Capacity Planning of Wind-PV-Thermal-Storage Energy Bases Considering Intraday Adjustment Costs via Nested Generalized Benders Decomposition

Summary

This protocol presents a capacity planning method for wind-PV-thermal-storage renewable energy bases, integrating uncertainty, intraday flexibility, and operational costs. It employs sequential production simulations and a nested Benders decomposition algorithm to optimize construction and operation.

Abstract

Large-scale renewable energy bases are increasingly deployed in arid regions, which offer favorable conditions for wind and PV generation supported by energy storage systems and long-distance transmission lines. However, the planning of such bases is complicated by the high variability of renewable generation, limited flexibility resources, and complex multi-objective trade-offs. To address these issues, this study proposes a capacity planning model for wind-PV-thermal-storage renewable energy bases, minimizing construction and operational costs while accounting for uncertainty and explicitly quantifying the value of flexibility resources. Compared with existing capacity planning models that rely on deterministic formulations or simplified two-stage stochastic representations, the proposed model explicitly embeds intraday operational flexibility and forecast-error costs into life-cycle planning. Operational costs are assessed through sequential production simulations, in which intraday forecast errors are incorporated via deviation costs and flexibility requirements. A hybrid sampling strategy combining Latin hypercube sampling and importance sampling is used for scenario generation, followed by scenario reduction to improve computational efficiency. To solve the optimization model, a nested generalized Benders decomposition framework is developed, decomposing the model into a master problem and multiple production simulation subproblems, which are further divided into mixed-integer and continuous-variable layers to enhance computational tractability and solution accuracy. Case studies demonstrate that the proposed model and algorithm demonstrate the role of flexibility resources, resulting in economically viable and practically implementable capacity under high renewable penetration. By explicitly accounting for intraday forecast deviations, the resulting plans ensure reserve adequacy for over 95% of uncertainty realizations while remaining economically viable and practically implementable. Moreover, the impact of carbon emission penalties on capacity allocation and renewable utilization is quantified, highlighting implications for system design and planning strategies for wind-PV-thermal-storage renewable energy bases.

Introduction

The accelerating transition toward carbon neutrality has driven large-scale deployment of wind and PV, creating new challenges for power-system flexibility and reliability¹. Desert and semi-arid regions offer abundant complementary wind and solar resources, as well as wide land availability². These characteristics make them attractive locations for utility-scale integrated wind-solar-thermal-storage bases, which rely on energy storage and long-distance transmission to align resource availability with system demand³.

Planning such large bases poses several challenges. Ca....

Protocol

Protocol overview

This study follows a three-step protocol to perform life-cycle capacity planning under intraday uncertainty. (i) Formulate and implement the integrated planning and operational model in MATLAB. An integrated capacity planning and operational model is formulated for a wind–PV–storage–transmission base. The objective function and constraints are implemented in MATLAB R2023a using YALMIP, decision variables are defined with sdpvar, and CPLEX 12.10 is configured as the mixed-integer solver. The model formulation includes the overall structure, objective function, and constraints. (ii) Generate uncertainty scen....

Results

Application of the proposed protocol generates representative planning and operational results that highlight the effectiveness of explicitly modeling intraday flexibility and carbon penalties.

Representative planning outcomes under carbon penalties

Using 400 representative scenarios across seasons, sequential production simulation produces the operational cost corresponding to each capacity expansion plan. Figure 3 pre.......

Discussion

The presented protocol provides a life-cycle capacity planning framework that integrates sequential production simulation, intraday adjustment modeling, and nested generalized Benders decomposition to explicitly quantify the value of flexibility under intraday uncertainty. Unlike conventional capacity planning approaches that typically rely on deterministic formulations or simplified two-stage stochastic models^16,17, the proposed protocol explicitly embeds intrad.......

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
Electricity market price data	Market operator / Open datasets	—	Day-ahead and intraday price inputs for operational cost modeling
Historical PV generation time-series data	Regional grid operator / Open datasets	—	Used for PV forecast modeling and scenario generation
Historical wind power time-series data	Regional grid operator / Open datasets	—	Used for wind forecast modeling and scenario generation
MATLAB / Python	MathWorks / Python Software Foundation	MATLAB R2025a / Python 3.11	Used to implement capacity planning model and sequential production simulation
Optimization solver (e.g., CPLEX, Gurobi)	IBM / Gurobi	CPLEX 22.1 / Gurobi 10.0	Solves the mixed-integer linear optimization problems
Scenario generation libraries	Python: pyDOE, NumPy, SciPy	pyDOE 0.3.1, NumPy 1.26, SciPy 1.11	Used for Latin Hypercube Sampling, importance sampling, and probability fitting
System load data	Regional grid operator / Open datasets	—	Used for load forecast and scenario generation
Visualization libraries	Python: Matplotlib, Seaborn	Matplotlib 3.8, Seaborn 0.12	Used to generate figures of planning results, operational trajectories, and reserve margins