Decoupling Control for the HVAC Port of Power Electronic Transformer

Abstract

For the high-voltage AC port of power electronic transformer (HVAC-PET) with three-phase independent DC buses on the low-voltage side, a decoupling control strategy, concerning the influence of grid voltage imbalance, three-phase active-load imbalance, and high-order harmonic distortion, is proposed in this paper to simultaneously realize the functions of active power control, reactive power compensation, and active power filtering. In the outer power control loop, according to the distribution rule of decoupled average active power components in three phases, stability control for the sum of cluster average active power flows is realized by injecting positive-sequence active current, so as to control the average cluster voltage (i.e., the average of all the DC-link capacitor voltages), and by injecting negative-sequence current, the cluster average active power flows can be controlled individually to balance the three cluster voltages (i.e., the average of the DC-link capacitor voltages in each cluster). The negative-sequence reactive power component is considered to realize the reactive power compensation. In the inner current control loop, the fundamental and high-order harmonic components are uniformly controlled in the positive-sequence dq frame using the PI + VPIs (vector proportional integral) controller, and the harmonic filtering function is realized while the fundamental positive-sequence current is adjusted. Experiments performed on the 380 V/50 kVA laboratory HVAC-PET verify the effectiveness of the proposed control strategy.

1. Introduction

With the increasing penetration rate of renewable energy sources (RESs) and distributed generation systems (DGS), and the widespread use of generalized DC equipment represented by the inverter air conditioner and electric vehicle, the scale of transmission and distribution systems is growing rapidly. Flexible interconnection between different power systems, which puts higher demands on power electronic converters, is receiving increasing attention [1]. In addition to the basic functions of voltage conversion and galvanic isolation of conventional transformer, the power electronic transformer (PET) is also able to isolate the faults of the distribution system [2,3], form plug-and-play energy ports for distributed RES and storage devices freely accessing the power system [4], and flexibly control the bidirectional power flows of each port for reasonable energy scheduling [5]. So, it is considered an enabling component to build the future smart grid. As shown in Figure 1, the modularized series-connected structure is usually adopted in the high-voltage AC port of PET (HVAC-PET). Cascaded H-bridge (CHB) [6,7] and modular multilevel converter (MMC) [8,9] are the most popular topologies to meet the high-voltage requirements. In this paper, the CHB topology is employed. As shown in Figure 2, in each phase, the secondary-side H-bridges of dual-active-bridge (DAB) converters are connected in parallel to form a low-voltage DC-link (LVDCL). Via the three separated LVDCLs, all port converters of the PET are interconnected.

For enhancing energy utilization and the power system stability, HVAC-PET requires the capability of reactive power compensation to regulate the reactive power flow, compensate for the reactive load, and improve the voltages at the point of common coupling (PCC) [10]. Nevertheless, the imbalanced grid voltages often occur stemming from voltage flicker, asymmetrical loads and faults, etc. [11], which accordingly results in the imbalance of the three cluster voltages. As a consequence, potential problems may arise, like disconnecting the HVAC port from the grid and thus degrading the reliability of the power system. Based on the generalized instantaneous power theory, a control strategy in the abc stationary frame is proposed in [12,13], and the control effects of grid voltage and load current under different objectives are compared. In [14], zero-sequence current injection is adopted, but it generates additional voltage stress in each phase and puts forward higher requirements for the rated voltage of the DC-link capacitor. Studies in [15] show that the active power adjustment ability of zero-sequence current is much smaller than that of negative-sequence current. In the case of a serious active-power imbalance, the three cluster voltages will be out of control. For the PET with three phases that are independent of each other from the input stage to the output stage, the balancing control of cluster voltages is proposed in [16]. However, it needs a large amount of calculation and has no consideration of the imbalanced grid voltages.

With more and more non-linear loads, such as electric arc furnace, electric locomotive, induction motor, and so on, connected to the distribution system, a large number of harmonics are generated in the grid to increase power losses. The HVAC-PET should integrate the function of an active power filter (APF), which utilizes a filtered measurement of the load currents to obtain current references for the current controllers, and injects the required harmonic currents back into the PCC to mitigate harmonics being drawn by non-linear loads. The common scheme of APF is to control the selected harmonic currents using multiple parallel resonant current controllers [17]. Four different resonant current controllers are compared in [18], for the vector–proportional–integral (VPI) controller, which has a zero-gain for DC component, proper design of the tunable control parameters can offset the pole in the controlled plant model, so it has better stability under high harmonic conditions, and is more suitable for harmonic current control. Moreover, a successful operation of the APF requires an accurate phase-locked loop (PLL) for the estimation and injection of harmonics. In [19], a variety of control strategies are proposed to mitigate the impact of grid-voltage harmonics on the PLL, while maintaining a high bandwidth and fast tracking of the phase of grid-voltage. In [20], a division-summation (D-Σ) digital-control scheme based on the SVPWM method for APF is proposed; it can effectively suppress the influence of grid-voltage harmonics on the frame transformations and accommodate filter-inductance variation, but experimental verification under the condition of a polluted grid is not presented. In [21], an artificial neural network (ANN) is applied to improve the harmonic detection and the current control, but it increases the difficulty of design and requires more computation resources from the controller.

