Ricardo Fernandez-Blanco

A Unified Bilevel Programming Framework for Price-Based Market Clearing Under Marginal Pricing

Market clearing in restructured power systems is mostly implemented through an offer-based setting with the goal of maximizing social welfare. This approach leads to sound results from an economic viewpoint when generation offers reflect true production costs. However, offers may significantly differ from actual costs in practice, thus yielding undesired distortion. Under a marginal pricing scheme, this paper presents a general bilevel programming framework for alternative market-clearing procedures dependent on market-clearing prices rather than on offers. The resulting nonlinear mixed-integer bilevel programming formulation is transformed into an equivalent single-level mixed-integer linear program suitable for efficient off-the-shelf software. The bilevel formulation is investigated through a particular instance of price-based market clearing driven by consumer payment minimization. This problem has recently received considerable attention due to the open challenges posed from both modeling and computational perspectives. Numerical results are provided to illustrate the performance of the proposed approach.

Network-Constrained Day-Ahead Auction for Consumer Payment Minimization

This paper presents an alternative day-ahead auction based on consumer payment minimization for pool-based electricity markets. This auction is an instance of price-based market clearing wherein market-clearing prices are explicitly modeled as decision variables of the optimization. The auction design includes network constraints, inter-temporal constraints associated with generation scheduling, and marginal pricing. Hence, consumer payment is expressed in terms of locational marginal prices. The proposed solution approach is based on bilevel programming. In the upper-level optimization, generation is scheduled with the goal of minimizing the total consumer payment while taking into account that locational marginal prices are determined by a multiperiod optimal power flow in the lower level. In this bilevel programming setting, locational marginal prices are the Lagrange multipliers or dual variables associated with the nodal power balance equations of the lower-level problem. The resulting mixed-integer linear bilevel program is transformed into an equivalent single-level mixed-integer linear program suitable for efficient off-the-shelf software. This transformation relies on the application of results from duality theory of linear programming and integer algebra. The proposed methodology has been successfully applied to several test systems including the IEEE 118-bus system. Numerical results have been compared with those obtained from declared social welfare maximization.

Optimal Energy Storage Siting and Sizing: A WECC Case Study

The large-scale integration of grid-scale energy storage and the increasing penetration of renewable resources motivate the development of techniques for determining the optimal ratings and locations of storage devices. This paper proposes a method for identifying the sites where energy storage systems should be located to perform spatio-temporal energy arbitrage most effectively and the optimal size of these systems. This method takes a centralized perspective where the objective is to minimize the sum of the expected operating cost and the investment cost of energy storage. It has been tested on a realistic 240-bus 448-line model of the Western Electricity Coordinating Council (WECC) interconnection. The influence on the results of the following parameters is analyzed: Maximum number of storage locations, maximum size of storage systems, capital cost of deploying storage, value assigned to spillage of renewable energy, marginal cost of conventional generation, and renewable generation capacity. These numerical results are used to characterize the benefits that energy storage can provide in prospective large-scale power systems with renewable generation.

Ensuring Profitability of Energy Storage

Energy storage (ES) is a pivotal technology for dealing with the challenges caused by the integration of renewable energy sources. It is expected that a decrease in the capital cost of storage will eventually spur the deployment of large amounts of ES. These devices will provide transmission services, such as spatiotemporal energy arbitrage, i.e., storing surplus energy from intermittent renewable sources for later use by loads while reducing the congestion in the transmission network. This paper proposes a bilevel program that determines the optimal location and size of storage devices to perform this spatiotemporal energy arbitrage. This method aims to simultaneously reduce the system-wide operating cost and the cost of investments in ES while ensuring that merchant storage devices collect sufficient profits to fully recover their investment cost. The usefulness of the proposed method is illustrated using a representative case study of the ISO New England system with a prospective wind generation portfolio.

Look-Ahead Bidding Strategy for Energy Storage

As the cost of battery energy storage continues to decline, we are likely to see the emergence of merchant energy storage operators. These entities will seek to maximize their operating profits through strategic bidding in the day-ahead electricity market. One important parameter in any storage bidding strategy is the state-of-charge at the end of the trading day. Because this final state-of-charge is the initial state-of-charge for the next trading day, it has a strong impact on the profitability of storage for this next day. This paper proposes a look-ahead technique to optimize a merchant energy storage operators bidding strategy considering both the day-ahead and the following day. Taking into account the discounted profit opportunities that could be achieved during the following day allows us to optimize the state-of-charge at the end of the first day. We formulate this problem as a bilevel optimization. The lower-level problem clears a ramp-constrained multiperiod market and passes the results to the upper-level problem that optimizes the storage bids. Linearization techniques and Karush–Kuhn–Tucker conditions are used to transform the original problem into an equivalent single-level mixed-integer linear program. Numerical results obtained with the IEEE Reliability Test System demonstrate the benefits of the proposed look-ahead bidding strategy and the importance of considering ramping and network constraints.

