Load Flow Study Made Simple | The Iteration Process

Equipment selection and specification is a basic requirement in the design of any electric power system. Typically, this starts with the determination of the system steady state operating conditions through a load flow study.

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Prior to commissioning of an electric power system, what is known are only the resistance and reactance of the lines, the loads connected, and an assumption of the voltage at the sending end.

The Iteration Process of Load Flow Study

From figure 1, V₁, Z, and S₂ are known. This leaves us with V₂. As an example, suppose that we have a load of S₂ = 1.5 ∠0 pu, a line impedance of Z = 0.05 ∠0 pu, and assuming that the voltage at the sending end, V₁ = 1 ∠0 pu, solving for V₂ using the equation presented above will require an iteration process.

Initial Value (Assumption)

V₂⁽⁰⁾ = 1∠0 pu

1st Iteration

V₂ ⁽¹⁾= 1∠0  – 0.05∠0(1.5∠0/1∠0)* = 0.925 pu

2nd Iteration

V₂ ⁽²⁾=1∠0-0.05∠0(1.5∠0/0.925∠0)* = 0.91892 pu

3rd Iteration

V₂ ⁽³⁾=1∠0-0.05∠0(1.5∠0/0.91892∠0)*= 0.91838 pu

4th Iteration

V₂ ⁽⁴⁾=1∠0-0.05∠0(1.5∠0/0.91838∠0)*= 0.91833 pu

5th Iteration

V₂ ⁽⁵⁾=1∠0-0.05∠0(1.5∠0/0.91833∠0)*= 0.91833 pu

Solving for I,

I = (V₁ – V₂)/Z = (1 – 0.91833)/0.05 = 1.6334 pu

This is just a simple illustration of how the iteration process is done in a load flow study. For more complex systems, methods such as Newton-Raphson or Gauss-Seidel is used. Manual calculations can be quite complex and time consuming that is why using computer-aided simulation software such as ETAP and others related software is preferred.

The results of the load flow study will become the basis in the selection and specification of continuous current rating, cable ampacity, transformer rating and tap position, capacitor bank rating among others, and the optimization of system operating conditions.