Electricity is an essential component of society that has implications for the economy, the environment and consumer welfare. The need for an affordable, secure and clean energy supply motivates us to continue improving electricity markets. In Colombia, electricity generation is organized on the basis of auctions where generators bid maximum generation capacities for each of the 24 hours of the following day, together with a unit price. The system operator, based on an allocation and payment rule, defines the number of units to be dispatched by each generator and the payment they will receive. In this context, the question arises as to how to design this auction to minimize the generation costs of the system to supply the electricity demand, encouraging generators to participate in the auction and disclose their true unit costs.
However, solving this question involves several challenges. First, it is important to consider that generators have private information about their unit costs and act strategically to maximize their profits by bidding a price above their real costs. In addition, there may be other objectives besides minimizing generation costs, such as reducing the environmental impact of thermal generation and ensuring the security of the system to meet demand. For example, hydropower is often a cost-effective source of generation in Colombia. However, as we have observed in the last month, extreme weather events such as the El Niño phenomenon can cause considerable increases in energy prices.
The literature on optimal auction design, starting with Myerson (1981), provides valuable insights on how to address this question. Recently, Dütting et al. (2019) propose a method for finding optimal auction designs using Deep Learning. Motivated by this context, my thesis work, titled Optimal Design for Electricity Auctions: A Deep learning approach aims to extend this method to discover electricity auction designs. In particular, the results to be presented in this space evaluate the impact of wind and solar integration on system generation costs, using data from the Colombian market during 2022.
The method employed consists of first modeling the multi-unit auction design problem to supply electricity demand during different time slots throughout the day. It is assumed that the generators have a single private unit cost during the day, which follows a known probability distribution. They also have capacities for each time slot. Through an auction, generators report their unit costs and the system operator defines how many units each generator will dispatch in each time slot, and the payment they will receive for generating these units. These allocation and payment rules are modeled through neural networks, which are trained to solve the optimal design problem.
The optimal design problem focuses on finding the allocation and payment rules that minimize the expected power generation costs and meet 4 constraints:
Then, the optimal design problem is reformulated as a learning problem. The incentive and capacity compatibility constraints are relaxed so that they are satisfied at expected value. The other two constraints are incorporated into the network architecture. The neural network is trained using random samples of the unit costs following their known joint distribution. The objective is to minimize a loss function that incorporates both generation costs and violations of these constraints.
Next, the results of the experiments are presented using real data from the Colombian electricity market during 2022 to estimate the distribution of unit costs, capacities and demand for each type of generator: (1) thermoelectric using liquid fuels, (2) thermoelectric using coal or gas, (3) hydroelectric, (4) wind and (5) solar. In addition, the dispatch is modeled during 2 time slots, one of low demand (between 10pm-8am) and the other of high demand (9am-9pm). The first scenario (A), considers only 3 generators: the two thermoelectric and one hydroelectric. From this reference scenario, experiments B-D expand the capacity by 10%, 20% and 30%, respectively, incorporating a wind and solar generator. In contrast, scenarios E-G incorporate two additional hydroelectric generators for each level of expansion.
Figura 1: Box plot of the unit costs for each generator (left side) and average capacity for each generator (right side) during each time frame for experiments B-D. The triangles and the + sign indicate the average and max/min values, respectively. The bars on the left in the left plot represent the average capacity during the first time window, while those on the right correspond to the second time window.
The left side of Figure 1 shows the distribution of unit costs for each generator. Although on average hydro, wind and solar generators have similar unit costs, a skewed distribution to the right is observed for the hydro generator. These high costs are often associated with periods of low rainfall: generation quickly depletes reservoir levels when there is drought. This leads to higher opportunity costs for hydroelectric generators: if electricity is generated, considerable payments are sacrificed in the future. On the other hand, for experiments B-D, the right side of Figure 1 shows the average capacity of each generator for the first and second band, along each level of aggregate capacity expansion. It is evident that, in the second band, the capacity increases more, which is due to the higher availability of solar energy.
Figure 2 compares the distributions of generator payments and generation costs between scenario D and G (a 30% capacity expansion) in the learned auction. Although average system generation costs are only reduced by 5.1%, it can be seen that integrating solar and wind power reduces the incidence of extreme generation costs compared to adding new hydroelectric generators. These extreme values usually occur when hydroelectric generator unit costs are high during periods of low rainfall.
Figura 2: Distribution of payments and generation costs for a 30% expansion level for scenarios D (left panel) and G (middle panel). The histogram of generation costs when wind and solar are introduced are shown in black and when additional hydroelectric generators are introduced in light blue.
Overall, this paper hopes to propose a method that allows exploring further applications for electricity auctions. Future work may include additional constraints related to pollution levels or modeling non-convex costs. In addition, the effect of demand response programs and reserve capacity strategies could be studied.
References:
Myerson, R. B. (1981): “Optimal auction design,” Mathematics of operations research, 6, 58–73.
Dütting, P., Z. Feng, H. Narasimhan, D. Parkes, and S. S. Ravindranath (2019): “Optimal auctions through deep learning,” in International Conference on Machine Learning, PMLR, 1706–1715.
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