Voltage stability enhancement based on DG units

Abstract

Dispersed generation is considered as a novel approach in the field of electricity production. In fact, there are no standard definitions, or a standard term has been approved for this type of power generation right now. However, various terms and definitions about distributed generation have been employed in the previous kinds of research. For instance, North American countries use the term ‘dispersed generation,’ Anglo-American centuries the term ‘embedded generation,’ and some parts of Asia as well as Europe countries, the term ‘decentralized generation’ is used for this kind of production. In general, distributed generation can be defined as small-scale electric power generation that is connected to the distribution system. DG term refers to using modular technology which is located throughout utility’s service region. Distributed generation units are energized by solar, the wind, and fuel cell. There are a set of dispersed generation technologies in the market such as the wind and solar that started dominating on the local electricity markets due to their availability of such resources and free emission characteristics. It is worth mentioning that integrating dispersed generation into current networks has altered power flow pattern from traditional vertical to bi-directional power flow which contributed to enhancing voltage stability and minimizing power losses of the whole system. However, arbitrary integration of DG units in the system may cause some technical issues. In this paper, Newton–Raphson method and modal analysis are employed to identify the proper allocation of DG in the system. The 14 IEEE system has been selected to implement this approach by using a MATLAB software.

Appendix

Newton–Raphson Load flow:

The load flow formulated in Jacobian form is as follows:

$$ [J]\left[ {\begin{array}{*{20}c} {\Delta \delta } \\ {\Delta v} \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {\Delta P} \\ {\Delta Q} \\ \end{array} } \right] $$

where the column vectors consist of corresponding mismatches in power which are formulated to the voltage and angle, respectively. The J is Jacobian matrix which consists of partial derivatives J1, J2, J3, J4, respectively

$$ \begin{aligned} \left[ {\begin{array}{*{20}c} {J1} & {J2} \\ {J3} & {J4} \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {\Delta \delta } \\ {\Delta v} \\ \end{array} } \right] & = \left[ {\begin{array}{*{20}c} {\Delta P} \\ {\Delta Q} \\ \end{array} } \right] \\ \left[ {\begin{array}{*{20}c} {\frac{{\partial P_{\text{IN}} }}{\partial \delta }} & {\frac{{\partial P_{\text{IN}} }}{\partial V}} \\ {\frac{{\partial Q_{\text{IN}} }}{\partial \delta }} & {\frac{{\partial Q_{\text{IN}} }}{\partial V}} \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {\Delta \delta } \\ {\Delta v} \\ \end{array} } \right] & = \left[ {\begin{array}{*{20}c} {\Delta P} \\ {\Delta Q} \\ \end{array} } \right] \\ \end{aligned} $$

The J1 value for main diagonal and off diagonal elements are given below

$$ \begin{aligned} J1_{ii} & = \frac{{\partial P_{{{\text{IN,}}i}} }}{{\partial \delta_{i} }} = V_{i} \sum\limits_{\begin{subarray}{l} j = 1 \\ \ne i \end{subarray} }^{N} {y_{ij} V_{j} \sin (\delta_{i} - \delta_{j} - \theta_{ij} )} \\ J1_{ik} & = \frac{{\partial P_{{{\text{IN,}}i}} }}{{\partial \delta_{k} }} = - V_{i} V_{k} y_{ik} \sin (\delta_{i} - \delta_{k} - \theta_{ik} )\quad i \ne k \\ \end{aligned}$$

The value of J2 for main and off diagonal elements are calculated as below

$$ \begin{aligned} J2_{ii} & = \frac{{\partial P_{{{\text{IN,}}i}} }}{{\partial V_{i} }} = - \sum\limits_{\begin{subarray}{l} j = 1 \\ \ne i \end{subarray} }^{N} {y_{ij} V_{j} \cos (\delta_{i} - \delta_{j} - \theta_{ij} ) - 2V_{i} y_{ii} \cos ( - \theta_{ii} )} \\ J2_{ik} & = \frac{{\partial P_{{{\text{IN,}}i}} }}{{\partial V_{k} }} = - V_{i} y_{ik} \cos (\delta_{i} - \delta_{k} - \theta_{ik} )\quad i \ne k \\ \end{aligned} $$

The value of J3 for main and off diagonal elements is calculated as below

$$ \begin{aligned} J3_{ii} = \frac{{\partial Q_{{{\text{IN,}}i}} }}{{\partial \delta_{i} }} = - V_{i} \sum\limits_{\begin{subarray}{l} j = 1 \\ \ne i \end{subarray} }^{N} {y_{ij} V_{j} \cos (\delta_{i} - \delta_{j} - \theta_{ij} )} \\ J3_{ik} = \frac{{\partial Q_{{{\text{IN,}}i}} }}{{\partial \delta_{k} }} = V_{i} V_{k} y_{ik} \cos (\delta_{i} - \delta_{k} - \theta_{ik} )\quad i \ne k \\ \end{aligned} $$

The value of J4 for main and off diagonal elements is calculated as below

$$ \begin{aligned} J4_{ii} & = \frac{{\partial Q_{{{\text{IN,}}i}} }}{{\partial V_{i} }} = - \sum\limits_{\begin{subarray}{l} j = 1 \\ \ne i \end{subarray} }^{N} {y_{ij} V_{j} \sin (\delta_{i} - \delta_{j} - \theta_{ij} ) - 2V_{i} y_{ii} \sin ( - \theta_{ii} )} \\ J4_{ik} & = \frac{{\partial Q_{{{\text{IN,}}i}} }}{{\partial V_{k} }} = - V_{i} y_{ik} \sin (\delta_{i} - \delta_{k} - \theta_{ik} ) \quad i \ne k \\ \end{aligned} $$

The matrices are formulated in every iteration, and the mismatches are calculated. The new matrix is formed using the mismatches, and the corresponding voltage and angles are updated. The iterations are carried out until the required level of error tolerance is achieved or the maximum number of iterations have been exhausted.