Load Flow or Power Flow Analysis

Load flow analysis is the computational process used to find the steady-state operating conditions of a power system network based on line and bus data.
Things you must know about load flow:

1. Load flow study is the steady-state analysis of a power system network.
2. Load flow study determines the operating condition of the system under a specific load.
3. Load flow solves a set of simultaneous non-linear algebraic equations to find the voltage magnitude (|V|) and phase angle (∠δ) at each node in a system.
4. Solving non-linear equations requires fast, efficient, and accurate numerical algorithms.
5. The output of the load flow analysis is the voltage and phase angle, real and reactive power (both sides in each line), line losses and slack bus power.

Load Flow Steps

The study of load flow involves the following three steps:

1. Modeling of power system components and network.
2. Development of load flow equations.
3. Solving the load flow equations using numerical techniques.

Modeling of Power System Components

Generator

Load


Transmission Line
A Transmission line is represented as a nominal π model.

Where, R + jX is the line impedance and Y/2 is called the half line charging admittance.

Off Nominal Tap Changing Transformer
For a nominal transformer the relation
But for an off nominal transformer

Thus for an off nominal transformer we define the transformation ratio (a) as follows

Now we would like to represent an off nominal transformer in a line by an equivalent model.

Fig 2: Line Containing an Off Nominal Transformer
We want to convert the above into an equivalent π model between bus p and q.

Fig 3: Equivalent π Model of Line

Our aim is to find these values of admittances Y₁, Y₂ and Y₃ so that fig2 can be represented by fig 3
From Fig 2 we have,


Now consider Fig 3, from fig3 we have,

From eqn I and III on comparing the coefficients of E_p and E_q we get,

Similarly from equation II and IV we have

Some useful observations

From above analysis we see that Y₂, Y₃ values can either be positive or negative depending on the value of transformation ratio.

Good question!
Y = – ve implies absorption of reactive power i.e it is behaving as an inductor.
Y = + ve implies generation of reactive power i.e it is behaving as a capacitor.
Modeling of a Network

Consider the two bus system as shown in figure above.
We have already seen that
Power generated at bus i is

Power demand at bus i is


Therefore we define the net power injected at bus i as follows