论文
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《Optimal Bidding Strategy of Power Generating Companies with Consideration of Load Forecast Uncertainty》
In recent decades, the electricity supply industry throughout the world has been moved from nationalized monopolies into competitive markets. Electricity is evolving into a distributed commodity in which market forces are bound to drive its price and reduce the net cost through increased competition. In such a market, the existence of an independent entity called Independent System Operator (ISO) is necessary. The ISO is a regulatory organization and one of its responsibilities is to balance the network in a manner that maximizes the welfare of the industry as a whole (Kirschen and Strbac, 2004; Shahidehpour et al., 2002).In a restructured electricity market, each Generating Company (GENCO) submits bids to the ISO with the goal of maximizing its own benefits. So, each GENCO tries to establish a suitable bidding strategy to maximize its potential profit (David and Wen, 2000). Finding the optimal bidding strategy of GENCOs depends on the type of competition. In the perfect competition, all of the market participants are called price takers and don’t have the ability to influence the market price through their individual actions. Developing bidding strategy in perfect competition is based on price forecasting. Forecasted price will be used in a Price-Based Unit Commitment (PBUC) program for determining the bid that maximizes profit. In Arroyo and Conejo (2000), Li et al. (2002) and Li and Shahidehpour (2005b) a deterministic PBUC was applied for developing bidding strategies. But due to the uncertainty in equipment outages, fuel prices and other price drivers, it could be difficult to forecast market prices accurately (Amjady and Hemmati, 2006). However, because of direct impact of the precision of market price forecasting on PBUC solution, it would be very important to consider the market price uncertainty. Mont-Carlo Simulation (MCS) is utilized (Li et al., 2007) to generate a set of discrete (deterministic) market prices based on forecasted market prices and then the bidding curve is constructed with the goal of maximizing the expected payoff.
There are several approaches to analyze the problem of developing optimal bidding strategy in electricity markets with imperfect competition. They could be categorized into non-equilibrium and equilibrium models (Li et al., 2007). The basic idea in non-equilibrium models is to use an approximate model for analyzing the impact of a GENCO’s bidding strategies on market clearing price. For example, an ordinal optimization method was used (Guan et al., 2001) to find the good enough bidding strategy for power suppliers. In equilibrium models, game theory concepts are utilized to simulate bidding behaviors of GENCOs. The solution of this game, if it exists, is the optimal bidding strategy of each GENCO and represents a market Nash Equilibrium (NE) which means that each GENCO’s profit will reduce if it unilaterally changes its bidding strategy while other GENCO’s bidding strategy remain fixed. If there is no collusion and each player’s payoff are known to all players, then the optimal bidding strategy problem could be considered as a non-cooperative game with complete information.
In recent research, the strategic bidding problem is formulated as a bilevel optimization problem using the Supply Function Equilibrium (SFE) model for modeling the imperfect competition among GENCOs. In this bilevel optimization problem, the upper level sub-problem maximizes the individual GENCOs’ payoffs and the lower sub-problem (convex quadratic programming) solves the ISO’s market clearing problem. Weber and Overbye (2002) represented the problem as a bilevel optimization problem and utilized price and dispatch sensitivity information, available from the OPF solution, to determine how a market participant should vary its bid in order to increase its profit. Via a bilevel optimization technique and Karush-Kuhn-Tucker (KKT) complementary conditions, Hobbs et al. (2000) transformed the strategic bidding problem to a nonlinear programming model or, more specifically, to a mathematical program involving linear complementary constraints. Also Li and Shahidepour (2005a) utilized the primal-dual interior point method and sensitivity functions to solve this bilevel problem.
One of the common uncertainties in equilibrium models of imperfect competition markets is the uncertainty of load forecasting. In fact, forecasted load has the direct impact on the solution of the game and it will be very important to be considered. There are two approaches to handle this uncertainty: probabilistic approach and fuzzy approach.
