Control / Math / Three-Phase PLL

Description

Three-phase Phase-Locked Loop (PLL).

Description

The three-phase Phase Locked Loop (PLL) proposes an estimation of the three-phase system frequency, signal amplitude and the phase-angle. This block implements two types of PLL which are described in Teoderescu et al.[^1]: an Synchronous Reference Frame(SRF) PLL and a Decoupled Double Reference Frame(DDSRF) PLL. At initialization, the phase angle and magnitude are derived from the input voltage vector when it is nonzero; Initial Angle and Initial Magnitude are used as fallbacks for a zero-voltage input.

Each PLL can be derived by three main functions: * a phase detector: generates an output signal that is proportional to the phase difference between the input signal and the signal generated by the PLL itself; this function will change according to the PLL type. * a low-pass filter : currently a PI controller to attenuate high-frequency components and to eliminate the steady-state phase-error. * a phase-angle generator: generates a phase-angle signal based on the estimated angular frequency (typically, it is a wrapping integrator).

Synchronous Reference Frame PLL (SRF-PLL)

The basic synchronization method in three-phase systems is the synchronous reference frame PLL(SRF - PLL) and the structure is shown below.

1. The three-phase voltage vector expressed in the natural reference frame is converted into a rotating reference frame through the Park transformation.
2. A feedback control loop (low-pass filter) adjusts the instantaneous phase angle by forcing the q - axis component to zero.In steady-state conditions, when the q component is null, the d-axis component corresponds to the magnitude of the input voltage vector.

This method performs effectively when the grid voltage is balanced and free of harmonic distortion. To reduce the influence of voltage harmonics on the estimation of phase angle and frequency, the PLL bandwidth should be increased. However, under unbalanced grid conditions, an excessively large control bandwidth introduces a double-frequency ripple in the PLL output signals. In this case, a Double Decoupled Reference Frame PLL should be preferred.

Decoupled Double Reference Frame PLL (DDSRF-PLL)

The decoupled double synchronous reference frame PLL is well - adapted in case of unblanced three - phase systmes. It uses two synchronous reference frames, rotating with positive and negative synchronous speeds, respectively. These two rotating frames are used to decouple of the effect of the negative sequence component on the dq - signals, as shown in the figure below. Since the double-frequency ripple caused by the unbalanced grid condition is avoided, a higher control bandwidth compared to the SRF-PLL can be set.

** Controller Design **

Two approaches to set the gains of the phase detector($K_{ i_{ pd} }$) and of the loop filter which is a PI controller($K_{ p_{ lf} }$ and $K_{ i_ { lf} }$).

• Auto approach: the parameters are automatically calculated from the nominal frequency $f_0$ in Hz. The calculation first converts it to the angular frequency $\omega_0 = 2\pi f_0$ in rad/s.

omega0 = 2 * pi * f0; // f0 in Hz, omega0 in rad/s
if type == SRF {
   wc = omega0 / 2; // SRF PLL
}
else
{
   wc = omega0; // DDSRF PLL
}
phase_margin = 60;
Kp = wc;
Ki = wc ^ 2 * tan(phase_margin * pi / 180.0);
wf = omega0 / sqrt(2); // for DDSRF only

• *Advanced approach * : $K_{p_{lf}}$, $K_{i_{lf}}$ and $\omega_f$ are defined by the user.

Info

The input signal of the PI controller is normalized in the PLL block so the parameters are not required to be scaled.

Important

The unit for phase-angle is the radian(rad) and the unit for the frequency is the Hertz(Hz).

References

R. Teodorescu, M. Liserre, and P. Rodriguez, "Chapter 8 - Grid Synchronization in Three-Phase Power Converters" in Grid Converters for Photovoltaic and Wind Power Systems, John Wiley and Sons, 2010.

Library

Control > Math

Parameters

Property	Display Name	Parameter Type	Description
Mode	PLL Mode	ThreePhasePLLModeParameter	PLL mode
ControllerDesign	Controller Design	PLLControllerDesignParameter	Controller design method
Kp_lf	Loop Filter Proportional Gain (Kp_lf)	DoubleParameter	Loop Filter Proportional Gain
Ki_lf	Loop Filter Integral Gain (Ki_lf)	DoubleParameter	Loop Filter Integral Gain
Wf	Decoupling Filter Pulsation (Wf)	DoubleParameter	DDSRF decoupling filter pulsation [rad/s]
InitFreq	Initial Frequency [Hz]	DoubleParameter	Initial Frequency [Hz]
InitMag	Initial Magnitude	DoubleParameter	Initial Magnitude
InitAngle	Initial Angle [deg]	DoubleParameter	Initial Angle [deg]

Pins

Property	Pin Name	Type	Description
A	A	ControlIn	Phase-A input signal
B	B	ControlIn	Phase-B input signal
C	C	ControlIn	Phase-C input signal
Freq	Freq	ControlOut	Estimated Frequency [Hz]
Angle	Angle	ControlOut	Estimated Phase-A Angle [rad]
Mag	Mag	ControlOut	Estimated phase magnitude

Default Size

Width	Height
8	8