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| Phase Estimation Error Detection and Compensation Method of DDSRF-PLL and DSOGI-PLL under Three-Phase Voltage Unbalance |
| Qi Yongsheng1,2, Li Kai1, Gao Changyu1, Xue Tengyue1, You Xiaojie1 |
1. School of Electrical Engineering Beijing Jiaotong University Beijing 100044 China;
2. State Grid Shanxi Electric Power Company Xinzhou Subsidiary Xinzhou 034000 China |
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Abstract Due to the combined effect of high-permeability distributed power supply and various types of loads, the three-phase voltage of the actual grid-connected point has deviations in amplitude and phase angle. However, phase-locking methods based on single synchronous reference frame phase-locked loop (SSRF-PLL), such as decoupled double synchronous reference frame phase-locked loop (DDSRF-PLL) and double second-order generalized integrator phase-lock loop (DSOGI-PLL), generally ignored these differences, and, hence, only acquiring synchronization information at phase-balanced three-phase voltage. More is needed to support coordinated control among devices at the grid-connected point. Recently, some methods were presented to obtain phase information of three-phase voltage under phase unbalance, but most suffered from high computation costs and poor expansibility. Therefore, a compensation method for phase estimation error is proposed. The phase estimation error can be accurately compensated under phase-balanced three-phase voltage by detecting the unbalanced phase angle deviation of B and C phases.
Firstly, the three-phase unbalanced voltage specified in the national standard is used as the input signal for DDSRF-PLL and DSOGI-PLL, and the equivalent relationship between unbalanced voltage and phase estimation error of the two phase-locked loops is obtained. The functional relationship between phase estimation error and unbalanced phase angle deviation is based on steady-state characteristics. Secondly, three approximate solutions for the phase estimation errors are given to simplify the calculation. Then, based on the zero-crossing point of the A phase, the unbalanced phase angle deviation of B and C phases is obtained by calculating the sample value of three-phase voltage. Finally, precise compensation of phase estimation error can be achieved by substituting the phase angle deviation in the function of phase estimation error, overlaying the output of phase estimation error to the original PLL reversely. The phase angle deviation detection and phase estimation error compensation method can realize open-loop compensation with a low computation cost and good expandability.
Simulation results under eight conditions of phase angle deviation show that the estimated phase curves of two PLLs always coincide when the unbalanced phase angle deviation of B and C phases change within the range of [-30 ° 30 °]. The maximum error between theoretical and simulation values is 0.230 °, and the relative error is only 2.3 %. It proves the rationality of the theoretical equivalence of two PLLs and the validity of the relationship between unbalanced phase angle deviation and phase estimation error. The results also show that the maximum delay time decreased from 1.126 ms to 28 μs, and the corresponding phase estimation error reduced from 20.268 ° to 0.501 °, indicating the method's high compensation accuracy. The experimental results also have similar conclusions. After the accurate compensation and three approximate methods, the phase estimation error was reduced from 1.425 ms to 75 μs, 250 μs, 325 μs, and 225 μs, respectively. The approximate method has a compromise between compensation accuracy and calculation burden.
The following conclusions can be drawn from the simulation and experimental results: (1) DDSRF-PLL and DSOGI-PLL are theoretically equivalent at phase-unbalanced three-phase voltage. (2) The relationship between phase estimation error and phase angle deviation is derived based on the steady-state characteristics of SSRF-PLL, which is suitable for a series of phase-locked methods based on SSRF-PLL and has a wide range of applications. (3) The proposed phase angle deviation detection and phase estimation error compensation method can realize open-loop compensation by simply calculating the sample value of three-phase voltage, which has the characteristics of low computational cost, easy expansion, and high compensation accuracy.
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Received: 17 September 2022
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2024, Vol. 39 