In this study, a fuzzy approach for modeling the uncertainty of load forecast in imperfect competition market is developed and its result is compared to probabilistic approach. In probabilistic approach, it’s assumed that future demand is normally distributed and each player attempts to solve a Chance Constrained Problem (CCP) (Chouchman et al., 2005). In fuzzy approach, possibility distributions are used for demand values in the future (Rosado and Navarrov, 2004; Popovic and Popovic, 2004) and fuzzy game theory is utilized for developing the optimal bidding strategy of each GENCO. Also, the bilevel optimization model, applied by Li and Shahidepour (2005a), or equivalently, the Mathematical Problem with Equilibrium Constraints (MPEC) model applied by Hobbs et al. (2000), is employed for developing optimal bidding strategy for competitor suppliers participating in the Day-Ahead (DA) energy market. In this market, it’s supposed that the ISO uses a DC Optimal Power Flow (DC OPF) to clear the market after collecting bids and pays the suppliers under pay-as-LMP pricing. Suppliers are assumed to bid affine non-decreasing supply curve. Strategic behavior is represented via a parameterized SFE model and the x α y parameterization technique is considered for the SFE model in which the suppliers can manipulate the slope and the intercept proportionally.
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《Agent-Based Modeling in Electricity Market Using Deep Deterministic Policy Gradient Algorithm》
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Abstract: Game theoretic methods and simulations based on reinforcement learning (RL) are often used to analyze electricity market equilibrium. However, the former is limited to a simple market environment with complete information, and difficult to visually reflect the tacit collusion; while the conventional RL algorithm is limited to low-dimensional discrete state and action spaces, and the convergence is unstable. To address the aforementioned problems, this paper adopts deep deterministic policy gradient (DDPG) algorithm to model the bidding strategies of generation companies (GenCos). Simulation experiments, including different settings of GenCo, load and network, demonstrate that the proposed method is more accurate than conventional RL algorithm, and can converge to the Nash equilibrium of complete information even in the incomplete information environment. Moreover, the proposed method can intuitively reflect the different tacit collusion level by quantitatively adjusting GenCos’ patience parameter, which can be an effective means to analyze market strategies.
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ISO来充当环境，提供反馈（包括next state, reward），博弈论（包括无限轮博弈和静态博弈）中的无限轮博弈来计算折现因子。 DDPG-based multiple agents 来模拟GENCO（发电企业）。
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术语:
load:
bus:
cost function:
marginal cost function:
maximum lines flow limits:
matrix of power transfer distribution factor:
demand curve:
supply function:
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基本概念
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DC power flow model：直流潮流模型（DC power flow model）是电力系统潮流计算中最简单的模型之一，通常用于大型电力系统的预测和规划。该模型通过假设电力系统中的所有元件都是直流元件，忽略了电力系统中的交流电流变化和变压器等元件的非线性特性。
在DC潮流模型中，电力系统中的每个节点被视为具有固定电压，而节点之间的电流是由电压差和电阻来计算的。该模型基于欧姆定律和基尔霍夫定律，使用线性代数方程组来求解电力系统的潮流分布情况。
DC潮流模型的优点是计算速度快，计算结果准确度高，且能够处理大型电力系统的潮流计算。然而，由于该模型忽略了电力系统中的许多非线性特性，如变压器的饱和和饱和磁导率等，因此在一些情况下，其计算结果可能与实际情况存在偏差。
总之，DC潮流模型是电力系统潮流计算中的一种简单而有效的方法，其可靠性和适用性取决于具体的应用场景和问题要求。 -
市场出清：在经济学中，市场出清（英语：market clearing）是在市场中，任何使交易的供给等于需求的过程，即为“清理”多余的供给或需求。新古典经济学假设在任何给定市场中，假设所有买家和卖家都可以全面获取信息并且没有阻碍价格变化的粘性，价格总是会向上或向下调整以确保市场出清。
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市场机制：市场出清价格是供给量等于需求量的商品或服务的价格，也就是均衡价格。 [1]该理论认为如果市场价格不为均衡价格，那么市场价格就一定在不断接近均衡价格直到二者相等。对于短期商品的销售，供应量是固定的，因此市场出清价格只是使得所有商品售尽的价格，但不会也无需更低。在这种情况下，市场上的所有商品就会刚好被买空。对于持续生产和销售商品的市场，该理论预测市场将朝着在较长的时间段上向供应量等于需求量的价格移动。这段时间可以是一周甚至是一年。为了消除由批量制造和提前约定的交付计划造成的供给不灵活性，卖家通常有库存进行缓冲，因此产品始终可供零售而不会留下多余的需求。
