Extended Version: Market-Driven Equilibria for Distributed Solar Panel Investment

2025-09-08

AI Summary

This paper investigates how short-term electricity market equilibria—specifically price formation and quantity allocation—affect long-term investment decisions of distributed photovoltaic (PV) individual investors, and comparatively evaluates the incentive efficiency of alternative market mechanisms. We employ a nonatomic game model to capture strategic interactions among heterogeneous investors and develop a nested analytical framework coupling short-term market equilibrium with long-term investment equilibrium. Theoretically, we prove that: (i) a product-differentiated market achieves socially optimal investment capacity; (ii) a single-product market induces systemic underinvestment; and (iii) a contract-based market may lead to overinvestment when marginal cost heterogeneity is high. Closed-form equilibrium capacity expressions are derived for each mechanism and validated via numerical experiments. Our primary contribution lies in the first integration of nonatomic game theory with multi-period market equilibrium modeling for distributed energy resources, thereby revealing the decisive role of market structure in shaping investment efficiency.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments

Abstract

This study investigates market-driven long-term investment decisions in distributed solar panels by individual investors. We consider a setting where investment decisions are driven by expected revenue from participating in short-term electricity markets over the panel's lifespan. These revenues depend on short-term markets equilibria, i.e., prices and allocations, which are influenced by aggregate invested panel capacity participating in the markets. We model the interactions among investors by a non-atomic game and develop a framework that links short-term markets equilibria to the resulting long-term investment equilibrium. Then, within this framework, we analyze three market mechanisms: (a) a single-product real-time energy market, (b) a product-differentiated real-time energy market that treats solar energy and grid energy as different products, and (c) a contract-based panel market that trades claims or rights to the production of certain panel capacity ex-ante, rather than the realized solar production ex-post. For each, we derive expressions for short-term equilibria and the associated expected revenues, and analytically characterize the corresponding long-term Nash equilibrium aggregate capacity. We compare the solutions of these characterizing equations under different conditions and theoretically establish that the product-differentiated market always supports socially optimal investment, while the single-product market consistently results in under-investment. We also establish that the contract-based market leads to over-investment when the extra valuations of users for solar energy are small. Finally, we validate our theoretical findings through numerical experiments.

Problem

• Modeling market-driven solar panel investment decisions
• Analyzing three market mechanisms for solar energy
• Comparing investment outcomes across different market structures

Innovation

• Non-atomic game modeling investor interactions and market equilibria
• Three market mechanisms analyzed for solar investment optimization
• Product-differentiated market achieves socially optimal investment levels