EFECTO MARGINAL

Further simulations are performed to examine the impact of the contribution rates vector [δR δT δD] on the DRX market outcome. As can be seen in Table 3.9, the total market net

Numerical example

benefit deviates from the global optimum as [δRδT δD] deviates from [1₃ 1₃ 1₃]. This is due

to theinconsistencies of payment contributions among buyers with respect to the benefits they get from trading DR. For example, as [δRδT δD] is [1₄ 1₂ 1₄], both the Reco and Disco

benefit more but contribute less, while the Transco benefits less but has to contribute more. Although this unfair situation is not a serious free-rider problem, it can still distort market efficiency [75]. An additional consequence is that an excess of payment (554.5$) occurs, meaning the buyers together have to pay more than the customers receive.

Table 3.9: The impact of contribution rates vector on DRX outcome (δR, δT, δD)

Total market Reco Transco Disco Payment benefit benefit benefit benefit excess (1 3, 1 3, 1 3) 2124.1 544.8 520.6 529.4 ≈0 (1 4, 1 2, 1 4) 2042.1 391.5 340.1 378.5 554.5

Although this contributions issue is not a major problem for DRX market-clearing, it demands that each DR buyer has to pay attention when signing onto the assurance contract. There is a requirement for choosing appropriate values for contribution rates, which should be proportional to the predicted benefits in the future DR trading [77].

The contributions issue also leads to an interesting observation that each buyer has a reasonable incentive totruthfully declare their own benefits when negotiating contracts with other buyers. If a buyer attempts to game the market by “lying” about its benefit, the [δRδT δD] that is determined using this false benefit will unfortunately becomeinconsistent

(i.e., deviating from the optimal value). As a consequence, the actual benefit the buyer eventually receives after the DRX is cleared will be lower than the benefit the buyer could receive if its claim has been more “honest”. Seeing Table 3.9 as an example, where [1₃ 1₃ 1₃] corresponds to “no buyer lied”, and [1₄ 1₂ 1₄] corresponds to “both the Reco and Disco lied but the Transco did not”.

In this example, the Transco who did not lie must also suffer from a benefit reduction caused by “dishonest” buyers. This unfair situation can be resolved introducing a mech- anism to refund the payment excess as an additional incentive for buyers not to lie. As indicated in Section 1.2.4, refunding the payment excess back to buyers is proportional to their own contributions. For example, in Table 3.9, the Transco, Reco, and Disco, who contribute at rates 1₂, 1₄, and 1₄, will receive 277.4$, 138.7$, and 138.7$, respectively (as- suming that the payment excess 554.5$ is fully refunded). Consequently, the total benefit for the Transco will be 617.5$ which is higher than the total benefits to the lying Reco and Disco (i.e. 530.2$ and 517.2$). In comparison to the [1₃ 1₃ 1₃] case, the Transco is rewarded while the lying buyers are penalized.

This result is also consistent with microeconomic theory. As shown in [79], a refund- ing mechanism under the assurance contract motivates any buyer to play a“dominant

strategy”, in which regardless of how much other buyers contribute to the public good, the buyer is better off contributing more based on its own true benefit. Such a strategy rewards the buyer with not only a better refund, but also a higher net benefit due to an improvement in the overall market efficiency. If every buyer plays the dominant strategy the market will reach an optimally efficient level with appropriate values for contribution rates (i.e., [1₃ 1₃ 1₃] in the above example). Playing the dominant strategies, each buyer will furthermore submit DR bids reflecting true benefits [79]. This, in turn, satisfies the marginal assumption made in Section 1.2.3.

