Investment in Electricity Generation and Transmission: Decision Making Under Uncertainty

Antonio J. Conejo, Luis Baringo, JK, and Afzal Siddiqui

Springer, Switzerland, 2016 [ link ]

This book provides an in-depth analysis of investment problems pertaining to electric energy infrastructure, including both generation and transmission facilities. The analysis encompasses decision-making tools for expansion planning, reinforcement, and the selection and timing of investment options. In this regard, the book provides an up-to-date description of analytical tools to address challenging investment questions such as:

• How can we expand and/or reinforce our aging electricity transmission infrastructure?

• How can we expand the transmission network of a given region to integrate significant amounts of renewable generation?

• How can we expand generation facilities to achieve a low-carbon electricity production system?

• How can we expand the generation system while ensuring appropriate levels of flexibility to accommodate both demand-related and production-related uncertainties?

• How can we choose among alternative production facilities?

• What is the right time to invest in a given production or transmission facility?

Written in a tutorial style and modular format, the book includes a wealth of illustrative examples to facilitate comprehension. It is intended for advanced undergraduate and graduate students in the fields of electric energy systems, operations research, management science, and economics. Practitioners in the electric energy sector will also benefit from the concepts and techniques presented here.

Flexibility of integrated power and gas systems: Gas flow modeling and solution choices matter

Enrica Raheli, Yannick Werner, and JK

IEEE Transactions on Power Systems, forthcoming [ link | arXiv | GitHub ] 

Abstract: Due to their slow gas flow dynamics, natural gas pipelines function as short-term storage, the so-called linepack. By efficiently utilizing linepack, the natural gas system can provide flexibility to the power system through the flexible operation of gas-fired power plants. This requires accurately representing the gas flow physics governed by partial differential equations. Although several modeling and solution choices have been proposed in the literature, their impact on the flexibility provision of gas networks to power systems has not been thoroughly analyzed and compared. This paper bridges this gap by first developing a unified framework. We harmonize existing approaches and demonstrate their derivation from and application to the partial differential equations. Secondly, based on the proposed framework, we numerically analyze the implications of various modeling and solution choices on the flexibility provision from gas networks to power systems. One key conclusion is that relaxation-based approaches allow charging and discharging the linepack at physically infeasible high rates, ultimately overestimating the flexibility.

Unit commitment predictor with a performance guarantee: A support vector machine classifier

Farzaneh Pourahmadi and JK

IEEE Transactions on Power Systems, forthcoming [ link | arXiv | GitHub ] 

Abstract: The system operators usually need to solve large-scale unit commitment problems within limited time frame for computation. This paper provides a pragmatic solution, showing how by learning and predicting the on/off commitment decisions of conventional units, there is a potential for system operators to warm start their solver and speed up their computation significantly. For the prediction, we train linear and kernelized support vector machine classifiers, providing an out-of-sample performance guarantee if properly regularized, converting to distributionally robust classifiers. For the unit commitment problem, we solve a mixed- integer second-order cone problem. Our results based on the IEEE 6- and 118- bus test systems show that the kernelized SVM with proper regularization outperforms other classifiers, reducing the computational time by a factor of 1.7. In addition, if there is a tight computational limit, while the unit commitment problem without warm start is far away from the optimal solution, its warmly-started version can be solved to (near) optimality within the time limit.

On the efficiency of energy markets with non-merchant storage

Linde Frölke, Eléa Prat, Pierre Pinson, Richard M. Lusby, and JK 

Energy Systems, forthcoming [ link | arXiv | GitHub ] 

Abstract: Energy market designs with non-merchant storage have been proposed in recent years, with the aim of achieving optimal market integration of storage. In order to handle the time-linking constraints that are introduced in such markets, existing works commonly make simplifying assumptions about the end-of-horizon storage level, e.g., by imposing an exogenous level for the amount of energy to be left for the next time horizon. This work analyzes market properties under such assumptions, as well as in their absence. We find that, although they ensure cost recovery for all market participants, these assumptions generally lead to market inefficiencies. Therefore we consider the design of markets with non-merchant storage without such simplifying assumptions. Using illustrative examples, as well as detailed proofs, we provide conditions under which market prices in subsequent market horizons fail to reflect the value of stored energy. We show that this problem is essential to address in order to preserve market efficiency and cost recovery. Finally, we propose a method for restoring these market properties in a perfect-foresight setting.

Bayesian regression markets

Thomas Falconer, JK, and Pierre Pinson

Journal of Machine Learning Research, vol. 25, no. 180, pp. 1-38, 2024 [ link | arXiv | GitHub ] 

Abstract: Although machine learning tasks are highly sensitive to the quality of input data, relevant datasets can often be challenging for firms to acquire, especially when held privately by a variety of owners. For instance, if these owners are competitors in a downstream market, they may be reluctant to share information. Focusing on supervised learning for regression tasks, we develop a regression market to provide a monetary incentive for data sharing. Our mechanism adopts a Bayesian framework, allowing us to consider a more general class of regression tasks. We present a thorough exploration of the market properties, and show that similar proposals in literature expose the market agents to sizeable financial risks, which can be mitigated in our setup.

Feature-driven strategies for trading wind power and hydrogen

Emil Helgren, JK, and Lesia Mitridati

Electric Power Systems Research, vol. 234, Article no. 110787, September 2024 [ link | arXiv | GitHub ] 

Presented at Power Systems Computation Conference (PSCC 2024), Paris, France [ PSCC ]

Abstract: This paper develops a feature-driven model for hybrid power plants, enabling them to exploit available contextual information such as historical forecasts of wind power, and make optimal wind power and hydrogen trading decisions in the day-ahead stage. For that, we develop different variations of feature-driven linear policies, including a variation where policies depend on price domains, resulting in a price–quantity bidding curve. In addition, we propose a real-time adjustment strategy for hydrogen production. Our numerical results show that the final profit obtained from our proposed feature-driven trading mechanism in the day-ahead stage together with the real-time adjustment strategy is very close to that in an ideal benchmark with perfect information.

Learning to bid in forward electricity markets using a no-regret algorithm

Arega Getaneh Abate, Dorsa Majdi, JK, and Maryam Kamgarpour

Electric Power Systems Research, vol. 234, Article no. 110693, September 2024 [ link | arXiv | GitHub ]

Presented at Power Systems Computation Conference (PSCC 2024), Paris, France [ PSCC ]

Abstract: It is a common practice in the current literature of electricity markets to use game-theoretic approaches for strategic price bidding. However, they generally rely on the assumption that the strategic bidders have prior knowledge of rival bids, either perfectly or with some uncertainty. This is not necessarily a realistic assumption. This paper takes a different approach by relaxing such an assumption and exploits a no-regret learning algorithm for repeated games. In particular, by using the a posteriori information about rivals’ bids, a learner can implement a no-regret algorithm to optimize her/his decision making. Given this information, we utilize a multiplicative weight-update algorithm, adapting bidding strategies over multiple rounds of an auction to minimize her/his regret. Our numerical results show that when the proposed learning approach is used the social cost and the market-clearing prices can be higher than those corresponding to the classical game-theoretic approaches. The takeaway for market regulators is that electricity markets might be exposed to greater market power of suppliers than what classical analysis shows.

Load shifting versus manual frequency reserve: Which one is more appealing to thermostatically controlled loads in Denmark?

Peter A. V. Gade, Trygve Skjøtskift, Charalampos Ziras, Henrik W. Bindner, and JK

Electric Power Systems Research, vol. 232, Article no. 110364, July 2024 [ link | arXiv | GitHub ] 

Abstract: This paper investigates demand-side flexibility provision in two distinct forms of manual Frequency Restoration Reserve (mFRR) services and load shifting, and explores which one is financially more appealing to Thermostatically Controlled Loads (TCLs) in Denmark. While mFRR is an ancillary service required for the system and being bought by the system operator, load shifting is an individual act of the TCL in response to the variation of hourly electricity prices. Without loss of generalization, we consider a supermarket freezer as a representative TCL, and develop a grey-box model describing its temperature dynamics using real data from a supermarket in Denmark. Taking into account price and activation uncertainties, a stochastic mixed-integer linear program is formulated to maximize the flexibility value from the freezer. Examined on an ex-post simulation based on Danish spot and balancing market prices in 2022, load shifting shows to be almost as profitable as mFRR provision, although it could be more consequential for temperature deviations in the freezer. This indicates the need for regulatory measures by the Danish system operator to make the attraction of ancillary service provision more obvious for TCLs in comparison to the load shifting alternative.

Electrolysis as a flexibility resource on energy islands: The case of the North sea

Alexandra Lüth, Yannick Werner, Ruud Egging-Bratseth, and JK

Energy Policy, vol. 185, Article no. 113921, February 2024 [ link | PDF | GitHub ]

Abstract: Energy islands are meant to facilitate offshore sector integration by combining offshore wind energy with power-to-x technologies and storage. In this study, we investigate the operation of electrolyzers on energy islands, assess their potential contribution to flexibility provision, and analyse different market integration strategies of the islands. For this purpose, a two-stage stochastic optimisation model is developed to determine the cost-efficient dispatch for an integrated day-ahead and balancing electricity market. For the market integration of the energy island, we align our approach to the current debate and compare the case of a single offshore bidding zone to a case where the energy island is integrated into a home market zone. We find that electrolysers on energy islands will run at low capacity factors and provide flexibility in 29–36% of their run time. In addition, offshore electrolysers produce more hydrogen when they are allocated to an offshore bidding zone, and thus earn higher profits. We conclude that combining offsore wind with electrolysers on an energy island relies on additional economic incentives if their main role is envisioned to be the delivery of balancing flexibility.

A market for trading forecasts: A wagering mechanism

Aitazaz Ali Raja, Pierre Pinson, JK, and Sergio Grammatico

International Journal of Forecasting, vol. 40, no. 1, pp. 142-159, January-March 2024 [ link | arXiv ]

Abstract: In many areas of industry and society, including energy, healthcare, and logistics, agents collect vast amounts of data that are deemed proprietary. These data owners extract predictive information of varying quality and relevance from data depending on quantity, inherent information content, and their own technical expertise. Aggregating these data and heterogeneous predictive skills, which are distributed in terms of ownership, can result in a higher collective value for a prediction task. In this paper, a platform for improving predictions via the implicit pooling of private information in return for possible remuneration is envisioned. Specifically, a wagering-based forecast elicitation market platform has been designed, in which a buyer intending to improve their forecasts posts a prediction task, and sellers respond to it with their forecast reports and wagers. This market delivers an aggregated forecast to the buyer (pre-event) and allocates a payoff to the sellers (post-event) for their contribution. A payoff mechanism is proposed and it is proven that it satisfies several desirable economic properties, including those specific to electronic platforms. Furthermore, the properties of the forecast aggregation operator and scoring rules are discussed in order to emphasize their effect on the sellers’ payoff. Finally, numerical examples are provided in order to illustrate the structure and properties of the proposed market platform.

Embedding dependencies between wind farms in distributionally robust optimal power flow

Adriano Arrigo, JK, Zacharie De Grève, Jean-François Toubeau, and François Vallée

IEEE Transactions on Power Systems, vol. 38, no. 6, pp. 5156-5169, November 2023 [ link | arXiv  | codes ]

Abstract: The increasing share of renewables in the electricity generation mix comes along with an increasing uncertainty in power supply. In the recent years, distributionally robust optimization has gained significant interest due to its ability to make informed decisions under uncertainty, which are robust to misrepresentations of the distributional information (e.g., from probabilistic forecasts). This is achieved by introducing an ambiguity set that describes the potential deviations from an empirical distribution of all uncertain parameters. However, this set typically overlooks the inherent dependencies of uncertainty, e.g., spatial dependencies of weather-dependent energy sources. This paper goes beyond the state-of-the-art models by embedding such dependencies within the definition of ambiguity set. In particular, we propose a new copula-based ambiguity set which is tailored to capture any type of dependencies. The resulting problem is reformulated as a conic program which is kept generic such that it can be applied to any decision-making problem under uncertainty in power systems. Given the Optimal Power Flow (OPF) problem as one of the main potential applications, we illustrate the performance of our proposed distributionally robust model applied to i) a DC-OPF problem for a meshed transmission system and ii) an AC-OPF problem using LinDistFlow approximation for a radial distribution system.

A conic model for electrolyzer scheduling

Enrica Raheli, Yannick Werner, and JK 

Computers & Chemical Engineering, vol. 179, Article no. 108450, November 2023 [ link | arXiv | GitHub ]

Abstract: The hydrogen production curve of the electrolyzer describes the nonlinear and nonconvex relationship between its power consumption and hydrogen production. An accurate representation of this curve is essential for the optimal scheduling of the electrolyzer. The current state-of-the-art approach is based on piecewise linear approximation, which requires binary variables and does not scale well for large-scale problems. To overcome this barrier, we propose two models, both built upon convex relaxations of the hydrogen production curve. The first one is a linear relaxation of the piecewise linear approximation, while the second one is a conic relaxation of a quadratic approximation. Both relaxations are exact under prevalent operating conditions. We prove this mathematically for the conic relaxation. Using a realistic case study, we show that the conic model, in comparison to the other models, provides a satisfactory trade-off between computational complexity and solution accuracy for large-scale problems.

Online decision making for trading wind energy

Miguel Angel Muñoz, Pierre Pinson, and JK

Computational Management Science, vol. 20. no. 33, pp. 1-31 [ link | arXiv ]

Abstract: We propose and develop a new algorithm for trading wind energy in electricity markets, within an online learning and optimization framework. In particular, we combine a component-wise adaptive variant of the gradient descent algorithm with recent advances in the feature-driven newsvendor model. This results in an online offering approach capable of leveraging data-rich environments, while adapting to the nonstationary characteristics of energy generation and electricity markets, also with a minimal computational burden. The performance of our approach is analyzed based on several numerical experiments, showing both better adaptability to nonstationary uncertain parameters and significant economic gains.

