Storage Size Determination for Grid-Connected Photovoltaic Systems (1109.4102v2)

Abstract: In this paper, we study the problem of determining the size of battery storage used in grid-connected photovoltaic (PV) systems. In our setting, electricity is generated from PV and is used to supply the demand from loads. Excess electricity generated from the PV can be stored in a battery to be used later on, and electricity must be purchased from the electric grid if the PV generation and battery discharging cannot meet the demand. Due to the time-of-use electricity pricing, electricity can also be purchased from the grid when the price is low, and be sold back to the grid when the price is high. The objective is to minimize the cost associated with purchasing from (or selling back to) the electric grid and the battery capacity loss while at the same time satisfying the load and reducing the peak electricity purchase from the grid. Essentially, the objective function depends on the chosen battery size. We want to find a unique critical value (denoted as $C_{ref}^c$) of the battery size such that the total cost remains the same if the battery size is larger than or equal to $C_{ref}^c$, and the cost is strictly larger if the battery size is smaller than $C_{ref}^c$. We obtain a criterion for evaluating the economic value of batteries compared to purchasing electricity from the grid, propose lower and upper bounds on $C_{ref}^c$, and introduce an efficient algorithm for calculating its value; these results are validated via simulations.

• The paper derives analytical bounds on critical battery storage size, establishing a cost-minimization criterion for grid-connected PV systems.
• It employs a bisection algorithm to optimize battery capacity while considering dynamic pricing, load demand, and battery aging.
• Simulations demonstrate significant savings and improved performance in both residential and commercial PV installations.

Determining Optimal Storage Size for Grid-Connected Photovoltaic Systems

The paper of optimal battery storage size for grid-connected photovoltaic (PV) systems, as explored by Yu Ru, Jan Kleissl, and Sonia Martinez, is an essential part of modern renewable energy applications. This paper primarily focuses on electricity consumers with rooftop PV arrays, such as residential and commercial buildings, aiming to reduce energy costs, minimize battery investment losses due to aging, and limit peak grid electricity purchase.

Problem Context:

Battery sizing for grid-connected PV systems deviates significantly from stand-alone systems, where the battery must cover energy needs during non-generational periods and cloudy days. In contrast, grid-connected systems can use grid power during deficits, placing different demands on battery storage regarding optimal size and economic feasibility.

Objective and Key Contributions:

A primary objective of the paper is to establish a critical battery size that minimizes the combined cost of net power purchase from the grid and battery capacity loss while adhering to load demand and peak shaving constraints. The paper uniquely proposes—including through theoretical analysis—lower and upper bounds for this critical battery size and offers an efficient algorithm for its calculation.

• The paper takes a novel approach by deriving analytical bounds on the storage size, distinct from previous works heavily reliant on simulations, providing a theoretical basis that aids economic evaluation of battery usage.
• It develops a decision-making criterion for judging battery storage feasibility against grid electricity procurement, essential for practical implementation in PV systems considering battery aging and time-of-use electricity pricing.

Methodological Approach:

The paper employs a detailed mathematical formulation of the storage size determination problem in a dynamic electricity pricing context, accounting for PV output variability, load demands, and battery aging. The effectiveness of the proposed solutions is validated through simulations, offering insights into real-world applications.

A critical contribution is the efficient bisection algorithm developed for determining optimal battery capacity. This approach, based on economic metrics and electrical constraints, allows for practical implementation and scale adaptation from theoretical optimal management insights to consumer-level applications.

Simulation Insights:

The simulations in different PV output and load scenarios underscore the relevance of considering PV variability and load profiles in battery sizing decisions. For instance, commercial loads, which often peak during high-priced periods, suggest greater savings potential with correctly sized batteries. In contrast, residential systems benefit primarily from strategic timing of battery use aligned with peak pricing.

Theoretical and Practical Implications:

This paper extends its practical relevance by suggesting that well-defined battery sizes aligned with economic and operational goals can lead to considerable savings and system performance improvements. From a theoretical perspective, the work highlights the importance of incorporating battery aging dynamics into energy storage optimization, an area often simplified in previous models.

Future Directions:

The paper acknowledges future research opportunities in incorporating more sophisticated dynamic pricing models and exploring more complex nonlinear battery models to adapt these findings to emerging hybrid and electric vehicle storage contexts.

In summary, this work offers a significant contribution to the field of renewable energy systems engineering, particularly in optimizing the economic and operational efficiency of PV-battery installations under market-driven constraints.