Different from the traditional STATCOM or APF, the HVAC port converter of PET should be able to operate in four quadrants, due to the active power following control used to achieve power balance among the ports of PET. However, for the HVAC port with three independent LVDCLs illustrated in Figure 1, active-load imbalance often occurs along with inconsistent submodule parameters, faults, and imbalanced energy control of other ports [22]. In order to realize the function integrations of active power control, reactive power compensation and active power filtering on the HVAC-PET, under the unfavorable conditions of grid-voltage imbalance, high-order harmonic distortion as well as uneven active loads, this paper proposes a decoupling control strategy, in which the cluster voltage is defined as the average of the DC-link capacitor voltages in each cluster of CHB, and the average cluster voltage denotes the average of three cluster voltages. For the active power control, ignoring the power losses of converters, the DC-link capacitor voltages of CHB fluctuate according to the average active power flowing between the power grid and the active loads of CHB. Thus, the sum of cluster average active power flows should meet the need of stability control for the average cluster voltage, and by the individual control for the cluster average active power flows, cluster voltage balance can be achieved. With the distribution rule of the decoupled average active power components in three phases, positive-sequence active current injection is adopted to realize the stability control for the sum of cluster average active power flows, and by injecting negative-sequence current, the cluster average active power flows can be controlled individually. Taking into consideration the reactive power component induced by negative-sequence voltage and negative-sequence current, the reactive power compensation control is realized by injecting the positive-sequence reactive current. In the inner current control loop, the fundamental and high-order harmonic components are uniformly controlled in the positive-sequence dq frame using the PI + VPIs controller to realize the function of active power filtering.

The rest of this paper is organized as follows: Section 2 introduces the decoupling principle of active power flows under imbalance operation. In Section 3, the outer power control loop is addressed. Following, Section 4 proposes the decoupling principle of voltages and currents, as well as the implementation of synchronous reference frame PLL (SRF-PLL) under distortion conditions. Section 5 illustrates the inner current control loop, while the overall control scheme is presented in Section 6. Experimental results are provided in Section 7 in order to verify the proposed control scheme. Finally, conclusions are drawn in Section 8.

2. Decoupling Principle of Active Power Under Imbalance Operation

For the HVAC port with a three-phase three-wire structure shown in Figure 2, if the controller of the port converter does not generate any zero-sequence voltage components, the line-to-neutral voltages of CHB can be calculated from the line-to-line voltages at the PCC. Ignoring the impact of non-characteristic harmonics, the line-to-neutral voltages of CHB can be defined as

$$u_s=u_s^{+}+u_s^{-}+u_s^{th}=u_s^{+}+u_s^{-}+{\displaystyle \sum _{\begin{array}{l}h=6 k\pm 1\\ k=1,2,3\dots \end{array}}{u}_s^h}$$

(1)

where ${\mathbf{u}}_s^{+}$ and ${\mathbf{u}}_s^{-}$ indicate the fundamental positive- and negative-sequence components, respectively, ${\mathbf{u}}_s^{th}$ is the high-order harmonic component can be formulated as

$$u_s^{+}=\left[\begin{array}{l}{u}_{sag}^{+}\\ u_{sbg}^{+}\\ u_{scg}^{+}\end{array}\right]=U_m^{+}\left[\begin{array}{l}\cos \left({\omega }_{0}t+{\sigma }_0^{+}\right)\\ \cos \left({\omega }_{0}t+{\sigma }_0^{+}-2\pi /3\right)\\ \cos \left({\omega }_{0}t+{\sigma }_0^{+}+2\pi /3\right)\end{array}\right]$$

(2)

$$u_s^{-}=\left[\begin{array}{l}{u}_{sag}^{-}\\ u_{sbg}^{-}\\ u_{scg}^{-}\end{array}\right]=U_m^{-}\left[\begin{array}{l}\cos \left(-{\omega }_{0}t+{\sigma }_0^{-}\right)\\ \cos \left(-{\omega }_{0}t+{\sigma }_0^{-}-2\pi /3\right)\\ \cos \left(-{\omega }_{0}t+{\sigma }_0^{-}+2\pi /3\right)\end{array}\right]$$

(3)

$$u_s^h=\left[\begin{array}{l}{u}_{sag}^h\\ u_{sbg}^h\\ u_{scg}^h\end{array}\right]=U_m^h\left[\begin{array}{l}\cos \left(h{\omega }_{0}t+{\sigma }_0^h\right)\\ \cos \left(h\left({\omega }_{0}t-{\displaystyle \raisebox{1ex}{$2\pi $}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right)+{\sigma }_0^h\right)\\ \cos \left(h\left({\omega }_{0}t+{\displaystyle \raisebox{1ex}{$2\pi $}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right)+{\sigma }_0^h\right)\end{array}\right]$$

(4)

where ω₀ denotes the fundamental angular frequency of the grid voltage, h = 6k ± 1 is the harmonic order, and k is a positive integer that k = 1, 2, 3….

