A Multi-Objective Genetic Algorithm methodology for sizing and power electronics selection of standalone renewable energy systems

This work proposes a design methodology to optimize multiple design metrics of a stand-alone PV/battery system at the same time. The relevance of each objective can be adjusted by the designer and this paper explores the correlations among them. An application example is proposed, where the objectives are the minimization of investment and operational cost, with a boundary set on the system reliability. The variables are six and represent the size of the generation, storage, and power conversion elements, as well as the converters selection. The example design is repeated with two battery types, Lead-Acid and Li-Ion. The use of a genetic algorithm reduces the computational power, allowing the quick execution of several optimizations with different settings.


INTRODUCTION
The switch to renewable energy is nowadays a reality with a bright future, but the increasing penetration of volatile energy sources risks compromising the reliability of national grids. Extensive research is being carried out to address this concern, exploring possibilities such as smart grids [1], energy storage technologies [2], energy management [3], and distributed energy systems [4]. Much of the research in the latter area revolves around using automated methods for either system-level [5,6,7,8] or component-level optimizations [9,10], which are usually treated separately, with simplifying assumptions. Such assumptions are also adopted by existing and widespread design software, like HOMER [11, 12,13], which make inaccessible their component specifications [14,15].
This paper attempts to make a step in exploring how these two design aspects affect each other while applying the findings of [16]. The dependency studied here is mono-directional (converters selection is based on system architecture, and not vice-versa), but an iterative approach will be adopted in future work.

PROBLEM FORMULATION AND METHODOLOGY
As shown in Fig. 1, the system architecture that this design method analyzes is composed by a photovoltaic element and a battery pack, each connected to a control system via an array of DC-DC converters. The size of PV and battery elements are the independent variables of the study. The sizing and selection of the converters arrays are carried out based on independent variables. In evolutionary terms, each design solution can be represented by a combination of 6 variables: 1) number of PV units ( ); 2) number of battery units ( ); 3) converter model for Array 1 ( ); 4) converter model for Array 2 ( ); 5) number of converters in Array 1 ( ); 6) number of converters in Array 2 ( ). The "quality" of the i-th combination is evaluated with the fitness function in eq. (1), which must be minimized: where and are the weights given to each objective, , , and , , are the investment and operational costs of the i-th combination, annualized [17] to the current year.
A solution to this problem is found using the Genetic Algorithm represented in Fig. 2: the GA is initialized by randomly creating different combinations of the two independent variables ( and ). Then, Figure 1: Schematic of the energy system.

Control system
Array 1

Array 2
Load the converters that are compatible with these are selected from a database of commercially available DC-DC converters. The compatibility is verified if the following conditions are satisfied: Once the 6 "genes" are available for all the individuals of the first generation, a typical year is simulated as described in the next section, and their fitness is calculated using (3). The individuals with the lowest survive to the next generation and are bred to produce "offspring" with mixed characteristics, which will become part of the next generation, together with random "mutations", generated to avoid local minimum traps. This iteration cycle continues until the relative improvement (the percentual difference between the fittest individuals of consecutive generations) becomes smaller than the threshold for consecutive times ( and are set by the designer). This method provides rapid convergence even in nonlinear scenarios.

EXAMPLE OF APPLICATION
The number of users is represented as a sinusoidal function of day and time, as suggested in [19]. When the percentage of users is under 5%, the idle mode is triggered to reduce the power consumption. A boundary condition discards the solutions providing less than a certain service availability (quote of users successfully served). The power generator is assumed to be working at its MPP for 95% of the active time. This allows to simplify the 5 parameters model [20] and calculate the MPP voltage and current at any irradiation and temperature conditions with (10) and (11) of [21]. Cell temperature is calculated as suggested in [22], with the irradiation (G) and ambient temperature (Ta) data provided by [23], and the technical data of the panel by its datasheet [24]. The energy stored in the battery pack at any time, ( ), is tracked using (2) [25]: Two battery types are compared: a lead-acid [26] and a lithium-ion battery pack [27]. The lifetime of the cells is estimated as a function of DoD and T by applying, respectively, the models in [28] and [29].

RESULTS
Six optimizations were carried out using different weights and two battery types to highlight their effect on the system design. The results are displayed in Table 1: focusing on the reduction of investment cost ( = 1000) produces an under-sized system, with a service availability near the lower boundary of 98%.
This has a negative impact on the overall cost because the operational cost soars; on the other hand, focusing on the operational cost produces the best availability results, showing how these two parameters are related.

CONCLUSIONS
In the present work, a methodology was proposed to design a stand-alone energy system with optimized investment and operational cost. The resulting design is a combination of six variables, plus the battery type, that is manipulated manually.  In the final submission, more information, both quantitative and qualitative, will be provided on the current research context, the methodology, the mathematical models, the economic parameters, and the results. The library of converters will be extended and the relation between system design and converters selection will be explored in more detail. Furthermore, the results provided by the Genetic Algorithm will be enhanced with the addition of a "surroundings exploration" technique.