Measure positive-, negative-, and zero-sequence components of three-phase signal
powerlib_extras/Measurements, powerlib_extras/Discrete Measurements
Note: The Measurements section of the Control and Measurements library contains the Sequence Analyzer block. This is an improved version of the Three-Phase Sequence Analyzer block. The new block features a mechanism that eliminates duplicate continuous and discrete versions of the same block by basing the block configuration on the simulation mode. If your legacy models contain the Three-Phase Sequence Analyzer block, they will continue to work. However, for best performance, use the Sequence Analyzer block in your new models. |
The Three-Phase Sequence Analyzer block outputs the magnitude and phase of the positive- (denoted by the index 1), negative- (index 2), and zero-sequence (index 0) components of a set of three balanced or unbalanced signals. The signals can contain harmonics or not. The three sequence components of a three-phase signal (voltages V1 V2 V0 or currents I1 I2 I0) are computed as follows:
V_{1} = (V_{a} + aV_{b}+ a^{2}V_{c})/3
V_{2} = (V_{a} + a^{2}V_{b} + aV_{c})/3
V_{0} = (V_{a} + V_{b} + V_{c})/3
where
V_{a}, V_{b}, V_{c} =
three voltage phasors at specified frequency
a = e^{j2π}/3
= 1∠120° complex operator.
A Fourier analysis over a sliding window of one cycle of the specified frequency is first applied to the three input signals. It evaluates the phasor values V_{a}, V_{b}, and V_{c} at the specified fundamental or harmonic frequency. Then the transformation is applied to obtain the positive sequence, negative sequence, and zero sequence.
The Three-Phase Sequence Analyzer block is not sensitive to harmonics or imbalances. However, as this block uses a running average window to perform the Fourier analysis, one cycle of simulation has to be completed before the outputs give the correct magnitude and angle. For example, its response to a step change of V_{1} is a one-cycle ramp.
The discrete version of this block allows you to specify the initial magnitude and phase of the output signal. For the first cycle of simulation the outputs are held to the values specified by the initial input parameter.
You can modify any parameter during the simulation in order to obtain the different sequence and harmonic components of the input signals.
The fundamental frequency, in hertz, of the three-phase input signal.
Specify the harmonic component from which you want to evaluate
the sequences. For DC, enter 0
. For fundamental,
enter 1
.
Specify which sequence component the block outputs. Select Positive
to
calculate the positive sequence, select Negative
to
calculate the negative sequence, select 0
to compute
the zero sequence of the fundamental or specified harmonic of the
three-phase input signal. Select Positive Negative Zero
to
get all the sequences.
abc
Connect to the input the vectorized signal of the three [a b c] sinusoidal signals.
Mag
The first output gives the magnitude (peak value) of the specified
sequence component, in the same units as the abc
input
signals.
Phase
The second output gives the phase in degrees of the specified component(s).
The power_3phsignalseq
example
illustrates the use of the Sequence Analyzer block
(the improved version of the Three-Phase Sequence Analyzer block)
to measure the fundamental and harmonic components of a three-phase
voltage. A 25kV, 100 MVA short-circuit level, equivalent network feeds
a 5 MW, 2 Mvar capacitive load. The internal voltage of the source is
controlled by the Programmable Voltage Source block.
A positive sequence of 1.0 pu, 0 degrees is specified for the fundamental signal. At t = 0.05 s a step of 0.5 pu is applied on the positive-sequence voltage magnitude, then at t = 0.1 s, 0.08 pu of fifth harmonic in negative sequence is added to the 1.5 pu voltage.
Two Sequence Analyzer blocks are used to measure the positive-sequence fundamental component and the negative-sequence fifth harmonic of the three-phase voltage.
As the Sequence Analyzer blocks use Fourier analysis, their response time is delayed by one cycle of the fundamental frequency.