In the same way, the cluster input currents of the CHB can be expressed by the sum of the fundamental positive-sequence component i⁺, the fundamental negative-sequence component i⁻, and the high-order harmonic components i^h, namely,

$$i=i^{+}+i^{-}+{\displaystyle \sum _{\begin{array}{l}h=6 k\pm 1\\ k=1,2,3\dots \end{array}}{i}^h}=\left[\begin{array}{l}{i}_a^{+}\\ i_b^{+}\\ i_c^{+}\end{array}\right]+\left[\begin{array}{l}{i}_a^{-}\\ i_b^{-}\\ i_c^{-}\end{array}\right]+{\displaystyle \sum _{\begin{array}{l}h=6 k\pm 1\\ k=1,2,3\dots \end{array}}\left[\begin{array}{l}{i}_a^h\\ i_b^h\\ i_c^h\end{array}\right]}$$

(5)

Under the assumption that the rotating angles of positive- and negative-sequence dq frames are ${\hat{\theta }}^{+}={\omega }_{0}t+{\sigma }_0^{+}$ and ${\widehat{\theta }}^{-}=- {\widehat{\theta }}^{+}$, respectively, the rotating matrices can be represented as

$$T_{dq/\alpha \beta }^{+}=\left[\begin{array}{l}\cos {\widehat{\theta }}^{+} -\sin {\widehat{\theta }}^{+}\\ \sin {\widehat{\theta }}^{+} \cos {\widehat{\theta }}^{+} \end{array}\right] , T_{dq/\alpha \beta }^{-}=\left[\begin{array}{l}\cos {\widehat{\theta }}^{+} \sin {\widehat{\theta }}^{+}\\ -\sin {\widehat{\theta }}^{+} \cos {\widehat{\theta }}^{+}\end{array}\right]$$

(6)

Taking no consideration of the high-order harmonics in (1) and (5), the line-to-neutral voltages and the cluster input currents of CHB can be transformed into their positive- and negative-sequence components in the dq frames as follows:

$$u_s=u_s^{+}+u_s^{-}=T_{\alpha \beta /abc}\cdot \left\{T_{dq/\alpha \beta }^{+}\cdot \left[\begin{array}{l}{U}_{sd}^{+}\\ U_{sq}^{+}\end{array}\right]+T_{dq/\alpha \beta }^{-}\cdot \left[\begin{array}{l}{U}_{sd}^{-}\\ U_{sq}^{-}\end{array}\right]\right\}$$

(7)

$$i=i^{+}+i^{-}=T_{\alpha \beta /abc}\cdot \left\{T_{dq/\alpha \beta }^{+}\cdot \left[\begin{array}{l}{I}_d^{+}\\ I_q^{+}\end{array}\right]+T_{dq/\alpha \beta }^{-}\cdot \left[\begin{array}{l}{I}_d^{-}\\ I_q^{-}\end{array}\right]\right\}$$

(8)

where subscripts sd and d stand for components in d-axis, subscripts sq and q stand for components in q-axis, and T_αβ/abc being the transform matrix given by

$$T_{\alpha \beta /abc}={\left[\begin{array}{lll}\hfill 1\hfill & \hfill {\displaystyle \raisebox{1ex}{$-1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\hfill & \hfill {\displaystyle \raisebox{1ex}{$-1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} \hfill \\ \hfill 0\hfill & \hfill {\displaystyle \raisebox{1ex}{$\sqrt{3}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\hfill & \hfill {\displaystyle \raisebox{1ex}{$-\sqrt{3}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\hfill \end{array}\right]}^T$$

(9)

The instantaneous active power flows, generated by the positive-sequence current i⁺, can be expressed in the form of vector as

$$P^{+}=P_p^{+}+P_n^{+}$$

(10)

where superscript + denotes the positive-sequence current component, subscripts p and n stand for the positive- and negative-sequence voltage components, respectively, which means that $P_p^{+}$ is the instantaneous active power flow induced by positive-sequence current i⁺ and positive-sequence voltage $u_s^{+}$, $P_n^{+}$ is the instantaneous active power flow induced by positive-sequence current i⁺ and negative-sequence voltage $u_s^{-}$. According to (2)~(9), they are derived as

$$\begin{array}{ll}{P}_p^{+}& =diag\left(u_s^{+}\right)\cdot i^{+}=\left[\begin{array}{l}{u}_{sag}^{+}{i}_a^{+}\\ u_{sbg}^{+}{i}_b^{+}\\ u_{scg}^{+}{i}_c^{+}\end{array}\right] ={\overline{P}}_p^{+}+{\tilde{P}}_p^{+} \\ & =\left[\begin{array}{l}{\overline{P}}_{pa}^{+}\\ {\overline{P}}_{pb}^{+}\\ {\overline{P}}_{pc}^{+}\end{array}\right]+{\tilde{P}}_p^{+}=\left[\begin{array}{l}{\displaystyle \frac{1}{2}}\left(U_{sd}^{+}{I}_d^{+}+U_q^{+}{I}_q^{+}\right)\\ {\displaystyle \frac{1}{2}}\left(U_{sd}^{+}{I}_d^{+}+U_{sq}^{+}{I}_q^{+}\right)\\ {\displaystyle \frac{1}{2}}\left(U_{sd}^{+}{I}_d^{+}+U_{sq}^{+}{I}_q^{+}\right)\end{array}\right]+{\tilde{P}}_p^{+} \end{array}$$

