RMS Measurement

R2026b

Calculate root-mean-square (RMS) properties of a signal

• 

RMS Measurement block

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Libraries:
Simscape / Electrical / Control / Measurements

Description

The RMS Measurement block measures root-mean-square (RMS) properties of the input signal. You can use it to measure one of these properties:

• The total RMS of the input signal

• The RMS of the individual harmonics of the input signal that you specify.

Use the total RMS configuration with appropriate sensors to perform RMS voltage, current, or power analyses in your system.

You can use the harmonics configuration to perform total harmonic distortion analyses on systems with nonlinear loads such as:

• Converters

• Motor drives

• Inverters

Equations

The total RMS value is calculated from the input signal x_RMS as:

$$x_{RMS}(t)=\sqrt{\frac{1}{T}{\displaystyle {\int }_{t-T}^{t}x{(t)}^{2}dt}},$$

where:

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

• x is the input signal.

Because the calculation is performed over a period of time, the block requires T seconds to respond to a step change in the input signal. This condition also applies to startup.

The harmonic RMS component x_k,RMS for harmonic k is calculated as:

$$x_{k,RMS}(t)=G\left(\frac{2}{T}\right)\sqrt{{\left({\displaystyle {\int }_{t-T}^{t}x(t)\sin \left(\frac{2\pi kt}{T}\right)dt}\right)}^2+{\left({\displaystyle {\int }_{t-T}^{t}x(t)\cos \left(\frac{2\pi kt}{T}\right)dt}\right)}^2},$$

where G is equal to 0.5 for the DC component (k = 0) and $$1/\sqrt{2}$$ for the AC components (k > 0).

Ports

Input

u — Input signal

scalar

Periodic input signal.

Data Types: single | double

Output

RMS — Root-mean-square of input signal

scalar or vector

Estimated RMS of the input signal.

If you select the Specify harmonics parameter, the output is a vector with each element corresponding to a specified harmonic. Otherwise, the output is a scalar representing the total RMS.

During the first cycle, the estimated RMS of the input signal is equal to the value of the Initial RMS parameter. (since R2026b)

Data Types: single | double

Parameters

Base frequency (Hz) — Fundamental frequency

60 (default) | scalar

Base frequency of the input signal corresponding to the first harmonic.

Specify harmonics — RMS output mode

off (default) | on

Specify whether to output the total RMS of the input signals or the individual harmonics that you specify.

Harmonic numbers — Harmonics specification

[0 1 2] (default) | vector

Specify the harmonics for which to output an RMS.

Dependencies

To enable this parameter, select the Specify harmonics parameter.

Initial RMS — Initial RMS value of input signal

0 (default) | scalar | vector

Since R2026b

Initial RMS value of the input signal.

• If you select the Specify harmonics parameter, you can specify this parameter as:

  • Scalar — All harmonics start from the same initial RMS value.

  • Vector with the same length as the Harmonic numbers parameter value — Each value of the vector specifies the initial RMS value of the corresponding harmonic.

• If you clear the Specify harmonics parameter, specify this parameter as a scalar. If you provide a vector, the block uses only the first element and the software throws a warning.

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 to a Mask.

Extended Capabilities

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

Version History

Introduced in R2017b

R2026b: Specify initial RMS value of input signal

Use the Initial RMS parameter to specify the initial RMS value of the input signal. If you select the Specify harmonics parameter, you can specify a single initial RMS value for all harmonics or a separate value for each harmonic.

From R2026b onwards, the value at the RMS output port during the first cycle is equal to the value of the Initial RMS parameter.