A MIP framework for non-convex uniform price day-ahead electricity auctions

It is well-known that a market equilibrium with uniform prices often does not exist in non-convex day-ahead electricity auctions. We consider the case of the non-convex, uniform-price Pan-European day-ahead electricity market "PCR" (Price Coupling of Regions), with non-convexities arising from so-called complex and block orders. Extending previous results, we propose a new primal-dual framework for these auctions, which has applications in both economic analysis and algorithm design. The contribution here is threefold. First, from the algorithmic point of view, we give a non-trivial exact (i.e. not approximate) linearization of a non-convex 'minimum income condition' that must hold for complex orders arising from the Spanish market, avoiding the introduction of any auxiliary variables, and allowing us to solve market clearing instances involving most of the bidding products proposed in PCR using off-the-shelf MIP solvers. Second, from the economic analysis point of view, we give the first MILP formulations of optimization problems such as the maximization of the traded volume, or the minimization of opportunity costs of paradoxically rejected block bids. We first show on a toy example that these two objectives are distinct from maximizing welfare. We also recover directly a previously noted property of an alternative market model. Third, we provide numerical experiments on realistic large-scale instances. They illustrate the efficiency of the approach, as well as the economics trade-offs that may occur in practice

Revisiting minimum profit conditions in uniform price day-ahead electricity auctions

We examine the problem of clearing day-ahead electricity market auctions where each bidder, whether a producer or consumer, can specify a minimum profit or maximum payment condition constraining the acceptance of a set of bid curves spanning multiple time periods in locations connected through a transmission network with linear constraints. Such types of conditions are for example considered in the Spanish and Portuguese day-ahead markets. This helps describing the recovery of start-up costs of a power plant, or analogously for a large consumer, utility reduced by a constant term. A new market model is proposed with a corresponding MILP formulation for uniform locational price day-ahead auctions, handling bids with a minimum profit or maximum payment condition in a uniform and computationally-efficient way. An exact decomposition procedure with sparse strengthened Benders cuts derived from the MILP formulation is also proposed. The MILP formulation and the decomposition procedure are similar to computationally-efficient approaches previously proposed to handle so-called block bids according to European market rules, though the clearing conditions could appear different at first sight. Both solving approaches are also valid to deal with both kinds of bids simultaneously, as block bids with a minimum acceptance ratio, generalizing fully indivisible block bids, are but a special case of the MP bids introduced here. We argue in favour of the MP bids by comparing them to previous models for minimum profit conditions proposed in the academic literature, and to the model for minimum income conditions used by the Spanish power exchange OMIE

A compensation-based pricing scheme in marketswith non-convexities

A compensation-based pricing scheme is a market clearing mechanism that may be applied when a uniform, linear pricing scheme cannot support equilibrium allocations in the auction markets. We analyze extensions of our previously proposed pricing scheme [14] to include various possible representations of bids that reflect some non-convex costs and constraints. We conclude with a discussion on directions for future research.auction design, electricity market, non-convex bids, minimum profit condition, unit commitment constraints

Power Exchange Auction Trading Platform Design (Ontwerp van een veilingsysteem voor elektrische energiebeurzen).

Deze studie analyseert de door elektrische energiebeurzen georganiseerde veilingen in Europa. Beurzen zijn instituties die de groothandel in elektrische energie vergemakkelijken. De meeste beurzen organiseren aparte veilingen een dag voordat de levering plaatsvindt voor elk uur van de volgende dag. Generatoren, grootverbruikers, leveranciers en handelaars optimaliseren hun portfolios via deze handelsplatformen.Initieel organiseerden de meeste beurzen in Europa handel binnen nationale grenzen. In toenemende mate worden ze ook betrokken bij het organiseren van grensoverschrijdende handel. De veranderende context impliceert nieuwe uitdagingen maar hernieuwt ook de discussie over hoe vroegere uitdagingen werden aangepakt.Dit werk geeft inzicht in de problemen waarmee beurzen te kampen hebben. Het veilingsysteem is gemodelleerd als een optimalisatieprobleem met beperkingen en alternatieve oplossingen worden onderzocht. In zijn rol als veilingmeester, ontvangt de beurs door marktpartijen geïntroduceerde orders en beslist dan welke orders te aanvaarden en aan welke prijzen de contracten worden afgerekend. Het nemen van deze beslissing is niet vanzelfsprekend door netwerkbeperkingen, order formaten (blokorders) en politieke beperkingen. De tekst is onderverdeeld in drie delen die respectievelijk deze themas bespreken.

