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In modern power systems, small distributed energy resources (DERs) are considered a valuable source of flexibility towards accommodating high penetration of Renewable Energy Sources (RES). In this paper we consider an economic dispatch problem for a community of DERs, where energy management decisions are made online and under uncertainty. We model multiple sources of uncertainty such as RES, wholesale electricity prices as well as the arrival times and energy needs of a set of Electric Vehicles. The economic dispatch problem is formulated as a multi-agent Markov Decision Process. The difficulties lie in the curse of dimensionality and in guaranteeing the satisfaction of constraints under uncertainty. A novel method, that combines duality theory and deep learning, is proposed to tackle these challenges. In particular, a Neural Network (NN) is trained to return the optimal dual variables of the economic dispatch problem. By training the NN on the dual problem instead of the primal, the number of output neurons is dramatically reduced, which enhances the performance and reliability of the NN. Finally, by treating the resulting dual variables as prices, each distributed agent can self-schedule, which guarantees the satisfaction of its constraints. As a result, our simulations show that the proposed scheme performs reliably and efficiently. [ABSTRACT FROM AUTHOR]

Marginal Utility Functions (MUFs) encapsulate the prosumer willingness to trade energy with other market agents. In large-scale distributed optimization schemes scalability and convergence are crucial, and the assumption of MUFs is common. In this work, instead of assuming the shape and coefficients of those functions, a method is proposed to derive them based on the optimization of a prosumer's energy procurement problem. We formulate a rolling-horizon optimization problem that considers asset characteristics and network tariffs, and we utilize forecasts to capture the effects of uncertainty. We use this formulation to calculate the true prosumer MUF. A test case with real data is used to investigate the shape of these functions. Our results reveal that they present a non-linear shape under certain conditions, they cannot be a priori derived, and their form is sensitive to a variety of factors. This indicates that MUFs should be constructed based on an approach similar to the one proposed in this paper to more accurately capture the prosumer's true willingness to trade. A linearized version of these functions, which is computationally attractive and scalable, can be determined using a least-squares estimator that achieves the best fit to the prosumer's preferences under a linearity constraint. [ABSTRACT FROM AUTHOR]

The large shares of wind power generation in electricity markets motivate higher levels of operating reserves. However, current reserve sizing practices fail to account for important topological aspects that might hinder their deployment, thus resulting in high operating costs. Zonal reserve procurement mitigates such inefficiencies, however, the way the zones are defined is still open to interpretation. This paper challenges the efficiency of predetermined zonal setups that neglect the location of stochastic power production in the system, as well as the availability, cost and accessibility of flexible generating units. To this end, we propose a novel reserve procurement approach, formulated as a two-stage stochastic bilevel model, in which the upper level identifies a number of contiguous reserve zones using dynamic grid partitioning and sets zonal requirements based on the total expected operating costs. Using two standard IEEE reliability test cases, we show how the efficient partitioning of reserve zones can reduce expected system cost and promote the integration of stochastic renewables. [ABSTRACT FROM AUTHOR]

