Equilibrium analysis of generator bidding in the electricity spot market considering medium- and long-term transactions

doi:10.11930/j.issn.1004-9649.202507063

Abstract

Abstract:

To examine how medium- and long-term (MLT) market transactions affect spot-market operations and to analyze generators' bidding strategies in the spot market, this paper proposes a bilevel optimization model and a multi-agent deep reinforcement learning (MADRL) algorithm to simulate the bidding equilibrium of generators in the electricity spot market. A supply–demand ratio is introduced to characterize spot-market tightness, and the prospect theory is employed to capture generators' bounded-rational behavior, thereby analyzing the impact of MLT transactions on bidding strategies of generators in the spot market. In the MADRL solution process, generators are modeled as agents and market clearing is modeled as the environment; iterative training yields equilibrium bidding strategies for each generator and the corresponding spot-market clearing prices. A case study on an actual power system in Eastern China involving eight generators demonstrates that the proposed MADRL approach effectively computes generators' bidding strategies and accurately simulates the influence of different MLT market settings on spot-market operations. The findings provide quantitative guidance for power trading institutions to assess strategic bidding and to design coordinated rules for the joint operation of MLT and spot markets.

Key words: medium- and long-term market, spot market, bilevel model, equilibrium analysis, reinforcement learning

LI Xiaogang, LIU Qiyuan, FENG Yuanhao, WU Min, CHEN Zhongyang, FENG Donghan. Equilibrium analysis of generator bidding in the electricity spot market considering medium- and long-term transactions[J]. Electric Power, 2026, 59(2): 127-137.

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URL: https://www.electricpower.com.cn/EN/10.11930/j.issn.1004-9649.202507063

https://www.electricpower.com.cn/EN/Y2026/V59/I2/127

Figures/Tables 15

References 30

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序号	步骤
1	初始化各智能体的策略网络参数$\theta $和价值网络参数$\omega $
2	初始化各智能体的两个目标网络参数$\theta '$和$\omega '$
3	for ${\text{episode}} = 1$ to $M$ do
4	for $t = 1$ to $T$ do
5	各智能体观测市场状态$s = \left[ {{o_1},{o_2},\cdots ,{o_N}} \right]$
6	各智能体策略网络输出动作$a = {\mu _\theta }\left( s \right)$
7	完成市场出清，获得奖励$r$和下一状态$s'$
8	储存状态转移矩阵$\left( {s,a,r,s'} \right)$至经验回放池
9	if $ {\text{episode}}\text{mod} {f^{\text{c}}} = 0 $ then
10	从经验回放池随机抽取四元组$\left( {s,a,r,s'} \right)$
11	计算目标策略网络${\mu _{\theta '}}$和目标价值网络${Q_{\omega '}}$
12	更新价值网络参数$ \omega \leftarrow \omega - {\alpha _{{\text{critic}}}} {\nabla _\omega }{L_{{\text{critic}}}} $
13	if $ {\text{episode}}\text{mod} {f^{\text{a}}} = 0 $ then
14	更新策略网络参数$ \theta \leftarrow \theta + {\alpha _{{\text{actor}}}} {\nabla _\theta }J $
15	end if
16	end if
17	更新目标价值网络参数$\omega ' = \left( {1 - \tau } \right)\omega + \tau \omega '$
18	更新目标策略网络参数$\theta ' = \left( {1 - \tau } \right)\theta + \tau \theta '$
19	end for
20	end for

序号	步骤
1	初始化各智能体的策略网络参数$\theta $和价值网络参数$\omega $
2	初始化各智能体的两个目标网络参数$\theta '$和$\omega '$
3	for ${\text{episode}} = 1$ to $M$ do
4	for $t = 1$ to $T$ do
5	各智能体观测市场状态$s = \left[ {{o_1},{o_2},\cdots ,{o_N}} \right]$
6	各智能体策略网络输出动作$a = {\mu _\theta }\left( s \right)$
7	完成市场出清，获得奖励$r$和下一状态$s'$
8	储存状态转移矩阵$\left( {s,a,r,s'} \right)$至经验回放池
9	if $ {\text{episode}}\text{mod} {f^{\text{c}}} = 0 $ then
10	从经验回放池随机抽取四元组$\left( {s,a,r,s'} \right)$
11	计算目标策略网络${\mu _{\theta '}}$和目标价值网络${Q_{\omega '}}$
12	更新价值网络参数$ \omega \leftarrow \omega - {\alpha _{{\text{critic}}}} {\nabla _\omega }{L_{{\text{critic}}}} $
13	if $ {\text{episode}}\text{mod} {f^{\text{a}}} = 0 $ then
14	更新策略网络参数$ \theta \leftarrow \theta + {\alpha _{{\text{actor}}}} {\nabla _\theta }J $
15	end if
16	end if
17	更新目标价值网络参数$\omega ' = \left( {1 - \tau } \right)\omega + \tau \omega '$
18	更新目标策略网络参数$\theta ' = \left( {1 - \tau } \right)\theta + \tau \theta '$
19	end for
20	end for

发电商	所在节点	容量/ MW	$ {a_i} $/ (元·(MW·h)^–2)	$ {b_i} $/ (元·(MW·h)^–1)
G1	1	150	0.175	16.0
G2	2	100	0.200	16.5
G3	3	100	0.160	18.0
G4	8	80	0.220	18.5
G5	9	100	0.180	20.0
G6	11	120	0.175	21.0
G7	18	100	0.225	22.0
G8	19	150	0.200	22.5

发电商	所在节点	容量/ MW	$ {a_i} $/ (元·(MW·h)^–2)	$ {b_i} $/ (元·(MW·h)^–1)
G1	1	150	0.175	16.0
G2	2	100	0.200	16.5
G3	3	100	0.160	18.0
G4	8	80	0.220	18.5
G5	9	100	0.180	20.0
G6	11	120	0.175	21.0
G7	18	100	0.225	22.0
G8	19	150	0.200	22.5

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