- The paper presents a two-stage stochastic robust optimization framework for scheduling VPPs that effectively handles both market and reserve uncertainties.
- It introduces decision-dependent uncertainty modeling and employs a Benders' decomposition algorithm to iteratively achieve an optimal solution.
- Case studies reveal a trade-off between reserve offers and operational costs, demonstrating enhanced profitability under dynamic market conditions.
Robust Scheduling of Virtual Power Plant under Exogenous and Endogenous Uncertainties
Introduction
The examined paper presents a robust scheduling methodology for Virtual Power Plants (VPPs) operating under uncertainty in the day-ahead (DA) energy and reserve markets. The presented approach tackles both exogenous uncertainties, such as market clearing prices and wind power availability, and endogenous uncertainties related to reserve deployment requests.
Model Description
DA Scheduling of VPP
The paper describes a model wherein a VPP aggregates multiple energy resources such as renewable and conventional power generation units, storage systems, and demand response capabilities. The objective is to optimize the VPP's performance in selling energy and reserves to the DA market while managing the operation cost of conventional plants.
Uncertainty Characterization
- Exogenous Uncertainties: These include DA market prices and wind power generation, modeled using a scenario-based stochastic program to capture variability and affect optimization decisions.
- Endogenous Uncertainties: These arise from reserve deployment requests, modeled as dependent on the VPP's decisions in the reserve market. This introduces complexity since the uncertainty set varies based on the VPP's market offerings.
The study employs a two-stage stochastic adaptive robust optimization framework. The framework ensures the feasibility of real-time operations under worst-case scenarios of uncertainties, leveraging a decision-dependent uncertainty model for reserve deployment requests.
Solution Methodology
Benders' Decomposition-Based Algorithm
The algorithm comprises two levels:
- Master Problem (MP): It iteratively optimizes the VPP's DA offerings subject to updated feasibility cuts derived from the subproblem.
- Robust Feasibility Examination Subproblem: It examines the feasibility of the MP solutions through the evaluation of the uncertainty effects on the VPP's operations. The subproblem uses linear surrogate formulations to handle bilinearity in decision dependency.
The iterative process converges to an optimal solution, balancing profitability against inherent uncertainties.
Case Studies
The paper includes case studies conducted on a VPP model involving multiple energy resources. Key aspects examined include:
- Impact of Wind Uncertainty Budget: The results reveal a trade-off between the reserve market offerings and the VPP's cost as the uncertainty budget varies.
- Effects of Pricing on Strategy: Changes in reserve energy prices influence the VPP's strategy in offering reserve capacities, affecting the system's cost and profitability.
Comparative Analysis
Decision-Independent vs. Decision-Dependent Uncertainty
Two models were compared, illustrating that decision-dependent formulations allow for a more dynamic adaptation to market conditions, potentially optimizing profitability and robustness.
C&CG Algorithm vs. Proposed Benders' Approach
The proposed method was shown to overcome limitations of the traditional Column-and-Constraint Generation algorithm when handling decision-dependent uncertainties, providing more accurate and less conservative solutions.
Conclusion
The paper's novel approach effectively models and optimizes VPP operations under complex uncertainty structures, highlighting a significant contribution to power system optimization under uncertainty. Future work could focus on algorithmic efficiency and broader applicability of decision-dependent uncertainty sets.