**4. Comparison of SRF-Based Control with a Conventional PQ (Active-Reactive Power)-Based Technique**

The PQ (active-reactive power) method of control for compensation by an active power filter (APF) is one of the most popular control methods. It is based on separating the average and harmonic power components. However, the SRF method is based on separating the average and harmonic components of the current. Under ideal sinusoidal supply conditions, both the SRF method and the conventional PQ method perform similarly. However, under non-sinusoidal supply conditions, the compensating power consists of additional disturbing factors in the PQ method (id-iq). Thus, under non-ideal supply voltage conditions, the SRF method is always a preferable option compared with the PQ method [5,22].

Under a non-sinusoidal supply, the compensating power by the APF for the PQ method is given by:

$$
\begin{bmatrix} \mathbf{P\_{C(PQ)}} \\ \mathbf{Q\_{C(PQ)}} \end{bmatrix} = -\nabla\_{\mathbf{sd}} \begin{bmatrix} \tilde{\mathbf{i\_{Ld}}} \\ -\tilde{\mathbf{i\_{Lq}}} \end{bmatrix} - \tilde{\mathbf{v\_{sd}}} \left( \begin{bmatrix} \tilde{\mathbf{i\_{Ld}}} \\ -\tilde{\mathbf{i\_{Lq}}} \end{bmatrix} + \begin{bmatrix} \tilde{\mathbf{i\_{Ld}}} \\ -\tilde{\mathbf{i\_{Lq}}} \end{bmatrix} \right) \tag{11}
$$

Under a non-sinusoidal supply, the compensating power by the APF for the SRF method is given by: the PQ method [5,22]. Under a non‐sinusoidal supply, the compensating power by the APF for the PQ method is given by:

supply voltage conditions, the SRF method is always a preferable option compared with

$$
\begin{bmatrix}
\mathbf{P\_{C(SRF)}} \\
\mathbf{Q\_{C(SRF)}}
\end{bmatrix} = - \begin{pmatrix}
\mathbf{\tilde{v\_{sd}}} + \mathbf{\tilde{v}\_{sd}}
\end{pmatrix} \begin{bmatrix}
\mathbf{\tilde{i\_{Ld}}} \\
\end{bmatrix} \tag{12}
$$

Thus, the difference between Equations (11) and (12) accounts for the additional disturbance in the PQ method. Another important degrading factor in the PQ method may arise if similar harmonic components are present in the voltage and current, resulting in a more fundamental power component. Under a non‐sinusoidal supply, the compensating power by the APF for the SRF method is given by: Pେሺୗୖሻ Qେሺୗୖሻ <sup>൨</sup> ൌ െሺvതୱୢ <sup>v</sup>ୱୢሻ <sup>ı</sup>̃ ୢ െı̃ ୯<sup>൨</sup> (12)

In Section 6.4, the performance difference is presented between the PQ method and the SRF method under non-sinusoidal voltage disturbances. Thus, the difference between Equations (11) and (12) accounts for the additional

disturbance in the PQ method. Another important degrading factor in the PQ method

#### **5. PA-UVT Controller for Series APF** may arise if similar harmonic components are present in the voltage and current, result‐

*Energies* **2022**, *15*, x FOR PEER REVIEW 5 of 19

As loads operate at a rated voltage, the reference voltage could be fixed and a unit vector template (UVT) generation method could be employed for the series APF, as illustrated in Figure 3. For incorporating the PA shift in the load voltage in reference to the source voltage, the transformation angle ωt was added with the PA δ. The transformation angle ωt was generated from the modified PLL, as stated in Section 2. The reference load voltage signal generated is depicted below: ing in a more fundamental power component. In Section 6.4, the performance difference is presented between the PQ method and the SRF method under non‐sinusoidal voltage disturbances. **5. PA‐UVT Controller for Series APF** As loads operate at a rated voltage, the reference voltage could be fixed and a unit vector template (UVT) generation method could be employed for the series APF, as il‐

$$\mathbf{V\_L}^\* = \mathbf{V\_m}\sin(\omega \mathbf{t} + \delta) \tag{13}$$

where V<sup>m</sup> is the maximum fixed reference rated voltage. The desired load voltage (V<sup>L</sup> ∗ ) was equated with the measured load voltage (VL) to produce the control signals for the series APF. angle ωt was generated from the modified PLL, as stated in Section 2. The reference load voltage signal generated is depicted below:

source voltage, the transformation angle ωt was added with the PA δ. The transformation

**Figure 3.** PAC‐SRF‐based series APF. **Figure 3.** PAC-SRF-based series APF.