Probabilistic Security-Constrained Unit Commitment With Generation and Transmission Contingencies

System operators maintain sufficient reserve in power systems in order to respond to generation and transmission contingencies. Traditionally, the reserve requirements have been determined using deterministic criteria (e.g., N - 1). These amounts of reserve allocate sufficient spare generation capacity and transmission margins to protect the system against any contingency of magnitude lower or equal to the chosen criterion. However, these criteria ignore the probability of individual contingencies as well as energy redistribution and transmission limitations in post-contingency states. In this paper, we propose to optimize the amount, location, and chronological procurement of the reserve in a given power system using probabilistic criteria. The proposed approach factors the probability of individual contingencies in a cost/benefit analysis, which balances the pre-contingency operating costs against the post-contingency cost of interruptions. The effectiveness of the proposed approach is demonstrated using a modified IEEE Reliability Test System.

Incorporating Price-Responsive Demand in Energy Scheduling Based on Consumer Payment Minimization

In the restructured power industry, demand responsiveness is a key factor whose importance will be boosted due to the impetus provided by the development of smart grids. Within the context of pool-based electricity markets, this paper addresses the incorporation of price-responsive demand in multiperiod energy scheduling driven by consumer payment minimization. Although consumer payment minimization has drawn considerable attention mainly in an operational setting and also recently under a planning framework, available models and solution approaches typically neglect demand-side participation. The proposed scheduling model considers a marginal pricing scheme as well as the effects of both network constraints and intertemporal constraints associated with generation operation. Modeling demand-side participation leads to bilinear payment terms that significantly increase the mathematical complexity of the optimization process.The resulting problem is formulated as a mixed-integer nonlinear bilevel program for which no exact solution technique is currently available. This paper presents a novel methodology by which the original bilevel and bilinear problem is converted into an equivalent single-level mixed-integer linear program suitable for efficient off-the-shelf software. This transformation is based on the application of duality theory of linear programming, integer algebra, and Karush-Kuhn-Tucker optimality conditions. The proposed approach has been successfully applied to the IEEE 118-bus system.

On the Solution of Revenue- and Network-Constrained Day-Ahead Market Clearing Under Marginal Pricing—Part I: An Exact Bilevel Programming Approach

The first of this two-paper series addresses a practical day-ahead auction model, where generation revenue constraints are explicitly incorporated in the problem formulation, as routinely done in several national electricity markets across Europe. The revenue-constrained market-clearing procedure includes the effect of the transmission network, inter-temporal constraints associated with generation scheduling, demand-side bidding, and marginal pricing. This auction design is an instance of price-based market clearing which features two major complicating factors. First, locational marginal prices become decision variables of the optimization process. In addition, producer revenues are formulated as bilinear and highly nonconvex products of power outputs and market-clearing prices. The resulting problem is formulated as a mixed-integer nonlinear bilevel program with bilinear terms for which available solution techniques rely on heuristics, approximations, or modeling simplifications. This paper presents a novel and exact methodology whereby the original problem is recast as an equivalent single-level mixed-integer linear program. As a consequence, finite convergence to optimality is guaranteed and the use of standard commercial software is allowed. The proposed transformation is based on duality theory of linear programming, Karush-Kuhn-Tucker optimality conditions, and integer algebra results. In the second part of this two-paper series, numerical results from several case studies illustrate the effective performance of the proposed solution approach.

On the Solution of Revenue- and Network-Constrained Day-Ahead Market Clearing Under Marginal Pricing—Part II: Case Studies

This paper presents the numerical analysis of the bilevel programming approach for revenue- and network-constrained market clearing developed in its companion paper. The impact of minimum revenue conditions and minimum declared profits on generation and consumption levels as well as on locational marginal prices for energy is examined in detail through three case studies. First, the results from an illustrative example including minimum revenue conditions are comprehensively analyzed. The second case study is based on the IEEE Reliability Test System and considers minimum declared profits. In the third case study, a modified version of the IEEE 118-bus system is tested while accounting for minimum revenue conditions. In addition, the computational behavior of the proposed approach is illustrated with several case studies including the IEEE 300-bus system. Numerical results show the effectiveness of the proposed approach to handle revenue constraints as well as its superiority over the heuristic currently implemented in the Iberian electricity market. Moreover, simulations reveal that, unlike previous works in the literature, generation revenue constraints can be precisely incorporated in day-ahead market clearing while explicitly considering the standard economic-dispatch-based marginal pricing scheme and without requiring price uplifts.

Scalable Planning for Energy Storage in Energy and Reserve Markets

Energy storage can facilitate the integration of renewable energy resources by providing arbitrage and ancillary services. Jointly optimizing energy and ancillary services in a centralized electricity market reduces the systems operating cost and enhances the profitability of energy storage systems. However, achieving these objectives requires that storage be located and sized properly. We use a bilevel formulation to optimize the location and size of energy storage systems, which perform energy arbitrage and provide regulation services. Our model also ensures the profitability of investments in energy storage by enforcing a rate of return constraint. Computational tractability is achieved through the implementation of a primal decomposition and a subgradient-based cutting-plane method. We test the proposed approach on a 240-bus model of the Western Electricity Coordinating Council system and analyze the effects of different storage technologies, rate of return requirements, and regulation market policies on energy storage participation on the optimal storage investment decisions. We also demonstrate that the proposed approach outperforms exact methods in terms of solution quality and computational performance.