## What is load flow analysis?

Load flow analysis is a study or numerical calculation of the power flow of power in steady-state conditions in any electrical system. It is used to determine the flow of power (real and reactive), voltage, or current in a system under any load conditions.

This analysis is required for designing a new project or making changes in an existing one. For example, if any line is to be removed from a power system, power flow analysis is used to determine if the existing lines will be able to handle the load without going over their rated value.

## Ways to Perform Load Flow Studies

**Mathematical Analysis**

From the information obtained from the power flow analysis, equations are obtained that comprises of the magnitudes and phase angles of load bus voltages, reactive powers and voltage phase angles at generator buses, real and reactive power flows on transmission lines together with power at the reference bus are known in the form of equations. These equations are non-linear and are known as the power flow equations. Various iterative techniques using numerical methods such as Newton-Raphson method, Gauss-Seidel method, Fast decoupled method, etc. are used to solve these equations. These techniques use arithmetic methods and give approximate solutions of the given equations.

**Software Analysis**

Using software simplifies the carrying out of a load flow study. Many software such as PSS, ETAP, SKM, Neplan, etc. are available to help to analyze the load flow, such as. However, a skilled electrical engineer needs to input the data required of the details of the model to be analysed .

These softwares are operated in real-time conditions by building a network of nodes that interconnected by impedances / admittances.

The node system has four important parameters:

- Active power (P)
- Reactive power (Q)
- Voltage magnitude (V)
- Voltage phase angle (δ)

In defining nodes in a software model, the engineer typically considers three types:

- Load Bus also called P-Q bus is where the real and reactive power i.e. P and Q, are specified.
- Generator Bus is also called P-V bus is where the voltage and real power generation is known.
- Slack Bus (Swing bus) is where the voltage magnitude and phase are known.

## Analysis methods

### Gauss–Seidel iterative method

When digital computers were initially used to solve load flow problems, the Gauss–Seidel iterative method was wide;y used. This method is based on a nodal admittance matrix. It is a simple method that requires relatively small memory. However, the convergence of the method was not enough as the number of iterations increased when the scale increased and sometimes the convergence was not satisfactory with sometimes no convergence of the iteration process..

This problem led to the use of the sequential substitution method based on the nodal impedance matrix (also called the impedance method).

### Impedance method

To improve the results from the Gauss–Seidel method, a sequential substitution method that was based on the nodal impedance matrix was used. The impedance matrix is a full matrix which requires a great amount of computer memory because every element in the impedance matrix is operated on in each iteration. This method has improved convergence and solved some load flow problems that admittance methods could not and was widely used in power system design.

The high memory requirement and computing burden are the main disadvantages of the impedance method. To overcome these disadvantages, a method which divides a large system up into several small local systems was used.

### Newton–Raphson method

Newton–Raphson method is the other method to overcome the disadvantages of the impedance method. The Newton method is a typical method used to solve nonlinear equations in mathematics with very favorable convergence. This strategy starts with the introductory estimates of every single obscure variable. Then, a Taylor series is composed, with the higher request terms overlooked, for every one of the power balance conditions remembered for the arrangement of conditions. This is still the favored method, and is widely used in load flow calculation today.

### Fast decoupled method

Many more methods were developed for the load flow calculations. Among them the most successful is the fast decoupled method, also called the P Q decoupled method. This is a simplified Newton–Raphson method but the precision is equivalent to that of the Newton–Raphson technique in power systems. It is simpler and algorithmically more efficient, and therefore more popular in many applications.

## Common Mistakes

- Mathematically, the load flow problem is a problem of solving a system of linear algebraic equations. Its solution usually cannot avoid some iteration process. Thus, reliable convergence becomes the prime criterion for a load flow calculation method.

## Context and Applications

In each of the expert exams for undergraduate and graduate publications, this topic is mainly used for:

- Bachelor of Electrical Engineering
- Bachelor of Electronics Engineering
- Masters of Electrical Engineering

## Related Concepts

- Load flow and Y bus
- Steady state stability
- Power system stability
- Medium transmission line

## Practice Problems

**Q1** What is best method of load flow analysis?

- Newton-Raphson method
- Gauss method
- Fast decoupled method
- None

**Correct option** – (1)

**Explanation** – Newton-Raphson method estimates every obscure variable.

**Q2** The voltage of a particular bus can be controlled by controlling ________.

- Reactive power
- Active power
- Phase angle
- None

**Correct option **– (1)

**Explanation** – Several components of power system are connected to each other.

**Q3** At the swing bus which components are specified with electrical parameters?

- P,Q
- |V|
- P,V
- None

**Correct option** – (2)

**Explanation-** Swing bus is where the voltage magnitude and phase are known.

**Q4** As the number of buses increases for the G - S method, the number of iterations _____.

- Increases
- Decreases
- Does not effect
- None

**Correct option** – (1)

**Explanation** – Iteration and buses are proportional to each other. So, when iteration increases, buses also increase.

**Q5** The time per iteration in the Decouple load flow is same as that of ____.

- Gauss – iteration
- Gauss–Seidel
- Newton–Raphson
- None

**Correct option** – (3)

**Explanation**- Decoupled load flow is same as the Newton-Raphson method.

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