On ambiguity-averse market equilibrium

Niklas Vespermann, Thomas Hamacher, and JK

Optimization Letters, vol. 17,  pp. 1379-1412, 2023 [ link | PDF | codes ]

Abstract: We develop a Nash equilibrium problem representing a perfectly competitive market wherein all players are subject to the same source of uncertainty with an unknown probability distribution. Each player—depending on her individual access to and confidence over empirical data—builds an ambiguity set containing a family of potential probability distributions describing the uncertain event. The ambiguity set of different players is not necessarily identical, yielding a market with potentially heterogeneous ambiguity aversion. Built upon recent developments in the field of Wasserstein distributionally robust chance-constrained optimization, each ambiguity-averse player maximizes her own expected payoff under the worst-case probability distribution within her ambiguity set. Using an affine policy and a conditional value-at-risk approximation of chance constraints, we define a tractable Nash game. We prove that under certain conditions a unique Nash equilibrium point exists, which coincides with the solution of a single optimization problem. Numerical results indicate that players with comparatively lower consumption utility are highly exposed to rival ambiguity aversion.

Moving from linear to conic markets for electricity 

Anubhav Ratha, Pierre Pinson, Hélène Le Cadre, Ana Virag, and JK

European Journal of Operational Research, vol. 309, no. 2, pp. 762-783, September 2023 [ link | arXiv ]

Abstract: We propose a new forward electricity market framework that admits heterogeneous market participants with second-order cone strategy sets, who accurately express the nonlinearities in their costs and constraints through conic bids, and a network operator facing conic operational constraints. In contrast to the prevalent linear-programming-based electricity markets, we highlight how the inclusion of second-order cone constraints improves uncertainty-, asset-, and network-awareness of the market, which is key to the successful transition towards an electricity system based on weather-dependent renewable energy sources. We analyze our general market-clearing proposal using conic duality theory to derive efficient spatially-differentiated prices for the multiple commodities, comprised of energy and flexibility services. Under the assumption of perfect competition, we prove the equivalence of the centrally-solved market-clearing optimization problem to a competitive spatial price equilibrium involving a set of rational and self-interested participants and a price setter. Finally, under common assumptions, we prove that moving towards conic markets does not incur the loss of desirable economic properties of markets, namely market efficiency, cost recovery, and revenue adequacy. Our numerical studies focus on the specific use case of uncertainty-aware market design and demonstrate that the proposed conic market brings advantages over existing alternatives within the linear programming market framework.

Power systems optimization under uncertainty: A review of methods and applications

Line Roald, David Pozo, Anthony Papavasiliou, Daniel K. Molzahn, JK, and Antonio J. Conejo 

Electric Power Systems Research, vol. 214,  Article no. 108725, January 2023 [ link ]

Presented at Power Systems Computation Conference (PSCC 2022), Porto, Portugal [ PSCC ]

Abstract: Electric power systems and the companies and customers that interact with them are experiencing increasing levels of uncertainty due to factors such as renewable energy generation, market liberalization, and climate change. This raises the important question of how to make optimal decisions under uncertainty. This paper aims to provide an overview of existing methods for modeling and optimization of problems affected by uncertainty, targeted at researchers with a familiarity with power systems and optimization. We also review some important applications of optimization under uncertainty in power systems and provide an outlook to future directions of research.

Ecosystem for demand-side flexibility revisited: The Danish solution

Peter A. V. Gade, Trygve Skjøtskift, Henrik W. Bindner, and JK

The Electricity Journal, vol. 35, no. 9, Article no. 107206, November 2022 [ link | arXiv ]

Abstract: Denmark has recently set a legislation called Market Model 3.0 to make the ecosystem for demand-side flexibility more attractive to stakeholders involved. The main change is to relax the previous mandate that required each aggregator to be associated with a retailer and a balance responsible party. We explain the rationale behind such a change and its implications, particularly on the pre-qualification of demand-side portfolios providing ancillary services.

Trading data for wind power forecasting: A regression market with lasso regularization

Liyang Han, Pierre Pinson, and JK

Electric Power Systems Research, vol. 212, Article no. 108442, November 2022 [ link | arXiv | video ]

Presented at Power Systems Computation Conference (PSCC 2022), Porto, Portugal [ PSCC ]

Abstract: This paper proposes a regression market for wind agents to monetize data traded among themselves for wind power forecasting. Existing literature on data markets often treats data disclosure as a binary choice or modulates the data quality based on the mismatch between the offer and bid prices. As a result, the market disadvantages either the data sellers due to the overestimation of their willingness to disclose data, or the data buyers due to the lack of useful data being provided. Our proposed regression market determines the data payment based on the least absolute shrinkage and selection operator (lasso), which not only provides the data buyer with a means for selecting useful features, but also enables each data seller to individualize the threshold for data payment. Using both synthetic data and real-world wind data, the case studies demonstrate a reduction in the overall losses for wind agents who buy data, as well as additional financial benefits to those who sell data.

Multi-stage linear decision rules for stochastic control of natural gas networks with linepack

Vladimir Dvorkin, Dharik Mallapragada, Audun Botterud, JK, and Pierre Pinson

Electric Power Systems Research, vol. 212, Article no. 108388, November 2022 [ link | arXiv | GitHub ]

Presented at Power Systems Computation Conference (PSCC 2022), Porto, Portugal [ PSCC ]

Abstract: The disturbances from variable and uncertain renewable generation propagate from power systems to natural gas networks, causing gas network operators to adjust gas supply nominations to ensure operational security. To alleviate expensive supply adjustments, we develop control policies to leverage instead the flexibility of linepack – the gas stored in pipelines – to balance stochastic gas extractions. These policies are based on multi-stage linear decision rules optimized on a finite discrete horizon to guide controllable network components, such as compressors and valves, towards feasible operations. Our approach offers several control applications. First, it treats the linepack as a main source of flexibility to balance disturbances from power systems without substantial impacts on nominal gas supply. Second, these policies can be optimized to minimize the variability (due to intermittency of renewables) and variance (due to their uncertainty) of network state variables, such as pressures. Finally, it enables topology optimization to decouple network parts and prevent uncertainty propagation through the network. This is demonstrated using illustrative numerical experiments.

Modeling gas flow directions as state variables: Does it provide more flexibility to power systems?

Junesoo Shin, Yannick Werner, and JK

Electric Power Systems Research, vol. 212, Article no. 108502, November 2022 [ link | arXiv | codes ]

Presented at Power Systems Computation Conference (PSCC 2022), Porto, Portugal [ PSCC ]

Abstract: As a common practice, the direction of natural gas flow in every pipeline is determined ex-ante for simplification purposes, and treated as a given parameter within the scheduling problem. However, in integrated gas and electric power networks with a large share of intermittent renewable power supply, it is no longer straightforward to optimally predetermine the gas flow directions. A wrong predetermination of gas flow directions may result in feasible but not necessarily optimal schedules. We propose a mixed-integer linear optimization model to determine the optimal gas flow directions while scheduling the system. This unlocks additional flexibility to power systems, provided that a tight coordination between power and gas systems exists. The increased flexibility, although it comes at the cost of increased computational complexity, is quantified by comparing the total operational cost of the entire system with bidirectional gas flows as opposed to unidirectional gas flows. We numerically show that modeling gas flow directions as state variables may bring added value not only in the meshed but also in the radial gas networks.

Market integration of excess heat

Linde Frölke, Ida-Marie Palm, and JK

Electric Power Systems Research, vol. 212, Article no. 108459, November 2022 [ link | arXiv ]

Presented at Power Systems Computation Conference (PSCC 2022), Porto, Portugal [ PSCC ]

Abstract: Excess heat will be an important heat source in future carbon-neutral district heating systems. A barrier to excess heat integration is the lack of appropriate scheduling and pricing systems for these producers, which generally have small capacity and limited flexibility. In this work, we formulate and analyze two methods for scheduling and pricing excess heat producers: self-scheduling and market participation. In the former, a price signal is sent to excess heat producers, based on which they determine their optimal schedule. The latter approach allows excess heat producers to participate in a market clearing. In a realistic case study of the Copenhagen district heating system, we investigate market outcomes for the two excess heat integration paradigms under increasing excess heat penetration. An important conclusion is that in systems of high excess heat penetration, simple price signal methods will not suffice, and more sophisticated price signals or coordinated dispatch become a necessity.

Regression markets and application to energy forecasting

Pierre Pinson, Liyang Han, and JK

TOP, vol. 30, pp. 533-573, October 2022 [ link | arXiv | video ]

Abstract: Energy forecasting has attracted enormous attention over the last few decades, with novel proposals related to the use of heterogeneous data sources, probabilistic forecasting, online learning, etc. A key aspect that emerged is that learning and forecasting may highly benefit from distributed data, though not only in the geographical sense. That is, various agents collect and own data that may be useful to others. In contrast to recent proposals that look into distributed and privacy-preserving learning (incentive-free), we explore here a framework called regression markets. There, agents aiming to improve their forecasts post a regression task, for which other agents may contribute by sharing their data for their features and get monetarily rewarded for it. The market design is for regression models that are linear in their parameters, and possibly separable, with estimation performed based on either batch or online learning. Both in-sample and out-of-sample aspects are considered, with markets for fitting models in-sample, and then for improving genuine forecasts out-of-sample. Such regression markets rely on recent concepts within interpretability of machine learning approaches and cooperative game theory, with Shapley additive explanations. Besides introducing the market design and proving its desirable properties, application results are shown based on simulation studies (to highlight the salient features of the proposal) and with real-world case studies.

A complementarity model for electric power transmission-distribution coordination under uncertainty

Alexander Hermann, Tue V. Jensen, Jacob Østergaard, and JK

European Journal of Operational Research, vol. 299, no. 1, pp. 313-329, May 2022 [ link | PDF | GitHub ]

Abstract: The growing penetration of stochastic renewable energy sources increases the need for operational flexibility to cope with imbalances. Existing proposals for flexibility procurement are envisioning markets where the transmission system operator (TSO) can access flexible resources located at the distribution system operator (DSO)-level and vice versa, but the coordination between these two entities is a matter of active research. We consider two trading floors, i.e., day-ahead and real-time markets, and propose a method for day-ahead coordination on how to share flexible resources, described as a complementarity model. The proposed coordination approach is to optimize prices and capacity limits at the physical interface of TSO and DSO, the so-called “coordination variables”. For given values of these variables, the DSO pre-qualifies the participation of DSO-level resources in the day-ahead market by capping their quantity bids. This way, the DSO ensures that the constraints of its system, modeled by a conic program, will be respected. Pursuing computational tractability, we decompose the model using a multi-cut Benders’ decomposition approach. It separates the conic modeling of real-time power flows under each scenario from the mixed-integer linear formulation of the day-ahead market-clearing problem. We quantify the potential benefit of the proposed coordination method in terms of improved social welfare. Using an ex-post out-of-sample simulation, the performance of the proposed coordination method is assessed against two benchmarks: (i) a fully uncoordinated scheme which obtains a lower bound for the expected social welfare, and (ii) an ideal benchmark which co-optimizes the TSO and DSO problems, providing an upper bound for the expected social welfare.

Stochastic control and pricing for natural gas networks

Vladimir Dvorkin, Anubhav Ratha, Pierre Pinson, and JK

IEEE Transactions on Control of Network Systems, vol. 9, no. 1, pp. 450-462, March 2022 [ link | arXiv | video | GitHub ]

Abstract: We propose stochastic control policies to cope with uncertain and variable gas extractions in natural gas networks. Given historical gas extraction data, these policies are optimized to produce the real-time control inputs for nodal gas injections and for pressure regulation rates by compressors and valves. We describe the random network state as a function of control inputs, which enables a chance-constrained optimization of these policies for arbitrary network topologies. This optimization ensures the real-time gas flow feasibility and a minimal variation in the network state up to specified feasibility and variance criteria. Furthermore, the chance-constrained optimization provides the foundation of a stochastic pricing scheme for natural gas networks, which improves on a deterministic market settlement by offering the compensations to network assets for their contribution to uncertainty and variance control. We analyze the economic properties, including efficiency, revenue adequacy, and cost recovery, of the proposed pricing scheme and make them conditioned on the network design.

Wasserstein distributionally robust chance-constrained optimization for energy and reserve dispatch: An exact and physically-bounded formulation

Adriano Arrigo, Christos Ordoudis, JK, Zacharie De Grève, Jean-François Toubeau, and François Vallée

European Journal of Operational Research, vol. 296, no. 1, pp. 304-322, January 2022 [ link | PDF | codes ]

Abstract: In the context of transition towards sustainable, cost-efficient and reliable energy systems, the improvement of current energy and reserve dispatch models is crucial to properly cope with the uncertainty of weather-dependent renewable power generation. In contrast to traditional approaches, distributionally robust optimization offers a risk-aware framework that provides performance guarantees when the distribution of uncertain parameters is not perfectly known. In this paper, we develop a distributionally robust chance-constrained optimization with a Wasserstein ambiguity set for energy and reserve dispatch, and provide an exact reformulation. While preserving the exactness, we then improve the model by enforcing physical bounds on the uncertainty space, resulting in a bilinear program. We solve the resulting bilinear model with an iterative algorithm which is computationally efficient and has convergence guarantee. A thorough out-of-sample analysis is performed to compare the proposed model against a scenario-based stochastic program. We also compare the performance of the proposed exact reformulation against an existing approximate technique in the literature, built upon a conditional-value-at-risk measure. We eventually show that the proposed physically-bounded exact reformulation outperforms the other methods by achieving a cost-optimal yet reliable trade-off between reserve procurement and load curtailment.

