# Optimized Multiport DC/DC Converter for Vehicle Drivetrains: Topology and Design Optimization
## 1 Introduction
[7] used the Augmented Lagrange Penalty Function (ALPF) technique to optimize a half-bridge dc-dc converter. [PERSON] et al. [8] utilized the Sequential Quadratic Programming (SQP) for a boost power-factor-correction converter optimization. However, the main drawback of gradient-based algorithms is that if the design space contains several local minima, there is a possibility that a gradient-based optimizer may be trapped by a local minimum, and the result depends on the selection of the initial design point. So far in the literature, no existing gradient-based algorithms are able to find the global optimization solution [9]. Furthermore, the gradient-based methods are mathematically guided algorithms, which require stringent mathematical formulations, causing a complexity of the system when variables increase. The metaheuristic-based optimization method was thus developed to solve the derivative-free and multi-objective problem with a large number of variables. Metaheuristic methods imitate the best features in nature, based on natural selection and social adaption. Among numerous metaheuristic methods, Genetic Algorithm (GA) [10] and Particle Swarm Optimization (PSO) [11] have been widely utilized to design the circuity of a power converter. The GA can be applied to optimize the medium-frequency transformer [12] of isolated converter, heatsink and bus capacitor volumes [13] of a three-phase inverter to archive minimum weight, losses and cost, with respect to constraints of design specification and physical limitation of components. The PSO, combined with Differential Evolution (DE), helps find an optimal transformer design for the Dual-Active-Bridge converter [14], the resonant tank of isolate bidirectional series resonant converter [15], and the inductor using EE core geometry [16]. So far, almost all researches have formulated a single objective formulation (efficiency, or weight, or cost [8]) or aggregated  
Figure 2: Non-isolated MPC using an interleaved bidirectional converter for each port in the Full Electric Bus powertrain. multiple conflicting objectives (weight, and loss, and cost) into one single objective. The multi-objective optimization of transformer design was solved by the Non-dominated Sorted Genetic Algorithm (NSGA-II) [12]; however, the final design selected from Pareto-solutions was not explained clearly. In this paper, a new optimization methodology as shown in Figure 3 is proposed for the non-isolated interleaved MPC. The main characteristics of the interleaved converter are analyzed by predefined specifications such as maximum power \(P_{max}\), input voltage \(V_{in}\), output voltage \(V_{out}\) and required input current ripples \(I_{ripple}\) for battery and Supercapacitor (SC) ports, to derive objective functions that can be used for optimization problem formulation. A multi-objective genetic algorithm and Average Ranking technique are then employed to find three design variables (the number of phases \(N_{ph}\), switching frequency \(f_{sw}\), and core index representing geometry parameters of the core) to simultaneously minimize three trade-off objectives: weight of inductors, converter losses and input current ripples. To closely attain a practical design, a database was developed, which included commercial available inductor cores (23 cores) and Insulated Gate Bipolar Transistor (IGBT) modules (8 IGBT modules) for the optimization process. A hypothesis is that an optimal solution can be found in the database. The SOLIDWORKS software (Solidworks Premium 2018, Dassault Systemes SolidWorks Corporation, Waltham, MA, USA, 2018) is then used to visualize the physical structure of optimal inductors that are imported into the COMSOL Multiphysics (Version 5.3a, COMSOL, Inc., Burlington, MA, USA, 2018), a Finite Element Method (FEM)-based software, to simulate the electromagnetic field of the designed inductor. The curve fitting Matlab function is also used to plot the inductance value in the function of air-gap and number of turns.