# Power Measurement

Measure single-phase real and reactive power

• Library:
• Simscape / Power Systems / Simscape Components / Control / Measurements

## Description

The Power Measurement block measures the real and reactive power of an element in a single-phase network. The block outputs the power quantities for each frequency component you specify. For three-phase measurements, consider using the Three-Phase Power Measurement block.

Use this block to measure power for both sinusoidal and nonsinusoidal periodic signals.

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 Pk and reactive power Qk from the phasor equation:

`${P}_{k}+j{Q}_{k}=G\left({V}_{k}{e}^{j{\theta }_{{V}_{k}}}\right)\left(\overline{{I}_{k}{e}^{j{\theta }_{{I}_{k}}}}\right),$`
where:

• G is equal to `0.25` for the DC component (k = 0) and `0.5` for the AC components (k > 0).

• ${V}_{k}{e}^{j{\theta }_{{V}_{k}}}$ is the phasor representation of the k-component input voltage.

• $\overline{{I}_{k}{e}^{j{\theta }_{{I}_{k}}}}$ is the complex conjugate of ${I}_{k}{e}^{j{\theta }_{{I}_{k}}}$, the phasor representation of the k-component input current.

The block estimates the real-time k-component voltage and current phasors using these relationships:

`${V}_{k}{e}^{j{\theta }_{{V}_{k}}}=\frac{2}{T}{\int }_{t-T}^{t}V\left(t\right)\mathrm{sin}\left(2\pi kFt\right)dt+j\frac{2}{T}{\int }_{t-T}^{t}V\left(t\right)\mathrm{cos}\left(2\pi kFt\right)dt$`
`${I}_{k}{e}^{j{\theta }_{{I}_{k}}}=\frac{2}{T}{\int }_{t-T}^{t}I\left(t\right)\mathrm{sin}\left(2\pi kFt\right)dt+j\frac{2}{T}{\int }_{t-T}^{t}I\left(t\right)\mathrm{cos}\left(2\pi kFt\right)dt.$`
In these phasor equations:

• V(t) and I(t) are the input voltage and current, respectively.

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

If the input signals have a finite number of harmonics n, the total real power P and total reactive power Q 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.

## Ports

### Input

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Voltage across element from which to measure power, in V.

Data Types: `single` | `double`

Current through element from which to measure power, in A.

Data Types: `single` | `double`

### Output

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Real power for selected frequency components, in W.

Data Types: `single` | `double`

Reactive power for selected frequency components, in var.

Data Types: `single` | `double`

## Parameters

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Fundamental frequency corresponding to component k=1.

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.

Sample time for the block. For continuous operation, set this property to `0`. For discrete operation, specify the sample time explicitly. This block does not support inherited sample time.