Price-region bids in electricity markets

Lucien Bobo, Lesia Mitridati, Josh A. Taylor, Pierre Pinson, and JK

European Journal of Operational Research, vol. 295, no. 3, pp. 1056-1073, December 2021 [ link | PDF | video ]

Abstract: Current bid formats in pool-based electricity markets are ill-equipped to accommodate the broad range of non-conventional sources of flexibility, such as demand response and interconnected heating, natural gas and water infrastructure networks. To address this issue, this paper introduces the novel price-region bid format to be used in both forward electricity markets and financial right auctions. We show that price-region bids are able to accommodate a broad range of techno-economic characteristics, including complex spatial and temporal couplings, and facilitate market access to non-conventional flexibility providers. We then show that this new bid format is compatible with existing market structures, and satisfies desirable market properties under common assumptions. Three numerical studies are provided: two motivating examples based on a district heating utility and a cascaded hydro power plant, and a case study based on an integrated power and heat system. These studies illustrate the inability of existing bid formats to accommodate flexible resources, and show how price-region bids overcome this shortcoming.

Coordination of power and natural gas markets via financial instruments

Anna Schwele, Christos Ordoudis, Pierre Pinson, and JK

Computational Management Science, vol. 18, pp. 505-538, October 2021 [ link | PDF | codes ]

Abstract: Current electricity and natural gas markets operate with deterministic description of uncertain supply, and in a temporally and sectorally decoupled way. This practice in energy systems is being challenged by the increasing integration of stochastic renewable energy sources. There is a growing need for exchanging operational flexibility among energy sectors, which requires to improve the sectoral coordination between electricity and natural gas markets. In addition, the dispatch of flexible units in both sectors needs to be made in a more uncertainty-aware manner, requiring to strengthen the temporal coordination between day-ahead and real-time energy markets. We explore the use of existing financial instruments in the form of virtual bidding (VB) as a market-based solution to enhance both sectoral and temporal coordination in energy markets. It is established in the literature that VB by purely financial players is able to enhance the temporal coordination between deterministic day-ahead and real-time markets. By developing various stochastic equilibrium and optimization models, we show that VB by physical players, i.e., gas-fired power plants, at the interface of power and natural gas systems is of great potential to improve not only the temporal coordination between deterministic day-ahead and real-time markets, but also the sectoral coordination between deterministic electricity and natural gas markets. We exploit a fully stochastic co-optimization model as an ideal benchmark, and numerically illustrate the benefits of VB for increasing the overall market efficiency in terms of reduced expected operational cost of the entire energy system. We eventually show that flexible resources in both electricity and natural gas markets are dispatched more efficiently in the day-ahead stage when VB exists.

Distributionally robust generation expansion planning with unimodality and risk constraints

Farzaneh Pourahmadi and JK

IEEE Transactions on Power Systems, vol. 36. no. 5, pp. 4281-4295, September 2021 [ link | PDF | GitHub ]

Abstract: As more renewables are integrated into the power system, capacity expansion planners need more advanced long-term decision-making tools to properly model short-term stochastic production uncertainty and to explore its effects on expansion decisions. We develop a distributionally robust generation expansion planning model, accounting for a family of potential probability distributions of wind forecast error uncertainty. Aiming to include more realistic distributions, we construct more informed moment-based ambiguity sets by adding structural information of unimodality. We include operational-stage unit commitment constraints and model the risk of operational limit violations in two distinct forms: chance and conditional value-at-risk (CVaR) constraints. In both forms, the resulting expansion planning model is a mixed-integer second-order cone program. Using a thorough out-of-sample numerical analysis, we conclude: (i) the distributionally robust chance-constrained generation expansion planning model exhibits a better out-of-sample performance only if sufficiently accurate information about the first- and the second-order moments as well as the mode location of potential distributions is available; (ii) conversely, if such accurate information is unavailable, the distributionally robust CVaR-constrained generation expansion planning model outperforms; (iii) these two models have a similar performance when unimodality information is excluded.

A local flexibility market mechanism with capacity limitation services

Carsten Heinrich, Charalampos Ziras, Tue V. Jensen, Henrik W. Bindner, and JK

Energy Policy, vol. 156, Article no. 112335, September 2021 [ link ]

Abstract: Local flexibility markets have a substantial potential to unlock the flexibility of distributed energy resources in the distribution level. Capacity limitation services have been perceived as one of the most appealing products to be traded in these markets. This work argues why classical market-clearing and pricing mechanisms such as pay-as-bid, uniform pricing and Vickrey-Clarke-Groves (VCG) are not compatible with a market that trades capacity limitations. As a solution, we propose a local flexibility market mechanism which is built upon an adapted VCG-based auction. The mechanism achieves a trade-off among various desirable economic properties, including budget-balancedness, incentive-compatibility and stability. The suitability of the proposed mechanism is illustrated using a case study which is based on a real medium voltage feeder, located on the Danish island of Bornholm. Results show that aggregators and the distribution system operator benefit from the trade of capacity limitation services. We eventually conclude by providing a set of policy recommendations for the real-life operation of such a market.

Access economy for storage in energy communities

Niklas Vespermann, Thomas Hamacher, and JK

IEEE Transactions on Power Systems, vol. 36, no. 3, pp. 2234-2250, May 2021 [ link | PDF | codes ]

Abstract: We address the market design issue for a local energy community, comprising prosumers, consumers, photovoltaic, and energy storage systems, all connected as a community to a distribution grid. Our work explores different market design options based on cooperative and non-cooperative game-theoretic models that enable an economic access to the benefits of energy storage for prosumers without a direct ownership of a storage system. We compare market outcomes in terms of the community cost as well as the individual cost. We pay special attention to potential uncertainties, and investigate financial instruments that allow storage systems to be utilized by multiple prosumers. In particular, we explore a case where a prosumer that owns a storage system provides rights, either physical or financial, rather than participating in the local market as an arbitrageur. Moreover, we consider a cooperative market design where energy community members agree on the Shapley value or the nucleolus as a community cost allocation rule. Our results show that an access economy for energy storage systems enhances energy communities by reducing the cost volatility for most prosumers, while the expected operational cost of the community as a whole remains unchanged.

Differentially private optimal power flow for distribution grids

Vladimir Dvorkin, Ferdinando Fioretto, Pascal Van Hentenryck, Pierre Pinson, and JK

IEEE Transactions on Power Systems, vol. 36, no. 3, pp. 2186-2196, May 2021 [ link | arXiv | video | GitHub ] 

Recognized as one of the 8 Best Papers of the IEEE Transactions on Power Systems in the time period of 2019 to 2021

Abstract: Although distribution grid customers are obliged to share their consumption data with distribution system operators (DSOs), a possible leakage of this data is often disregarded in operational routines of DSOs. This paper introduces a privacy-preserving optimal power flow (OPF) mechanism for distribution grids that secures customer privacy from unauthorised access to OPF solutions, e.g., current and voltage measurements. The mechanism is based on the framework of differential privacy that allows to control the participation risks of individuals in a dataset by applying a carefully calibrated noise to the output of a computation. Unlike existing private mechanisms, this mechanism does not apply the noise to the optimization parameters or its result. Instead, it optimizes OPF variables as affine functions of the random noise, which weakens the correlation between the grid loads and OPF variables. To ensure feasibility of the randomized OPF solution, the mechanism makes use of chance constraints enforced on the grid limits. The mechanism is further extended to control the optimality loss induced by the random noise, as well as the variance of OPF variables. The paper shows that the differentially private OPF solution does not leak customer loads up to specified parameters.

Risk trading in energy communities 

Niklas Vespermann, Thomas Hamacher, and JK

IEEE Transactions on Smart Grid, vol. 12, no. 2, pp. 1249-1263. March 2021 [ link | PDF | codes ] 

Abstract: Local energy communities are proposed as a regulatory framework to enable the market participation of end-consumers. However, volatile local market-clearing prices, and consequently, volatile cost give rise to local market participants with generally heterogeneous risk attitudes. To prevent the increased operational cost of communities due to conservative trading decisions in the forward stage, e.g., a day-ahead market, we propose risk trading in energy communities via financial hedging products, the so-called Arrow-Debreu securities. The conditional value-at-risk serves as our risk measure for players to study different degrees of market completeness for risk. We define a risk-averse Nash game with risk trading and solve the Nash equilibrium problem for an incomplete market for risk as a mixed complementarity problem. We show that such a Nash equilibrium problem reduces to a single optimization problem if the market is complete for risk. Numerical findings indicate that a significant community cost saving can be realized when players engage in risk trading and sufficient financial hedging products are available. Moreover, risk trading efficiently protects less risk-averse players from highly risk-averse decision-making of rival players.

Energy security through demand side flexibility: The case of Denmark

Jacob Østergaard, Charalampos Ziras, Henrik W. Bindner, JK, Mattia Marinelli, Peter Markussen, Signe H. Rosted, and Jorgen S. Christensen

IEEE Power & Energy Magazine, vol. 19, no. 2, pp. 46-55, March-April 2021 [ link ]

Abstract: The Danish government has set very ambitious binding targets regarding decarbonization. By 2030, carbon dioxide emissions must be reduced by 70% compared to the 1990 level. This can be achieved primarily through a predominantly renewables-based electricity system and the electrification of energy demand.

Design and game-theoretic analysis of community-based market mechanisms in heat and electricity systems

Lesia Mitridati, JK, and Pierre Pinson

Omega, vol. 99, Article no. 102177, pp. 1-24, March 2021 [ link | PDF ]

Abstract: In an increasingly decentralized energy system with tight interdependencies with heat and electricity markets, prosumers, who act both as consumers and producers at the interface between the markets, are becoming important operational flexibility providers. Policy-makers and market operators need a better understanding of the motivations and behavior of prosumers in order to harness their underlying flexibility. In that context, existing market mechanisms must be accompanied by decision-making tools which enable direct participation of prosumers and cooperation among them towards a social choice. This work focuses on designing a community-based market mechanism, in which prosumers can pool their heat and electricity production and consumption, and coordinate their participation in heat and electricity wholesale markets. A central research question that is addressed, is to understand how this mechanism can affect the outcomes of the interactions among individuals towards a social choice, and in particular incentivize cooperation among prosumers. Game-theoretic concepts are used to analyze the properties of the proposed market mechanism with different allocation schemes, namely uniform pricing, Vickrey-Clarke-Groves, Shapley value, and nucleolus. This analysis shows that it is beneficial for the community as a whole to cooperate and that there exists a set of stable allocations for the proposed mechanism. Additionally, although no allocation can satisfy all fundamental desirable market properties, this study demonstrates that the proposed mechanism based on a nucleolus allocation can provide an interesting trade-off between stability, efficiency, and incentive compatibility. Finally, the concepts and properties discussed in this work are illustrated in a case study.

Affine policies for  flexibility provision by natural gas networks to power systems

Anubhav Ratha, Anna Schwele, JK, Pierre Pinson, Shahab S. Torbaghan, and Ana Virag

Electric Power Systems Research, vol. 189, Article no. 106565, pp. 1-9, December 2020  [ link | PDF | codes ]

Presented at Power Systems Computation Conference (PSCC 2020), Porto, Portugal [ PSCC | video ]

Abstract: Using flexibility from the coordination of power and natural gas systems helps with the integration of variable renewable energy in power systems. To include this flexibility into the operational decision-making problem, we propose a distributionally robust chance-constrained co-optimization of power and natural gas systems considering flexibility from short-term gas storage in pipelines, i.e., linepack. Recourse actions in both systems, based on linear decision rules, allow adjustments to the dispatch and operating set-points during real-time operation when the uncertainty in wind power production is revealed. We convexify the non-linear and non-convex power and gas flow equations using DC power flow approximation and second-order cone relaxation, respectively. Our coordination approach enables a study of the mitigation of short-term uncertainty propagated from the power system to the gas side. We analyze the results of the proposed approach on a case study and evaluate the solution quality via out-of-sample simulations performed ex-ante.

Coordination of electricity, heat, and natural gas systems accounting for network flexibility

Anna Schwele, Adriano Arrigo, Charlotte Vervaeren, JK, and François Vallée

Electric Power Systems Research, vol. 189, Article no. 106776, pp. 1-9, December 2020 [ link | PDF ] 

Presented at Power Systems Computation Conference (PSCC 2020), Porto, Portugal [ PSCC | video ]

Among top 15 papers selected for the PSCC 2020 Highlights Playlist

Abstract: Existing energy networks can foster the integration of uncertain and variable renewable energy sources by providing additional operational flexibility. In this direction, we propose a combined power, heat, and natural gas dispatch model to reveal the maximum potential “network flexibility”, corresponding to the ability of natural gas and district heating pipelines to store energy. To account for both energy transport and linepack in the pipelines in a computational efficient manner, we explore convex quadratic relaxations of the nonconvex flow dynamics of gas and heat. The resulting model is a mixed-integer second-order cone program. An ex-post analysis ensures feasibility of the heat dispatch, while keeping the relaxation of the gas flow model sufficiently tight. The revealed flexibility is quantified in terms of system cost compared to a dispatch model neglecting the ability of natural gas and district heating networks to store energy.

Market-based coordination for integrated electricity and natural gas systems under uncertain supply

Christos Ordoudis, Stefanos Delikaraoglou, JK, and Pierre Pinson

European Journal of Operational Research, vol. 287, no. 3, pp. 1105-1119, December 2020 [ link | PDF ]

Abstract: The interdependence between electricity and natural gas systems has lately increased due to the wide deployment of gas-fired power plants (GFPPs). Moreover, weather-driven renewables introduce uncertainty in the operation of the integrated energy system, increasing the need for operational flexibility. Recently proposed stochastic dispatch models optimally use the available flexibility and minimize the total expected system cost. However, these models are incompatible with the current sequential market design. We propose a novel method to optimally define the available natural gas volume for power production scheduling, anticipating the real-time flexibility needs. This volume-based model is formulated as a stochastic bilevel program that aims to enhance the inter-temporal coordination of scheduling and balancing operations, while remaining compatible with the sequential clearing of day-ahead and real-time markets. The proposed model accounts for the inherent flexibility of the natural gas system via the proper modeling of linepack capabilities and reduces the total expected system cost by the optimal definition of natural gas volume availability for GFPPs at the forward phase. The volume-based coordination model is compared with a price-based coordination alternative, which was recently proposed. In the latter one, the natural gas price perceived by GFPPs is similarly adjusted to enhance the temporal coordination of scheduling and balancing stages. This comparison enables us to highlight the main properties and differences between the two coordination mechanisms.

