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# Find symmetrical components in MATLAB Simulink

This article deals with the procedure to find symmetrical components in MATLAB Simulink. Blocks, schematic diagram, simulation results, and test bed to find symmetrical components in MATLAB Simulink will also be discussed.

## Introduction

Symmetrical components are imaginary components which represents currents and voltages in the poly phase system. Unbalance three phase voltages and currents can be represented by balanced three phase components. The algebraic sum of these symmetrical components is always equal to the system voltage and currents. Three symmetrical components are

• Positive sequence: It consists of a balanced three phase components with a sequence abc.
• Negative Sequence: It consists of a balanced three phase components with a sequence acb.
• Zero Sequence components consists of three single phase components all equal in magnitude but with same phase angles.  In component form, the calculation for symmetrical components is   ### Significance of Symmetrical Components

In balanced condition, the power system can be analyzed using per phase approach. However in case of unbalanced fault, all the phases become unequal. Therefore usual per phase method is no more applicable for fault analysis. In such cases, the currents and voltages are divided into its balanced symmetrical components. Unbalanced faults are computed using  these symmetrical components.

Unbalance fault relays like negative sequence relays, earth fault relays, positive sequence relays etc are based on the symmetrical components of the current.

## Building Blocks

Following blocks are used to find symmetrical components in MATLAB Simulink.

• Gain: This block is used to multiply certain value or signal with a specific number or term.
• Summation: It adds or subtracts input. When there is only one input port, it add or subtract elements over all dimensions or one specified dimension
• Complex to magnitude-Angle: This block split up complex value or signal into magnitude and angle
• From: This block can receive signal from another block without physical connection. It is used to reduce the complexity of the diagram.
• Display: This block can display the value at its input.

Using from block, the value of current and voltage of the system is fed into the gain blocks. The gain blocks implements the equation 1, 2 and 3 by multiplying phase current (or voltage) with the respective operators according to the given equations. It must be noted that operators are entered in gain blocks in exponential form.

After multiplying each term, they are added using the summation block. Another gain block following the summation has value 1/3 which completes the implementation of equation 1, 2 and 3. The answer is immediately displayed in rectangular form using a display. Also for convenience, the components are split into its magnitude and angle and displayed in polar form as well. ## Test Bed.

To test the proposed system, simplest test bed is selected which consists of a three phase source and a load. Three phase measurement block is connected named as bus 1 to take current and voltage values from the system For convenience all the phase voltages and their respective angles are displayed so that the calculation can be confirmed. An unbalanced fault is also introduced in the system to create unbalance phase condition. The value of currents after introducing unbalance fault is shown in the figure ## Simulation Results

In order to verify our modeling, result of the modeled block is also verified by manual calculation. Due to the introduction of unbalance fault, phase and current of system becomes unbalance and the symmetrical components are calculated by MATLAB Simulink block is shown below To verify our results, symmetrical components are calculated manually using excel sheet. The manual calculation is shown in the following figure. By comparing values it can be seen that the symmetrical components calculated by MATLAB Simulink is same as manual calculation. Comparison verifies our exercise to find symmetrical components in MATLAB Simulink.

### About Syed Noman ud din Syed Noman ud din is an Electrical Engineer and working in Industry from last 3 years. He writes technical articles for electrical and electronic engineers. He has also published several research publications in renowned international journals.

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### 2 comments

1. dude,
i am not sure how you got your configuration to run, but apparently, you cannot sum the elements without first extracting the real and imaginary components. MATLAB has a build in sequence analyzer and it uses a fourier block for the extraction. anyhow, it would be nice to have a further explanation on how you got your specifc configuration to work

• Thanks for your comment
This model is built in phasor simulation environment. The gain block with braces treats the input as vector quantity and apply vector functions. Therefore it is not required to separate real and imaginary parts. Your tool may be applicable in other mode of simulation however in phasor mode, there is no need to treat quantities separately.