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Significance Statement
An efficient methodology for decision-making: optimal operation of photovoltaic devices, batteries, thermal energy storage, and heat source systems using metaheuristics
This article consists of two parts: the optimization of operating schedules for energy systems, and the proposal of a new index for decision-making to decide the schedules. The former focuses on how to optimize an operating schedule for photovoltaic (PV) devices, batteries, water thermal storage, and heat source machines. We adopted the epsilon constrained differential evolution (εDE) algorithm to efficiently find the best solution under the nonlinear configuration of heat source machines. εDE is one of the metaheuristic methods that use iterative calculations to find a solution.
An advantage of this method is that it solves almost all functions, whether they are linear, nonlinear, convex, concave, continuous, or discrete. Hence, a complex mathematical formulation such as integer linear programming is not needed, and it enables an end-user to easily decide an optimal operating schedule within a short computation time.
In the second part of this article, we propose a new index, the area rate of prices (ARP), through analysis of many results that were obtained using the optimization method mentioned previously. The ARP is designed for easy decision-making of optimal operations of electricity systems and uses only day-ahead information of electricity purchased and sale prices to decide optimal operations. We validated this index under three different curves of cooling and electricity demand, and electricity price.
The result was that generated electricity from PV should be sold to the grid when the ARP value is less than a certain number (0.2 in this case). On the other hand, when the value is greater than the same value, electricity from PV should be used in buildings. This threshold was the same value in three different demand curves. Thus, when the PV power generation profile is the same, the threshold can be used even if the demand and price curves are different.
Therefore, εDE can be used in practical situations because of its low computation cost and easy adaptation. The new index, ARP, has substantial advantages for energy system optimization.
Journal Reference
Sustainable Cities and Society, Volume 21, 2016, Pages 1–11.
Shintaro Ikeda1 , Ryozo Ooka2
[expand title=”Show Affiliations”]- Department of Architecture, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
- Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
Abstract
Thermal energy storage (TES) and batteries have recently become increasingly important for peak-load shifting in energy systems. However, optimizing energy systems is difficult because each machine has multiple combinations of operations, and the objective function contains transformed nonlinear or non-convex characteristics. Therefore, we adopted the epsilon-constrained differential evolution (ɛDE) in order to minimize operating costs.
We demonstrate that the ɛDE method efficiently solved strict constraint optimization problems on three energy systems: a self-consumption model (Case 1), total amount of a purchased model (Case 2), and a full connection model (Case 3) under 126 case studies. Although 216 decision variables were used under the nonlinear condition, we were able to obtain the optimal solution within a short time period, 16 min on an ordinary PC. Moreover, we proposed a new index “Area rate of prices (ARP)” in order to evaluate the effects of purchased and sold electricity prices on the operating costs.
The results showed that when the area rates of purchased price to sold price are higher than 0.2 (ARP > 0.2), Case 1 was superior to Case 2. On the other hand, when the ARP value was less than 0.2, Case 2 was superior to Case 1. Therefore, we can conduct the optimization on everyday practical situations because ɛDE requires low computational cost. Even if the operators cannot conduct the optimization in practical energy management, they can easily determine the operation strategy by calculation of the ARP value. Therefore, the ɛDE and ARP methods have substantial advantages for energy system optimization.
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