A local market mechanism for physical storage rights

Dimitrios Thomas, JK, Athanasios Papakonstantinou, Pierre Pinson, Olivier Deblecker, and Christos S. Ioakimidis

IEEE Transactions on Power Systems, vol. 35, no. 4, pp. 3087-3099, July 2020 [ link | PDF ]

Abstract: This paper proposes a two-stage auction-based local market mechanism to allocate physical storage rights (PSRs). As a market product, PSRs are provided by a storage owner and enable the local market participants (including renewable producers, consumers and prosumers) to access the storage. That is, they can book storage in the form of PSRs and dispatch it at a given time aiming to maximize their utility function. The business options we examine to evaluate the position of storage in the market range from storage owner entirely participating in day-ahead (DA) and real-time (RT) markets as an inter-temporal arbitrager, to exclusively acting as a PSR provider in DA only - this way, the storage owner is fully paid upfront in DA. Considering the context above, we propose an equilibrium model where each player optimizes its operational objective. We prove that the equilibrium model can be substituted with an equivalent optimization formulation which clears the proposed market ensuring the same desirable market properties, such as efficiency and revenue adequacy. Results suggest that the certain revenues earned by the storage owner in DA when acting as a PSR provider is equal to its expected profit as a regular market participant, mitigating however its payoff uncertainty and resulting in the same economic return.

Distributionally robust chance-constrained generation expansion planning

Farzaneh Pourahmadi, JK, Christos Ordoudis, Pierre Pinson, and Seyed Hamid Hosseini

IEEE Transactions on Power Systems, vol. 35, no. 4, pp. 2888-2903, July 2020 [ link | PDF | video ]

Abstract: This article addresses a centralized generation expansion planning problem, accounting for both long- and short-term uncertainties. The long-term uncertainty (demand growth) is modeled via a set of scenarios, while the short-term uncertainty (wind power generation) is described by a family of probability distributions with the same first- and second-order moments obtained from historical data. The resulting model is a distributionally robust chance-constrained optimization problem, which selects the conventional generating units to be built among predefined discrete options. This model includes a detailed representation of unit commitment constraints. To achieve computational tractability, we use a tight relaxation approach to convexify unit commitment constraints and solve the model with linear decision rules, resulting in a mixed-integer second-order cone program. It is observed that the proposed model exhibits better out-of-sample performance in terms of total expected system cost and its standard deviation compared to a chance-constrained model that assumes a Gaussian distribution of short-term uncertainty. A similar observation is made when comparing the proposed model against a chance-constrained program that uses empirical renewable power generation data with unknown type of distribution, recasting as either a robust optimization or a stochastic program.

Heat and electricity market coordination: A scalable complementarity approach

Lesia Mitridati, JK, and Pierre Pinson

European Journal of Operational Research, vol. 283, no. 3, pp. 1107–1123, June 2020 [ link | PDF ]

Abstract: The large penetration of stochastic and non-dispatchable renewable energy sources increases the need for operational flexibility in power systems. Flexibility can be unlocked by aligning the existing interactions and synergies between heat and power systems. However, in the current sequential order of heat and electricity market clearings, the heat market is myopic to its interactions with the electricity market. This paper designs a heat market, aimed at achieving the optimal coordination of heat and power systems while respecting the current market regulations. The proposed electricity-aware heat market yields a soft coordination between heat and power systems by endogenously modeling their interactions in the day-ahead heat market clearing. The proposed market framework requires to solve a hierarchical optimization problem under uncertainty, which can be computationally challenging in large-scale energy systems with many scenarios. To resolve this potential scalability issue, this paper develops an augmented regularized Benders decomposition algorithm. The performance of the proposed market framework is compared against the fully integrated and sequential market frameworks using an ex-post out-of-sample simulation. This comparison reveals that there is a significant room for improvement in the cost-effective operation of the overall energy system. In particular, the proposed electricity-aware heat market framework provides a trade-off between the sequential and fully integrated market frameworks by significantly reducing the inefficiencies in both heat and electricity systems while respecting the current sequence of clearing heat and electricity markets.

Do unit commitment constraints affect generation expansion planning? A scalable stochastic model

Anna Schwele, JK, and Pierre Pinson

Energy Systems, vol. 11, no. 2, pp. 247-282, May 2020 [ link | PDF ]

Abstract: Due to increasing penetration of stochastic renewable energy sources in electric power systems, the need for flexible resources especially from fast-start conventional generation units (e.g., combined cycle gas turbine plants) is growing. The fast-start conventional units are being operated more frequently in order to respond to the variability and uncertainty of stochastic generation. This raises two important technical questions: as it is common in the literature, is it still an appropriate simplification to ignore the operational unit commitment (UC) constraints of conventional units within the generation expansion planning optimization? And if not, which UC constraint impacts most the expansion planning outcomes? To answer these questions, this paper aims at measuring the planning inefficiency (i.e., the underestimation of need for new generation capacity) caused by ignoring each UC constraint. To this purpose, we develop a centralized network-constrained generation expansion planning model incorporating UC constraints. In particular, we model start-up and shut-down costs, minimum production level and hourly ramping limits of conventional units. Wind power production is considered as the only source of uncertainty, and is modeled through a set of scenarios. A two-stage stochastic programming tool is used, whose first stage determines the long-term expansion and short-term UC decisions over different hours of representative days, while the second stage models the real-time operation for accommodating imbalances arising from wind deviation under different scenarios. Since this problem is potentially hard to solve especially with a large number of representative days and scenarios, a multi-cut Benders’ decomposition algorithm is implemented. The well-functioning of the proposed model and the impact of each UC constraint on planning outcomes are evaluated using an extensive numerical study. In our case studies, the exclusion of ramping constraints from planning optimization causes large error and is the most distorting simplification.

Incorporating non-convex operating characteristics into bi-level optimization electricity market models

Yujian Ye, Dimitrios Papadaskalopoulos, JK, and Goran Strbac

IEEE Transactions on Power Systems, vol. 35, no. 1, pp. 163-176, January 2020 [ link | PDF ]

Abstract: Bi-level optimization constitutes the most popular mathematical methodology for modeling the deregulated electricity market. However, state-of-the-art models neglect the physical non-convex operating characteristics of market participants, due to their inherent inability to capture binary decision variables in their representation of the market clearing process, rendering them problematic in modeling markets with complex bidding and unit commitment (UC) clearing mechanisms. This paper addresses this fundamental limitation by proposing a novel modeling approach enabling incorporation of these non-convexities into bi-level optimization market models, which is based on the relaxation and primal-dual reformulation of the original, non-convex lower level problem and the penalization of the associated duality gap. Case studies demonstrate the ability of the proposed approach to closely approximate the market clearing solution of the actual UC clearing algorithm and devise more profitable bidding decisions for strategic producers than the state-of-the-art bi-level optimization approach, and reveal the potential of strategic behavior in terms of misreporting non-convex operating characteristics.

A mid-term DSO market for capacity limits: How to estimate opportunity costs of aggregators?

Charalampos Ziras, JK, Emre Can Kara, Henrik W. Bindner, Pierre Pinson, and Sila Kiliccote

IEEE Transactions on Smart Grid, vol. 11, no. 1, pp. 334-345, January 2020 [ link | PDF ]

Abstract: A large number of mechanisms are proposed to manage potential problems in distribution networks caused by the participation of distributed energy resources (DERs) in the wholesale markets. In this paper, we first introduce a practical and straightforward mechanism, based on capacity limits, which avoids conflicts between the transmission system operator and the distribution system operators (DSOs). Using a large number of real electric vehicle (EV) commercial charging stations we then show how an EV aggregator can forecast the opportunity cost incurred by offering a mid-term capacity limit service to the DSO. This cost is computed based on the estimated profit that the aggregator could gain in the day-ahead and real-time markets. The proposed methodology guarantees robustness against evolving EV uncertainty, both in terms of service delivery and driving requirements. It also allows the use of a variety of time-series forecasting methods without forecasting electricity prices and EV scenarios. The results of our empirical analysis show the exponential increase of opportunity cost and the considerable increase of the prediction intervals as the capacity limit decreases. The produced offering curves can be used as an indication of the underutilization cost of DERs caused by the DSO's limitations.

Congestion management in distribution networks with asymmetric block offers

Alexander Hermann, JK, Shaojun Huang, and Jacob Østergaard

IEEE Transactions on Power Systems, vol. 34, no. 6, pp. 4382-4392, November 2019 [ link | PDF ]

Abstract: In current practice, the day-ahead market-clearing outcomes are not necessarily feasible for distribution networks, i.e., the network constraints might not be satisfied. Hence, the distribution system operator may consider an ex-post re-dispatch mechanism, exploiting potential flexibility of local distributed energy resources including demand response (DR) units. Many DR units have an inherent “rebound effect,” meaning a decrease in power demand (response) must be followed by an increase (rebound) or vice versa, due to their underlying physical properties. A naive re-dispatch mechanism relying on DR units with non-negligible rebound effect may fail, since those units may cause another congestion in the rebound period. We propose a mechanism, which models the rebound effect of DR units using asymmetric block offers-this way, those units offer their flexibility using two subsequent blocks (response and rebound), each one representing the load decrease/increase in a time period. We demonstrate that though linear approximations of optimal power flow (OPF) models as potential re-dispatch mechanisms are more computationally efficient, they can result in a different dispatch of the asymmetric blocks than an exact convex relaxation of an AC-OPF model, and therefore, must be used with caution.

Electricity market equilibrium under information asymmetry

Vladimir Dvorkin, JK, and Pierre Pinson

Operations Research Letters, vol. 47, no. 6, pp. 521-526, November 2019 [ link | arXiv ]

Abstract: We study a competitive electricity market equilibrium with two trading stages, day-ahead and real-time. The welfare of each market agent is exposed to uncertainty (here from renewable energy production), while agent information on the probability distribution of this uncertainty is not identical at the day-ahead stage. We show a high sensitivity of the equilibrium solution to the level of information asymmetry and demonstrate economic, operational, and computational value for the system stemming from potential information sharing.

Incentive-compatibility in a two-stage stochastic electricity market with high wind power penetration

Lazaros Exizidis, JK, Athanasios Papakonstantinou, Pierre Pinson, Zacharie De Grève, and François Vallée

IEEE Transactions on Power Systems, vol. 34, no. 4, pp. 2846-2858, July 2019 [ link | PDF ]

Abstract: A major restructuring of electricity markets takes place worldwide, pursuing maximum economic efficiency. In most modern electricity markets, including the widely adapted Locational Marginal Price (LMP) market, efficiency is only guaranteed under the assumption of perfect competition. Moreover, market design is heavily focused on deterministic conventional generation. Electricity markets, though, are vulnerable to strategic behaviors and challenged by the increased penetration of renewable energy generation. In this paper, we cope with the aforementioned bottlenecks by investigating the application of Vickrey-Clarke-Groves (VCG) auction in a two-stage stochastic electricity market. The VCG mechanism achieves incentive-compatibility by rewarding market participants for their contribution towards market efficiency, being attractive from both market operation and participants perspectives. Both traditional and VCG market-clearing approaches are explored and compared, investigating as well the impact of increasing wind power penetration. The main shortcoming of VCG, i.e., not ensuring revenue adequacy, is quantified in terms of market budget imbalance for various levels of wind power penetration. To this end, a novel ex-post budget redistribution scheme is proposed, which achieves to partially recover budget deficit.

Cost-optimal ATCs in zonal electricity markets 

Tue V. Jensen, JK, and Pierre Pinson

IEEE Transactions on Power Systems, vol. 33, no. 4, pp. 3624-3633, July 2018 [ link | PDF ]

Abstract: In contrast to existing frameworks for available transfer capacity (ATC) determination, we propose to define ATCs in an integrated and data-driven manner, optimizing for expected operational costs of the whole system to derive cost-optimal ATCs. These ATCs are purely financial parameters, separated from the physical ATCs based on security indices only typically used in zonal electricity markets today. Determining cost-optimal ATCs requires viewing ATCs as an endogenous market construct, and leads naturally to the definition of a market entity whose responsibility is to optimize ATCs. The optimization problem that this entity solves is a stochastic bilevel problem, which we decompose to yield a computationally tractable formulation. We show that cost-optimal ATCs depend nontrivially on the underlying network structure, and the problem of finding a set of cost-optimal ATCs is in general nonconvex. On a European-scale test system, cost-optimal ATCs achieve expected total costs midway between those for nonintegrated ATCs and a fully stochastic nodal setup. This benefit comes from qualitatively different ATCs compared to typical definitions, with ATCs which exceed the physical cross-border capacity by a factor of 2 or more, and ATCs which are zero between well-connected areas. Our results indicate that the perceived efficiency gap between zonal and nodal markets may be exaggerated if nonoptimal ATCs are used.

