All market clearing optimization models, including DRX and partial, are simulated using the non-linear programming solver called General Algebraic Modeling System (GAMS), with the same data inputs applied. The simulation here is assumed to be within a single- hour period. The results are given in Tables 3.7 and 3.8. Table 3.7 shows the net benefits (that is gross benefit less the cost) for each individual player and for all players together (total market benefit). Table 3.7 presents total DR quantity, payment made by each buyer, and the total revenue of all customers combined. In the simulation, the contribution rates vector [δR δT δD] of the DRX model is set at approximately [13 13 13].
Table 3.7: Comparative net benefit ($)
Model Total market Reco Transco Disco Customers benefit benefit benefit benefit benefit
Reco based 1521.5 121.3 641.3 621.6 137.3
Transco based 1562.3 644.5 126.2 649.1 142.5
Disco based 1565.3 645.2 661.7 129.2 129.2
DRX 2124.1 544.8 520.6 529.4 529.3
Table 3.8: Comparative DR quantities (MW) and payments($)
Model DR Reco Transco Disco Cons
quantity payment payment payment revenue
Reco based 15.2 516.4 0 0 516.4
Transco based 15.8 0 539.2 0 539.2
Disco based 15.7 0 0 526.5 526.5
DRX 32.2 517.6 566.1 548.7 1632.4
As can be seen from the simulation output, results of the DRX are significantly better than those of partial DR approaches. The total market benefit is improved by more than
Figure 3.8:Load curtailment (in MWh on the right axis) versus customer willingness (on left axis with no unit). Note: the horizontal axis represents customer index
35%. At the same time, the customer benefit is improved by approximately 300%; total DR quantity, increased by more than 100%; and the corresponding customer revenue increased by nearly 220%.
In partial approaches, there are some players who do not pay for DR. However, their free benefits are only about 15% (Reco), 20% (Transco), and 18% (Disco) higher than would be the case in the DRX. This is because when all players contribute, both the total payment and the resultant DR quantity are improved. Consequently, the gross benefit for each player significantly increases, which compensates for the player’s payment.
With these results, we can argue that a DRX is more efficient than partial approaches. This argument is consistent with the microeconomic theory. As indicated in [75, p. 362], “private provision leads to an inefficient level of a desirable public good”. In the context of DR scheduling, a private provision refers to partial approaches since DR, as a public good, is sold to only one buyer. The term “inefficient” here means that the total market benefit cannot reach the global maximum value due to insufficient good being provided. The above results support the claim that partial approaches lead to inefficient DR markets.
Fig. 3.8 examines the relationship between the individual curtailment amount (xi,l)
and the curtailment willingness (θi,l) of various customers. Here xi,l generally increases
following the increasing value ofθi,l, which implies that customers would curtail more load
for supplying DR as they are more willing to do so. However, there are certain customers (i.e., 3, 4, 5) having relatively low willingness but curtailing more load than some others.
Numerical example
Figure 3.9:Net benefit (on the right axis) versus load curtailment (on the left axis). Here the horizontal axis represents customer index
This result can be explained by the effect of DRX market clearing, where the curtailment amount (or rather DR supply) isjointly decided by the customers and the DR buyers. In this situation, if the DRs from some customers are more valuable for the buyers than those from other customers, the former would be purchased at higher quantities and, of course, higher prices than the latter regardless of the curtailment willingness of each customer. For example, the Transco will be likely to buy more DR quantities of those customers at “critical” locations of the transmission network (that is, the locations significantly affecting the network security) than DR quantities of other customers. These results demonstrate the advantage of using market clearing for scheduling DR, where the outcome is given by an optimal balance of the curtailment willingness (or DR supply capability of the customers) and the buyer demand.
Fig. 3.9 shows the net benefit for each individual customer according to their DR quantities supplied. Since such benefits are the difference between DR payments and DR provision costs, they give the “ultimate” incentives for load curtailments. As can be seen from the graph, there is a near-perfect correlation between the curtailments and the net benefits across all customers, that is, those customers curtailing more load than others enjoy higher monetary gains. What is surprising, this correlation is independent of other market clearing parameters such as the curtailment willingness of customers (θi,l) and
the buyer demand for DR. This result demonstrate the very fairness across all types of customers when supplying DR, that is, regardless of which condition the power system is in (normal or contingencies, or with electricity market volatility) and regardless of how much the customers are willing to curtail loads, the more they do the more they gain.
Figure 3.10: The relationship of DR market clearing prices, quantities purchased, gross benefit for the Disco (the results here are normalized by the corresponding peak values.)
In addition to the customers as DR providers, here we examine the market clearing outcome from a DR buyer perspective. For illustrative purposes, we choose the Disco as it deals with all customers at the individual level and consequently gives more diversified results than other buyers including the Reco and the Transco, who deals with only a limited number of aggregated customers (i.e., 2 as of Table 3.3). Fig. 3.10 presents the correlation between DR quantities and their market clearing prices paid by the Disco. It is observed that the former isinversely proportional to the latter, which can be explained by the law of demand in microeconomics. That is, people tend to buy more of the cheaper products and avoid purchasing the expensive unless necessary.
Fig. 3.10 also gives the relationship between the purchased quantities and the gross benefit derived from each quantity. As can be seen, those DRs giving more benefits than other DRs will be purchased by the Disco at higher quantities. In order words, higher DR quantities must bring out more gross benefits, otherwise they would not be cleared in the market. Such an argument can be referred as “rationality” in DRX market clearing.