## 4 System Loss Optimized Control for PMSM Drive System  
From Equations (14) and (53), the system loss of PMSM drive system can be expressed as:  
\[ \begin{array}{ll}P_{loss\_system}&=P_{loss\_inter}+P_{loss\_motor}\\ &=6\left\{\begin{array}{l}\frac{a_{r}+a_{f}}{\pi}I_{0}+\frac{2\left(c_{r}+ c_{f}\right)}{3\pi}I_{0}^{3}+\frac{b_{r}+b_{f}}{4\pi}I_{0}^{2}+\frac{a_{r}-a_{f}}{4}M \cos\varphi I_{0}\\ \frac{1}{4}\left(2\left(b_{r}-b_{r}\right)-M\cos\varphi I_{0}^{2}+\frac{3\left( c_{r}-c_{f}\right)}{16}M\cos\varphi I_{0}^{3}\right.\end{array}\right\}\\ &\left.\frac{f_{sw}\omega I_{0}}{L_{dec}\omega_{r}}\left[\frac{f_{sw}\omega I_ {0}}{4}+\frac{f_{sw}\omega I_{0}}{16}+\frac{1}{2}\left(b_{on}+b_{off}+b_{rec} \right)I_{0}+\frac{1}{2}\left(a_{on}+a_{off}+a_{rec}\right)\right]\\ &+\frac{3}{2}R_{s\_f}\left(\left(i_{old}+\frac{L_{dec}\omega_{r}}{2}-\frac{a_ {off}}{R_{e}}\omega_{r}L_{out}\omega_{r}\right)^{2}+\left(i_{old}+\frac{L_{out }\omega_{r}}{2}+\frac{a_{off}}{R_{e}}\omega_{r}L_{out}\omega_{r}\right)^{2} \right)^{2}\end{array} \right.\end{array} \tag{54}\]  
Equation (54) shows that the system loss of a PMSM drive system is so complicated that it is impossible to directly optimize the system loss by an analytical method. Therefore, to maximize the system efficiency of PMSM system, the system loss can be divided into two parts: one part is the loss only affected by motor operation state and the other part is the loss affected by motor and inverter operation state, which can be shown as:  
\[P_{loss\_system}=P_{Motor\_affect\_loss}+P_{Double\_affect\_loss} \tag{55}\]  
where the loss only affected by motor state in the steady state can be expressed as:  
\[ \begin{array}{ll}P_{Motor\_affect\_loss}&=\frac{6\left(a_{c}+a_{f}\right)} {\pi}I_{0}+\frac{4\left(c_{c}+c_{f}\right)}{\pi}I_{0}^{3}+\frac{6\left(b_{c}+ b_{f}\right)}{4\pi}I_{0}^{2}+\frac{3\left(a_{c}-a_{f}\right)}{2}M\cos\varphi \cdot I_{0}\\ &+\frac{4\left(b_{c}-b_{f}\right)}{\pi}M\cos\varphi\cdot I_{0}^{2}+\frac{9 \left(c_{c}-c_{f}\right)}{2}M\cos\varphi\cdot I_{0}^{3}\\ &+\frac{3}{2}R_{s\_f}\left[\left(i_{old}-\frac{n_{p}\omega_{r}L_{s}n_{id}}{R_ {e}}\right)^{2}+\left(i_{old}+\frac{n_{p}\omega_{r}\psi_{f}+n_{p}\omega_{r}L _{out}a_{id}}{R_{e}}\right)^{2}\right]\\ &+\frac{3}{2}\left(\frac{n_{p}\omega_{r}L_{s}n_{id}}{R_{e}}\right)^{2}+\left( n_{p}\omega_{r}\psi_{f}+n_{p}\omega_{r}L_{out}a_{id}\right)^{2}\\ &=P_{conduction\_intercept}+P_{motor\_f}\end{array}  \tag{56}\]  
and the loss affected by motor and inverter operation state in the steady state can be shown as:  
\[ \begin{array}{ll}P_{Double\_affect\_loss}&=\frac{f_{sw}L_{dec}}{L_{dec} \omega_{r}}\left[\frac{3}{2}\left(c_{on}+c_{off}+c_{rec}\right)I_{0}^{2}+\frac {6}{\pi}\left(b_{on}+b_{off}+b_{rec}\right)I_{0}+3\left(a_{on}+a_{off}+a_{rec} \right)\right]\\ &+3\left[\sum\limits_{n=2}^{\infty}I_{2,0n}^{2}\cdot R_{s,mn}+\sum\limits_{m=1 }^{\infty}\sum\limits_{n\underset{n\rightarrow\infty}{n\rightarrow\infty}}^{ \infty}I_{s,mn}^{2}\cdot R_{s,mn}+\sum\limits_{n=2}^{\infty}I_{cs,0n}^{2}\cdot R _{e}+\sum\limits_{m=1}^{\infty}\sum\limits_{n\underset{n\rightarrow\infty}{n \rightarrow\infty}}^{\infty}I_{cs,mn}^{2}\cdot R_{e}\right]\\ &=P_{switch\_intercept}+P_{motor\_h}\end{array}  \tag{57}\]Based on the system loss model, this paper proposes a system efficiency improvement control which aims to optimize the system loss and improve the system efficiency of a PMSM system over the whole operation condition range of EVs. As the system loss model is too complex to solve, the proposed control strategy optimizes the system efficiency by minimizing the loss affected by motor operation condition (\(P_{Motor\_affect\_loss}\)) and the loss affected by motor and inverter operation state (\(P_{Double\_affect\_loss}\)). Equation (57) shows that \(P_{Motor\_affect\_loss}\) is only affected by the motor drive parameters (\(i_{od}\), \(i_{od}\), \(M\), \(\omega_{r}\)).