The rapid growth of distributed energy resources results in the proliferation of prosumers at the distribution level, who can both produce and consume energy. In order to harvest benefits of aggregation to obtain revenues in wholesale market and encourage direct interactions among prosumers and other flexible players at the same time, this paper proposes an aggregation framework for prosumers based on transactive energy, in which prosumers aggregate and trade in an independent, proactive and privacy-preserved manner without relying on a real central entity, while other flexible players could be benefited equally. The aggregation of prosumers as a whole behaves as a retailer that trades in wholesale market and towards end-users in retail market. Therefore, the problem is generalized as a bi-level multi-leader multi-follower game in which prosumers are leaders and end-users are followers. To realize the transactive energy based trading framework, an inner-outer iteration approach is proposed, where the outer iteration involves interactions among prosumers and end-users, and achieves final results including the retail price and optimal behaviors of all players. The inner iteration is conducted during each time of the outer iteration to solve end-users’ optimal consuming profiles. The whole iteration process involves the independent decision makings of players, and only relies on exchange of information of retail price and prosumers’ offers instead of players’ private information. Case studies are then carried out demonstrating the proposed transactive energy based aggregation framework for prosumers could decrease the retail price, increase revenues for both prosumers and end-users, and reduce the peak load. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Wind power producers participating in today's electricity markets face significant variability in revenue streams, with potential high losses mostly due to wind's limited predictability and the intermittent nature of the generated electricity. In order to further expand wind power generation despite such challenges, it is important to maximize its market value and move decisively towards economically sustainable and financially viable asset management. In this paper, we introduce a decision‐making framework based on stochastic optimization that allows wind power producers to hedge their position in the market by trading physically settled options in futures markets in conjunction with their participation in the short‐term electricity markets. The proposed framework relies on a series of two‐stage stochastic optimization models that identify a combined trading strategy for wind power producers actively participating in both financial and day‐ahead electricity markets. The proposed models take into consideration penalties from potential deviations between day‐ahead market offers and real‐time operation and incorporates different preferences of risk aversion, enabling a trade‐off between the expected profit and its variability. Empirical analysis based on data from the Nordic region illustrates high efficiency of the stochastic model and reveals increased revenues for both risk neutral and risk averse wind producers opting for combined strategies. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper deals with the impact of linear approximations for the unknown nonconvex confidence region of chance-constrained ac optimal power flow problems. Such approximations are required for the formulation of tractable chance constraints. In this context, we introduce the first formulation of a chance-constrained second-order cone (SOC) OPF. The proposed formulation provides convergence guarantees due to its convexity, while it demonstrates high computational efficiency. Combined with an ac feasibility recovery, it is able to identify better solutions than chance-constrained nonconvex ac-OPF formulations. To the best of our knowledge, this paper is the first to perform a rigorous analysis of the ac feasibility recovery procedures for robust SOC-OPF problems. We identify the issues that arise from the linear approximations, and by using a reformulation of the quadratic chance constraints, we introduce new parameters able to reshape the approximation of the confidence region. We demonstrate our method on the IEEE 118-bus system. [ABSTRACT FROM AUTHOR]

Despite substantial improvement in the development of forecasting approaches, conditional and dynamic uncertainty estimates ought to be accommodated in decision-making in power system operation and market, in order to yield either cost-optimal decisions in expectation, or decision with probabilistic guarantees. The representation of uncertainty serves as an interface between forecasting and decision-making problems, with different approaches handling various objects and their parameterization as input. Following substantial developments based on scenario-based stochastic methods, robust and chance-constrained optimization approaches have gained increasing attention. These often rely on polyhedra as a representation of the convex envelope of uncertainty. In this paper, we aim to bridge the gap between the probabilistic forecasting literature and such optimization approaches by generating forecasts in the form of polyhedra with probabilistic guarantees. For that, we see polyhedra as parameterized objects under alternative definitions (under $L_1$ and $L_\infty$ norms), the parameters of which may be modeled and predicted. We additionally discuss assessing the predictive skill of such multivariate probabilistic forecasts. An application and related empirical investigation results allow us to verify probabilistic calibration and predictive skills of our polyhedra. [ABSTRACT FROM AUTHOR]

While substantial advances are observed in probabilistic forecasting for power system operation and electricity market applications, most approaches are still developed in a univariate framework. This prevents from informing about the interdependence structure among locations, lead times, and variables of interest. Such dependencies are key in a large share of operational problems involving renewable power generation and electricity prices for instance. The few methods that account for dependencies translate to sampling scenarios based on given marginals and dependence structures. However, for classes of decision-making problems based on robust, interval, and chance-constrained optimization, necessary inputs take the form of multivariate prediction regions rather than scenarios. The current literature is at a very primitive stage of characterizing multivariate prediction regions to be employed in these classes of optimization problems. To address this issue, we introduce a new class of multivariate forecasts, which form as multivariate ellipsoids for non-Gaussian variables. We propose a data-driven systematic framework to readily generate and evaluate ellipsoidal prediction regions, with predefined probability guarantees and minimum conservativeness. A skill score is proposed for quantitative assessment of the quality of prediction ellipsoids. A set of experiments is used to illustrate the discrimination ability of the proposed scoring rule for potential misspecification of ellipsoidal prediction regions. Application results based on three datasets with wind, photovoltaic power, and electricity prices allow us to assess the skill of the resulting ellipsoidal prediction regions, in terms of calibration, sharpness, and overall skill. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

