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Sinusoidal Measurement (PLL)

Estimate sinusoidal characteristics using a phase-locked loop

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

Description

The Sinusoidal Measurement (PLL) block estimates the frequency, phase angle, and magnitude of a single-phase sinusoidal signal or individual phases of a multiphase sinusoidal signal. The block uses an enhanced phase-locked loop (PLL) strategy to estimate these sinusoidal characteristics of the input signal.

Use this block in control applications when the frequency, phase angle, or magnitude is required and cannot be measured directly. To provide faster phase locking for balanced three-phase input signals, use the Three-Phase Sinusoidal Measurement (PLL) block.

Equations

The phase-locked loop generates a sinusoid that approximates the input signal u(t) with the form:

y(t)=A(t)sin(ϕ0+2πf(t)dt),

where:

  • y is the estimate of the input signal.

  • A is the estimate of the amplitude of the input signal.

  • ϕ0 is the initial phase angle of the input signal.

The estimated phase angle ϕ is the angle of this generated sinusoid:

ϕ(t)=ϕ0+2πf(t)dt,

where f if the frequency of the sinusoid, and ϕ0 is the initial phase angle.

This diagram shows the overall structure of the phase-locked loop.

In the diagram:

  • The phase detector produces an error signal relative to the phase difference eϕ between the input sinusoid u and the synthesized sinusoid y. It also outputs an estimate of the amplitude A.

  • The loop filter provides an estimate of the input angular frequency ω by filtering out the high-frequency components of the phase difference. The block also outputs the converted frequency f in Hz.

  • The voltage-controlled oscillator integrates the angular speed to produce the phase estimate ϕ. The oscillator also generates the normalized synthesized sinusoid (1/A)y which it sends to the Phase Detector for comparison.

Ports

Input

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Periodic input signal.

Data Types: single | double

Output

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Estimated frequency of the input signal, in Hz.

Data Types: single | double

Estimated phase angle of the input signal, in rad.

Data Types: single | double

Estimated magnitude of the input signal.

Data Types: single | double

Parameters

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Integral gain for the phase detector. This determines the aggressiveness of the PLL in tracking and locking to the magnitude.

If the input signal is a vector, use scalar parameters or use vector parameters that are the same size as the input signal.

Proportional gain for the loop filter. This determines the aggressiveness of the PLL in tracking and locking to the phase angle. Increase this value to improve reaction time of the tracking to step changes in the phase angle.

If the input signal is a vector, use scalar parameters or use vector parameters that are the same size as the input signal.

Integral gain for the loop filter. Increase this value to increase the rate at which steady-state error is eliminated in the phase angle. This value also determines the aggressiveness of the PLL in tracking and locking to the phase.

If the input signal is a vector, use scalar parameters or use vector parameters that are the same size as the input signal.

Initial estimate of the input frequency. If the input signal is a vector, use scalar parameters or use vector parameters that are the same size as the input signal.

Initial estimate of the phase angle. If the input signal is a vector, use scalar parameters or use vector parameters that are the same size as the input signal.

Initial estimate of the magnitude. If the input signal is a vector, use scalar parameters or use vector parameters that are the same size as the input signal.

Sample time for the block (-1 for inherited). Set this to 0 for continuous operation, or explicitly for discrete operation. If you use this block inside a triggered subsystem, set the sample time to -1. If you use this block in a continuous variable-step model, you can specify the sample time explicitly.

References

[1] Karimi-Ghartemani, M., and M. R. Iravani. "A New Phase-Locked Loop (PLL) System." IEEE Transactions on Industrial Electronics. Proceedings of the 44th IEEE Symposium on Circuits and Systems, vol. 1, pp. 421-424. IEEE, 2001..

Introduced in R2017b

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