This paper outlines a strawman proposal for ensuring electricity supply adequacy by means of contracting obligations imposed on load serving entities (LSE). The mandatory contracts take the form of physically covered back stop call options with a high strike price so as not to interfere with normal risk management practices. These call options which can be covered by existing capacity, new investment in generation, or curtailable load contracts are of one year duration and a two year lead time so as to enable new entrant participation. The obligation, which is based on forecasted peak load plus adequate planning reserves, can be met with any forward or option contract that meets the physical cover requirement, has the same delivery period, and has a strike or forward price at or below the backstop strike price. The proposed mechanisms is intended to facilitate smooth transition to an energy only market where voluntary bilateral contracting and spot prices provide the needed incentives for adequate investment in generation capacity. We also describe a central procurement alternative that alleviates the credit problems associated with carrying long term option contracts. The features of the proposed approach are compared to those of the controversial LICAP mechanism proposed by the NEISO and endorsed by FERC.

In this dissertation we develop models, solution techniques, and derive policy implications for a number of important applications in improving power system resilience and flexibility: black start allocation and power system restoration, optimal islanding, stochastic unit commitment and flexible wind dispatch. The models we employ are predominantly mixed integer programs (MIPs), i.e. optimization problems in which some of the variables must take integer values. These problems are NP-hard in general, so there is no guarantee that we will be able to obtain solutions within acceptable time and accuracy as the scale of the problem increases. For that reason, we also develop or utilize specialized computational techniques, which broadly fall into one of the following categories: decomposition algorithms that exploit the problem structure (sparsity), reformulations of the problem constraints, and customized heuristics.

We start by exploring the problem of restoring the normal operation of the power system after a blackout. The restoration of the system builds around specific units with the ability to start autonomously (black start units). We formulate a planning problem for deciding the allocation of these units on the grid - black start allocation (BSA) - in an optimal way, while simultaneously optimizing over the possible restoration plans. We include, among others, considerations for thermal limits of lines, alleviating overvoltages, and constraints to model the startup curves of generators. Due to the size and complexity of the resulting MIP, commercial solvers are unable to tackle it directly. We construct a randomized heuristic based on linear programming relaxations of the optimization problem and an understanding of the underlying physics of the power grid to aid the solvers. The heuristic execution is parallelized and implemented on a high-performance computing environment. We are able to obtain solutions with optimality guarantees within reasonable times for test power systems with a few hundred buses.

We proceed to extract a substructure of the feasible region from any problem in power systems that employs reconfiguration of the physical topology (i.e. switching on/off of generators, branches, and buses): each energized island in the power system needs to contain at least one energized generator. We explore reformulations that describe the feasible region corresponding to this requirement. We employ two families of valid inequalities to strengthen the formulation, both exponential in size, but separable in polynomial time. We study polyhedral properties of the integer hull and the strength of some of these inequalities under simplifying assumptions. We proceed to conduct computational experiments for two problems in which the substructure appears: the optimal islanding problem and a simplified version of the BSA problem. We are able to observe significant computational benefits by using suitable reformulations for both problems. Finally, we describe an approach to obtain solutions with an optimality guarantee for a simplified model of BSA in a synthetic test case with 2000 nodes representative of Texas.

We extend the modeling framework of the BSA problem to accommodate for uncertainty in the power outages. Specifically, we consider optimal allocations of the black start units over a number of scenarios of partial or total outages. These scenarios may also include irreparable damage caused to components of the system. The resulting stochastic mixed integer program exhibits sparsity, so we employ a decomposition algorithm by scenario to solve instances of the problem.

We then return to the optimal islanding problem to examine it in more detail. We observe that, despite the formulation improvements, the branch and cut algorithm is still fairly slow for an online application of that scale, which requires to act within seconds to prevent a cascaded outage of the system. For that reason, we propose a heuristic based on a reformulation of the optimization into a problem in graph theory. We utilize an algorithm to obtain heuristic solutions with high computational efficiency and good quality compared to state-of-the-art techniques.

To conclude this dissertation, we introduce a framework for evaluating the cost of priority dispatch for wind power. Renewable generation is commonly considered a must-take resource in power systems, despite the technical capabilities of current wind turbines to dispatch at levels lower than their available output. The cost of that policy compared to one that instead optimizes over the available wind output is evaluated for a reduced California system, by employing a two-stage stochastic program for stochastic unit commitment. A scenario decomposition algorithm for the resulting large-scale MIP, parallelized on a high-performance computing environment, enables us to obtain near optimal solutions and calculate the difference in cost between the two policies.