A stochastic market design with revenue adequacy and cost recovery by scenario: Benefits and costs

JK, Pierre Pinson, and Benjamin F. Hobbs

IEEE Transactions on Power Systems, vol. 33, no. 4, pp. 3531-3545, July 2018 [ link | PDF ]

Abstract: Two desirable properties of electricity market mechanisms include: 1) revenue adequacy for the market, and 2) cost recovery for all generators. Previously proposed stochastic market-clearing mechanisms satisfy both properties in expectation only, or satisfy one property by scenario and another in expectation. Consequently, market parties may perceive significant risks to participating in the market since they may lose money in one or more scenarios, and therefore be discouraged from offering in the market or perhaps even from investing. We develop a stochastic two-stage market-clearing model including day-ahead and real-time settlements with an energy-only pricing scheme that ensures both properties by scenario. However, this approach is cost-inefficient in general and may sacrifice other desirable market attributes. Undesirable consequences include: One group of participants will have to pay more to ensure that all other participants have their costs covered, and thus their prices will not be equilibrium supporting; and day-ahead and real-time prices are not arbitraged in expectation, although this can be fixed by allowing virtual bidders to arbitrage but at the potential cost of increased market inefficiency. Considering these pros and cons, we propose our model as an appropriate tool for market analysis, and not for clearing actual markets. Numerical results from case studies illustrate the benefits and costs of the proposed stochastic market design.

A bilevel model for participation of a storage system in energy and reserve markets

Ehsan Nasrolahpour, JK, Hamidreza Zareipour, and William D. Rosehart

IEEE Transactions on Sustainable Energy, vol. 9, no. 2, pp. 582-598, April 2018 [ link | PDF ]

Abstract: We develop a decision-making tool based on a bilevel complementarity model for a merchant price-maker energy storage system to determine the most beneficial trading actions in pool-based markets, including day-ahead (as joint energy and reserve markets) and balancing settlements. The uncertainty of net load deviation in real-time is incorporated into the model using a set of scenarios generated from the available forecast in the day-ahead. The objective of this energy storage system is to maximize its expected profit. The day-ahead products of energy storage system include energy as well as reserve commitment (as one of the ancillary services), whereas its balancing product is the energy deployed from the committed reserve. The proposed model captures the interactions of different markets and their impacts on the functioning of the storage system. It also provides an insight for storage system into clearing process of multiple markets and enables such a facility to possibly affect the outcomes of those markets to its own benefit through strategic price and quantity offers. The validity of the proposed approach is evaluated using a numerical study.

Price-taker offering strategy in electricity pay-as-bid markets

Nicolò Mazzi, JK, and Pierre Pinson

IEEE Transactions on Power Systems, vol. 33, no. 2, pp. 2175-2183, March 2018 [ link | PDF ]

Abstract: The recent increase in the deployment of renewable energy sources may affect the offering strategy of conventional producers, mainly in the balancing market. The topics of optimal offering strategy and self-scheduling of thermal units have been extensively addressed in the literature. The feasible operating region of such units can be modeled using a mixed-integer linear programming approach, and the trading problem as a linear programming problem. However, the existing models mostly assume a uniform pricing scheme in all market stages, while several European balancing markets (e.g., in Germany and Italy) are settled under a pay-as-bid pricing scheme. The existing tools for solving the trading problem in pay-as-bid electricity markets rely on nonlinear optimization models, which, combined with the unit commitment constraints, result in a mixed-integer nonlinear programming problem. In contrast, we provide a linear formulation for that trading problem. Then, we extend the proposed approach by formulating a two-stage stochastic problem for optimal offering in a two-settlement electricity market with a pay-as-bid pricing scheme at the balancing stage. The resulting model is mixed-integer and linear. The proposed model is tested on a realistic case study against a sequential offering approach, showing the capability of increasing profits in expectation.

Impacts of ramping inflexibility of conventional generators on strategic operation of energy storage facilities

Ehsan Nasrolahpour, JK, Hamidreza Zareipour, and William D. Rosehart

IEEE Transactions on Smart Grid, vol. 9, no. 2, pp. 1334-1344, March 2018 [ link | PDF ]

Abstract: This paper proposes an approach to assist a price-maker merchant energy storage facility in making its optimal operation decisions. The facility operates in a pool-based electricity market, where the ramping capability of other resources is limited. Also, wind power resources exist in the system. The merchant facility seeks to maximize its profit through strategic inter-temporal arbitrage decisions, when taking advantage of those ramp limitations. The market operator, on the other hand, aims at maximizing the social welfare under wind power generation uncertainty. Thus, a stochastic bi-level optimization model is proposed, taking into account the interactions between the storage facility and the market operator, and the existing market opportunities for the storage facility. The proposed bi-level model is then transformed into a mathematical program with equilibrium constraints that can be recast as a mixed-integer linear programming problem. Different case studies are presented and discussed using a six-bus illustrative example and the IEEE one-area reliability test system to evaluate the performance of the proposed approach.

Value of flexible resources, virtual bidding, and self-scheduling in two-settlement electricity markets with wind generation – Part I: Principles and competitive model

JK and Benjamin F. Hobbs

IEEE Transactions on Power Systems, vol. 33, no. 1, pp. 749-759, January 2018 [ link | PDF ] 

Recognized with an Honorable Mention by INFORMS ENRE Best Publication Award Committee in 2020

Abstract: Part one of this two-part paper presents new models for evaluating flexible resources in two-settlement electricity markets (day-ahead and real-time) with uncertain net loads (demand minus wind). Physical resources include wind together with fast- and slow-start demand response and thermal generators. We also model financial participants (virtual bidders). Wind is stochastic, represented by a set of scenarios. The two-settlement system is modeled as a two-stage process in which the first stage involves unit commitment and tentative scheduling, while the second stage adjusts flexible resources to resolve imbalances. The value of various flexible resources is evaluated through four two-settlement models: 1) an equilibrium model in which each player independently schedules its generation or purchases to maximize expected profit; 2) a benchmark (expected system cost minimization); 3) a sequential equilibrium model in which the independent system operator first optimizes against a deterministic wind power forecast; and 4) an extended sequential equilibrium model with self-scheduling by profit-maximizing slow-start generators. A tight convexified unit commitment allows for demonstration of certain equivalencies of the four models. We show how virtual bidding enhances market performance, since, together with self-scheduling by slow-start generators, it can help a deterministic day-ahead market to choose the most efficient unit commitment.

Value of flexible resources, virtual bidding, and self-scheduling in two-settlement electricity markets with wind generation – Part II: ISO models and application

JK and Benjamin F. Hobbs

IEEE Transactions on Power Systems, vol. 33, no. 1, pp. 760-770, January 2018 [ link | PDF ]

Abstract: In Part II of this paper, we present formulations for three two-settlement market models: Baseline cost-minimization (Stoch-Opt); and two sequential market models in which an independent system operator (ISO) runs real-time (RT) balancing markets after making day-ahead (DA) generating unit commitment decisions based upon deterministic wind forecasts, while virtual bidders arbitrage the two markets (Seq and Seq-SS). The latter two models differ in terms of whether some slow-start generators can self-schedule in the DA market while anticipating probabilities of RT prices. Models in Seq and Seq-SS build on components of the two-settlement equilibrium model (Stoch-MP) defined in Part I of this paper [J. Kazempour and B. F. Hobbs, “Value of flexible resources, virtual bidding, and self-scheduling in two-settlement electricity markets with wind generation - Part I: Principles and competitive model,” IEEE Trans. Power Syst., vol. 33, no. 1, pp. 749-759, Jan. 2018]. We then provide numerical results for all four models. A simple single-node case illustrates the economic impacts of flexibility, virtual bidding, and self-schedules, and is followed by a larger case study based on the 24-node IEEE reliability test system. Their results confirm that flexible resources, including fast-start generators and demand response, can reduce expected costs in a sequential two-settlement market. In addition, virtual bidders can also improve the functioning of sequential markets. In some circumstances, virtual bidders (together with self-scheduling by slow-start generators) enable deterministic ISO DA markets to obtain the least (expected) cost unit commitments.

Impact of public aggregate wind forecasts on electricity market outcomes

Lazaros Exizidis, JK, Pierre Pinson, Zacharie De Grève, and François Vallée

IEEE Transactions on Sustainable Energy, vol. 8, no. 4, pp. 1394-1405, October 2017 [ link | PDF ]

Abstract: Following a call to foster a transparent and more competitive market, member states of the European transmission system operator are required to publish, among other information, aggregate wind power forecasts. The publication of the latter information is expected to benefit market participants by offering better knowledge of the market operation, leading subsequently to a more competitive energy market. Driven by the above regulation, we consider an equilibrium study to address how public information of aggregate wind power forecasts can potentially affect market results, social welfare, as well as the profits of participating power producers. We investigate, therefore, a joint day-ahead energy and reserve auction, where producers offer their conventional power strategically based on a complementarity approach and their wind power at generation cost based on a forecast. In parallel, an iterative game-theoretic approach (diagonalization) is incorporated in order to investigate the existence of an equilibrium for various values of aggregate forecast. As anticipated, variations in public forecasts will affect market results and, more precisely, underforecasts can mislead power producers to make decisions that favor social welfare, while overforecasts will cause the opposite effect. Furthermore, energy and reserve market prices can also be affected by deviations in aggregate wind forecasts altering, inevitably, the profits of all power producers.

Transmission expansion in an oligopoly considering generation investment equilibrium

S. Saeid Taheri, JK, and Seyedjalal Seyedshenava

Energy Economics, vol. 64, pp. 55-62, May 2017 [ link | PDF ]

Abstract: Transmission expansion planning (TEP) is a sophisticated decision-making problem, especially in an oligopolistic electricity market in which a number of strategic (price-maker) producers compete together. A transmission system planner, who is in charge of making TEP decisions, requires considering the future generation investment actions. However, in such an oligopolistic market, each producer makes its own strategic generation investment decisions. This motivates the transmission system planner to consider the generation investment decision-making problem of all producers within its TEP model. The strategic generation investment problem of each producer can be represented by a complementarity bi-level model. The joint consideration of all bi-level models, one per producer, characterizes the generation investment equilibrium that identifies the future evolution of generation investment in the market. This paper proposes a tri-level TEP decision-making model to be solved by the transmission system planner, whose objective is to maximize the social welfare of the market minus the expansion costs, and whose constraints are the transmission expansion limits as well as the generation investment equilibrium problem. This model is then recast as a mixed-integer linear programming problem and solved. Numerical results from an illustrative example and a case study based on the IEEE 14-bus test system demonstrate the usefulness of the proposed approach.

Strategic sizing of energy storage facilities in electricity markets

Ehsan Nasrolahpour, JK, Hamidreza Zareipour, and William D. Rosehart

IEEE Transactions on Sustainable Energy, vol. 7, no. 4, pp. 1462-1472, October 2016 [ link | PDF ]

Abstract: This paper proposes a model to determine the optimal size of an energy storage facility from a strategic investor's perspective. This investor seeks to maximize its profit through making strategic planning, i.e., storage sizing, and strategic operational, i.e., offering and bidding, decisions. We consider the uncertainties associated with rival generators' offering strategies and future load levels in the proposed model. The strategic investment decisions include the sizes of charging device, discharging device, and energy reservoir. The proposed model is a stochastic bi-level optimization problem; the planning and operation decisions are made in the upper-level, and market clearing is modeled in the lower-level under different operating scenarios. To make the proposed model computationally tractable, an iterative solution technique based on Benders' decomposition is implemented. This provides a master problem and a set of subproblems for each scenario. Each subproblem is recast as an mathematical programs with equilibrium constraints. Numerical results based on real-life market data from Alberta's electricity market are provided.

Strategic demand-side response to wind power integration

Ali Daraeepour, JK, Dalia Patino-Echeverri, and Antonio J. Conejo

IEEE Transactions on Power Systems, vol. 31, no. 5, pp. 3495 - 3505, September 2016 [ link | PDF ]

Abstract: This paper explores the effects of allowing large, price-responsive consumers to provide reserves in a power system with significant penetration of wind energy. A bilevel optimization model represents the utility maximization problem of a large consumer, subject to a stochastic day-ahead co-optimization of energy and reserves that a system operator would solve to clear the market while considering wind power uncertainty. An examination of the market outcomes from both an illustrative and a large-scale study using this model allows analysis of a) the effects of the type of behavior of the large consumer (i.e., strategic vs competitive), b) limits on the amount of reserves it is allowed to provide, and c) variability and accuracy of characterization of wind power uncertainty.

Sharing wind power forecasts in electricity markets: A numerical analysis

Lazaros Exizidis, JK, Pierre Pinson, Zacharie De Grève, and François Vallée

Applied Energy, vol. 176, pp. 65-73, August 2016 [ link | PDF ]

Abstract: In an electricity pool with significant share of wind power, all generators including conventional and wind power units are generally scheduled in a day-ahead market based on wind power forecasts. Then, a real-time market is cleared given the updated wind power forecast and fixed day-ahead decisions to adjust power imbalances. This sequential market-clearing process may cope with serious operational challenges such as severe power shortage in real-time due to erroneous wind power forecasts in day-ahead market. To overcome such situations, several solutions can be considered such as adding flexible resources to the system. In this paper, we address another potential solution based on information sharing in which market players share their own wind power forecasts with others in day-ahead market. This solution may improve the functioning of sequential market-clearing process through making more informed day-ahead schedules, which reduces the need for balancing resources in real-time operation. This paper numerically evaluates the potential value of sharing forecasts for the whole system in terms of system cost reduction. Besides, its impact on each market player’s profit is analyzed. The framework of this study is based on a stochastic two-stage market setup and complementarity modeling, which allows us to gain further insights into information sharing impacts.

Network-constrained AC unit commitment under uncertainty: A Benders' decomposition approach

Amin Nasri, JK, Antonio J. Conejo, and Mehrdad Ghandhari

IEEE Transactions on Power Systems, vol. 31, no. 1, pp. 412-422, January 2016 [ link | PDF ]

Abstract: This paper proposes an efficient solution approach based on Benders' decomposition to solve a network-constrained AC unit commitment problem under uncertainty. The wind power production is the only source of uncertainty considered in this paper, which is modeled through a suitable set of scenarios. The proposed model is formulated as a two-stage stochastic programming problem, whose first-stage refers to the day-ahead market, and whose second-stage represents real-time operation. The proposed Benders' approach allows decomposing the original problem, which is mixed-integer nonlinear and generally intractable, into a mixed-integer linear master problem and a set of nonlinear, but continuous subproblems, one per scenario. In addition, to temporally decompose the proposed ac unit commitment problem, a heuristic technique is used to relax the inter-temporal ramping constraints of the generating units. Numerical results from a case study based on the IEEE one-area reliability test system (RTS) demonstrate the usefulness of the proposed approach.

