# Very Fast Phase Angle Estimation Algorithm for a Single Phase System

The phase angle of a source voltage is used to construct the current reference for controlling the ﬂow of active/reactive power, and transform the feedback variables to a synchronous reference frame (SRF). The phase angle, therefore, is a critical piece of information for the operation of most power conditioning equipment such as: pulse width modulation (PWM)rectiﬁer, uninterruptable power supply (UPS), active harmonic ﬁlters, etc. For example, when an electrical railway traction crosses over to the power section supplied by another voltage source, the phase angle as well as the amplitude may change in a step manner. Under such a step change condition, the phase angle detector of normal use such as a phase locked loop (PLL), a low pass or notch ﬁlter typically generates phase delay and results in a sluggish response, and causes some time-critical machine to malfunction. Obviously, one can enhance the tracking speed of a PLL or ﬁlters by adopting a small time-constant. However, then, it may make them very sensitive to the harmonic disturbances and the measurement noises. Thus, it seems to be very diﬃcult to achieve both the fast tracking and the strong robustness (or insensitiveness)against the harmonics and measurement noises. Sidhu and Sachdev presented an iterative technique for estimating frequency and phase. However, since their method requires a great deal of computational eﬀort, it does not seem to be appropriate for the control of UPS or PWM converters.

In this work, we propose a very fast and robust (insensitive)phase angle estimation algorithm that operates well even under a sudden voltage changing conditions, and a frequency update law to accommodate a frequency varying environment. The algorithm is derived from the weighted least-squares estimation (WLSE)method having the covariance resetting technique. With the proposed estimation method, one can ﬁnd the phase angle within a few sampling periods even when both the phase angle and the amplitude change in a step manner. II. Principles of the Proposed Phase Angle Estimation Algorithm In this section, a phase-angle estimation algorithm for a single-phase system is developed with the use of the weighted least-squares estimation (WLSE)method. A frequency update algorithm is also proposed to track the source frequency when it is varying.

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