(11)

$$\begin{array}{ll}{P}_n^{+}& =diag\left(u_s^{-}\right)\cdot i^{+}=\left[\begin{array}{l}{u}_{sag}^{-}{i}_a^{+}\\ u_{sbg}^{-}{i}_b^{+}\\ u_{scg}^{-}{i}_c^{+}\end{array}\right] ={\overline{P}}_n^{+}+{\tilde{P}}_n^{+}=\left[\begin{array}{l}{\overline{P}}_{na}^{+}\\ {\overline{P}}_{nb}^{+}\\ {\overline{P}}_{nc}^{+}\end{array}\right]+{\tilde{P}}_n^{+}\\ & =\left[\begin{array}{cc}\hfill {\displaystyle \frac{1}{2}}{U}_{sd}^{-}\hfill & \hfill -{\displaystyle \frac{1}{2}}{U}_{sq}^{-}\hfill \\ \hfill -{\displaystyle \frac{1}{4}}{U}_{sd}^{-}-{\displaystyle \frac{\sqrt{3}}{4}}{U}_{sq}^{-}\hfill & \hfill {\displaystyle \frac{1}{4}}{U}_{sq}^{-}-{\displaystyle \frac{\sqrt{3}}{4}}{U}_{sd}^{-}\hfill \\ \hfill -{\displaystyle \frac{1}{4}}{U}_{sd}^{-}+{\displaystyle \frac{\sqrt{3}}{4}}{U}_{sq}^{-}\hfill & \hfill {\displaystyle \frac{1}{4}}{U}_{sq}^{-}+{\displaystyle \frac{\sqrt{3}}{4}}{U}_{sd}^{-}\hfill \end{array}\right]\left[\begin{array}{l}{I}_d^{+}\\ I_q^{+}\end{array}\right]+{\tilde{P}}_n^{+}\end{array}$$

(12)

Similarly, the instantaneous active power flows generated by the negative-sequence current i⁻ can be expressed as

$$P^{-}=P_p^{-}+P_n^{-}$$

(13)

where $P_p^{-}$ is the instantaneous active power flow induced by negative-sequence current $i^{-}$ and positive-sequence voltage $u_s^{+}$, $P_n^{-}$ is the instantaneous active power flow induced by negative-sequence current $i^{-}$ and negative-sequence voltage $u_s^{-}$. They are calculated as

$$\begin{array}{ll}{P}_p^{-}& =diag\left(u_s^{+}\right)\cdot i^{-}=\left[\begin{array}{l}{u}_{sag}^{+}{i}_a^{-}\\ u_{sbg}^{+}{i}_b^{-}\\ u_{scg}^{+}{i}_c^{-}\end{array}\right] ={\overline{P}}_p^{-}+{\tilde{P}}_p^{-}=\left[\begin{array}{l}{\overline{P}}_{pa}^{-}\\ {\overline{P}}_{pb}^{-}\\ {\overline{P}}_{pc}^{-}\end{array}\right]+{\tilde{P}}_p^{-} \\ & =\left[\begin{array}{cc}\hfill {\displaystyle \frac{1}{2}}{U}_{sd}^{+}\hfill & \hfill -{\displaystyle \frac{1}{2}}{U}_{sq}^{+}\hfill \\ -{\displaystyle \frac{1}{4}}{U}_{sd}^{+}-{\displaystyle \frac{\sqrt{3}}{4}}{U}_{sq}^{+}& \hfill {\displaystyle \frac{1}{4}}{U}_{sq}^{+}-{\displaystyle \frac{\sqrt{3}}{4}}{U}_{sd}^{+}\hfill \\ \hfill -{\displaystyle \frac{1}{4}}{U}_{sd}^{+}+{\displaystyle \frac{\sqrt{3}}{4}}{U}_{sq}^{+}\hfill & \hfill {\displaystyle \frac{1}{4}}{U}_{sq}^{+}+{\displaystyle \frac{\sqrt{3}}{4}}{U}_{sd}^{+} \hfill \end{array}\right]\left[\begin{array}{l}{I}_d^{-}\\ I_q^{-}\end{array}\right]+{\tilde{P}}_p^{-} \end{array}$$

(14)

$$\begin{array}{ll}{P}_n^{-}& =diag\left(u_s^{-}\right)\cdot i^{-}=\left[\begin{array}{l}{u}_{sag}^{-}{i}_a^{-}\\ u_{sbg}^{-}{i}_b^{-}\\ u_{scg}^{-}{i}_c^{-}\end{array}\right] ={\overline{P}}_n^{-}+{\tilde{P}}_n^{-} \\ & =\left[\begin{array}{l}{\overline{P}}_{na}^{-}\\ {\overline{P}}_{nb}^{-}\\ {\overline{P}}_{nc}^{-}\end{array}\right]+{\tilde{P}}_n^{-}=\left[\begin{array}{l}{\displaystyle \frac{1}{2}}\left(U_{sd}^{-}{I}_d^{-}+U_{sq}^{-}{I}_q^{-}\right) \\ {\displaystyle \frac{1}{2}}\left(U_{sd}^{-}{I}_d^{-}+U_{sq}^{-}{I}_q^{-}\right) \\ {\displaystyle \frac{1}{2}}\left(U_{sd}^{-}{I}_d^{-}+U_{sq}^{-}{I}_q^{-}\right) \end{array}\right]+{\tilde{P}}_n^{-} \end{array}$$

(15)

In (11), (12), (14), and (15), the average value of each element in the oscillating power vectors that ${\tilde{P}}_p^{+}$, ${\tilde{P}}_n^{+}$, ${\tilde{P}}_p^{-}$, and ${\tilde{P}}_n^{-}$ is zero, so these power components have no contribution to the cluster voltage. On the contrary, with the average power vectors ${\overline{P}}_p^{+}$, ${\overline{P}}_n^{+}$, ${\overline{P}}_p^{-}$, and ${\overline{P}}_n^{-}$, the cluster average active power flows that affect the cluster voltages can be extracted as

$$\overline{P}={\left[{\overline{P}}_a {\overline{P}}_b {\overline{P}}_c\right]}^T={\overline{P}}^{+}+{\overline{P}}^{-}={\overline{P}}_p^{+}+{\overline{P}}_n^{+}+{\overline{P}}_n^{-}+{\overline{P}}_p^{-}$$

