A simple implementation of power mismatch STATCOM model into current injection Newton–Raphson power-flow method

Abstract

This paper presents a simple implementation of Static Shunt Compensator (STATCOM) into Newton–Raphson current injection load flow method. The controlled STATCOM bus in the network is represented by voltage-controlled bus with zero active power generation at the required voltage magnitudes. The power mismatch equation of the connected STATCOM bus is included in Newton–Raphson current injection load flow algorithm, while the other PQ buses are represented by current mismatch equations. Moreover, the parameters of STATCOM can be calculated during iterative process and the final value will be updated after the convergence is achieved. This representation of generator buses reduces the number of required equations with respect to the classical and improved versions of the current injection methods. In addition of that the developed model reduces the complexities of the computer program codes and enhances the reusability by avoiding modifications in the Jacobian matrix. The performance of the developed STATCOM model has been tested using standard IEEE systems.

Appendix

The parameters $(a_{f},\; b_{f},\; c_{f}$ and $d_{f})$ in Eq. (1) can be given as following:

$$\begin{aligned} a_f&= \left[ \frac{Q_f^{\prime } (V_{\mathrm{r}f} {2}-V_{\mathrm{m}f} {2})-2P_f^{\prime } V_{\mathrm{r}f} V_{\mathrm{m}f} }{V_f^4 }\nonumber \right. \\&+\left. \frac{V_{\mathrm{r}f} b_p P_{0f} V_{\mathrm{m}f} +b_p Q_{\mathrm{0}f} V_{\mathrm{m}f} ^{2}}{V_f^3 }+c_q Q_{0f}\right] \end{aligned}$$

(24)

$$\begin{aligned} b_f&= \left[ \frac{(P_f^{\prime } (V_{\mathrm{r}f} {2}-V_{\mathrm{m}f} {2})+2V_{\mathrm{r}f} V_{\mathrm{m}f} Q_f^{\prime } )}{V_f^4 }\nonumber \right. \\&- \left. \frac{(b_p Q_{0f} V_{\mathrm{m}f} V_{\mathrm{r}f} +b_p P_{0f} V_{\mathrm{r}f} {2})}{V_{f}^{3}}-c_p P_{0f} \right] \end{aligned}$$

(25)

$$\begin{aligned} c_f&= \left[ \frac{P_f^{\prime } ((V_{\mathrm{m}f} {2}-V_{\mathrm{r}f} {2})-2Q_f^{\prime } V_{\mathrm{r}f} V_{\mathrm{m}f} )}{V_f^4 }\nonumber \right. \\&+ \left. \frac{b_p Q_{0f} V_{\mathrm{m}f} V_{\mathrm{r}f} -b_p P_{0f} V_{\mathrm{m}f} {2})}{V_f^3 }-c_p P_{0f} \right] \end{aligned}$$

(26)

$$\begin{aligned} d_f&= \left[ \frac{Q_f^{\prime } (V_{\mathrm{r}f} {2}-V_{\mathrm{m}f} {2})-2P_f^{\prime } V_{\mathrm{r}f} V_{\mathrm{m}f} }{V_f^4 }\nonumber \right. \\&+ \left. \frac{(V_{\mathrm{m}f} b_p P_{0f} V_{\mathrm{r}f} -b_p Q_{0f} V_{\mathrm{r}f} {2})}{V_f^3 }-c_q Q_{0f}\! \right] \!, \end{aligned}$$

(27)

where

$$\begin{aligned}&P_f^{\prime } =P_{G(f)} -P_{L(f)} =P_{G(f)} -P_{0f} a_p\end{aligned}$$

(28)

$$\begin{aligned}&Q_f^{\prime } =Q_{G(f)} -Q_{L(f)} =Q_{G(f)} -Q_{0f} a_q \end{aligned}$$

(29)

When the bus has only a constant power load, the parameters are simplified to

$$\begin{aligned}&a_f =d_f =\frac{Q_f^{\prime } (V_{\mathrm{r}f} ^{2}-V_{\mathrm{m}f} ^{2})-2P_f^{\prime } V_{\mathrm{r}f} V_{\mathrm{m}f}}{V_f^4 }\end{aligned}$$

(30)

$$\begin{aligned}&b_f =-c_f =\frac{P_f^{\prime } (V_{\mathrm{r}f} ^{2}-V_{\mathrm{m}f} ^{2})+2V_{\mathrm{r}f} V_{\mathrm{m}f} Q_f^{\prime } }{V_f^4} \end{aligned}$$

(31)

These parameters are updated during the iterative load flow process.