Implements a phasor measurement unit using a phase-locked loop
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The PMU (PLL-Based, Positive-Sequence) block implements a phasor measurement unit (PMU) using a phase-locked loop (PLL), which computes the positive-sequence component of the input abc signal over a running window of one cycle of fundamental frequency given by input abc. The signal can be a set of three balanced or unbalanced signals which may contain harmonics. The PMU (PLL-Based, Positive-Sequence) block is inspired by the IEEE Std C37.118.1-2011.
The PLL (3ph) block tracks the frequency and phase of a sinusoidal
three-phase signal (abc) by using an internal frequency oscillator.
The control system adjusts the internal oscillator frequency to keep the phase
The Positive-Sequence (PLL-Driven) block computes the positive-sequence components (magnitude and phase) of a sinusoidal three-phase input signal (abc) over a running window of one cycle of the fundamental frequency tracked by the PLL (3ph) closed-loop control system. The reference frame required for the computation is given by the angle (rad, varying between 0 and 2*pi), synchronized on zero crossings of the fundamental (positive-sequence) of phase A. The angle is also tracked by the PLL (3ph) closed-loop control system.
Because the block uses a running average window to perform the Fourier analysis, one cycle of simulation must complete before the outputs give the correct magnitude and angle. For example, the block response to a step change in the positive-sequence component of a three-phase signal is a one-cycle ramp. For the first cycle of simulation, the output is held constant at the values specified by the initial input parameters.
The three outputs of the PMU (PLL-Based, Positive-Sequence) block return the magnitude (same units as the input signal), the phase (in degrees relative to the PLL phase), and the frequency of the positive-sequence component of the abc input at the fundamental frequency, respectively.
The sample time (Ts) of the block, in seconds, is a function of the nominal frequency fn and the sampling rate Nsr, as follows:
Finally, the reporting rate (Rt), that determines the length of the interval over which an event will be reported, is related to the sample time using a reporting rate factor k, as follows:
Rt = k × Ts
Under subsynchronous conditions, the phasor estimation may present erroneous results.
Time synchronization from the common time source of a global positioning systems (GPS) radio clock is implicit in the model.
Three-phase sinusoidal voltage or current.
Magnitude of the positive-sequence component of the abc input at the fundamental frequency in the same units as the input signal.
The phase, in degrees, relative to the PLL phase of the positive-sequence component of the abc input at the fundamental frequency.
F— Frequency, Hz
Frequency, in Hz, relative to the PLL phase of the positive-sequence component of the abc input at the fundamental frequency.
fixed point |
Nominal frequency fn (Hz)— Frequency
Nominal frequency, fn, in Hz, of the three-phase input.
Sampling rate Nsr (point/cycle)— Sampling rate
Sampling rate, Nsr, in point/cycle.
Reporting rate factor [k]— Reporting rate
Sampling rate of the PMU. This parameter multiplies the sample time to calculate the reporting rate. The reporting rate factor must be equal to or greater than 1.
 IEEE Standard for Synchrophasor Measurements for Power Systems. IEEE Std C37.118.1-2011 (Revision of IEEE Std C37.118-2005), pp. 1–61, 2011.
 P. Kundur, N. J. Balu, and M. G. Lauby, Power system stability and control. Vol. 7. New York: McGraw-Hill, 1994.