Search

Currently, there is a national push for a smarter electric grid, one that is more controllable and flexible. Only limited control and flexibility of electric assets is currently built into electric network optimization models. Optimal transmission switching is a low cost way to leverage grid controllability: to make better use of the existing system and meet growing demand with existing infrastructure. Such control and flexibility can be categorized as a “smart grid application” where there is a co-optimization of both generators or loads and transmission topology. In this paper we form the dual problem and examine the multi-period N-1 reliable unit commitment and transmission switching problem with integer variables fixed to their optimal values. Results including LMPs and marginal cost distributions are presented for the IEEE RTS 96 test problem. The applications of this analysis in improving the efficiency of ISO and RTO markets are discussed.

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.

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 wholesale electricity markets call on the independent system operator (ISO) to determine day-ahead schedules for generators based on a centralized unit commitment. Up until recently, the Lagrangian relaxation (LR) algorithm was the only practical means of solving an ISO-scale unit commitment problem, and it was the solution technique used by most ISOs. Johnson et al. [1] demonstrate, however, that equity, incentive, and efficiency issues will arise from use of LR solutions, because different commitments that are similar in terms of total system costs can result in different surpluses to individual units. Recent advances in computing capabilities and optimization algorithms now make solution of the mixed-integer programming (MIP) formulation by means of branch and bound (B&B) tractable, often with optimality gaps smaller than those of LR algorithms, which has led some ISOs to adopt B&B algorithms and others proposing to do so.With the move towards B&B, one obvious question is whether the use of MIP will eliminate or reduce the issues with LR raised by Johnson et al. Using actual market data from an ISO, we demonstrate that both LR and MIP solutions will suffer the same equity issues, unless the ISO unit commitment problems can be solved to complete optimality within the allotted timeframe—which is beyond current computational capabilities. Our results further demonstrate that the size of the payoff deviations are not monotone in the size of the optimality gap, meaning smaller optimality gaps from B&B will not necessarily mitigate the issues Johnson et al. raise. We show that the use of “make-whole” payments, which ensure units recover any startup and no-load costs not recovered by inframarginal energy rents, can help to reduce surplus volatility and differences to some extent.

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 sub-problems 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.

We present an empirical analysis of a supply function equilibrium model in the Texas spot electricity market. We derive condititions for optimal bidding behavior in a spot market with ex ante bilaterally contracted sales. By using generation cost information, we are able to derive a set of ex post- and ex ante-optimal supply functions and use a nonparametric model of firm behavior to compare our theoretically-optimal supply functions to actual offers made in years 2002 and 2003. Our results show that with markups and markdowns far in excess of what a model of profit-maximizing behavior suggests. For small generators, municipalities, and cogenerators we find evidence suggesting these firms may be acting to exclude themselves from the market by economically witholding their generation.By using partial-linear behavior model we demonstrate some learning effects to have taken place during the first quarter of 2002.

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.

System operators in the electricity industry are required to procure reserve capacity to deal with unanticipated outages, demand shocks, and transmission constraints. One traditional method of procuring reserves is through a separate capacity auction with two-part bids. We analyze an alternative scheme whereby reserves are procured through the energy market using only energy bids, and capacity payments are made based on a generator's implied opportunity cost. By using the revelation principle, we are able to derive the equilibrium bidding function in this market and show that generators have a clear incentive to understate their costs in order to capture higher capacity rents. We then give a numerical example for a special case and examine the effect of the equilibrium bidding behavior on the generators' total revenues and on the energy payments.

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.

The physical nature of electricity generation and delivery creates special problems for the design of efficient markets, notably the need to manage delivery in real time and the volatile congestion and associated costs that result. Proposals for the operation of the deregulated electricity industry tend towards one of two paradigms: centralized and decentralized. Transmission congestion management can be implemented in the more centralized point-to-point approach, a in New York state, where derivative transmission congestion contracts (TCCs) are traded, or in the more decentralized flowgate-based approach. While it is widely accepted that theoretically TCCs have attractive properties as hedging instruments against congestion cost uncertainty, whether efficient markets for them can be established in practice has been questioned. Based on an empirical analysis of publicly available data from years 2000 and 2001, it appears that New York TCCs provided marketparticipants with a potentially effective hedge against volatile congestion rents. However, the prices paid for TCCs systematically diverged from the resulting congestion rents for distant locations and at high prices. The price paid for the hedge not being in line with the congestion rents, i.e. unreasonably high risk premiums are being paid, suggests an inefficient market. The low liquidity of TCC markets and the deviation of TCC feasibility requirements from actual energy flows are possible explanations.