Algorithms for Operation Planning of Electric Distribution Networks

Abstract

In this paper, two algorithms for solving the problem of operation planning of electric power distribution systems are presented. This problem consists in defining the values of a set of continuous and discrete control variables to obtain better system performance. Given the large number of possible combinations of the settings of the control variables, the problem presents combinatorial explosion. To work around it, two procedures are proposed. In the first one, the genetic algorithm developed by Chu and Beasley (GACB) is used with a special mechanism of creation of the initial population. In the second procedure, a simplified algorithm which is capable of obtaining good quality solutions at a much lower computational time complexity than GACB is proposed. The results for the 34- and 70-bus IEEE test systems show that the proposed algorithms are promising.

Appendix

The equations of active and reactive powers and calculated active power losses in the branches are given by:

$$\begin{aligned}&P_{k}^\mathrm{cal}= V_{k}\sum \limits _{m \in \Omega _{k}}V_{m}(G_{km}\cos (\theta _{k} -\theta _{m}) + B_{km}\sin (\theta _{k} -\theta _{m}))\nonumber \\ \end{aligned}$$

(16)

$$\begin{aligned}&Q_{k}^\mathrm{cal}= V_k\sum \limits _{m \in \Omega _{k}}V_m(G_{km}\sin (\theta _{k} -\theta _{m}) - B_{km}\cos (\theta _{k} -\theta _{m}))\nonumber \\ \end{aligned}$$

(17)

$$\begin{aligned}&P_{j}^\mathrm{l}= \sum \limits _{r=1}^{nr}g_{km}(V_{k}^{2}t_{km}^{2} + V_{m}^2 - 2V_{k}V_{m}t_{km}cos(\theta _{k} -\theta _{m})).\nonumber \\ \end{aligned}$$

(18)

$\Omega _{k}$ is the set of all neighboring buses to bus $k$; $V_{k},$ $V_m,$ $\theta _{k}$ and $\theta _{m}$ are the magnitudes and angles of voltage in the buses at the branch terminals $k m,$ and $G_{km}$ and $B_{km}$ are the real and imaginary parts of each element of the nodal admittance matrix. Furthermore, $r$ is the branch between the buses $k m,$ and $nr$ is the total number of branches, while $g_{km}$ is the conductance of the branch $k m.$