Strategic bidding for a large consumer

JK, Antonio J. Conejo, and C. Ruiz

IEEE Transactions on Power Systems, vol. 30, no. 2, pp. 848-856, March 2015 [ link ]

Abstract: The smart grid technology enables an increasing level of responsiveness on the demand side, facilitating demand serving entities-large consumers and retailers-to procure their electricity needs under the best conditions. Such entities generally exhibit a proactive role in the pool, seeking to procure their energy needs at minimum cost. Within this framework, we propose a mathematical model to help large consumers to derive bidding strategies to alter pool prices to their own benefit. Representing the uncertainty involved, we develop a stochastic complementarity model to derive bidding curves, and show the advantages of such bidding scheme with respect to non-strategic ones.

Minimizing wind power spillage using an OPF with FACTS devices

Amin Nasri, Antonio J. Conejo, JK, and Mehrdad Ghandhari

IEEE Transactions on Power Systems, vol. 29, no. 5, pp. 2150 - 2159, September 2014 [ link ]

Abstract: This paper proposes an optimal power flow (OPF) model with flexible AC transmission system (FACTS) devices to minimize wind power spillage. The uncertain wind power production is modeled through a set of scenarios. Once the balancing market is cleared, and the final values of active power productions and consumptions are assigned, the proposed model is used by the system operator to determine optimal reactive power outputs of generating units, voltage magnitude and angles of buses, deployed reserves, and optimal setting of FACTS devices. This system operator tool is formulated as a two-stage stochastic programming model, whose first-stage describes decisions prior to uncertainty realization, and whose second-stage represents the operating conditions involving wind scenarios. Numerical results from a case study based on the IEEE RTS demonstrate the usefulness of the proposed tool.

Equilibria in an oligopolistic market with wind power production

JK and Hamidreza Zareipour

IEEE Transactions on Power Systems, vol. 29, no. 2, pp. 686-697, March 2014 [ link ]

Abstract: This paper proposes an approach for analyzing the impacts of large-scale wind power integration on electricity market equilibria. A pool-based oligopolistic electricity market is considered including a day-ahead market and a number of real-time markets. Wind power is considered within the generation portfolio of the strategic producers, and the uncertainty of wind power production is modeled through a set of plausible scenarios. The strategic behavior of each producer is modeled through a stochastic bilevel model. The resulting nonlinear equilibrium problem with equilibrium constraints (EPEC) is linearized and then solved. Numerical results for a test case with increasing levels of the wind power penetration is provided.

Generation investment equilibria with strategic producers – Part I: Formulation

JK, Antonio J. Conejo, and Carlos Ruiz

IEEE Transactions on Power Systems, vol. 28, no. 3, pp. 2613 - 2622, August 2013 [ link ]

Abstract: The first of this two-paper series proposes a methodology to characterize generation investment equilibria in a pool-based network-constrained electricity market, where the producers behave strategically. To this end, the investment problem of each strategic producer is represented using a bilevel model, whose upper-level problem determines the optimal investment and the supply offering curves to maximize its profit, and whose several lower-level problems represent different market clearing scenarios. This model is transformed into a mathematical program with equilibrium constraint (MPEC) through replacing the lower-level problems by their optimality conditions. The joint consideration of all producer MPECs, one per producer, constitutes an equilibrium problem with equilibrium constraints (EPEC). To identify the solutions of this EPEC, each MPEC problem is replaced by its Karush-Kuhn-Tucker (KKT) conditions, which are in turn linearized. The resulting mixed-integer linear system of equalities and inequalities allows determining the EPEC equilibria through an auxiliary MILP problem.

Generation investment equilibria with strategic producers – Part II: Case studies

JK, Antonio J. Conejo, and Carlos Ruiz

IEEE Transactions on Power Systems, vol. 28, no. 3, pp. 2623 - 2631, August 2013 [ link ]

Abstract: This paper analyzes numerically the approach reported in the companion paper for identifying generation investment equilibria in an electricity market where the producers behave strategically. To this end, a two-node illustrative example and a large-scale case study based on the IEEE reliability test system (RTS) are examined and the results obtained are reported and discussed.

Strategic generation investment considering futures and spot markets

JK, Antonio J. Conejo, and Carlos Ruiz

IEEE Transactions on Power Systems, vol. 27, no. 3, pp. 1467-1476, August 2012 [ link ]

Abstract: Futures markets are increasingly relevant for trading electric energy as they help to hedge the volatility of the pool prices. In this paper, we analyze the effect of such futures markets on the investment decisions of a strategic electricity producer. To this end, we propose a bilevel model whose upper-level problem represents the investment and offering actions of the producer, and whose multiple lower-level problems represent the clearing of both the futures markets and the pool under different operating conditions. Such model is equivalent to a mathematical program with equilibrium constraints that can be recast as a tractable mixed-integer linear programming problem and that allows assessing the impact of the futures markets on the investment decisions of a strategic producer.

Equilibria in futures and spot electricity markets

Carlos Ruiz, JK, and Antonio J. Conejo

Electric Power Systems Research, vol. 84, no. 1, pp. 1-9, March 2012 [ link ]

Abstract: We describe a model to analyze the equilibrium encompassing an electricity futures market and a number of electricity spot markets sequentially arranged along the time horizon spanned by the futures market. Profit-maximizing strategic electricity producers react to both prices and rival production changes, in both the spot and the futures markets. At each time period, the total demand is considered to depend linearly on the spot price of the considered time period, and the futures market price is assumed to equal the average spot price over the time horizon. Equilibrium conditions at each spot market are described as a function of the futures market decision variables, which in turn allows describing the equilibrium in the futures market implicitly enforcing equilibrium in each spot market. The proposed model allows deriving analytical expressions that characterize such multi-market equilibrium and that can be recast as a mixed linear complementarity problem. This model is useful to gain insight on the outcomes and characteristics of the considered multi-market equilibrium. Such insight may allow the regulator to better design the futures and spot trading floors, their rules and sequential timing. It may also allow producers to increase the effectiveness of their respective offering strategies.

Strategic generation investment under uncertainty via Benders decomposition

JK and Antonio J. Conejo

IEEE Transactions on Power Systems, vol. 27, no. 1, pp. 424-432, February 2012 [ link ]

Abstract: We address the generation investment problem faced by a strategic power producer and consider a detailed description of the uncertain parameters involved, namely, rival producer investment and market offering, and demand growth. To identify optimal investment decisions, we consider a target year and propose a bilevel model whose upper-level problem determines investment and offering decisions to maximize expected profit, and whose many lower-level problems represent market clearing conditions per demand block and scenario. Since the producer total expected profit is sufficiently convex with respect to investment decisions, a Benders' decomposition approach is proposed that results in a tractable formulation even if hundred of scenarios are used to describe uncertain parameters. Extensive numerical simulations based on realistic case studies show the good performance of the proposed decomposition approach.

Strategic generation investment using a complementarity approach

JK, Antonio J. Conejo, and Carlos Ruiz

IEEE Transactions on Power Systems, vol. 26, no. 2, pp. 940-948, May 2011 [ link ]

Abstract: This paper provides a methodology to assist a strategic producer in making informed decisions on generation investment. A single target year is considered with demand variations modeled through blocks. The strategic behavior of the producer is represented through a bilevel model: the upper-level considers both investment decisions and strategic production actions and the lower-level corresponds to market clearing. Prices are obtained as dual variables of power balance equations. Rival uncertainties (on offering and investment) are characterized through scenarios. The resulting model is a large-scale mixed-integer LP problem solvable using currently available branch-and-cut techniques. Results pertaining to an illustrative example and a case study are reported and discussed.

Risk-constrained self-scheduling of a fuel and emission constrained power producer using rolling window procedure

JK and Mohsen Parsa Moghaddam

International Journal of Electrical Power and Energy Systems, vol. 33, no. 2, pp. 359-368, February 2011 [ link ]

Abstract: This work addresses a relevant methodology for self-scheduling of a price-taker fuel and emission constrained power producer in day-ahead correlated energy, spinning reserve and fuel markets to achieve a trade-off between the expected profit and the risk versus different risk levels based on Markowitz’s seminal work in the area of portfolio selection. Here, a set of uncertainties including price forecasting errors and available fuel uncertainty are considered. The latter uncertainty arises because of uncertainties in being called for reserve deployment in the spinning reserve market and availability of power plant. To tackle the price forecasting errors, variances of energy, spinning reserve and fuel prices along with their covariances which are due to markets correlation are taken into account using relevant historical data. In order to tackle available fuel uncertainty, a framework for self-scheduling referred to as rolling window is proposed. This risk-constrained self-scheduling framework is therefore formulated and solved as a mixed-integer non-linear programming problem. Furthermore, numerical results for a case study are discussed.

Electric energy storage systems in a market-based economy: Comparison of emerging and traditional technologies

JK, Mohsen Parsa Moghaddam, Mahmoud Reza Haghifam, and Gholam Reza Yousefi

Renewable Energy, vol. 34, no. 12, pp. 2630 - 2639, December 2009 [ link ]

Abstract: Unlike markets for storable commodities, electricity markets depend on the real-time balance of supply and demand. Although much of the present-day grid operate effectively without storage technologies, cost-effective ways of storing electrical energy can make the grid more efficient and reliable. This work addresses an economic comparison between emerging and traditional Electric Energy Storage (EES) technologies in a competitive electricity market. In order to achieve this goal, an appropriate Self-Scheduling (SS) approach must first be developed for each of them to determine their maximum potential of expected profit among multi-markets such as energy and ancillary service markets. Then, these technologies are economically analyzed using Internal Rate of Return (IRR) index. Finally, the amounts of needed financial supports are determined for choosing the emerging technologies when an investor would like to invest on EES technologies. Among available EES technologies, we consider NaS battery (Natrium Sulfur battery) and pumped-storage plants as emerging and traditional technologies, respectively.

Risk-based self-scheduling of a pumped-storage plant in energy and ancillary service markets

JK, Mohsen Parsa Moghaddam, Mahmoud Reza Haghifam, and Gholam Reza Yousefi

Energy Conversion and Management, vol. 50, no. 5, pp. 1368-1375, May 2009 [ link ]

Abstract: This work addresses a new framework for self-scheduling of an individual price-taker pumped-storage plant in a day-ahead (DA) market. The goal is achieving the best trade-off between the expected profit and the risks when the plant participates in DA energy, spinning reserve and regulation markets. In this paper, a set of uncertainties including price forecasting errors and also the uncertainty of power delivery requests in the ancillary service markets are contemplated. Considering these uncertainties, a new approach is proposed which is called dynamic self-scheduling (DSS). This risk-constrained dynamic self-scheduling problem is therefore formulated and solved as a mixed integer programming (MIP) problem. Numerical results for a case study are discussed.

Evaluation of TCSC efficiency on lines overloads reduction and voltage stability enhancement in fault conditions

Mehrdad Tarafdar Hagh and JK

Journal of Faculty of Engineering (University of Tehran), vol. 117, no. 7, pp. 891-899, February 2009 [In Persian] [ link ]

Abstract: Although many mathematics-based and heuristic approaches have been recently developed on optimally allocation of TCSCs for lines overloads reduction and buses voltage stability enhancement during fault conditions, the works on the TCSCs efficiency to achieve the abovementioned goals are rare. This idea that TCSCs can surely enhance the system’s security must be comprehensively investigated. In this paper, after the optimal allocation of TCSCs, their efficiencies on lines overloads reduction and buses voltage stability enhancement during fault conditions are investigated using two new indices named “transmission index” and “voltage stability index”. The numerical results show TCSCs can remarkably enhance the buses voltage stability, but they can not significantly reduce the lines overloads. In addition, the impact of TCSCs installation on mitigation of load shedding aim to enhance the buses voltage stability is presented as a new work. The IEEE standard 14 and 30 buses systems are selected as case studies.

How satisfactory can deep reinforcement learning methods simulate electricity market dynamics?  Benchmarking via bi-level optimization

Nick Harder, Lesia Mitridati, Farzaneh Pourahmadi, Anke Weidlich, and JK

The 13th DACH+ Energy Informatics Conference, Lugano, Switzerland, October 2024

Also, published in the ACM SIGEnergy Energy Informatics Review, vol. 4, no. 4, October 2024 [ link ]

Abstract: Various factors make electricity markets increasingly complex, making their analysis challenging. This complexity demands advanced analytical tools to manage and understand market dynamics. This paper explores the application of deep reinforcement learning (DRL) and bi-level optimization models to analyze and simulate electricity markets. We introduce a bi-level optimization framework incorporating realistic market constraints, such as non-convex operational characteristics and binary decision variables, to establish an upper-bound benchmark for evaluating the performance of DRL algorithms. The results confirm that DRL methods do not reach the theoretical upper bounds set by the bi-level models, thereby confirming the effectiveness of the proposed model in providing a clear performance target for DRL. This benchmarking approach demonstrates DRL’s current capabilities and limitations in complex market environments but also aids in developing more effective DRL strategies by providing clear, quantifiable targets for improvement. The proposed method can also identify the information gap cost since DRL methods operate under more realistic conditions than optimization techniques, given that they don’t need to assume complete knowledge about the system. This study thus provides a foundation for future research to enhance market understanding and possibly its efficiency in the face of increasing complexity in the electricity market. Our methodology’s effectiveness is further validated through a large-scale case study involving 150 power plants, demonstrating its scalability and applicability to real-world scenarios.