(16)

And the sum of cluster average power flows, which determines the average cluster voltage of CHB, is derived as

$${\overline{P}}_{3-p}={\overline{P}}_a+{\overline{P}}_b+{\overline{P}}_c ={\displaystyle \frac{3}{2}}\left[\left(U_{sd}^{+}{I}_d^{+}+U_{sq}^{+}{I}_q^{+}\right)+\left(U_{sd}^{-}{I}_d^{-}+U_{sq}^{-}{I}_q^{-}\right)\right]$$

(17)

From the above derivations, the decoupled average active power flows of the CHB can be depicted in Figure 3 in detail. There are two forms of power flows among the three clusters: (1) cluster-balanced average active power flows ${\overline{P}}_p^{+}$ and ${\overline{P}}_n^{-}$, and (2) cluster-imbalanced average active power flows ${\overline{P}}_n^{+}$ and ${\overline{P}}_p^{-}$.

For the power vectors ${\overline{P}}_p^{+}$ and ${\overline{P}}_n^{-}$, the cluster power elements are balanced with each other, i.e., ${\overline{P}}_{pa}^{+}={\overline{P}}_{pb}^{+}={\overline{P}}_{pc}^{+}$ and ${\overline{P}}_{na}^{-}={\overline{P}}_{nb}^{-}={\overline{P}}_{nc}^{-}$. So adjusting the positive- and negative-sequence currents will only change the sum of the cluster power elements in vectors ${\overline{P}}_p^{+}$ and ${\overline{P}}_n^{-}$, respectively, but will not affect their cluster-balanced performance. For the power vectors ${\overline{P}}_n^{+}$ and ${\overline{P}}_p^{-}$, for which the sum of the cluster power elements is zero, it denotes that the average cluster voltage is independent of ${\overline{P}}_n^{+}$ and ${\overline{P}}_p^{-}$. However, the individual control of cluster average active power flows can be achieved by tuning the positive- or negative-sequence current. Therefore, if individual control for the cluster average active power flows is realized by injecting negative-sequence current, the sum of cluster average active power flows can be stabilized by adjusting positive-sequence current further.

3. Average Power Control Strategy

The outer power control loop includes the average active power control and the reactive power compensation control. The sum of cluster average active power flows is controlled to stabilize the average cluster voltage, and by the individual control for the cluster average active power flows, the three cluster voltages will be balanced.

3.1. Stability Control for the Sum of Cluster Average Active Power Flows

From (11), (15)~(17), the sum of cluster average power flows can be rewritten as

$${\overline{P}}_{3-p}={\overline{P}}_{3-p}^{+}+{\overline{P}}_{3-p}^{-}={\left(u_s^{+}\right)}^T\cdot i^{+}+{\left(u_s^{-}\right)}^T\cdot i^{-}$$

(18)

Stability control for the sum of cluster average active power flows is mainly realized by adjusting the positive-sequence current. Supposing that i⁻ = 0, and substituting it into (18) yields

$$i^{+\ast }={\displaystyle \frac{{\overline{P}}_{3-p}^{+*}}{{\left|u_s^{+}\right|}^2}}{u}_s^{+}={\displaystyle \frac{2}{3}}{\displaystyle \frac{{\overline{P}}_{3-p}^{+*}}{{\left(U_m^{+}\right)}^2}}{u}_s^{+}$$

(19)

where superscript * stands for the reference value.

With the transform matrices in (6) and (9), (19) can be transformed into the positive-sequence dq frame as follows

$$\left[\begin{array}{l}{I_d^{+}}^{*}\\ {I_q^{+}}^{*}\end{array}\right]={\displaystyle \frac{2}{3}}{\displaystyle \frac{{\overline{P}}_{3-p}^{+*}}{{\left(U_m^{+}\right)}^2}}\left[\begin{array}{l}{U}_{sd}^{+}\\ U_{sq}^{+}\end{array}\right]=\left[\begin{array}{l}{\displaystyle \frac{2}{3}}{\displaystyle \frac{{\overline{P}}_{3-p}^{+*}}{U_{sd}^{+}}}\\ \hfill 0\hfill \end{array}\right]$$

(20)

From (20), the control structure for the sum of cluster average active power flows can be depicted in Figure 4. $U_{dc}^{\ast }$ and ${\overline{u}}_{dc}$ are the reference and observed value of the average cluster voltage, respectively, which is regulated by a PI controller.

3.2. Individual Control for the Cluster Average Active Power Flows

From Figure 3, the vector of average active power deviation can be derived as

$$\Delta \overline{P}={\overline{P}}_p^{-}+{\overline{P}}_n^{+}$$

(21)

Moreover

$${\overline{P}}_p^{-}=\left[\begin{array}{ll}\hfill {\displaystyle \frac{1}{2}}{U}_{sd}^{+}\hfill & \hfill 0\hfill \\ \hfill -{\displaystyle \frac{1}{4}}{U}_{sd}^{+}\hfill & \hfill -{\displaystyle \frac{\sqrt{3}}{4}}{U}_{sd}^{+}\hfill \\ \hfill -{\displaystyle \frac{1}{4}}{U}_{sd}^{+}\hfill & \hfill {\displaystyle \frac{\sqrt{3}}{4}}{U}_{sd}^{+}\hfill \end{array}\right]\left[\begin{array}{l}{I}_d^{-}\\ I_q^{-}\end{array}\right]=M\cdot \left[\begin{array}{l}{I}_d^{-}\\ I_q^{-}\end{array}\right]$$

