**2. Shunt APF Reference Signal Generation with SRF-Based Approach**

By an orthodox approach of VAR sharing between the shunt and series APFs as presented in [4,5], the series APF part of handling VAR arose after the load VAR surpassed a specific maximum.

The shunt APF of the UPC was used for serving the following two purposes in our system:

1. Providing source current harmonic compensation. The shunt APF of the UPC was used for serving the following two purposes in our

passed a specific maximum.

*Energies* **2022**, *15*, x FOR PEER REVIEW 3 of 19

2. Providing 50% of load reactive power compensation. system:

**2. Shunt APF Reference Signal Generation with SRF‐Based Approach**

The SRF control algorithm is a popular control approach for custom power devices as it involves the direct controlling of the d (active) and q (reactive) elements of the current drawn by the load. As shown in Figure 2, initially, the single-phase load current was treated as a load component iL<sup>α</sup> in stationary reference frame; the other component iL<sup>β</sup> was derived by orthogonally shifting iLα. The transformation angle ωt was generated from the modified PLL (phase-locked loop) due to the source voltage with the harmonics for a proper synchronization [14]. With the following transformations, the direct and quadrature components of the current in a rotating reference frame were obtained from iL<sup>α</sup> and iLβ. 1. Providing source current harmonic compensation. 2. Providing 50% of load reactive power compensation. The SRF control algorithm is a popular control approach for custom power devices as it involves the direct controlling of the d (active) and q (reactive) elements of the cur‐ rent drawn by the load. As shown in Figure 2, initially, the single‐phase load current was treated as a load component i in stationary reference frame; the other component iஒ was derived by orthogonally shifting i. The transformation angle ωt was generated from the modified PLL (phase‐locked loop) due to the source voltage with the harmonics

By an orthodox approach of VAR sharing between the shunt and series APFs as presented in [4,5], the series APF part of handling VAR arose after the load VAR sur‐

(1)

**Figure 2.** SRF method-based shunt APF.

**Figure 2.** SRF method‐based shunt APF.

 <sup>൨</sup> ൌ <sup>ቂ</sup> െ ቃ <sup>൨</sup> (1) The direct component of the current, i.e., iLd, was considered to be an active component of the current whereas the quadrature component of the current iLq was considered to be a reactive element of the load current.

The direct component of the current, i.e., iୢ, was considered to be an active com‐ ponent of the current whereas the quadrature component of the current i୯ was consid‐ ered to be a reactive element of the load current. These two components involved fundamental and harmonic terms and could be separated by a different HPF (high‐pass filter) derived from an LPF (low‐pass filter). The loss element of the UPC, acquired from a PI compensator by comparing the DC‐link ref‐ erence voltage with the measured DC‐link voltage, was combined with the harmonic content of the active current. The VAR harmonic current element was combined with 50% of the fundamental reactive current to allow half of the load VAR to be remunerated These two components involved fundamental and harmonic terms and could be separated by a different HPF (high-pass filter) derived from an LPF (low-pass filter). The loss element of the UPC, acquired from a PI compensator by comparing the DC-link reference voltage with the measured DC-link voltage, was combined with the harmonic content of the active current. The VAR harmonic current element was combined with 50% of the fundamental reactive current to allow half of the load VAR to be remunerated by the shunt APF. The compensating d and q axis currents thus obtained were transformed to a reference shunt APF-injecting current. This current was compared with the measured shunt APF current and fed to a hysteresis controller to produce a gating signal for the shunt APF.

#### by the shunt APF. The compensating d and q axis currents thus obtained were trans‐ formed to a reference shunt APF‐injecting current. This current was compared with the **3. PA Calculation for Equal Reactive Power Sharing**

Considering the non-ideal conditions of the supply voltage and the load current, the d and q axis voltage and current parameters, obtained from the SRF control algorithm of the shunt APF, were utilized to estimate the power demand by load as:

Load active power (fundamental), P<sup>L</sup> = vsd· iLd (2)

Load reactive power (fundamental), Q<sup>L</sup> = vsd· iLq (3)

The source side power could be calculated as:

Source active power, P<sup>S</sup> = vsd· iLd + i<sup>0</sup> (4)

Source reactive power, Q<sup>S</sup> = 0 (5)

where i0, the active component of the current drawn from the source, denotes the loss component of the UPC.

The VAR rating of the series APF could be articulated as [4]:

$$\mathbf{Q\_{sr}} = |\mathbf{I\_{s}}| \cdot |\mathbf{V\_{L}^{\*}}| \cdot \sin \delta \tag{6}$$

$$\sin \delta = \frac{\mathbf{Q\_{sr}}}{|\mathbf{I\_{s}}| \cdot |\mathbf{V\_{L}^\*}|} = \frac{\mathbf{Q\_{sr}}}{\mathbf{P\_S}} \tag{7}$$

$$\delta = \sin^{-1}\left[\frac{\mathbf{Q\_{sr}}}{\mathbf{P\_s}}\right] \tag{8}$$

For equivalent VAR sharing among the shunt and series APF we obtained:

$$\mathbf{Q\_{sr}} = \mathbf{0.5Q\_{L}} \tag{9}$$

Therefore, from Equations (3), (4), (8) and (9), we obtained:

$$\delta = \sin^{-1}\left[\frac{\mathbf{i}\_{\rm Lq}}{2\cdot\left(\hat{\mathbf{i}}\_{\rm Ld} + \hat{\mathbf{i}}\_{0}\right)}\right] \tag{10}$$

Thus, as is clear from the above equation, for half of the load VAR sharing by the series APF, the PA could be directly derived from the load current parameters. As the estimation of the PA was independent of any voltage component, in reference to the PA estimation presented in [11,12] (where the PA estimation was based on the PQ theory), the number of variables involved were reduced in the PA estimation. Therefore, the PA estimation was much simpler to implement. In [12], a PA estimation was carried out where the supply voltage was considered to be completely sinusoidal. With a non-sinusoidal supply voltage and the methods proposed in [11,12], an additional disturbance needs to be accounted for, as discussed in Section 4. A comparative analysis is presented in Section 5 to understand the efficacy of the SRF-based PA estimation over the others.
