The PLL, 3-ph component models a Phase Lock Loop (PLL) closed-loop control system, which tracks the frequency and phase of a sinusoidal signal by using an internal frequency oscillator.

The input signal u is mixed with an internal oscillator signal. The DC component of the mixed signal is extracted with a variable frequency mean value (Phase detector section). A Proportional-Integral-Derivative (PID) controller keeps the phase difference to 0 by acting on a controlled oscillator.

The controlled oscillator output corresponds to the output angular velocity signal defined by wt. The PID output is filtered using a low-pass filter (rate limited) and converted to frequency, which is used by the mean value. The filtered signal corresponds to the output frequency signal defined by f.

Symbol

Mask Parameters

Main tab

Name	Description	Unit	Variable = {Possible Values}
Description	Use this field to add all kinds of information about the component		Description = {'string'}
Initial frequency	Initial frequency for the first simulation cycle. This value cannot be modified during the simulation	Hz	Finit = { [0, 1e12] }
Minimum frequency	Minimum expected frequency of the input signal. This value cannot be modified during the simulation	Hz	Fmin = { [0, 1e12] }
Initial phase	Initial value of the phase of the output signal for the first simulation cycle. This value cannot be modified during the simulation	deg.	InitialPhase = { [0, 360] }

PID Controller tab

Name	Description	Unit	Variable = {Possible Values}
Kp	Internal PID controller proportional gain		Kp = { [0, 1e12] }
Ki	Internal PID controller integral gain		Ki = { [0, 1e12] }
Kd	Internal PID controller derivative gain		Kd = { [0, 1e12] }
Lower limit	Lower limit of the PI integral action. This value cannot be modified during the simulation		LowerLimit = { [-1e64, 1e64] }
Upper limit	Upper limit of the PI integral action. This value should be greater than the value of the Lower limit parameter. This value cannot be modified during the simulation		UpperLimit = { [-1e64, 1e64] }
Initial condition	Integrator initial condition. This value cannot be modified during the simulation		Integrator_InitialCondition = { [0, 1e12] }
Time constant for derivative action	Time constant for the first-order filter of the derivative action from the internal PID controller	s	Tc_Derivative = { [0, 1e12] }
Duration of initial value	Duration of the initial value of the internal PID controller output signal. This value cannot be modified during the simulation	s	Tinit = { [0, 1e12] }

Second-Order FIlter tab

Name	Description	Unit	Variable = {Possible Values}
Maximum rate of change of frequency	Maximum positive and negative slope of the frequency of the second-order low pass filter input signal	Hz/s	Freq_RateLimiter = { [0, 1e12] }
Filter natural frequency	Internal second-order natural low-passe filter frequency	Hz	FreqFilter_fn = { [0, 1e12] }
Filter damping ratio	Second-order low-pass filter damping rate. The damping ratio is typically a value between 0 and 1		FreqFilter_zeta = { [0, 1] }

Input/Output Signals

Name	Description	Unit	Type
abc	Vectorized signal that can contain phase-to-ground voltages (Va, Vb and Vc) or phase-to-ground currents (Ia, Ib and Ic)	pu	Input
f	Measured frequency signal	Hz	Output
wt	Angle signal varying between 0 and 2 * pi, synchronized to the zero-crossing (ascending) of the fundamental of the input signal	rad	Output

Sensor Descriptions

Name	Description	Unit
abc[a]	Input signal that may contain the voltage or current of phase A	pu
abc[b]	Input signal that may contain the voltage or current of phase B	pu
abc[c]	Input signal that may contain the voltage or current of phase C	pu
f	Measured frequency signal	Hz
wt	Angle signal varying between 0 and 2 * pi, synchronized to the zero-crossing (ascending) of the fundamental of the input signal	rad

Internal Circuit of Component

Limitations

In the PLL, 3-ph component, since the internal Proportional-Integral-Derivative (PID) controller has no automatic gain control, the input signal should be in pu and have a value not too distant from one.