(22)

Then the injected negative-sequence current can be determined as follows

$$\begin{array}{ll}\left[\begin{array}{l}{I_d^{-}}^{\ast }\\ {I_q^{-}}^{\ast }\end{array}\right]& ={\left(T_{abc/\alpha \beta }\cdot M\right)}^{-1}\cdot T_{abc/\alpha \beta }\cdot {{\overline{P}}_p^{-}}^{\ast }\\ & ={\displaystyle \frac{1}{U_{sd}^{+}}}\cdot {\displaystyle \frac{2}{3}}\left[\begin{array}{lll}\hfill 2\hfill & \hfill -1\hfill & \hfill -1\hfill \\ \hfill 0\hfill & \hfill -\sqrt{3}\hfill & \hfill \sqrt{3}\hfill \end{array}\right]\cdot \left(\Delta {\overline{P}}^{\ast }-{\overline{P}}_n^{+}\right)\hfill \end{array}$$

(23)

The individual control structure for the cluster average active power flows is illustrated in Figure 5. The subscript m represents the cluster number that a, b, or c, as shown in Figure 2. The average active power deviation of each cluster $\Delta {\overline{P}}_m^{*}$ can be obtained by closed-loop regulation of the cluster voltage ${\overline{u}}_{dcm}$ individually with a PI controller.

3.3. Reactive Power Compensation Control

The total average reactive power can be expressed as

$$\overline{Q}={\overline{Q}}^{+}+{\overline{Q}}^{-}={\left(u_{s\perp }^{+}\right)}^T\cdot i^{+}+{\left(u_{s\perp }^{-}\right)}^T\cdot i^{-}$$

(24)

Therein, $u_{s\perp }$ denotes the orthogonal vector of u_s.

The negative-sequence current, injected for cluster voltage balanced control in the previous Section 3.2, generates average reactive power ${\overline{Q}}^{-}$ as follows

$${\overline{Q}}^{-}={\displaystyle \frac{3}{2}}\left(-U_{sd}^{-}{I}_q^{-}+U_{sq}^{-}{I}_d^{-}\right)$$

(25)

Assuming that the average reactive power to be absorbed by the HVAC port is ${\overline{Q}}^{\ast }$, which is set by the energy dispatch system or determined by real-time reactive power detection of the grid loads, the reactive power that should be compensated by injecting positive-sequence current is

$${{\overline{Q}}^{+}}^{\ast }={\overline{Q}}^{\ast }-{\overline{Q}}^{-}$$

(26)

Supposing that i⁻ = 0, and substituting it into (24) yields

$${i^{+}}^{\ast }={\displaystyle \frac{{{\overline{Q}}^{+}}^{*}}{{\left|u_{s\perp }^{+}\right|}^2}}{u}_{s\perp }^{+}={\displaystyle \frac{2}{3}}{\displaystyle \frac{{{\overline{Q}}^{+}}^{*}}{{\left(U_m^{+}\right)}^2}}{u}_{s\perp }^{+}$$

(27)

With the transform matrices in (6) and (9), (27) can be transformed into the positive-sequence dq frame as follows

$$\left[\begin{array}{l}{I_d^{+}}^{*}\\ {I_q^{+}}^{*}\end{array}\right]={\displaystyle \frac{2}{3}}{\displaystyle \frac{{{\overline{Q}}^{+}}^{*}}{{\left(U_m^{+}\right)}^2}}\left[\begin{array}{l} U_{sq}^{+}\\ -U_{sd}^{+}\end{array}\right]=\left[\begin{array}{l}\hfill 0\hfill \\ -{\displaystyle \frac{2}{3}}{\displaystyle \frac{{{\overline{Q}}^{+}}^{*}}{U_{sd}^{+}}}\end{array}\right]$$

(28)

Therefore, the reference of positive-sequence reactive current ${I_q^{+}}^{*}$, injected for average reactive power compensation control, can be calculated with (25), (26), and (28).

4. Decoupling Principle of Voltage and Current Under Distorted Conditions

In this section, the decoupling principle of voltages and currents in the positive- and negative-sequence dq frames is mainly carried out, as well as the implementation of SRF-PLL under distortion conditions.

4.1. Voltage Decoupling Principle and the Implementation of SRF-PLL

As depicted in (1)~(4), if the rotating angle of positive-sequence dq frame is consistent with the phase of fundamental positive-sequence component ${\mathbf{u}}_s^{+}$, i.e., ${\widehat{\theta }}^{+}={\omega }_{0}t+{\sigma }_0^{+}$, the voltage u_s can be transformed as

