The theory used by economists to support restructuring of the electric power industry has ignored several important technological constraints and public goods that affect the way in which power is delivered. Similarly, engineers, by using security-constrained optimization to incorporate the demand for reliability, have failed to properly define the economic problem. In this two-part paper we attempt to remedy the deficiencies of both the economists’ approach and the security-constrained optimization approach through a collaboration of economists and engineers to examine the theoretical properties of a networked power system that provides optimal resource allocation.

Electric power is traditionally comprised of valued services, including real and reactive power, voltage, frequency and reliability in its most general sense. In this second part of our two-part paper we show mathematically that of these, only real and reactive power are purely private goods, in that power consumed by one customer cannot be used by another and customers can be excluded from receiving any power. The other ancillary services, including voltage, frequency and reliability are shown to be public goods. The first order conditions presented clearly illustrate that the public goods occurring in electric power systems comprise a significant problem for market design.

and the army of past and present students who worked on parts of this project over the years for their support and for helpful comments during the course of this work. All conclusions, recommendations, and remaining errors are the sole responsibility of the authors.

The economic theory that has been used to support restructuring of the electric power industry has ignored several important technological constraints and public goods that affect the way in which power is delivered. Some of these public goods include voltage, frequency, and reliability of lines. Similarly, engineers, by using security-constrained optimization to incorporate the demand for reliability, have failed to properly define the economic problem. This research attempts to remedy this deficiency through a collaborative effort between economists and engineers to examine the theoretical and empirical properties of a networked power system that provides economically optimal reliability and draw conclusions regarding efficient market design.

How line flows, capacity requirements and system design might be altered under deregulated market structures is explored through simulations of experimentally-obtained loads and generator dispatches under alternative market structures, including a regulated base-case dispatch. Eight generators were located on the Power Web 30 bus simulated transmission network, and the 19 buyers were randomly allocated over thirty different trials to busses on the network. Line flows were estimated using a DC optimal power flow routine. Unambiguously, the sum of maximum flows over all lines is lower (by from one to ten percent) under a real-time pricing (RTP) regime, as compared to a simulation of the former regulated regime with fixed price (FP). Furthermore, a demand response program (DRP) is shown to perform nearly as well, resulting in lower maximum line flows in all but one of the allocations. RTP also restores line flow predictability close to operation under regulation.

Robert Thomas has shown, using simulations of experimental results, that the power flow on any line in an electric network is linearly proportional to the total system load when that system is optimally dispatched using accurate generator cost data. By comparison, when offers from generators obtained in a wholesale market that is not perfectly competitive are used to dispatch the system, that relationship between line flow and system load becomes nearly random. These simulations were conducted in a single-sided market environment, however, that is typical of most wholesale market regimes around the world. Here the central dispatcher (ISO, RTO, etc.) accumulates the demand from various buyers and satisfies that load with a least-cost purchase schedule, regardless of price, subject to all of the physical and reliability constraints imposed on the system. If buyers were also able to submit a schedule of bids that are related to price, does the same random relationship between line-flows and system load prevail? This experimental analysis demonstrates that letting the customers participate fully in the market re-establishes the predictability of line flows as a function of system load. In all of these experiments there are no restrictions on permissible offering behavior by suppliers (e.g. no price caps, prohibitions on withholding capacity or automated mitigation procedures). Two alternative forms of demand side participation are considered: 1) a demand response program (DRP) where customers are alerted to high prices in the subsequent period and are paid a pre-specified amount for each kWh less than their benchmark level of usage for that period, and 2) a real time pricing program (RTP) where customers are given forecasts of prices for each period over the subsequent day and they then pay the actual period-by-period market clearing price. As a benchmark, these experiments with six suppliers and seventeen buyers are also repeated where customers pay an average constant price in all periods (FP); although in all cases sellers receive the market-clearing price in each period. R-squares were greater, variances were smaller and the t-tests on regression coefficients were stronger on the relationship between line-flow and system load for RTP, as compared to - the FP system that is commonly used in most electricity markets. DRP was usually somewhere in between. Not only does inducing active customer participation in the market through RTP lead to better system predictability, it also reduces price spikes and leads to greater overall economic efficiency in these markets. It is a winner on both economic and operational grounds.

An experimental structure is demonstrated that represents end-use customers in electricity markets who can substitute part of their usage between day and night. Each customer’s demand relationship is represented by a two-step value function for each period, disaggregated from observed market demand relationships, that varies between day and night and during heat-waves. Three alternative demand-side market structures are evaluated: 1) customers pay the same fixed price (FP) in all periods the base case, 2) a demand response feature (DRP) is added to the fixed price case in periods of supply shortages, wherein buyers receive a pre-specified credit for reduced purchases, and 3) a real time pricing (RTP) case where prices are forecast for the upcoming day/night pair, then buyers select their quantity purchases sequentially and are charged the actual market-clearing price, period-by-period. After demonstrating the ability of buyers to make efficient purchases, six experienced sellers with experience in exercising market power were paired with seventeen buyers over twenty two auctions (eleven day-night pairs) that included heat waves and unit outages. The same periods were repeated under each of the three different market treatments, and the RTP structure resulted in the greatest market efficiency, despite the difficult cognitive problem it poses for buyers. Both DRP and RTP reduced the severity of price spikes as compared to the FP structure. A preference poll comparing DRP and RTP was conducted after each treatment. In one experiment, 74% of the participants said they preferred DRP before trying RTP, but 64% chose RTP afterward, a statistically significant reversal of preferences, and in a second experiment, 53% preferred DRP initially, but 68% selected RTP after experiencing both treatments. Finally, the relationship between total system load and line flows was examined under each of the three market treatments and for a simulated fully-regulated regime. The relationship demonstrated under the regulated regime deteriorates under FP, but is re-established under the DRP and RTP market structures.

An experimental structure is demonstrated that represents end-use customers in electricity markets who can substitute part of their usage between day and night. Individuals' demand relationships are represented by a two-step value function for each period that are disaggregated from observed market demand relationships. Demand varies between day and night and during heat waves. Three alternative demand-side market structures are evaluated: 1) customers pay the same fixed price (FP) in all periods - the base case, 2) a demand response feature (DRP) is added in periods of supply shortages, wherein buyers receive a prespecified credit for reduced purchases, and 3) a real time pricing (RTP) case where prices are forecast for the upcoming day/night pair, then buyers select their quantity purchases sequentially and are charged the actual market-clearing prices. Initial experiments were conducted with active demand-participants, but with a predetermined typical "hockey-stick" supply structure that was varied randomly, over eleven day-night pairs that included heat wave and supply shortages. The RTP structure resulted in the greatest market efficiency, despite the more difficult cognitive problem it poses for buyers. Furthermore, a preference poll comparing DRP and RTP was conducted after each trial; and while 64% of the participants said they preferred DRP before RTP experiments, 76% selected the RTP structure afterwards, a statistically significant reversal of preferences.