Shmuel S. Oren

Reserve Requirements for Wind Power Integration: A Scenario-Based Stochastic Programming Framework

We present a two-stage stochastic programming model for committing reserves in systems with large amounts of wind power. We describe wind power generation in terms of a representative set of appropriately weighted scenarios, and we present a dual decomposition algorithm for solving the resulting stochastic program. We test our scenario generation methodology on a model of California consisting of 122 generators, and we show that the stochastic programming unit commitment policy outperforms common reserve rules.

Co-Optimization of Generation Unit Commitment and Transmission Switching With N-1 Reliability

Currently, there is a national push for a smarter electric grid, one that is more controllable and flexible. The full control of transmission assets are not currently built into electric network optimization models. Optimal transmission switching is a straightforward way to leverage grid controllability: to make better use of the existing system and meet growing demand with existing infrastructure. Previous papers have shown that optimizing the network topology improves the dispatch of electrical networks. Such optimal topology dispatch can be categorized as a smart grid application where there is a co-optimization of both generators and transmission topology. In this paper we present a co-optimization formulation of the generation unit commitment and transmission switching problem while ensuring N-1 reliability. We show that the optimal topology of the network can vary from hour to hour. We also show that optimizing the topology can change the optimal unit commitment schedule. This problem is large and computationally complex even for medium sized systems. We present decomposition and computational approaches to solving this problem. Results are presented for the IEEE RTS 96 test case.

Optimal Transmission Switching With Contingency Analysis

In this paper, we analyze the N-1 reliable DC optimal dispatch with transmission switching. The model is a mixed integer program (MIP) with binary variables representing the state of the transmission element (line or transformer) and the model can be used for planning and/or operations. We then attempt to find solutions to this problem using the IEEE 118-bus and the RTS 96 system test cases. The IEEE 118-bus test case is analyzed at varying load levels. Using simple heuristics, we demonstrate that these networks can be operated to satisfy N-1 standards while cutting costs by incorporating transmission switching into the dispatch. In some cases, the percent savings from transmission switching was higher with an N-1 DCOPF formulation than with a DCOPF formulation.

Folk theorems on transmission access: Proofs and counterexamples

Nodal prices, congestion revenues, transmission capacity rights, and compensation for wire ownership are key concepts used to formulate claims about proposals to organize competitive and open transmission access. Underlying those claims are implicit assertions (folk theorems) concerning the regulation of transmission access, the determination of power flows, properties of economic dispatch, and the operations of competitive nodal markets for power. The paper has two objectives. We first formulate these folk theorems as explicit mathematical assertions. We then prove that some of these assertions are true, and we present counterexamples to other assertions.The counterexamples are interesting because they negate plausible propositions, including: (1) uncongested lines do not receive congestion rents (defined through node price differences); (2) nodal prices clear markets for power only if the allocation is efficient; (3) in an efficient allocation power can only flow from nodes with lower prices to nodes with higher prices; (4) strengthening transmission lines or building additional lines increases transmission capacity; (5) transmission capacity rights are compatible with any economically efficient dispatch.

Flow-Based Transmission Rights and Congestion Management

Abstract Combining the advantages of financial and physical rights, a flow-based transmission reservation approach facilitates liquidity and efficient risk management.

Optimal Transmission Switching—Sensitivity Analysis and Extensions

In this paper, we continue to analyze optimal dispatch of generation and transmission topology to meet load as a mixed integer program (MIP) with binary variables representing the state of the transmission element (line or transformer). Previous research showed a 25% savings by dispatching the IEEE 118-bus test case. This paper is an extension of that work. It presents how changing the topology affects nodal prices, load payment, generation revenues, cost, and rents, congestion rents, and flowgate prices. Results indicate that changing the topology to cut costs typically results in lower load payments and higher generation rents for this network. Computational issues are also discussed.

Nodal prices and transmission rights: A critical appraisal

This article challenges several prevalent claims about the role of nodal prices and transmission rights which underlie Poolco proposals. The application of nodal prices for pricing transmission services in networks with parallel path flows can have perverse consequences due to the interaction of power flows.

Modeling and Computing Two-Settlement Oligopolistic Equilibrium in a Congested Electricity Network

A model of two-settlement electricity markets is introduced, which accounts for flow congestion, demand uncertainty, system contingencies, and market power. We formulate the subgame perfect Nash equilibrium for this model as an equilibrium problem with equilibrium constraints (EPEC), in which each firm solves a mathematical program with equilibrium constraints (MPEC). The model assumes linear demand functions, quadratic generation cost functions, and a lossless DC network, resulting in equilibrium constraints as a parametric linear complementarity problem (LCP). We introduce an iterative procedure for solving this EPEC through repeated application of an MPEC algorithm. This MPEC algorithm is based on solving quadratic programming subproblems and on parametric LCP pivoting. Numerical examples demonstrate the effectiveness of the MPEC and EPEC algorithms and the tractability of the model for realistic-size power systems.

Economic Criteria for Planning Transmission Investment in Restructured Electricity Markets

From an economic perspective, a common criterion for assessing the merits of a transmission investment is its impacts on social welfare. The underlying assumption in using this criterion is that side payments may be used to distribute the social gains among all market players. In reality, however, since the impacts of an electricity transmission project on different players may vary, such side payments are rather difficult to implement. This paper focuses on different economic criteria that should be considered when planning electricity transmission investments. We propose an electricity transmission investment assessment methodology that is capable of evaluating the economic impacts on the various effected stakeholders and account for strategic responses that could enhance or impede the investments objectives. We formulate transmission planning as an optimization problem under alternative conflicting objectives and investigate the policy implications of divergent expansion plans resulting from the planners level of anticipation of strategic responses. We find that optimal transmission expansion plans may be very sensitive to supply and demand parameters. We also show that the transmission investments have significant distributional impact, creating acute conflicts of interests among market participants. We use a 32-bus representation of the main Chilean grid to illustrate our results.

Supplying renewable energy to deferrable loads: Algorithms and economic analysis

In this paper we propose a direct coupling of renewable generation with deferrable demand in order to mitigate the unpredictable and non-controllable fluctuation of renewable power supply. We cast our problem in the form of a stochastic dynamic program and we characterize the value function of the problem in order to develop efficient solution methods. We develop and compare two algorithms for optimally supplying renewable power to time-flexible electricity loads in the presence of a spot market, backward dynamic programming and approximate dynamic programming. We describe how our proposition compares to price responsive demand in terms capacity gains and energy market revenues for renewable generators, and we determine the optimal capacity of deferrable demand which can be reliably coupled to renewable generation.