A New Approach to Electricity Market Clearing With Uniform Purchase Price and Curtailable Block Orders

The European market clearing problem is characterized by a set of heterogeneous orders and rules that force the implementation of heuristic and iterative solving methods. In particular, curtailable block orders and the uniform purchase price (UPP) pose serious difficulties. A block is an order that spans over multiple hours, and can be either fully accepted or fully rejected. The UPP prescribes that all consumers pay a common price, i.e., the UPP, in all the zones, while producers receive zonal prices, which can differ from one zone to another. The market clearing problem in the presence of both the UPP and block orders is a major open issue in the European context. The UPP scheme leads to a non-linear optimization problem involving both primal and dual variables, whereas block orders introduce multi-temporal constraints and binary variables into the problem. As a consequence, the market clearing problem in the presence of both blocks and the UPP can be regarded as a non-linear integer programming problem involving both primal and dual variables with complementary and multi-temporal constraints. The aim of this paper is to present a non-iterative and heuristic-free approach for solving the market clearing problem in the presence of both curtailable block orders and the UPP. The solution is exact, with no approximation up to the level of resolution of current market data. By resorting to an equivalent UPP formulation, the proposed approach results in a mixed-integer linear program, which is built starting from a non-linear integer bilevel programming problem. Numerical results using real market data are reported to show the effectiveness of the proposed approach. The model has been implemented in Python, and the code is freely available on a public repository.Comment: 15 pages, 7 figure

Pricing in Non-Convex Markets: How to Price Electricity in the Presence of Demand Response

A Walrasian competitive equilibrium defines a set of linear and anonymous prices where no coalition of market participants wants to deviate. Walrasian prices do not exist in non-convex markets in general, with electricity markets as an important real-world example. However, the availability of linear and anonymous prices is important for derivatives markets and as a signal for scarcity. Prior literature on electricity markets assumed price-inelastic demand and introduced numerous heuristics to compute linear and anonymous prices on electricity markets. At these prices market participants often make a loss. As a result, market operators provide out-of-market side-payments (so-called make-whole payments) to cover these losses. Make-whole payments dilute public price signals and are a significant concern in electricity markets. Besides, demand-side flexibility becomes increasingly important with growing levels of renewable energy sources. Demand response implies that different flexibility options come at different prices, and the proportion of price-sensitive demand that actively bids on power exchanges will further increase. We show that with price-inelastic demand there are simple pricing schemes that are individually rational (participants do not make a loss), clear the market, support an efficient solution and do not require make-whole payments. With the advent of demand-side bids, budget balanced prices (no subsidies are necessary) cannot exist anymore, and we propose a pricing rule that minimizes make-whole payments. We describe design desiderata that different pricing schemes satisfy and report results of experiments that evaluate the level of subsidies required for linear and anonymous prices on electricity spot markets with price-sensitive demand