On the other side of the DRX market, electricity customers, as the DR suppliers, have even more incentive to offer DR at marginal rates that reflect true costs. If a supplier attempts to raise the offering price above the marginal rate, it might simply lose the op- portunity to sell DR to other suppliers who offer a cheaper price. Under a DRX market withseveral million DR suppliers (electricity customers) no one can hold significant “mar- ket power”, so the loss of a DR sales opportunity from one supplier to another due to price competition is likely to happen [75]. Consequently, any supplier is better off offering the DR at a minimal price (that is equal to the marginal rate [75]) to compete well with the other suppliers in the DRX market. If every supplier offers the marginal rate, the market will achieve near-perfect competition in DR supply.

The above observations are mainly based on the general microeconomic theory. The issues related to individual buyer contributions and true-benefit gaming in the particular context of a DRX market obviously need further investigation. In our opinion, the proposed DRX market-clearing scheme under an assurance contract provides a good starting point as it offers clear advantages compared with conventional DR approaches.

A DRX market under the assurance contract can be cleared on an hourly basis. During each hour, buyers receiving a greater benefit contribute more than other buyers, and buyers receiving no benefit are not required to contribute. This hourly arrangement is included in the assurance contract. Note that the contributions among buyers in different hours of the day can differ, depending on their own time-varying benefits. Furthermore, there may exist some off-peak hours when no player benefits from DR. In these hours, no payment is made, and thus no DR is supplied. Such special cases, however, still fall well within the assurance contract arrangement.

3.5

Summary

This chapter developed a pool-based market clearing model for DRX in the restructured power system. Here the DRXO collects bids and offers from DR buyers and sellers, respec- tively. It then clears the market by maximizing the total market benefit for all participants. The theory behind the pool-based DRX is based on a well-known demand-supply model

Summary

incorporated with an assurance contract used for solving the free-riding problems associ- ated with public good contributions. Most importantly, such a theory brings together DR buyers (i.e., Transco, Recos, Discos, each with their own reasons to demand some DR from time to time) and sellers (i.e., ESCos on behalf of electricity customers) under a common DRX umbrella.

The DRX market clearing model has an additional advantage in that it rewards cus- tomers better by allowing them to deal with multiple buyers in a competitive way. This reward and competition based model can motivate customers to participate in DR pro- grams more actively than in the past.

Numerical simulations have been performed to examine the “core” properties of a pool- based DRX. It was observed that the proposed approach is significantly better than the conventional partial approaches, in the sense that it increases the total market benefit for all participants. In addition, many critical aspects of the DRX were shown to be consistent with microeconomic theory. These are fairness across all customers as DR providers, price- quantity relationship, and truthfulness in submitting demand and supply data for market clearing.

Agent–based Market Clearing

4.1

Overview

This chapter presents the design and evaluation of an agent-based market clearing mecha- nism for DRX, in which each market participant (i.e., buyers and selers) is represented by an economic agent behaving in a self-interested manner. This means that the agent always attemps to maximize its local benefit based on the available information about actions taken by other agents participating in the same DRX market. The proposed market clear- ing mechanism uses Walrasian auctions, where the agents update their locally optimal bids for DR quantities in response to prices adjusted by the DRXO. This auction is repeated iteratively until market equilibrium is obtained at the point where the market outcome is Pareto efficient from a global perspective. Both analytical proof and numerical simulation are provided to support key arguments.

Convex optimization theory is used as the mathematical background to formulate the market clearing problem with the aim of maximizing total market benefit for all partic- ipating agents. This problem is then converted into a set of equivalent conditions using Karush–Kuhn–Tucker (KKT) theorems. Such conditions which constitute a market equi- librium point are solved iteratively using Walrasian auction design.

This chapter is structured as following. Section 4.2 describes the concept of economic agent and its implications for a DRX. Section 4.3 formulates the market clearing problem from an agent-based perpective. With this formulation Section 4.4 designs the Walrasian auction mechanism, which will then be theoritically evaluated in terms of optimality and convergence in Section 4.5. Numerical studies of the proposed mechanism are given in 4.6 and concluding remarks due in Section 4.7.

Agent-based market concepts

Figure 4.1:Agent with a local view into the world