$$\begin{array}{ll}\left[\begin{array}{l}{u}_{sd}\\ u_{sq}\end{array}\right]& =\left[\begin{array}{l}{U}_m^{+}\\ 0\end{array}\right]+U_m^{-}\left[\begin{array}{l}\cos (2{\omega }_{0}t+{\sigma }_0^{+}-{\sigma }_0^{-})\\ -\sin (2{\omega }_{0}t+{\sigma }_0^{+}-{\sigma }_0^{-})\end{array}\right] \\ & +U_m^5\left[\begin{array}{l}\cos (6{\omega }_{0}t+{\sigma }_0^{+}+{\sigma }_0^5)\\ -\sin (6{\omega }_{0}t+{\sigma }_0^{+}+{\sigma }_0^5)\end{array}\right]+U_m^7\left[\begin{array}{l}\cos (6{\omega }_{0}t+{\sigma }_0^7-{\sigma }_0^{+})\\ \sin (6{\omega }_{0}t+{\sigma }_0^7-{\sigma }_0^{+})\end{array}\right]\\ & +U_m^{11}\left[\begin{array}{l}\cos (12{\omega }_{0}t+{\sigma }_0^{+}+{\sigma }_0^{11})\\ -\sin (12{\omega }_{0}t+{\sigma }_0^{+}+{\sigma }_0^{11})\end{array}\right]+U_m^{13}\left[\begin{array}{l}\cos (12{\omega }_{0}t+{\sigma }_0^{13}-{\sigma }_0^{+})\\ \sin (12{\omega }_{0}t+{\sigma }_0^{13}-{\sigma }_0^{+})\end{array}\right]+\dots \end{array}$$

(29)

which shows that the transformation from the abc stationary frame to the positive-sequence dq frame results in harmonics of the order h = 6k ± 1 being transformed to h = 6k. In addition, the transformation for the fundamental negative-sequence component $u_s^{-}$ would also induce a second-order harmonic. Here, conventional notch filters are adopted to eliminate the selective harmonics, and the transfer function of the notch filter for eliminating $\mathcal{l}$-order harmonic is given by

$$F_{N\mathcal{l}}\left(s\right)={\displaystyle \frac{s^2+{\left(\mathcal{l}\cdot {\omega }_0\right)}^2}{s^2+Qs+{\left(\mathcal{l}\cdot {\omega }_0\right)}^2}}$$

(30)

where Q is the quality factor of the notch filter determining the rejection bandwidth, and $\mathcal{l}\cdot {\omega }_0$ being the notch frequency. For instance, F_N2 (i.e., $\mathcal{l}=2$) is used for the second-order harmonic elimination, while multiple notch filters integrated in series are employed for filtering higher-order harmonics, with the transfer function as follows

$$F_{Nth}\left(s\right)={\displaystyle \sum _{\begin{array}{l}\mathcal{l}=6k\\ k=1, 2, 3\dots \end{array}}{F}_{N\mathcal{l}}\left(s\right)}$$

(31)

For obtaining the rotating angle ${\widehat{\theta }}^{+}$ depicted in (6) and (29), the SRF-PLL scheme, as shown in Figure 6, is used to drive the phase estimate of the fundamental positive-sequence component $u_s^{+}$, in which a PI regulator is adopted as the PLL controller.

$$G_{PIpll}\left(s\right)=k_{Ppll}\left(1+{\displaystyle \frac{1}{T_{Ipll}s}}\right)$$

(32)

In this scheme, ${\omega }_c$ is a given center frequency supplied to the PLL as a feed-forward parameter, and the output frequency $\mathit{\omega }$ is shifted with respect to it. If it is assumed that the negative-sequence and high-order harmonic components are eliminated by F_N2 and F_Nth, respectively, the frequency $\mathit{\omega }$ is well tuned to the frequency of $u_s^{+}$ (i.e., $\omega ={\omega }_0$), and the component $u_s^{+}$ can be extracted in the positive-sequence dq frame as

$$\left[\begin{array}{l}{U}_{sd}^{+}\\ U_{sq}^{+}\end{array}\right]=U_m^{+}\left[\begin{array}{l}\cos ({\theta }^{+}-{\widehat{\theta }}^{+})\\ \sin ({\theta }^{+}-{\widehat{\theta }}^{+})\end{array}\right]$$

(33)

where ${\theta }^{+}$ is the phase of the input voltage $u_s^{+}$. From the q-axis in Figure 6, if the phase error ${\theta }^{+}-{\widehat{\theta }}^{+}$ is very small, $U_{sq}^{+}$ can be linearized since $\sin ({\theta }^{+}-{\widehat{\theta }}^{+})\approx {\theta }^{+}-{\widehat{\theta }}^{+}$, then the closed-loop of PLL will be equivalent to a second-order linear system, and the conclusions of $U_{sd}^{+}=U_m^{+}$, $U_{sq}^{+}=0$, and ${\theta }^{+}={\widehat{\theta }}^{+}$ will be achieved on the steady state.

As depicted in Figure 6, from the difference between input and output of the notch filter F_N2, the voltage components of $u_s^{-}$ in the positive-sequence dq frame are induced, and then, with two rotating transformations illustrated in (6), the component $u_s^{-}$ can be extracted in the negative-sequence dq frame; if the SRF-PLL is steady, it can be simplified as

$$\left[\begin{array}{l}{U}_{sd}^{-}\\ U_{sq}^{-}\end{array}\right]=U_m^{-}\left[\begin{array}{l}\cos ({\sigma }_0^{-}+{\sigma }_0^{+})\\ \sin ({\sigma }_0^{-}+{\sigma }_0^{+})\end{array}\right]$$

(34)

Finally, the voltage u_s in (1) can be rewritten as

$$u_s=u_{sbh}+u_s^{-}$$

(35)

where u_sbh indicates the sum of $u_s^{+}$ and $u_s^{th}$, so as well to $u$ and $i$, namely

$$u=u_{bh}+u^{-}, i=i_{bh}+i^{-}$$

(36)

where the voltage vector u = [u_ag, u_bg, u_cg]^T is generated by the H-bridges of CHB.

