Power Measurement (Three-Phase)

Calculate three-phase real and reactive power

Libraries:
Simscape / Electrical / Control / Measurements

Description

The Power Measurement (Three-Phase) block measures the real and reactive power of an element in a three-phase network. The block outputs the power quantities for each frequency component you specify in the selected symmetrical sequence.

Use this block to measure power for both sinusoidal and nonsinusoidal periodic signals. For single-phase power measurement, consider using the Power Measurement block.

Set the Sample time parameter to 0 for continuous-time operation, or explicitly for discrete-time operation.

Specify a vector of all frequency components to include in the power output using the Harmonic numbers parameter:

To output the DC component, specify 0.
To output the component corresponding to the fundamental frequency, specify 1.
To output components corresponding to higher-order harmonics, specify n > 1.

Equations

For each specified harmonic k, the block calculates the real power P_k and reactive power Q_k for the specified sequence from the phasor equation:

$P_{k} + j Q_{k} = \frac{3}{2} (V_{k} e^{j θ_{V_{k}}}) (\bar{I_{k} e^{j θ_{I_{k}}}}),$

where:

$V_{k} e^{j θ_{V_{k}}}$ is the phasor representing the k-component voltage of the selected sequence.
$\bar{I_{k} e^{j θ_{I_{k}}}}$ is the complex conjugate of $I_{k} e^{j θ_{I_{k}}}$ , the phasor representing the k-component current of the selected sequence.

Select the symmetrical sequence used in the power calculation using the Sequence parameter:

Positive:

$V_{k} e^{j θ_{V_{k}}} = V_{k +} e^{j θ_{V_{k +}}}, I_{k} e^{j θ_{I_{k}}} = I_{k +} e^{j θ_{I_{k +}}}$
Negative:

$V_{k} e^{j θ_{V_{k}}} = V_{k -} e^{j θ_{V_{k -}}}, I_{k} e^{j θ_{I_{k}}} = I_{k -} e^{j θ_{I_{k -}}}$
Zero:

$V_{k} e^{j θ_{V_{k}}} = V_{k 0} e^{j θ_{V_{k 0}}}, I_{k} e^{j θ_{I_{k}}} = I_{k 0} e^{j θ_{I_{k 0}}}$

The block calculates the symmetrical set of +-0 voltage phasors from the set of abc voltage phasors using the symmetrical components transform S:

$[\begin{matrix} V_{k +} e^{j θ_{V_{k +}}} \\ V_{k -} e^{j θ_{V_{k -}}} \\ V_{k 0} e^{j θ_{V_{k 0}}} \end{matrix}] = S [\begin{matrix} V_{k a} e^{j θ_{V_{k a}}} \\ V_{k b} e^{j θ_{V_{k b}}} \\ V_{k c} e^{j θ_{V_{k c}}} \end{matrix}] .$

For more information about this transform, see Symmetrical Components Transform.

The block obtains this set of abc voltage phasors from the three-phase input voltage V(t) as:

$[\begin{matrix} V_{k a} e^{j θ_{V_{k a}}} \\ V_{k b} e^{j θ_{V_{k b}}} \\ V_{k c} e^{j θ_{V_{k c}}} \end{matrix}] = \frac{2}{T} \int_{t - T}^{t} V (t) \sin (2 π k F t) d t + j \frac{2}{T} \int_{t - T}^{t} V (t) \cos (2 π k F t) d t,$

where T is the period of the input signal, or equivalently the inverse of its base frequency F.

The block calculates the symmetrical set of current phasors in the same way as it does the voltage.

If the input signals have a finite number of harmonics n, the total real power P and total reactive power Q for the specified sequence can be calculated from their components:

$P = \sum_{k = 0}^{n} P_{k}$

$Q = \sum_{k = 1}^{n} Q_{k} .$

The summation for Q does not include the DC component (k = 0), because this component only contributes to real power.

Examples

Load Side Converter Control

Control the RMS voltage in a load-side converter. The load is provided by a three-phase series RL element. The Control subsystem uses a PI-based cascade control structure with two control loops, an outer voltage control loop and an inner current control loop. The simulation uses step references. The Scopes subsystem contains scopes that allow you to see the simulation results.

Open Model

Vienna Rectifier Control

Control a Vienna rectifier. The Vienna rectifier subsystem consists of three-phase legs. Each leg has one power switch and six power diodes. The Control subsystem implements a closed-loop control strategy for the Vienna rectifier using space-vector modulation. Total simulation time is 0.1 s. At time 0.1 s, the Vienna Rectifier is engaged. At times 0.4 s and 0.6 s, the load steps up on the DC side.

Open Model

Ports

Input

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V — Input voltage
vector

Three-phase voltage across element from which to measure power, in V.

Data Types: single | double

I — Input current
vector

Three-phase current through element from which to measure power, in A.

Data Types: single | double

Output

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P — Real power
scalar or vector | vector

Real power for selected frequency components, in W. If the Harmonic numbers parameter value is a scalar, this output is also a scalar.

Data Types: single | double

Q — Reactive power
scalar or vector | vector

Reactive power for selected frequency components, in var. If the Harmonic numbers parameter value is a scalar, this output is also a scalar.

Data Types: single | double

Parameters

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Base frequency (Hz) — Fundamental frequency
`60` (default) | positive number

Fundamental frequency corresponding to component k=1.

Harmonic numbers — Frequency components
`[0 1 2 3]` (default) | scalar or vector

Frequency components to include in the output. Specify either a scalar value corresponding to the desired component or a vector of all desired components.

The value k = 0 corresponds to the DC component.
The value k = 1 corresponds to the fundamental frequency.
Values k > 1 correspond to higher-level harmonics.

If you specify a vector, the order of the power outputs correspond to the order of this vector.

Sequence — Symmetrical sequence
`Positive` (default) | `Negative` | `Zero`

Symmetrical sequence of the power output.

Sample time — Block sample time
`0` (default) | positive number

Time between consecutive block executions. During execution, the block produces outputs and, if appropriate, updates its internal state. For more information, see What Is Sample Time? and Specify Sample Time.

For continuous operation, set this property to 0. For discrete operation, specify the sample time explicitly as a positive number. This block does not support inherited sample time.

If this block is in a masked subsystem, or other variant subsystem that allows either continuous and discrete operation, promote the sample time parameter. Promoting the sample time parameter ensures correct switching between the continuous and discrete implementations of the block. For more information, see Promote Block Parameters on a Mask.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2017b

Power Measurement (Three-Phase)