Question

For the six-bus system shown in Figure 2, use DC Power Flow method to find all line flows and bus 1 (slack bus) power. Line and bus data are shown in Tables 1 and 2 respectively. The base is 100 MVA.

Answer 1

In DC load flow method we estimate power flows on AC power systems. This looks only at active power flows and neglects reactive power flows. Hee we simplify nonlinear model of the AC system is simplified to a linear form through these assumptions:-

• Line resistances (active power losses) are negligible

• Voltage angle differences are assumed to be small

• Magnitudes of bus voltages are set to 1.0 per unit (flat voltage profile).

• Tap settings are ignored.

The real power equation after above approximations used to solve the DC load flow are:-

$P_i=\sum_{j=1}^{N}B_i_j(\Theta _i-\Theta_j)$

Bij is the reciprocal of the reactance between bus i and bus j and Bij is the imaginary part of Yij.

Similarly the active power flow through transmission line i, between buses s and r, can be calculated as

$P_L_i=\frac{1}{X_L_i}B_i_j(\Theta _s-\Theta_r)$

where XLi is the reactance of line i.

DC power flow equations in the matrix form are given as

$\Theta=[B]^{^{-1}}P$

$P_L=(bXA)\Theta$

where P is Nx1 vector of bus active power injections for buses 1, …, N

B is N XN admittance matrix with R = 0

$\Theta$ is  N X1 vector of bus voltage angles for buses 1, …, N

PL is MX1 vector of branch flows (M is the number of branches)

b is M X M matrix (bkk is equal to the susceptance of line k and non-diagonal elements are zero)

A is M X N bus-branch incidence matrix

By applying to this problem and solving the appropriate $\Theta$ the solution for this is given as:-

Sl.no	From Bus	To Bus	pu MW flows
1	1	2	0.253
2	1	4	0.416
3	1	5	0.331
4	2	3	0.019
5	2	4	0.325
6	2	5	0.162
7	2	6	0.248
8	3	5	0.169
9	3	6	0.449
10	4	5	0.04
11	5	6	0.003

The slack bus(Bus 1) power flow is 1pu MW