TITLE:
Stochastic Social Welfare Maximization for Wind Power Integration in Electricity Spot Markets: A DC-OPF Approach with Nodal Pricing and Penetration Sensitivity Analysis
AUTHORS:
Ye Cao
KEYWORDS:
Stochastic Optimal Power Flow, Locational Marginal Price, Wind Power Integration, Social Welfare Maximization, DC Power Flow, PTDF, Curtailment, IEEE 30-Bus System, Scenario-Based Optimization
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.16 No.5,
May
25,
2026
ABSTRACT: The rapid growth of variable renewable energy—in particular utility-scale wind power—raises fundamental questions about social efficiency, price formation, and network adequacy in liberalized electricity spot markets. This paper formulates and solves a scenario-based stochastic social welfare maximization (SWM) problem on the IEEE 30-bus test system using a DC power-flow representation based on Powe Transfer Distribution Factors (PTDFs). Wind generation uncertainty is captured through a discrete scenario set, and nodal Locational Marginal Prices (LMPs) are recovered from the dual variables of the market-clearing optimization. A sign correction methodology is introduced to reconcile the CVXPY maximization convention with standard market pricing practice, ensuring that LMPs are positive under normal operating conditions and negative only when genuine local over-supply is present. Penetration levels are swept from 5% to 50% in 5 percentage-point increments, enabling a high-resolution analysis of social welfare, marginal welfare, wind curtailment, generation mix, and the hourly/nodal structure of prices. Results show that social welfare increases monotonically with penetration (from approximately $450 × 103/h to $473 × 103/h), yet marginal welfare declines from around $554/h per percentage-point at low penetration to $387/h at 50%, indicating diminishing systemic benefits. Wind curtailment remains negligible below 30% but accelerates sharply beyond that threshold, with the curtailment-to-accepted ratio reaching approximately 187% at 50% penetration (i.e., curtailed wind volume exceeds the actually accepted wind output) due to binding transmission and load-balance constraints. The expected system LMP peaks at approximately $1.09/MWh in the 15% - 20% range and declines to $1.03/MWh at 50%, while hourly LMP profiles reveal that the price-suppression effect of wind intensifies during peak-generation hours and at high penetrations. The nodal LMP heatmap at 30% penetration exposes persistent spatial price differentials driven by transmission congestion. These findings provide quantitative guidance for renewable integration policy, transmission planning, and market-design reform.