#### 期刊菜单

A General Software Phase-Locked Loop Compatible with Single-Phase System
DOI: 10.12677/JEE.2022.101002, PDF , HTML, XML, 下载: 196  浏览: 325

Abstract: When the high-power onboard charger works as V2G mode, there will be an application scenario of single-phase three-phase system switching. In this paper, a general three-phase system phase- locked loop control method is proposed. This method regards the single-phase system as a special case of three-phase unbalanced fault, and realizes the positive and negative sequence separation of the voltage signal based on the phase-shift control method. The universal software phase- locked loop makes it not only suitable for three-phase systems, but also compatible with single- phase systems. Finally, through model simulation, for the application scenarios of three-phase voltage unbalance and single-phase three-phase system switching, the simulation verifies the correctness of the phase-locked loop design.

1. 引言

2. 单相电压的同步旋转坐标等效模型分析

2.1. 单相电压等效为三相不平衡故障的电压模型

$\left\{\begin{array}{l}{u}_{a}\left(t\right)=A\mathrm{sin}\left(\omega t+\phi \right)\hfill \\ {u}_{b}\left(t\right)=0\hfill \\ {u}_{c}\left(t\right)=0\hfill \end{array}$ (1)

Figure 1. Three-phase unbalanced voltage model of single-phase grid voltage

$\left\{\begin{array}{l}{u}_{a}={u}_{a}^{+}{\text{e}}^{j0˚}+{u}_{a}^{-}{\text{e}}^{j0˚}+{u}_{a}^{0}{\text{e}}^{j0˚}\\ 0={u}_{a}^{+}{\text{e}}^{j240˚}+{u}_{a}^{-}{\text{e}}^{j120˚}+{u}_{a}^{0}{\text{e}}^{j0˚}\\ 0={u}_{a}^{+}{\text{e}}^{j120˚}+{u}_{a}^{-}{\text{e}}^{j240˚}+{u}_{a}^{0}{\text{e}}^{j0˚}\end{array}$ (2)

${u}_{a}^{+}={u}_{a}^{-}={u}_{a}^{0}=\frac{A}{3}$ (3)

$\left[\begin{array}{c}{u}_{a}\\ 0\\ 0\end{array}\right]=\frac{A}{3}\left[\begin{array}{c}{\text{e}}^{j0˚}\\ {\text{e}}^{j240˚}\\ {\text{e}}^{j120˚}\end{array}\right]+\frac{A}{3}\left[\begin{array}{c}{\text{e}}^{j0˚}\\ {\text{e}}^{j120˚}\\ {\text{e}}^{j240˚}\end{array}\right]+\frac{A}{3}\left[\begin{array}{c}{\text{e}}^{j0˚}\\ {\text{e}}^{j0˚}\\ {\text{e}}^{j0˚}\end{array}\right]$ (4)

2.2. 双同步旋转坐标系下的特性分析

Figure 2. Double synchronous rotating coordinate

$\left[\begin{array}{c}{V}_{d}^{+}\\ {V}_{q}^{+}\end{array}\right]=\frac{A}{3}\left[\begin{array}{c}\mathrm{cos}\left(\phi \right)\\ \mathrm{sin}\left(\phi \right)\end{array}\right]+\left[\begin{array}{cc}\mathrm{cos}\left(-2\omega t\right)& -\mathrm{sin}\left(-2\omega t\right)\\ \mathrm{sin}\left(-2\omega t\right)& \mathrm{cos}\left(-2\omega t\right)\end{array}\right]×\frac{A}{3}\left[\begin{array}{c}\mathrm{cos}\left(-\phi \right)\\ \mathrm{sin}\left(-\phi \right)\end{array}\right]$ (5)

$\left[\begin{array}{c}{V}_{d}^{-}\\ {V}_{q}^{-}\end{array}\right]=\frac{A}{3}\left[\begin{array}{c}\mathrm{cos}\left(-\phi \right)\\ \mathrm{sin}\left(-\phi \right)\end{array}\right]+\left[\begin{array}{cc}\mathrm{cos}\left(2\omega t\right)& -\mathrm{sin}\left(2\omega t\right)\\ \mathrm{sin}\left(2\omega t\right)& \mathrm{cos}\left(2\omega t\right)\end{array}\right]×\frac{A}{3}\left[\begin{array}{c}\mathrm{cos}\left(\phi \right)\\ \mathrm{sin}\left(\phi \right)\end{array}\right]$ (6)

3. 兼容单相系统的通用型锁相环控制设计

3.1. 移相控制器实现正负序分离

$\left\{\begin{array}{l}{u}_{d}={U}^{+}\mathrm{cos}{\phi }^{+}+{U}^{-}\mathrm{cos}\left(2{\omega }_{0}t+{\phi }^{-}\right)\\ {u}_{q}={U}^{+}\mathrm{sin}{\phi }^{+}-{U}^{-}\mathrm{sin}\left(2{\omega }_{0}t+{\phi }^{-}\right)\end{array}$ (7)

${u}_{d}$${u}_{q}$ 相移90˚，得到：

$\left\{\begin{array}{l}\stackrel{¯}{{u}_{d}}={U}^{+}\mathrm{cos}{\phi }^{+}+{U}^{-}\mathrm{sin}\left(2{\omega }_{0}t+{\phi }^{-}\right)\\ \stackrel{¯}{{u}_{q}}={U}^{+}\mathrm{sin}{\phi }^{+}+{U}^{-}\mathrm{cos}\left(2{\omega }_{0}t+{\phi }^{-}\right)\end{array}$ (8)

$\left\{\begin{array}{l}{u}_{d}^{+}={U}^{+}\mathrm{cos}{\phi }^{+}=0.5\left({u}_{d}+{u}_{q}+\stackrel{¯}{{u}_{d}}-\stackrel{¯}{{u}_{q}}\right)\\ {u}_{q}^{+}={U}^{+}\mathrm{sin}{\phi }^{+}=0.5\left(-{u}_{d}+{u}_{q}+\stackrel{¯}{{u}_{d}}+\stackrel{¯}{{u}_{q}}\right)\end{array}$ (9)

3.2. 移相控制器

$\left\{\begin{array}{l}\mathrm{cos}2\omega t+\mathrm{cos}2\omega \left(t-\frac{T}{4}\right)=0\\ \mathrm{sin}2\omega t+\mathrm{sin}2\omega \left(t-\frac{T}{4}\right)=0\end{array}$ (10)

Figure 3. Discrete block diagram of a phase-shift controller

3.3. 通用性锁相环控制框图

Figure 4. Control block of phase-locked loop

Figure 5. Phase-shift control based on second-order generalized integrator

Figure 6. Software phase locked loop based on second order generalized integrator

4. 仿真与实验效果

Figure 7. The simulated three-phase voltage

Figure 8. The output of the phase-locked loop

Figure 9. Single-phase three-phase voltage switching simulation waveform

Figure 10. Phase-locked loop output when single-phase three-phase voltage switching

5. 结论

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