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We propose a chance-constrained formulation for the problem of dimensioning frequency restoration reserves on a power transmission network. We cast our problem as a two-stage stochastic mixed integer linear program, and propose a heuristic algorithm for solving the problem. Our model accounts for the simultaneous sizing of both upward and downward reserves, and uncertainty driven by imbalances, contingencies and available transmission capacity. Our core methodology is further adapted in order to minimize inter-zonal flows and in order to split reserve requirements between automatic and manual frequency restoration reserves. We apply our methodology to the problem of sizing reserves in the four load frequency control areas of the Swedish power system. We demonstrate the benefits of our method in terms of decreasing reserve requirements in the absence of reserve sharing, we analyze the spatial allocation of reserves, and we perform various sensitivity analyses. [ABSTRACT FROM AUTHOR]

The European balancing market is undergoing radical transformation through numerous market design initiatives. These initiatives aim at improving geographical coordination among European transmission system operators, and better positioning the European system for integrating renewable resources through short-term operational efficiency and long-term investment in flexible resources. However, the European design is characterized by a missing market for real-time reserve capacity, that has been inherited from a failure to recognize the central role of real-time operations as the spot market of the electric power industry. This missing market undermines the valuation of reserve capacity, and the back-propagation of price signals to forward reserve markets that can support investment in reserves. The goal of the present paper is to develop a methodology that exposes the implications of this missing market. The methodology relies on analytical insights that can be derived under an assumption of price-taking behavior. These insights are validated by a simulation model which represents the European balancing market as a Markov Decision Process. The simulation model is used for validating the analytical insights and testing the ability of various balancing market design options to back-propagate the real-time value of reserve to forward reserve markets. [ABSTRACT FROM AUTHOR]

In this paper, we present a two-stage model of zonal electricity markets with day-ahead market clearing, and real-time re-dispatch and balancing that accounts for transmission line switching at both stages. We show how the day-ahead problem with switching can be formulated as an adaptive robust optimization problem with mixed integer recourse, and present a new algorithm for solving the adversarial max-min problem that obeys the structure of an interdiction game. We apply the model on a realistic instance of the Central Western European system, and comment on the impacts of both proactive, and reactive transmission switching on the operating costs of the system. Part I presents day-ahead models of a short-term zonal electricity market with switching, and describes our algorithmic approach for solving these models efficiently. Part II describes variants of the real-time model, and presents the results of our case study on the Central Western European market. [ABSTRACT FROM AUTHOR]

The increasing integration of renewable resources in electricity markets has increased the need for producers to correct their trading position close to real time in order to avoid volatile real-time prices. The closest option to delivery time in European markets is to trade in the continuous intraday market. This market is therefore an attractive trading outlet for assets that target at extracting value from their flexibility. Trading in this market is challenging due to the multistage nature of the problem, its high uncertainty and the fact that decisions need to be reached rapidly, in order to lock in profitable trades. We model the trading problem of a storage unit in the Markov Decision Process framework. We present an approach based on policy function approximation for tackling the problem. We provide relevant parameters for defining our policy, and demonstrate the effectiveness of our approach by comparing it to the rolling intrinsic policy on real historical data. Our proposed approach outperforms the rolling intrinsic policy, which is commonly employed in practice for storage units, by increasing profitability by $\text{17.8}\%$ on out-of-sample testing for a storage with perfect round-trip efficiency and by $\text{13.6}\%$ for a storage unit with a round-trip efficiency of $\text{81}\%$. [ABSTRACT FROM AUTHOR]

Low-voltage distribution networks are emerging as an increasingly important component of power system operations due to the deployment of distributed renewable resources (e.g., rooftop solar supply) and the need to mobilize the flexibility of consumers that are connected to the low-voltage grid. The pricing of electric power at distribution nodes follows directly from the theory of spot pricing of electricity. However, in contrast to linearized lossless models of transmission networks, an intuitive understanding of prices at the distribution level presents challenges due to voltage limits, reactive power flows, and losses. In this paper, we present three approaches toward understanding distribution locational marginal prices by decomposing them: 1) through a duality analysis of the problem formulated with a global power balance constraint; 2) through a duality analysis of a second-order cone program relaxation; and 3) through an analysis of the impact of marginal losses on price. We discuss the relative strengths and weaknesses of each approach in terms of computation and physical intuition, and demonstrate the concepts on a 15-bus radial distribution network. [ABSTRACT FROM AUTHOR]

This paper presents a multistage stochastic programming formulation of a transmission-constrained economic dispatch subject to multiarea renewable production uncertainty, with a focus on optimizing the dispatch of storage in real-time operations. This problem is resolved using stochastic dual dynamic programming. The applicability of the proposed approach is demonstrated on a realistic case study of the German power system calibrated against the solar and wind power integration levels of 2013–2014, with a 24-h horizon and 15-min time step. The value of the stochastic solution relative to the cost of a deterministic policy amounts to 1.1%, while the value of perfect foresight relative to the cost of the stochastic programming policy amounts to 0.8%. The relative performance of various alternative real-time dispatch policies is analyzed, and the sensitivity of the results is explored. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate the impact of zonal network management in the operation of power systems with significant levels of renewable energy integration. Our study is inspired by the current state of the European energy market, and we focus on a case study of the Central Western European (CWE) system. First, we present a hierarchy of models that account for unit commitment, the separation of energy and reserves, and the simplified representation of transmission constraints in a zonal market, in order to examine the impact of these factors on efficiency in a regime of large-scale renewable energy integration. Second, we simulate operations of the CWE system under the zonal market design using a detailed instance that consists of 656 thermal generators, 679 nodes, and 1073 lines, with multiarea renewable energy production and 15-minute time resolution. Zonal market operations are compared against deterministic and stochastic unit commitment using high-performance computing in order to tackle the scale of the resulting models. We find that market design can have an influence on cost efficiency which far exceeds the benefits of stochastic unit commitment relative to deterministic unit commitment. We conduct a detailed analysis of the numerical results in order to explain the relative performance of the different models. [ABSTRACT FROM AUTHOR]

Day-ahead energy market clearing relies on a deterministic equivalent model with a limited time horizon, which may lead to inefficient scheduling of generating units from the point of view of generators. For this reason, generators may wish to assume the risk of self-committing their units with the hope of securing greater profits. This phenomenon may reduce the room for economic signals in the day-ahead market. In this paper we investigate the influence of risk aversion and price volatility on the decision of generators to self-commit units. We present a stochastic programming model for self-committing combined cycle units under price uncertainty with a conditional value at risk criterion. We use Benders decomposition to solve the problem and present results on a case study to draw conclusions. [ABSTRACT FROM PUBLISHER]