Leveraging P90 requirement: Flexible resources bidding in Nordic ancillary service markets

Peter A. V. Gade, Henrik W. Bindner, and JK

IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids (SmartGridComm 2024), Oslo, Norway, September 2024 [ link | arXiv | GitHub ] 

Abstract: The P90 requirement of the Danish transmission system operator, Energinet, incentivizes flexible resources with stochastic power consumption/production baseline to bid in Nordic ancillary service markets with the minimum reliability of 90%, i.e., letting them cause reserve shortfall with the probability of up to 10%. Leveraging this requirement, we develop a distributionally robust joint chance-constrained optimization model for aggregators of flexible resources to optimize their volume of reserve capacity to be offered. Having an aggregator of electric vehicles as a case study, we show how distributional robustness is key for the aggregator when making bidding decisions in a non-stationary uncertain environment. We also develop a heuristic based on a grid search for the system operator to adjust the P90 requirement and the level of conservativeness, aiming to procure the maximum reserve capacity from stochastic resources with least expected shortfall.

Energy-intensive industries providing ancillary services: A real case of zinc galvanizing process

Peter A. V. Gade, Trygve Skjøtskift, Henrik W. Bindner, and JK

IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids (SmartGridComm 2024), Oslo, Norway, September 2024 [ link |  arXiv | GitHub ] 

Abstract: Energy-intensive industries can adapt to help balance the power grid. By using a real-world case study of a zinc galvanizing process in Denmark, we show how a modest investment in power control of the furnace enables the provision of various ancillary services. We consider two types of services, namely frequency containment reserve (FCR) and manual frequency restoration reserve (mFRR), and numerically conclude that the monetary value of both services is significant, such that the pay-back time of investment is potentially within a year. The FCR service provision is more preferable as its impact on the temperature of the zinc is negligible.

Electrolyzer scheduling for Nordic FCR services

Marco Saretta, Enrica Raheli, and JK 

IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids (SmartGridComm 2023), Glasgow, Scotland, November 2023 [ link | arXiv | PDF | GitHub ] 

Recipient of the Best Paper Award

Abstract: The cost competitiveness of green hydrogen production via electrolysis presents a significant challenge for its large-scale adoption. One potential solution to make electrolyzers profitable is to diversify their products and participate in various markets, generating additional revenue streams. Electrolyzers can be utilized as flexible loads and participate in various frequency-supporting ancillary service markets by adjusting their operating set points. This paper develops a mixed-integer linear model, deriving an optimal scheduling strategy for an electrolyzer providing Frequency Containment Reserve (FCR) services in the Nordic synchronous region. Depending on the hydrogen price and demand, results show that the provision of various FCR services, particularly those for critical frequency conditions (FCR-D), could significantly increase the profit of the electrolyzer.

Synergy among flexible demands: Forming a coalition to earn more from reserve market

Peter A. V. Gade, Trygve Skjøtskift, Henrik W. Bindner, and JK

IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids (SmartGridComm 2023), Glasgow, Scotland, November 2023 [ link | PDF | GitHub ] 

Abstract: We address potential synergy among flexible demands and how they may earn more collectively than individually by forming a coalition and bidding to the reserve market. We consider frequency-supporting ancillary service markets, particularly the manual Frequency Restoration Reserve (mFRR) market. The coalition of flexible demands provides more reliable mFRR services, where in comparison to individual demands, is penalized less for their potential failure and is paid more for their successful activation. This synergy effect is quantified as a function of the number of homogeneous assets in the coalition. A subsequent payment allocation mechanism using Shapley values is proposed to distribute the total earnings of the coalition among demands, while incentivizing them to remain in the coalition. For our numerical study, we use real price data from the Danish mFRR market in 2022.

Optimization of hybrid power plants: When is a detailed electrolyzer model necessary?

Manuel Tobias Baumhof, Enrica Raheli, Andrea Gloppen Johnsen, and JK

IEEE PowerTech Conference 2023, Belgrade, Serbia, June 2023 [ link | arXiv | GitHub ]

Abstract: Hybrid power plants comprising renewable power sources and electrolyzers are envisioned to play a key role in accelerating the transition towards decarbonization. It is common in the current literature to use simplified operational models for electrolyzers. It is still an open question whether this is a good practice, and if not, when a more detailed operational model is necessary. This paper answers it by assessing the impact of adding different levels of electrolyzer details, i.e., physics and operational constraints, to the optimal dispatch problem of a hybrid power plant in the day-ahead time stage. Our focus lies on the number of operating states (on, off, standby) as well as the number of linearization segments used for approximating the non-linear hydrogen production curve. For that, we develop several mixed-integer linear models, each representing a different level of operational details. We conduct a thorough comparative ex-post performance analysis under different price conditions, wind farm capacities, and minimum hydrogen demand requirements, and discuss under which operational circumstances a detailed model is necessary. In particular, we provide a case under which a simplified model, compared to a detailed one, results in a decrease in profit of 1.8 % and hydrogen production of 13.5% over a year. The key lesson learned is that a detailed model potentially earns a higher profit in circumstances under which the electrolyzer operates with partial loading. This could be the case for a certain range of electricity and hydrogen prices, or limited wind power availability. The detailed model also provides a better estimation of true hydrogen production, facilitating the logistics required.

Monetizing customer load data for an energy retailer: A cooperative game approach

Liyang Han, JK, and Pierre Pinson

IEEE PowerTech 2021 Conference, Madrid, Spain, June 2021 [ link | arXiv | video ]

Abstract: When energy customers schedule loads ahead of time, this information, if acquired by their energy retailer, can improve the retailer’s load forecasts. Better forecasts lead to wholesale purchase decisions that are likely to result in lower energy imbalance costs, and thus higher profits for the retailer. Therefore, this paper monetizes the value of the customer schedulable load data by quantifying the retailer’s profit gain from adjusting the wholesale purchase based on such data. Using a cooperative game theoretic approach, the retailer translates their increased profit in expectation into the value of cooperation, and redistributes a portion of it among the customers as monetary incentives for them to continue providing their load data. Through case studies, this paper demonstrates the significance of the additional profit for the retailer from using the proposed framework, and evaluates the long-term monetary benefits to the customers based on different payoff allocation methods.

Design of a continuous local flexibility market with network constraints

Eléa Prat, Lars Herre, JK, and Spyros Chatzivasileiadis

IEEE PowerTech 2021 Conference, Madrid, Spain, June 2021 [ link | arXiv ]

Abstract: To the best of our knowledge, this paper proposes for the first time a design of a continuous local flexibility market that explicitly considers network constraints. Continuous markets are expected to be the most appropriate design option during the early stages of local flexibility markets, where insufficient liquidity can hinder market development. At the same time, increasingly loaded distribution systems require to explicitly consider network constraints in local flexibility market clearing in order to help resolve rather than aggravate local network problems, such as line congestion and voltage issues. This paper defines the essential design considerations, introduces the local flexibility market clearing algorithm, and – aiming to establish a starting point for future research – discusses design options and research challenges that emerge during this procedure which require further investigation.

Enhanced Wasserstein distributionally robust OPF with dependence structure and support information

Adriano Arrigo, JK, Zacharie De Grève, Jean-François Toubeau, and François Vallée

IEEE PowerTech 2021 Conference, Madrid, Spain, June 2021 [ link | PDF | video | codes ]

Abstract: This paper goes beyond the current state of the art related to Wasserstein distributionally robust optimal power flow problems, by adding dependence structure (correlation) and support information. In view of the space-time dependencies pertaining to the stochastic renewable power generation uncertainty, we apply a moment-metric-based distributionally robust optimization, which includes a constraint on the second-order moment of uncertainty. Aiming at further excluding unrealistic probability distributions from our proposed decision-making model, we enhance it by adding support information. We reformulate our proposed model, resulting in a semi-definite program, and show its satisfactory performance in terms of the operational results achieved and the computational time.

Differentially private distributed optimal power flow

Vladimir Dvorkin, Pascal Van Hentenryck, JK, and Pierre Pinson

IEEE Conference on Decision and Control (CDC 2020), Jeju Island, Republic of Korea, December 2020 [ link | arXiv | video | GitHub ]

Abstract: Distributed algorithms enable private Optimal Power Flow (OPF) computations by avoiding the need in sharing sensitive information localized in algorithms sub-problems. However, adversaries can still infer this information from the coordination signals exchanged across iterations. This paper seeks formal privacy guarantees for distributed OPF computations and provides differentially private algorithms for OPF computations based on the consensus Alternating Direction Method of Multipliers (ADMM). The proposed algorithms attain differential privacy by introducing static and dynamic random perturbations of OPF sub-problem solutions at each iteration. These perturbations are Laplacian and designed to prevent the inference of sensitive information, as well as to provide theoretical privacy guarantees for ADMM sub-problems. Using a standard IEEE 118-node test case, the paper explores the fundamental trade-offs among privacy, algorithmic convergence, and optimality losses.

Chance-constrained equilibrium in electricity markets with asymmetric forecasts

Vladimir Dvorkin, JK, and Pierre Pinson 

International Conference on Probabilistic Methods Applied to Power Systems (PMAPS 2020), Liege, Belgium, August 2020 [ link | PDF ]

Abstract: We develop a stochastic equilibrium model for an electricity market with asymmetric renewable energy forecasts. In our setting, market participants optimize their profits using public information about a conditional expectation of energy production but use private information about the forecast error distribution. This information is given in the form of samples and incorporated into profit-maximizing optimizations of market participants through chance constraints. We model information asymmetry by varying the sample size of participants' private information. We show that with more information available, the equilibrium gradually converges to the ideal solution provided by the perfect information scenario. Under information scarcity, however, we show that the market converges to the ideal equilibrium if participants are to infer the forecast error distribution from the statistical properties of the data at hand or share their private forecasts.

Exploring market properties of policy-based reserve procurement for power systems

Anubhav Ratha, JK, Ana Virag, and Pierre Pinson

IEEE Conference on Decision and Control (CDC 2019), Nice, France, December 2019 [ link | PDF ]

Abstract: This paper proposes a market mechanism for co-optimization of energy and reserve procurement in day-ahead electricity markets with high shares of renewable energy. The single-stage chance-constrained day-ahead market clearing problem takes uncertain wind in-feed into account, resulting in optimal day-ahead dispatch schedule and an affine participation policy for generators for the real-time reserve provision. Under certain assumptions, the chance-constrained market clearing is reformulated as a convex quadratic program. Using tools from equilibrium modeling and variational inequalities, we explore the existence and uniqueness of a Nash equilibrium. Under the assumption of perfect competition in the market, we evaluate the satisfaction of desirable market properties, namely cost recovery, revenue adequacy, market efficiency, and incentive compatibility. To illustrate the effectiveness of the proposed market clearing, it is benchmarked against a deterministic co-optimization of energy and reserve procurement. Biased and unbiased out-of-sample simulation results for a power systems test case highlight that the proposed market clearing results in lower expected system operations cost than the deterministic benchmark, without the loss of any desirable market properties.

Optimal power flow under uncertainty: An extensive out-of-sample analysis

Adriano Arrigo, Christos Ordoudis, JK, Zacharie De Grève, Jean-François Toubeau, and François Vallée

IEEE ISGT-Europe, Bucharest, Romania, September 2019 [ link | PDF ]

Abstract: The uncertainty induced by high penetration of stochastic generation in power systems requires to be properly taken into account within Optimal Power Flow (OPF) problems to make informed day-ahead decisions that minimize the social cost in view of potential balancing actions. This ends up in a two-stage OPF problem that is usually solved using two-stage stochastic programming or adaptive robust optimization. Another alternative is the use of chance-constrained programming that allows to control the conservativeness of the decisions. In this paper, we aim at defining a fair basis for assessing the performance of these three techniques, using an extensive out-of-sample evaluation. Considering a common wind power database, each technique leads to optimal day-ahead decisions that are a posteriori assessed through the real-time stage on unseen realizations of the uncertainty. Our main conclusion is that undertaking conservative decisions results in lower standard deviations of the cost, but at the expense of higher expected cost.

Coordination of power and natural gas systems: Convexification approaches for linepack modeling

Anna Schwele, Christos Ordoudis, JK, and Pierre Pinson

IEEE PES PowerTech 2019 Conference, Milan, Italy, June 2019 [ link | PDF | codes ] 

Recipient of the 2nd Best Student Paper Award

Abstract: Utilizing operational flexibility from natural gas networks can foster the integration of uncertain and variable renewable power production. We model a combined power and natural gas dispatch to reveal the maximum potential of linepack, i.e., energy storage in the pipelines, as a source of flexibility for the power system. The natural gas flow dynamics are approximated by a combination of steady-state equations and varying incoming and outgoing flows in the pipelines to account for both natural gas transport and linepack. This steady-state natural gas flow results in a nonlinear and nonconvex formulation. To cope with the computational challenges, we explore convex quadratic relaxations and linear approximations. We propose a novel mixed-integer second-order cone formulation including McCormick relaxations to model the bidirectional natural gas flow accounting for linepack. Flexibility is quantified in terms of system cost compared to a dispatch model that either neglects linepack or assumes infinite storage capability.

A DSO-level contract market for conditional demand response

Corey Kok, JK, and Pierre Pinson

IEEE PES PowerTech 2019 Conference, Milan, Italy, June 2019 [ link | PDF ]

Abstract: This paper proposes a fixed-term (e.g., monthly) Demand Response (DR) contract market. Based on the outcomes of this market, the Distribution System Operator (DSO) pays DR aggregators to modify power consumption within a fixed window each day. Two contract types are introduced: Scheduled contracts require the DR daily, while conditional contracts require the DR after an activation signal from the DSO. Asymmetric block offers, introducing integer variables, are used to model DR with a rebound effect, potentially causing the DR offers to clear at a loss for the aggregators. Without an activation cost for conditional contracts, the DSO has the incentive to dispatch DR, despite consumer discomfort exceeding grid security benefits. Thus, the proposed market incorporates side-payments. A numerical study shows that among all DR services considered, the proposed market determines the optimal service for the whole system, ensuring the profitability of each market participant.