With increased competition in wholesale electricity markets, the need for new decision-making tools for strategic producers has arisen. Optimal bidding strategies have traditionally been modeled as stochastic profit maximization problems. However, for producers with non-negligible market power, modeling the interactions with rival participants is fundamental. This can be achieved through equilibrium and hierarchical optimization models. The efficiency of these methods relies on the strategic producer's ability to model rival participants’ behavior and supply curve, but a substantial gap remains in the literature on modeling this uncertainty. In this study, we introduce a Bayesian inference approach to reveal the aggregate supply curve in a day-ahead electricity market. The proposed algorithm relies on Markov Chain Monte Carlo and sequential Monte Carlo methods. The major appeal of this approach is that it provides a complete model of the uncertainty of the aggregate supply curve, through an estimate of its posterior distribution. We show on a small case study that we are able to reveal accurately the aggregate supply curve with no prior information on rival participants. Finally, we show how this piece of information can be used by a price-maker producer in order to devise an optimal bidding strategy. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM AUTHOR]

Power generation expansion planning needs to deal with future uncertainties carefully, given that the invested generation assets will be in operation for a long time. Many stochastic programming models have been proposed to tackle this challenge. However, most previous works assume predetermined future uncertainties (i.e., fixed random outcomes with given probabilities). In several recent studies of generation assets’ planning (e.g., thermal versus renewable), new findings show that the investment decisions could affect the future uncertainties as well. To this end, this paper proposes a multistage decision-dependent stochastic optimization model for long-term large-scale generation expansion planning, where large amounts of wind power are involved. In the decision-dependent model, the future uncertainties are not only affecting but also affected by the current decisions. In particular, the probability distribution function is determined by not only input parameters but also decision variables. To deal with the nonlinear constraints in our model, a quasi-exact solution approach is then introduced to reformulate the multistage stochastic investment model to a mixed-integer linear programming model. The wind penetration, investment decisions, and the optimality of the decision-dependent model are evaluated in a series of multistage case studies. The results show that the proposed decision-dependent model provides effective optimization solutions for long-term generation expansion planning. [ABSTRACT FROM AUTHOR]

The participation of wind farm-energy storage systems (WF-ESS) in electricity markets calls for an integrated view of day-ahead offering strategies and real-time operation policies. Such an integrated strategy is proposed here by co-optimizing offering at the day-ahead stage and operation policy to be used at the balancing stage. Linear decision rules are seen as a natural approach to model and optimize the real-time operation policy. These allow enhancing profits from balancing markets based on updated information on prices and wind power generation. Our integrated strategies for WF-ESS in electricity markets are optimized under uncertainty in both wind power and price predictions. The resulting stochastic optimization problem readily yields optimal offers and linear decision rules. By adding a risk-aversion term in form of conditional value at risk into the objective function, the optimization model additionally provides flexibility in finding a trade-off between profit maximization and risk management. Uncertainty in wind power generation, as well as day-ahead and balancing prices, takes the form of scenario sets, permitting to reformulate the optimization problem as a linear program. Case studies validate the effectiveness of the strategy proposed by highlighting and quantifying benefits w.r.t. other existing strategies. [ABSTRACT FROM PUBLISHER]

Wind power generation is to play an important role in supplying electric power demand, and will certainly impact the design of future energy and reserve markets. Operators of wind power plants will consequently develop adequate offering strategies, accounting for the market rules and the operational capabilities of the turbines, e.g., to participate in primary reserve markets. We consider two different offering strategies for joint participation of wind power in energy and primary reserve markets, based on the idea of proportional and constant splitting of potentially available power generation from the turbines. These offering strategies aim at maximizing expected revenues from both market floors using probabilistic forecasts for wind power generation, complemented with estimated regulation costs and penalties for failing to provide primary reserve. A set of numerical examples, as well as a case-study based on real-world data, allows illustrating and discussing the properties of these offering strategies. An important conclusion is that, even though technically possible, it may not always make sense for wind power to aim at providing system services in a market environment. [ABSTRACT FROM PUBLISHER]

Renewable energy sources such as wind and solar have received much attention in recent years, and large amounts of renewable generation are being integrated into electricity networks. A fundamental challenge in power system operation is to handle the intermittent nature of renewable generation. In this paper, we present a stochastic programming approach to solve a multiperiod optimal power flow problem under renewable generation uncertainty. The proposed approach consists of two stages. In the first stage, operating points of the conventional power plants are determined. The second stage realizes generation from the renewable resources and optimally accommodates it by relying on the demand-side flexibilities. The proposed model is illustrated on a 4-bus and a 39-bus system. Numerical results show that substantial benefits in terms of redispatch costs can be achieved with the help of demand side flexibilities. The proposed approach is tested on the standard IEEE test networks of up to 300 buses and for a wide variety of scenarios for renewable generation. [ABSTRACT FROM PUBLISHER]