This paper discusses alternative approaches that have been adopted around the world for guaranteeing the appropriate level of investment in electric generation capacity. We argue that long term reserves should be viewed as price insurance and be treated as a private good. However, political realities and asymmetries and distortions in risk management incentives may necessitate imposition of mandatory levels of such insurance on load serving entities. Furthermore, centralized markets may be needed as a supplement to bilateral contracting in order to facilitate efficient procurement of such insurance and to bridge the gap between the needs of generators and load serving entities with regard to duration of hedging instruments. We discuss the origins and shortcomings of capacity payments and capacity obligations and explain how long term supply contracts in the form of call options with premiums that depend on the contracts' strike prices can meet the need for ensuring supply adequacy and the financial health of the generator sector. We also outline a scheme where regulatory intervention in generation adequacy assurance takes the form of a hedging requirement imposed at the state level on load serving entities.

We present an empirical analysis of a supply function equilibrium model in the Texas spot electricity market. We derive conditions for optimal bidding behavior in a spot market with ex ante bilaterally contracted sales. By estimating costs, we are able to derive a set of ex post-and ex ante-optimal supply functions and use a non-parametric behavioral model to compare our theoretically optimal supply functions to actual offers made. Our results show that with the exception of the largest generators, firms make offers with markups and markdowns far in excess of what a model of profit-maximizing behavior suggests.

The prevalence of commercial activities whose profit and cost are correlated with weather risk makes weather derivatives valuable financial instruments that enable hedging of price or volumetric (quantity) risk in many industries. This paper proposes a multi-period equilibrium pricing model for weather derivative. In our stylized economy representative agents of weather-sensitive industries optimizes their hedging portfolios that drive the supply and demand for weather derivative which are dynamically determined based on a utility indifference pricing framework. At equilibrium the weather derivative market will be cleared and their market price can be obtained. Numerical examples illustrate the equilibrium prices and optimal choices for the weather derivative as function of the correlation between weather indices and demand for the underlying commodity. We also demonstrate the benefit of multiple trading opportunities which allows rebalancing of the hedging portfolio prior to the commodity delivery date, as compared to a single shot framework.

Many industries are exposed to weather risk. Weather derivatives can play a key role in hedging and diversifying such risk because the uncertainty in a company’s profit function can be correlated to weather condition which affects diverse industry sectors differently. Unfortunately the weather derivatives market is a classical example of an incomplete market that is not amenable to standard methodologies used for derivative pricing in complete markets. In this paper, we develop an equilibrium pricing model for weather derivatives in a multi-commodity setting. The model is constructed in the context of a stylized economy where agents optimize their hedging portfolios which include weather derivatives that are issued in a fixed quantity by a financial underwriter. The supply and demand resulting from hedging activities and the supply by the underwriter are combined in an equilibrium pricing model under the assumption that all agents maximize some risk averse utility function. We analyze the gains due to the inclusion of weather derivatives in hedging portfolios and examine the components of that gain attributable to hedging and to risk sharing.

This dissertation presents an equilibrium framework for analyzing the impact of cap-and-trade regulation on transmission-constrained electricity market. The cap-and-trade regulation of greenhouse gas emissions has gained momentum in the past decade. The impact of the regulation and its efficacy in the electric power industry depend on interactions of demand elasticity, transmission network, market structure, and strategic behavior of firms. I develop an equilibrium model of an oligopoly electricity market in conjunction with a market for tradable emissions permits to study the implications of such interactions. My goal is to identify inefficiencies that may arise from policy design elements and to avoid any unintended adverse consequences on the electric power sector.

I demonstrate this modeling framework with three case studies examining the impact of carbon cap-and-trade regulation. In the first case study, I study equilibrium results under various scenarios of resource ownership and emission targets using a 24-bus IEEE electric transmission system. The second and third case studies apply the equilibrium model to a realistic electricity market, Western Electricity Coordinating Council (WECC) 225-bus system with a detailed representation of the California market.

In the first and second case studies, I examine oligopoly in electricity with perfect competition in the permit market. I find that under a stringent emission cap and a high degree of concentration of non-polluting firms, the electricity market is subject to potential abuses of market power. Also, market power can occur in the procurement of non-polluting energy through the permit market when non-polluting resources are geographically concentrated in a transmission-constrained market.

In the third case study, I relax the competitive market structure assumption of the permit market by allowing oligopolistic competition in the market through a conjectural variation approach. A short-term equilibrium analysis of the joint markets in the presence of market power reveals that strategic permit trading can play a vital role in determining economic outcomes in the electricity market. In particular, I find that a firm with more efficient technologies can employ strategic withholding of permits, which allows for its increase in output share in the electricity market at the expense of other less efficient firms. In addition, strategic permit trading can influence patterns of transmission congestion.

