# Load Flow Study – how they work

A load flow study is the analysis of an electrical network carried out by an electrical engineer. The purpose is to understand how power flows around the electrical network. Carrying out a load flow study assists the engineer in designing electrical systems which work correctly, have sufficient power supplied by the power grid, where equipment is correctly sized, reactive power compensation is correctly placed and transformer taps are optimised.

A load flow study is the analysis of an electrical network carried out by an electrical engineer. The purpose is to understand how power flows around the electrical network. Carrying out a load flow study assists the engineer in designing electrical systems which work correctly, have sufficient power supplied by the power grid, where equipment is correctly sized, reactive power compensation is correctly placed and transformer taps are optimised.

Understanding how power flows is crucial to the design of any system. For simple radial systems, often no formal ‘load flow study’ is carried out, but invariably it is part of any analysis carried out during the design of the system. For larger power distribution systems, a formal ‘load flow study’ is carried out; typically using software, with the results presented in a report.

Primarily the load flow study investigates power flow (both real and reactive). If you need a better understanding of real and reactive power is, you can review our Alternating Current Circuits Note. In addition to power flow, a load flow study is often used to investigate other parameters such as current flow, system power factors, losses, and equipment loading.

The image (click for a larger version), shows a typical load flow study. This diagram illustrates part of the network and shows the calculated the flow of real power (P) and reactive power (Q), with the arrows indicating the direction of flow. In addition, busbar voltages are shown.

## Theory

In carrying out a load flow study, it is necessary to mathematically describe the electrical network and carry out calculations to obtain the desired results. Most real life studies are solved using software, so we will only briefly touch on the mathematics (numerous text books deal with load flow if the reader is interested in more depth).

The basic representation of an electrical network is given by:

$$\left[\begin{array}{ccc}{Y}_{11}& \dots & {Y}_{1n}\\ \vdots & \ddots & \vdots \\ {Y}_{n1}& \cdots & {Y}_{nn}\end{array}\right]\left[\begin{array}{l}{V}_{1}\\ \vdots \\ {V}_{n}\end{array}\right]=\left[\begin{array}{l}{I}_{1}\\ \vdots \\ {I}_{n}\end{array}\right]$$

The admittance matrix (Y_{11} … Y_{nn}) represents the admittance of between each network node (typically each busbar) of the electrical system. At each node, the voltages (V_{1} … V_{n}) and currents (I_{1} … I_{n}) are represented by it’s appropriate matrix It should be noted that the admittances, voltages and current are complex.

Given the network matrix above, expressed as:

$$\left[Y\right]\left[V\right]=\left[I\right]$$

and at each node, the complex power S = (P+jQ) is given by:

S=VI*

At the start of the load flow study, many of the voltages and currents are unknown. An iterative approach is required to find the value of these voltages and currents. Several methods exist (Gauss-Seidel, Newton-Raphson, and others). It is the iterative nature of solving the equations that make hand calculation difficult except for all but the smallest systems.

## Practice

Most real-life load flow studies are carried out using software. In doing this, the electrical engineer builds a network of nodes interconnected by admittances (impedances).

Each system node has four key parameters:

- the active power (P)
- the reactive power (Q )
- the voltage magnitude (V)
- the voltage phase angle (δ)

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

**Load Bus [P-Q bus]**– a bus where the real and reactive power are specified. The voltage (magnitude and phase angle) is calculated by the study.**Generator Bus [P-V bus]**– a bus a which the voltage and real power generation is known. The reactive power and phase angle of the voltage are calculated by the study.**Slack Bus (Swing bus)**– where the voltage magnitude and phase are assumed known. The active and reactive power are calculated by the study.

In a study most, nodes are of the load bus type. Any nodes with a generator connected are of the generator bus type. While more than one slack bus could be defined, it is usual to have only one, and this is chosen as the connection point to the main grid supply.

The engineer will build the network model by placing grid connections, generators, busbars, interconnections (cables, overhead lines, etc.) and major items of equipment (transformers, motors, loads, capacitors, etc.). The software will then carry out the necessary calculations.

Using software simplifies the carrying out of a load flow study. However, the selection of input data required, level of detail to model, verification and interpretation of the output and utilising this to achieve the required design still requires the input of a skilled electrical engineer. A knowledge of the underlying mechanics of what the software is doing will enable the engineer to employ software modelling in his everyday work to achieve the required system design.

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