Efficient Load Flow Techniques Based on Holomorphic Embedding for Distribution Networks

The Holomorphic Embedding Load flow Method (HELM) employs complex analysis to solve the load flow problem. It guarantees finding the correct solution when it exists, and identifying when a solution does not exist. The method, however, is usually computationally less efficient than the traditional Newton-Raphson algorithm, which is generally considered to be a slow method in distribution networks. In this paper, we present two HELM modifications that exploit the radial and weakly meshed topology of distribution networks and significantly reduce computation time relative to the original HELM implementation. We also present comparisons with several popular load flow algorithms applied to various test distribution networks.Comment: Accepted for publication in the Proceedings of 2019 IEEE PES General Meeting, 5 Page

Learning from past bids to participate strategically in day-ahead electricity markets

We consider the process of bidding by electricity suppliers in a day-ahead market context, where each supplier bids a linear non-decreasing function of her generating capacity with the goal of maximizing her individual profit given other competing suppliers' bids. Based on the submitted bids, the market operator schedules suppliers to meet demand during each hour and determines hourly market clearing prices. Eventually, this game-theoretic process reaches a Nash equilibrium when no supplier is motivated to modify her bid. However, solving the individual profit maximization problem requires information of rivals' bids, which are typically not available. To address this issue, we develop an inverse optimization approach for estimating rivals' production cost functions given historical market clearing prices and production levels. We then use these functions to bid strategically and compute Nash equilibrium bids. We present numerical experiments illustrating our methodology, showing good agreement between bids based on the estimated production cost functions with the bids based on the true cost functions. We discuss an extension of our approach that takes into account network congestion resulting in location-dependent pricesFirst author draf

Impact of Reserve and Fixed Costs on the Day-Ahead Scheduling Problem in Greece’s Electricity Market

We sketch the main aspects of Greece’s electricity system from a market-based point of view. First, we provide data concerning the mix of generating units, the system load and the frequency-related ancillary services. Then, we formulate a simplified model of Greece’s Day-Ahead Scheduling (DAS) problem that constitutes the basis for our analysis. We examine various cases concerning the format of the objective function as well as the pricing and compensation schemes. An illustrative example is used to indicate the impact of reserve and fixed (start-up, shut-down, and minimum-load) costs on the resulting dispatching of units and on clearing prices, under the different cases. Our analysis aims at unveiling the impact of cost components other than energy offers on the DAS problem, and provide the grounds for future research on the design of the electricity market.Electricity Market, Day-Ahead Scheduling

Learning from Past Bids to Participate Strategically in Day-Ahead Electricity Markets

We consider the process of bidding by electricity suppliers in a day-ahead market context where each supplier bids a linear non-decreasing function of her generating capacity with the goal of maximizing her individual profit given other competing suppliers' bids. Based on the submitted bids, the market operator schedules suppliers to meet demand during each hour and determines hourly market clearing prices. Eventually, this game-theoretic process reaches a Nash equilibrium when no supplier is motivated to modify her bid. However, solving the individual profit maximization problem requires information of rivals' bids, which are typically not available. To address this issue, we develop an inverse optimization approach for estimating rivals' production cost functions given historical market clearing prices and production levels. We then use these functions to bid strategically and compute Nash equilibrium bids. We present numerical experiments illustrating our methodology, showing good agreement between bids based on the estimated production cost functions with the bids based on the true cost functions. We discuss an extension of our approach that takes into account network congestion resulting in location-dependent prices

Computation of Convex Hull prices in electricity markets with non-convexities using Dantzig-Wolfe decomposition

The presence of non-convexities in electricity markets has been an active research area for about two decades. The — inevitable under current marginal cost pricing — problem of guaranteeing that no market participant incurs losses in the day-ahead market is addressed in current practice through make-whole payments a.k.a. uplift. Alternative pricing rules have been studied to deal with this problem. Among them, Convex Hull (CH) prices associated with minimum uplift have attracted significant attention. Several US Independent System Operators (ISOs) have considered CH prices but resorted to approximations, mainly because determining exact CH prices is computationally challenging, while providing little intuition about the price formation rationale. In this paper, we describe the CH price estimation problem by relying on Dantzig-Wolfe decomposition and Column Generation, as a tractable, highly paralellizable, and exact method — i.e., yielding exact, not approximate, CH prices — with guaranteed finite convergence. Moreover, the approach provides intuition on the underlying price formation rationale. A test bed of stylized examples provide an exposition of the intuition in the CH price formation. In addition, a realistic ISO dataset is used to support scalability and validate the proof-of-concept.Accepted manuscrip

The Value of Distributed Energy Resources (DER) to the Grid: Introductionto the concepts of Marginal Capital Cost and Locational Marginal Value

Distributed Energy Resources (DERs) are argued to be a significant benefit to the electric utility grid. While DERs generate significant benefits to their owners and as well as society, the compensation and operating structure of the distribution system of most utilities is such that DERs result in minimal benefits to the distribution system. As we show, the benefits correctly attributed to the distribution company (the wires company) are a function of what service (real, reactive power) the DER is able to provide, when and where, and at what level of certainty the DER is able to provide the service. We introduce the concepts of Marginal Cost of Capacity (MCC) and Locational Marginal Value (LMV) in the calculation of the value of DERs to the distribution system