These results illustrate that market structure and transmission congestion can have a significant impact on the market performance and environmental outcome of the regulation while the interactions of such factors can lead to unintended consequences. The proposed approach is proven useful as a tool for market monitoring purposes in the short run from the perspective of a system operator, whose responsibility has become indirectly intertwined with emission trading regulation.

There has been multiple national directives to enhance the economic operations of the power transmission system and promote the efficient use of the current grid configuration and resources. Transmission switching has been proposed as a new control method for various benefits, including improving the economic efficiency and meeting the reliability requirements. Optimal Transmission Switching model has been introduced to find an optimal generation dispatch and network topology to minimize the dispatch cost. Binary decision variables are used to denote the control of the transmission lines, which makes the model a nonlinear program. It suffers from curse of dimensionality and faces serious computational challenges.

To tackle the computational challenge of the Optimal Transmission Switching model, we propose three greedy algorithms in which only one line is switched at an iteration. In each iteration we solve a series of linear programs or smaller MIP programs, which can be implemented in parallel with the aid of high performance computing. The first algorithm enumerates all the possible line switching actions. The second algorithm produces a priority list ranking lines by a sensitivity factor based on dual criterion, and evaluate lines starting from the top of the list. The last one divides lines into small groups and consider each group at one time. We test the algorithms on the IEEE 118-Bus network and the FERC 13,867-Bus network which is representative of PJM Regional Transmission Organization. The results show that all three proposed algorithms result in cost reduction close to the best known optimal within a reasonable timeframe for IEEE network. For the FERC network which can not be solved directly by the OTS, the first two greedy algorithms are able to produce switching sequences which result in considerable cost reduction.

Furthermore we propose three machine learning based methods to produce priority lists for ranking possible line switching actions to facilitate faster searching. The algorithms take in the parameters from network status and network configuration to produce a standardized score representing the possible cost reduction of the line switching action. The numerical results on IEEE network and FERC network are presented. We evaluate the effectiveness of the priority lists based on dual criterion and machine learning methods by both regression analysis and comparison with random lists.

Based on the algorithms in literature and those we develop, we propose an algorithm selection method which selects the algorithm to optimize the cost improvement at each iteration. They show improvement in the cost reduction compared to the individual algorithms, especially for the FERC network.

The evolution of policy objectives and emergence of new technologies continually challenge the existing wholesale electricity market design. In the framework of standard market design based on locational marginal pricing (LMP) and two-settlement electricity markets, this dissertation investigates two topics for existing and future power systems -- Convergence Bidding (CB) and distribution locational marginal pricing (DLMP). The central theme that connects these two topics is market design -- determining how to create proper incentives to compensate market participants that ensures efficiency and reliability of the power grid.

We first empirically test whether the California Independent System Operator's (CAISO) existing two-settlement electricity markets are efficient, and if not, to what extent CB improves market efficiency. We examine the theoretical and empirical tools intended for other financial markets to help us understand the efficacy of CB in the forward and spot electricity markets. In the light of the efficient market hypothesis, Jensen uses the zero-profit competitive equilibrium to describe the condition for market efficiency. This definition of market efficiency directly converts the test of market efficiency into the assessment of return behavior. Following this methodology, we empirically test for market efficiency by evaluating the performance of trading strategies based on market data in the CAISO electric power markets. Our backtest results show that profitable trading opportunities continue to exist in the post-CB period, but the profitability decreases substantially. The decrease in profitability in the post-CB period indicates the improvement of market efficiency, and demonstrates the benefit of CB. The profitability in the post-CB period, however, conveys empirical implications that can be interpreted differently, depending on the level of competition and the level of risk aversion of virtual traders.

We further examine the use of DLMP to improve system efficiency in future power systems. DLMP is a modified form of LMP to alleviate congestion induced by electric vehicle (EV) loads on the distribution network. The distribution system operator (DSO) determines distribution locational marginal prices (DLMPs) by solving the social welfare optimization for both the conventional household demand and the EV demand with marginal costs exogenously set to LMPs. We show mathematically that the socially optimal charging schedule can be implemented through a decentralized mechanism where retailers and EV aggregators respond autonomously to the posted DLMPs by maximizing their individual net surplus in the perfectly competitive local DSO market. We further investigate the problem of designing pricing mechanism when LMPs are uncertain. A robust DLMP method is developed for EV charging management under price uncertainty. The efficacy of the proposed use of DLMP is demonstrated by means of case studies using the Bus 4 distribution system of the Roy Billinton Test System (RBTS) and the Danish driving data.