Power Flow Analysis: Transmission and Distribution Systems: An Introduction

Power flow or load flow is one of the important power system analyses. Problem. This problem is determining the unspecified (dependent) parameters of the power network by some specified (independent) parameters.

It is known that the power system consists of generators, loads, transformers, transmission lines and other protective devices. In power flow every bus (node) is having four parameters.

1. Real Power P

2. Reactive power Q

3. Voltage magnitude [V]

4. Voltage magnitude φ

Depending on the type of the bus two out the four variables are specified and the remaining two has to be determined. The specified two variables and unspecified two variables of each bus are related by the kirchoff’s network laws.

The network elements are modeled according to their steady state characteristics.

1. Generator –voltage source with series impedance

2. Loads: constant power or constant admittance (impedance)

3. Transmission line: pi model

4. Transformers are to be incorporated in the transmission line model.

The specified and unspecified parameters
Type of the bus	Specified variables	Unspecified variables
Slack	[V],φ	P,Q
Generator	[V],P	Q, φ
Load(Constant power)	P,Q	[V], φ

When the power is transmitted from the generators to the loads through the transmission line the loss occurring in the transmission line is unavoidable. It is call the transmission loss and it not known in advance so there must be a provision that a generator should include the transmission loss in its generation.

This is the reason why the slack bus concept is included in the power flow analysis. The generator having largest capacity is chosen as the slack bus. Depending on the selection of the slack bus generator the power flow solution will vary.

Procedure to solve transmission system power flow

The following steps are to be followed to carry out power flow analysis. Here it is assumed that the three phase network is a balanced one.

1. Collect the specified data of generators, loads, transmission lines, and transformers. You can follow some matrix format like matpower.
2. Convert the network as per unit equivalent.
3. Formulate the equations as per kirchooff’s law.

These equations can be written in either polar form or rectangular form. In polar form no of equation are to be solved in 2(n-1)-m, wherein the rectangular form the no of equations are 2(n-1).

1. The system of non linear (polar trigonometric, rectangular quadratic) equations are to be solved by numerical methods only because so far no analytical solution is derived to sole this problem.
2.   Newton Raphson method, Decupled and gauss seidal are methods used to solve this problem. Among this N-R and Decoupled are preferred for their quadratic convergence.

Distribution Power flow.

The distribution systems are characterized by their nature of high R/X ration and radial nature (no loop).The admittance matrix is sparse and the Newton Raphson method may fail to converge for some networks. So the modeling of the problem as well as the solution methodology is different.

 The power flow equations for a radial distribution system are derived as the relationship between the specified complex bus powers and the bus voltages. If the network has n (total number) buses and ‘m’ generator buses the power flow equations are written as follows

k(i) is the set of nodes connected to node i, and P_i /Q_i denote the real/reactive power at node i. The complex non linear equations (B2) are to be solved to determine the bus voltages. So many methods ranging form sweep methods to conic programming methods available in the literature 

 to solve this problem..

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