Accurate and reliable forecast of wind power is essential to power system operation and control. However, due to the nonstationarity of wind power series, traditional point forecasting can hardly be accurate, leading to increased uncertainties and risks for system operation. This paper proposes an extreme learning machine (ELM)-based probabilistic forecasting method for wind power generation. To account for the uncertainties in the forecasting results, several bootstrap methods have been compared for modeling the regression uncertainty, based on which the pairs bootstrap method is identified with the best performance. Consequently, a new method for prediction intervals formulation based on the ELM and the pairs bootstrap is developed. Wind power forecasting has been conducted in different seasons using the proposed approach with the historical wind power time series as the inputs alone. The results demonstrate that the proposed method is effective for probabilistic forecasting of wind power generation with a high potential for practical applications in power systems. [ABSTRACT FROM PUBLISHER]

A generic method for the providing of prediction intervals of wind power generation is described. Prediction intervals complement the more common wind power point forecasts, by giving a range of potential outcomes for a given probability, their so-called nominal coverage rate. Ideally they inform of the situation-specific uncertainty of point forecasts. In order to avoid a restrictive assumption on the shape of forecast error distributions, focus is given to an empirical and nonparametric approach named adapted resampling. This approach employs a fuzzy inference model that permits to integrate expertise on the characteristics of prediction errors for providing conditional interval forecasts. By simultaneously generating prediction intervals with various nominal coverage rates, one obtains full predictive distributions of wind generation. Adapted resampling is applied here to the case of an onshore Danish wind farm, for which three point forecasting methods are considered as input. The probabilistic forecasts generated are evaluated based on their reliability and sharpness, while compared to forecasts based on quantile regression and the climatology benchmark. The operational application of adapted resampling to the case of a large number of wind farms in Europe and Australia among others is finally discussed. [ABSTRACT FROM PUBLISHER]

Due to the fluctuating nature of the wind resource, a wind power producer participating in a liberalized electricity market is subject to penalties related to regulation costs. Accurate forecasts of wind generation are therefore paramount for reducing such penalties and thus maximizing revenue. Despite the fact that increasing accuracy in spot forecasts may reduce penalties, this paper shows that, if such forecasts are accompanied with information on their uncertainty, i.e., in the form of predictive distributions, then this can be the basis for defining advanced strategies for market participation. Such strategies permit to further increase revenues and thus enhance competitiveness of wind generation compared to other forms of dispatchable generation. This paper formulates a general methodology for deriving optimal bidding strategies based on probabilistic forecasts of wind generation, as well as on modeling of the sensitivity a wind power producer may have to regulation costs. The benefits resulting from the application of these strategies are clearly demonstrated on the test case of the participation of a multi-MW wind farm in the Dutch electricity market over a year. [ABSTRACT FROM AUTHOR]

We propose a shift from the current paradigm of electricity markets treating stochastic producers similarly to conventional ones in terms of their offers. We argue that the producers' offers should be probabilistic to reflect the limited predictability of renewable energy generation, while we should design market mechanisms to accommodate such offers. We argue that the transition from deterministic offers is a natural next step in electricity markets, by analytically proving our proposal's equivalence with a two-price conventional market. [ABSTRACT FROM PUBLISHER]

• A chance-constrained DCOPF with non-parametric correlated probabilistic forecasts of DLR and wind power. • The model co-optimizes energy and reserves with typical risk aversion levels of TSOs. • Assuming a normal distribution overestimates the probabilistic forecasts of DLR. • DLR reduces wind power curtailment and dispatch costs in highly congested networks. Compared to Seasonal Line Rating (SLR), Dynamic Line Rating (DLR) allows for higher power flows on overhead transmission lines, depending on the actual weather conditions. Nevertheless, the potential of DLR has to be traded off against the additional uncertainty associated with varying ratings. This paper proposes a DC-Optimal Power Flow (DCOPF) algorithm that accounts for DLR uncertainty by means of Chance-Constraints (CC). The goal is to determine the optimal day-ahead dispatch taking the cost of reserve procurement into account. The key contribution of this paper consists in considering both non-parametric predictive distributions of DLR and the combined wind power uncertainty in the optimization problem. Our results highlight the benefits of DLR in wind-dominated power systems, assuming typical risk aversion levels in the line rating estimation. [ABSTRACT FROM AUTHOR]