## 4 Conclusions  
The flow characteristics of the cooling system used in OBC/LDC integrated power inverters were analyzed through flow analysis of different design models. In addition, based on these characteristics, an optimization method was applied to achieve the same flow rate through each channel in the cooling system. Then, the obtained optimized model was verified via a flow uniformity evaluation method. In summary, the following conclusions can be drawn from this study:  
1. For the improved prediction accuracy of the optimized approximation values, the product and error distance functions, and normalized functions of the target value to the response were proposed as the optimization functions to ensure target distribution control in each multi-response. 2. The effective variables for controlling the distribution of flow rate in each channel of a planar cooling structure include the cooling water inlet volume flow rate, ratio of the width of the rear pipeline to that of the channel, and ratio of the length of the gap between the channel and wall to that of first channel and wall. Among these, the most effective variable was found to be the ratio of the length of the gap between the channel and wall to that of the first channel and wall. 3. The product and error distance functions and normalized response functions were applied as the optimization functions to ensure uniform distribution of water in each cooling water channel; it was found that this improved the prediction accuracy of the optimized approximation values. 4. The results of surface response optimization using the desirability function with the central composite design approach for our experimental evaluation indicated that the accuracy of optimization could be more significantly improved using a multi-response object function compared with using single-response object functions. 5. The proposed method was applied to the cooling system of the OBC/LDC integrated power inverter and was found to be highly effective in controlling uniform flow distribution in each cooling water channel. In particular, the flow uniformity among the different channels using the optimized design was more than or equal to 90% than the initial design model in terms of standard deviation, error distance, and maximum-minimum difference. This study was carried out using an analytical method in a design stage, and will be verified later by an experimental method. **Author Contributions:** [PERSON]-[PERSON] designed the equations of motion, conducted numerical programing and simulation, analyzed the results, composed and organized the data, and wrote the paper; [PERSON]-[PERSON] contributed to the numerical analysis and experiment design and data analysis; [PERSON]-[PERSON] contributed to the design and [PERSON]; [PERSON]-[PERSON] contributed to the CFD numerical analysis. All authors read and approved the final manuscript. **Funding:** This research was funded by the Korea Evaluation Institute of Industrial Technology (KEIT), Ministry of Trade, Industry & Energy (MOTIE), and Daewoo Electronic Components Co. Ltd. via Grant Number No. 10077362. **Conflicts of Interest:** The authors declare no conflict of interest. Figure 8: Velocity and pressure distributions for the optimal M6 model based on CFD analysis: (a) velocity (m/s); (b) pressure (kPa).