A consensus-ADMM approach for strategic generation investment in electricity markets

Vladimir Dvorkin, JK, Luis Baringo, and Pierre Pinson

IEEE Conference on Decision and Control (CDC 2018) , Miami Beach, FL, December 2018 [ link | PDF | codes ]

Abstract: This paper addresses a multi-stage generation investment problem for a strategic (price-maker) power producer in electricity markets. This problem is exposed to different sources of uncertainty, including short-term operational (e.g., rivals' offering strategies) and long-term macro (e.g., demand growth) uncertainties. This problem is formulated as a stochastic bilevel optimization problem, which eventually recasts as a large-scale stochastic mixed-integer linear programming (MILP) problem with limited computational tractability. To cope with computational issues, we propose a consensus version of alternating direction method of multipliers (ADMM), which decomposes the original problem by both short- and long-term scenarios. Although the convergence of ADMM to the global solution cannot be generally guaranteed for MILP problems, we introduce two bounds on the optimal solution, allowing for the evaluation of the solution quality over iterations. Our numerical findings show that there is a trade-off between computational time and solution quality.

Offering strategy of a flexibility aggregator in a balancing market using asymmetric block offers

Lucian Bobo, Stefanos Delikaraoglou, Niklas Vespermann, JK, and Pierre Pinson

Power Systems Computation Conference (PSCC 2018), Dublin, Ireland, June 2018 [ link | PDF | PSCC ]

Abstract: In order to enable large-scale penetration of renew-abies with variable generation, new sources of flexibility have to be exploited in the power systems. Allowing asymmetric block offers (including response and rebound blocks) in balancing markets can facilitate the participation of flexibility aggregators and unlock load-shifting flexibility from, e.g., thermostatic loads. In this paper, we formulate an optimal offering strategy for a risk-averse flexibility aggregator participating in such a market. Using a price-taker approach, load flexibility characteristics and balancing market price forecast scenarios are used to find optimal load-shifting offers under uncertainty. The problem is formulated as a stochastic mixed-integer linear program and can be solved with reasonable computational time. This work is taking place in the framework of the real-life demonstration project EcoGrid 2.0, which includes the operation of a balancing market on the island of Bornholm, Denmark. In this context, aggregators will participate in the market by applying the offering strategy optimization tool presented in this paper.

Evaluating the cost of line capacity limitations in aggregations of commercial buildings

Charalampos Ziras, Stefanos Delikaraoglou, JK, Shi You, and Henrik W. Bindner

International Universities Power Engineering Conference, Heraklion, Greece, August 2017 [ link | PDF ] 

Abstract: The trend towards electrification of the heating sector in many cases leads to the replacement of fossil-fueled heating systems with electric heat pumps. This may result to significantly higher consumption and potentially violations of the distribution grid operational limits. We propose a day-ahead optimization strategy to assess the cost of imposing capacity limitations in the total consumption of individual buildings, as well as aggregations of buildings. We show that such capacity limitations lead to an increase for the buildings operational costs, which can be interpreted as the value of these limitations. Based on such calculations, the aggregator can value capacity-limitation services to the distribution system operator. Moreover, the value of aggregation is also highlighted, since it leads to lower costs than imposing the same total capacity limitation on individual buildings.

Exploiting flexibility in coupled electricity and natural gas markets: A price-based approach

Christos Ordoudis, Stefanos Delikaraoglou, Pierre Pinson, and JK

IEEE PES PowerTech 2017 Conference, Manchester, UK, June 2017 [ link | PDF ]

Abstract: Natural gas-fired power plants (NGFPPs) are considered a highly flexible component of the energy system and can facilitate the large-scale integration of intermittent renewable generation. Therefore, it is necessary to improve the coordination between electric power and natural gas systems. Considering a market-based coupling of these systems, we introduce a decision support tool that increases market efficiency in the current setup where day-ahead and balancing markets are cleared sequentially. The proposed approach relies on the optimal adjustment of natural gas price to modify the scheduling of power plants and reveals the necessary flexibility to handle stochastic renewable production. An essential property of this price-based approach is that it guarantees no financial imbalance (deficit or surplus) for the system operator at the day-ahead stage. Our analysis shows that the proposed mechanism reduces the expected system cost and efficiently accommodates high shares of renewables.

Strategic wind power trading considering rival wind power production

Lazaros Exizidis, JK, Pierre Pinson, Zacharie De Grève, and François Vallée

IEEE ISGT Asia, Melbourne, Australia, November 2016 [ link | PDF ]

Abstract: In an electricity market with high share of wind power, it is expected that wind power producers may exercise market power. However, wind producers have to cope with wind's uncertain nature in order to optimally offer their generation, whereas in a market with more than one wind producers, uncertainty of rival wind power generation should also be considered. Under this context, this paper addresses the impact of rival wind producers on the offering strategy and profits of a price-maker wind producer. A stochastic day-ahead market setup is considered, which optimizes the day-ahead schedules considering a number of foreseen real-time scenarios. The results indicate that strategic wind producer is more likely to exercise market power having a mid-mean or low-mean forecast distribution, rather than having a high-mean one. Furthermore, it is observed that its offering strategy varies considerably depending on the rival's wind generation, given that its own expected generation is not high. Finally, as anticipated, expected system cost is higher when both wind power producers are expected to have low wind power generation.

Effects of risk aversion on market outcomes: A stochastic two-stage equilibrium model

JK and Pierre Pinson

International Conference on Probabilistic Methods Applied to Power Systems (PMAPS 2016), Beijing, China, October 2016 [ link | PDF ]

Abstract: This paper evaluates how different risk preferences of electricity producers alter the market-clearing outcomes. Toward this goal, we propose a stochastic equilibrium model for electricity markets with two settlements, i.e., day-ahead and balancing, in which a number of conventional and stochastic renewable (e.g., wind power) producers compete. We assume that all producers are price-taking and can be risk-averse, while loads are inelastic to price. Renewable power production is the only source of uncertainty considered. The risk of profit variability of each producer is incorporated into the model using the conditional value-at-risk (CVaR) metric. The proposed equilibrium model consists of several risk-constrained profit maximization problems (one per producer), several curtailment cost minimization problems (one per load), and power balance constraints. Each optimization problem is then replaced by its optimality conditions, resulting in a mixed complementarity problem. Numerical results from a case study based on the IEEE one-area reliability test system are derived and discussed.

Bidding strategy for an energy storage facility

Ehsan Nasrolahpour, Hamidreza Zareipour, William D. Rosehart, and JK

Power Systems Computation Conference (PSCC 2016), Genoa, Italy, June 2016 [ link | PDF | PSCC ]

Abstract: This paper studies operation decisions of energy storage facilities in perfectly and imperfectly competitive markets. In a perfectly competitive market, the storage facility is operated to maximize the social welfare. However, in a imperfectly competitive market, the storage facility operates to maximize its profit, while the market operator aims at maximizing the social welfare. In this case, the storage facility adapts its strategic behavior to take advantage of market conditions. To model the imperfectly competitive market, a bi-level optimization model is implemented to present the interactions between the storage facility and the market operator. In an illustrative test system, operation of the storage facility in these two market structures is compared and discussed.

Self-scheduling of a joint hydro and pumped-storage plant in energy, spinning reserve and regulation markets

JK, Majid Hosseinpour, and Mohsen Parsa Moghaddam

IEEE PES 2009 General Meeting, Calgary, AB, Canada, July 2009 [ link ]

Abstract: This paper addresses the self-scheduling problem for a price-taker hydro generating company. This company is comprised of several cascaded hydro plants along a river basin as well as a pumped-storage plant. Due to existence of a suitable zone as a natural reservoir, it is assumed that the hydro generating company has constructed a pumped-storage plant using the mentioned natural zone as upper reservoir and one of its hydro dams as lower reservoir. The goal is maximizing the profit of company through participating in the day-ahead energy and ancillary service markets. In order to reach this goal, it is essential to have an appropriate approach to self-schedule of company. The spinning reserve and regulation markets are considered as ancillary services in which the company can participate. The self-scheduling problem of hydro generating company is therefore formulated and solved as a mixed integer non-linear programming (MINLP) problem. Numerical results for a case study are discussed.

Economic viability of NaS battery plant in a competitive electricity market

JK and Mohsen Parsa Moghaddam

International Conference on Clean Electrical Power, Capri, Italy, June 2009 [ link ]

Abstract: Unlike markets for storable commodities, electricity markets depend on the real-time balance of supply and demand. Although much of the present-day grid operate effectively without storage technologies, cost-effective ways of storing electrical energy can make the grid more efficient and reliable. One of the emerging electric energy storage technologies is NaS (Natrium Sulfur) battery system. Recently, this technology is strongly considered due to its enough technological maturation and less environmental impacts. This work addresses the economic viability of NaS battery plant for participation in a competitive electricity market as a power producer. In order to achieve this goal, first an appropriate Self-Scheduling (SS) approach must be developed to determine its maximum potential of expected profit among multi-markets such as energy and ancillary service markets. Then, the utilization of this technology is economically analyzed using Internal Rate of Return (IRR) index. Finally, the amounts of needed financial supports are determined for choosing the NaS battery technology when an investor would like to invest on electric energy storage technologies. Two conventional financial support mechanisms are considered: decreasing the tax rate and dedicating the gratuitous loan. Numerical results for a case study are discussed.

Coupling fuel-constrained power plant and NaS battery systems for profit increment in a competitive electricity market

JK, Majid Hosseinpour, Mohsen Parsa Moghaddam, and Gholam Reza Yousefi

Power Systems Conference & Exposition (PSCE 2009), Seattle, WA, March 2009 [ link ]

Abstract: This work introduces coupling fuel-constrained power plant and electric energy storage plant aim to overall profit increment in a restructured electricity market. Among electric energy storage technologies, we select NaS battery (Natrium Sulfur battery) systems for coupling with power plant because of their enough technological maturation and less environmental impacts. The goal is investigating the coupling efficiency on profit increment considering various intensities of power plant's fuel constraint. In order to reach this goal, the amount of overall profits of fuel-constrained power plant, NaS battery plant and their coupling are first calculated in a specific time interval. Then, the coupling efficiency is determined using incremental profit rate. Having an appropriate strategy to calculate this parameter is essential. Hence, a comprehensive approach to self-schedule of individual and coupled plants is developed. This comprehensive self-scheduling approach is therefore formulated and solved as a mixed integer non-linear programming (MINLP) problem. Numerical results for a case study are discussed.

Dynamic self-scheduling of a fuel and emission constrained power producer under uncertainties

JK, Mohsen Parsa Moghaddam, Mahmoud Rrza Haghifam, and Gholam Reza Yousefi

Power Systems Conference & Exposition (PSCE 2009), Seattle, WA, March 2009 [ link ]

Abstract: This work addresses a new framework for self-scheduling of a price-taker fuel and emission constrained power producer in a day-ahead market. The goal is determination of a trade-off between the expected profit and the risk when the power producer participates in day-ahead energy and spinning reserve markets. In this paper, a set of uncertainties including price forecasting uncertainty and available fuel uncertainty are contemplated. The latter uncertainty is raised due to the uncertainty of calling the power plant to generate in the spinning reserve market as well as forced outages of power plant. With considering of these uncertainties, a new framework for self-scheduling problem is proposed which is called dynamic self-scheduling. This risk-constrained dynamic self-scheduling framework is therefore formulated and solved as a mixed integer non-linear programming problem. Numerical results for a case study are discussed.

Self-scheduling of a price-taker hydro producer in day-ahead energy and ancillary service markets

JK, Mohsen Parsa Moghaddam, and Gholam Reza Yousefi

IEEE Canada Electric Power Conference (EPEC 2008), Vancouver, BC, Canada, October 2008 [ link ]

Abstract: This paper addresses the self-scheduling of a price-taker hydro generating company in a pool-based electricity market. This company comprises several cascaded hydro plants along a river basin. The goal is maximizing the profit of company from participating in the day-ahead energy and ancillary service markets. The spinning reserve and regulation services are considered as ancillary services that hydro producer can participate in their markets. The self-scheduling problem of hydro producer is therefore formulated and solved as a mixed integer non-linear programming (MINLP) problem. Numerical results for a case study are discussed.

A MIP-based optimal operation scheduling of pumped-storage plant in the energy and regulation markets

JK, Ashkan Yousefi, Kazem Zare, and Mohsen Parsa Moghaddam

Universities Power Engineering Conference (UPEC 2008), Padova, Italy, September 2008 [ link ]

Abstract: This paper addresses the problem of optimal operation scheduling of an individual pumped-storage plant to participate in the energy and regulation markets simultaneously. The goal is achieving of the maximum expected profit when the plant participates in a day-ahead (DA) energy and regulation markets while all of the technical constraints are satisfied. This optimal operation scheduling problem is formulated and solved as a mixed integer programming (MIP) problem. Numerical results for a case study are discussed.

Static security enhancement by means of optimal utilization of NaS battery systems

JK and Mohsen Parsa Moghaddam

IEEE PowerTech 2007 Conference, Lausanne, Switzerland, July 2007 [ link ]

Abstract: This paper addresses the problem of utilization of NAS battery systems as energy storage facility for the enhancement of static security of power systems. NAS battery can be used effectively in maintaining systems security in case of a contingency, by eliminating line overloads and voltage stability control. A new methodology is introduced for optimal allocation and sizing of such batteries together with operational schemes. Numerical studies based on IEEE 14-bus system are performed for the evaluation of the method.