Pricing Schemes in Electric Energy Markets

abstract: Two thirds of the U.S. power systems are operated under market structures. A good market design should maximize social welfare and give market participants proper incentives to follow market solutions. Pricing schemes play very important roles in market design. Locational marginal pricing scheme is the core pricing scheme in energy markets. Locational marginal prices are good pricing signals for dispatch marginal costs. However, the locational marginal prices alone are not incentive compatible since energy markets are non-convex markets. Locational marginal prices capture dispatch costs but fail to capture commitment costs such as startup cost, no-load cost, and shutdown cost. As a result, uplift payments are paid to generators in markets in order to provide incentives for generators to follow market solutions. The uplift payments distort pricing signals. In this thesis, pricing schemes in electric energy markets are studied. In the first part, convex hull pricing scheme is studied and the pricing model is extended with network constraints. The subgradient algorithm is applied to solve the pricing model. In the second part, a stochastic dispatchable pricing model is proposed to better address the non-convexity and uncertainty issues in day-ahead energy markets. In the third part, an energy storage arbitrage model with the current locational marginal price scheme is studied. Numerical test cases are studied to show the arguments in this thesis. The overall market and pricing scheme design is a very complex problem. This thesis gives a thorough overview of pricing schemes in day-ahead energy markets and addressed several key issues in the markets. New pricing schemes are proposed to improve market efficiency.Dissertation/ThesisMasters Thesis Electrical Engineering 201

Building and investigating generators' bidding strategies in an electricity market

In a deregulated electricity market environment, Generation Companies (GENCOs) compete with each other in the market through spot energy trading, bilateral contracts and other financial instruments. For a GENCO, risk management is among the most important tasks. At the same time, how to maximise its profit in the electricity market is the primary objective of its operations and strategic planning. Therefore, to achieve the best risk-return trade-off, a GENCO needs to determine how to allocate its assets. This problem is also called portfolio optimization. This dissertation presents advanced techniques for generator strategic bidding, portfolio optimization, risk assessment, and a framework for system adequacy optimisation and control in an electricity market environment. Most of the generator bidding related problems can be regarded as complex optimisation problems. In this dissertation, detailed discussions of optimisation methods are given and a number of approaches are proposed based on heuristic global optimisation algorithms for optimisation purposes. The increased level of uncertainty in an electricity market can result in higher risk for market participants, especially GENCOs, and contribute significantly to the drivers for appropriate bidding and risk management tasks for GENCOs in the market. Accordingly, how to build an optimal bidding strategy considering market uncertainty is a fundamental task for GENCOs. A framework of optimal bidding strategy is developed out of this research. To further enhance the effectiveness of the optimal bidding framework; a Support Vector Machine (SVM) based method is developed to handle the incomplete information of other generators in the market, and therefore form a reliable basis for a particular GENCO to build an optimal bidding strategy. A portfolio optimisation model is proposed to maximise the return and minimise the risk of a GENCO by optimally allocating the GENCO's assets among different markets, namely spot market and financial market. A new market pnce forecasting framework is given In this dissertation as an indispensable part of the overall research topic. It further enhances the bidding and portfolio selection methods by providing more reliable market price information and therefore concludes a rather comprehensive package for GENCO risk management in a market environment. A detailed risk assessment method is presented to further the price modelling work and cover the associated risk management practices in an electricity market. In addition to the issues stemmed from the individual GENCO, issues from an electricity market should also be considered in order to draw a whole picture of a GENCO's risk management. In summary, the contributions of this thesis include: 1) a framework of GENCO strategic bidding considering market uncertainty and incomplete information from rivals; 2) a portfolio optimisation model achieving best risk-return trade-off; 3) a FIA based MCP forecasting method; and 4) a risk assessment method and portfolio evaluation framework quantifying market risk exposure; through out the research, real market data and structure from the Australian NEM are used to validate the methods. This research has led to a number of publications in book chapters, journals and refereed conference proceedings

Uncapacitated Lot-Sizing with Stock Upper Bounds, Stock Fixed Costs, Stock Overloads and Backlogging: A Tight Formulation

For an n-period uncapacitated lot-sizing problem with stock upper bounds, stock fixed costs, stock overload and backlogging, we present a tight extended shortest path formulation of the convex hull of solutions with O(n^2) variables and constraints, also giving an O(n^2) algorithm for the problem. This corrects and extends a formulation in [11] for the problem with just stock upper bounds