[Paper Review] Integrated Planning of a Solar/Storage Collective

Jesus E. Contreras-Ocaña, Arshpreet Singh+2 more|arXiv (Cornell University)|Aug 27, 2020

Smart Grid Energy Management29 references27 citations

TL;DR

This paper presents an integrated long-term planning and model predictive control (MPC) framework for a solar-plus-storage energy collective under French collective self-consumption regulations. It jointly optimizes system sizing, equitable energy allocation, and real-time operation to minimize cost and mismatch, achieving a 3–11% surplus in energy delivery with equitable distribution across 15 consumers.

ABSTRACT

French regulation allows consumers in low-voltage networks to form collectives to produce, share, and consume local energy under the collective self-consumption framework. A natural consequence of collectively-owned generation projects is the need to allocate production among consumers. In long-term plans, production allocation determines each of the consumers' benefits of joining the collective. In the short-term, energy should be dynamically allocated to reflect operation. This paper presents a framework that integrates long and short-term planning of a collective that shares a solar plus energy storage system. In the long-term planning stage, we maximize the collective's welfare and equitably allocate expected energy to each consumer. For operation, we propose a model predictive control algorithm that minimizes short-term costs and allocates energy to each consumer on a 30-minute basis (as required by French regulation). We adjust the energy allotment ex-post operation to reflect the materialization of uncertainty. We present a case study where we showcase the framework for a 15 consumer collective.

Motivation & Objective

• To design a cooperative, financially sustainable framework for a solar-plus-storage collective under French collective self-consumption regulations.
• To jointly optimize long-term system sizing and equitable energy allocation to maximize collective welfare and ensure investor profitability.
• To develop a real-time control and post-operation settlement mechanism that minimizes energy mismatch between planned and actual delivery.
• To ensure transparency and simplicity in pricing and allocation rules to foster trust and participation among consumers and investors.
• To evaluate the framework’s performance under realistic conditions, including uncertainty in solar generation and grid pricing.

Proposed method

• Formulates a mixed-integer linear program (MILP) for long-term planning to size the PV+storage system and maximize collective welfare over a 20-year horizon.
• Uses an optimization model to equitably allocate expected annual energy to each consumer based on load profiles and system capacity.
• Employs a model predictive control (MPC) algorithm with a rolling 30-minute horizon to dynamically manage energy dispatch and minimize operational costs.
• Introduces an ex-post settlement algorithm that adjusts energy allocations based on actual generation and consumption, reducing mismatch.
• Applies a weighted objective in MPC that balances operational cost minimization and deviation from planned energy allocations.
• Uses convex optimization for both control and settlement problems, ensuring fast and reliable computation (≈0.006s and ≈0.005s per iteration).

Experimental results

Research questions

• RQ1 What is the optimal size of a PV+storage system for a 15-consumer collective to maximize long-term collective welfare under French regulations?
• RQ2 What range of energy prices ensures financial sustainability for both investors and consumers in a collective self-consumption model?
• RQ3 How can energy be equitably allocated among heterogeneous consumers over a year while respecting regulatory 30-minute reporting requirements?
• RQ4 How does the proposed MPC and settlement framework compare to alternative control strategies in minimizing energy mismatch between planned and actual delivery?
• RQ5 To what extent does the framework maintain fairness and surplus delivery when solar generation exceeds expectations?

Key findings

• The proposed framework ensures financial sustainability for the collective, with a viable price range of 0.10–0.13 EUR/kWh for PV+storage energy in the pessimistic case.
• Even when the investor captures 50% of the net benefits, consumers still achieve 3–5% savings compared to grid electricity, demonstrating strong financial incentives.
• All consumers received at least as much energy as promised over the year, with a total surplus of 276 ± 2 kWh (over 2% of total load), due to 6% higher-than-expected PV generation.
• The MPC and ex-post settlement algorithm reduced end-of-year mismatch to between +3% and +11% across consumers, outperforming alternatives that showed deficits of up to 1.2 MWh.
• In the pessimistic scenario with no grid export compensation, the system still achieved Pareto-optimality, indicating that collective investment remains beneficial.
• The framework maintains equitable distribution: under the proposed method, no consumer received less than promised, unlike alternative approaches that led to deficits of up to 15%.