In this paper, the high-order harmonics would not be extracted separately from the fundamental positive-sequence components.

4.2. Current Decoupling Principle

Similarly to the voltage decoupling principle, in the current decoupling scheme, the same notch filters F_N2 and F_Nth are used to eliminate the negative-sequence and high-order harmonic components, respectively, and the rotating angle for the rotating matrices is the estimated phase of SRF-PLL, too.

The decoupling scheme of the cluster input current i is provided in Figure 7, for controlling the combination of fundamental positive-sequence component and high-order harmonics to realize the function of APF illustrated in the next section, the components ${\widehat{i}}_{bh\_d}$ and ${\widehat{i}}_{bh\_q}$ of the sum of i⁺ and ith are extracted in the positive-sequence dq frame.

As depicted in Figure 8, for the grid load currents, only the high-order harmonics that ${\widehat{i}}_{lh\_d}$ and ${\widehat{i}}_{lh\_q}$ would be extracted will be used as partial references of the current control.

5. Current Control Strategy

For the CHB configured in Figure 1 and Figure 2, applying Kirchhoff’s voltage law to the ac side yields

$$R_s\cdot i+L_s{\displaystyle \frac{d i}{dt}}+u=u_s$$

(37)

where L_s represents the inductance of the filtering inductor, and the series resistance associated is R_s.

In order to integrate the function of APF, that is to compensate the harmonic currents of grid loads, the harmonic currents are controlled together with the fundamental positive-sequence current. According to (35) and (36), the state-space equation in (37) can be separated into two parts as follows

$$R_s\cdot i_{bh}+L_s{\displaystyle \frac{d i_{bh}}{dt}}+u_{bh}=u_{sbh}$$

(38)

$$R_s\cdot i^{-}+L_s{\displaystyle \frac{d i^{-}}{dt}}+u^{-}=u_s^{-}$$

(39)

Using the transformation matrices in (6) and (9), the positive-sequence plant model, induced by the transformation for the state-space equation illustrated in (38) from the abc stationary frame to the positive-sequence dq frame, is set up as

$$\begin{array}{l}{R}_s\cdot i_{bh\_d}+L_s{\displaystyle \frac{d{i}_{bh\_d}}{dt}}=u_{sbh\_d}-u_{bh\_d}+\omega L_s{i}_{bh\_q}\\ R_s\cdot i_{bh\_q}+L_s{\displaystyle \frac{d{i}_{bh\_q}}{dt}}=u_{sbh\_q}-u_{bh\_q}-\omega L_s{i}_{bh\_d}\end{array}$$

(40)

where i_{bh_d} and i_{bh_q} are the d-axis and q-axis components of the current vector i_bh, respectively, and more d-axis and q-axis components, i.e., u_{sbh_d} and u_{sbh_q} of the voltage vector u_sbh, u_{bh_d} and u_{bh_q} of the voltage vector u_bh, are presented.

With the plant model in (40), the block diagram of current control in the positive-sequence dq frame can be depicted in Figure 9. The fundamental positive-sequence current is controlled by a PI regulator with zero steady-state error, and the regulator is given by

$$G_{PIi}^{+}\left(s\right)=k_{Pi}^{+}\left(1+{\displaystyle \frac{1}{T_{Ii}^{+}s}}\right)$$

(41)

while the VPI controller is employed for the selective harmonic compensation, and the transfer function of a single VPI controller is given by

$$G_{VPI}^h\left(s\right)={\displaystyle \frac{k_{Ph}{s}^2+k_{Rh}s}{s^2+{(h\cdot {\omega }_0)}^2}}$$

(42)

where h indicates the order of harmonic being compensated, k_Ph is the proportional gain, k_Rh is the resonant gain, and $h\cdot {\omega }_0$ is the resonant frequency. To compensate for the high-order harmonics, a set of VPI controllers is employed, which can be expressed as

$$G_{VPI}^{th}\left(s\right)={\displaystyle \sum _{\begin{array}{l}h=6k\\ k=1, 2, 3\dots \end{array}}{G}_{VPI}^h\left(s\right)}$$

(43)

Specifically, $G_{VPI}^2$ shown in Figure 9 is adopted to attenuate the influence of the fundamental negative-sequence current.

Furthermore, the negative-sequence plant model can be deduced from (39) as follows:

$$\begin{array}{l}{R}_s\cdot i_d^{-}+L_s{\displaystyle \frac{d{i}_d^{-}}{dt}}=u_{sd}^{-}-u_d^{-}-\omega L_s{i}_q^{-}\\ R_s\cdot i_q^{-}+L_s{\displaystyle \frac{d{i}_q^{-}}{dt}}=u_{sq}^{-}-u_q^{-}+\omega L_s{i}_d^{-}\end{array}$$

(44)

where $i_d^{-}$ and $i_q^{-}$, $u_{sd}^{-}$ and $u_{sq}^{-}$, $u_d^{-}$ and $u_q^{-}$ are the d-axis and q-axis components of the input current vector i⁻, the voltage vector $u_s^{-}$, and the voltage vector $u^{-}$, respectively.

Figure 10 shows the fundamental negative-sequence current control scheme, $G_{PIi}^{-}$ is the current controller given by

$$G_{PIi}^{-}\left(s\right)=k_{Pi}^{-}\left(1+{\displaystyle \frac{1}{T_{Ii}^{-}s}}\right)$$

(45)

In Figure 9 and Figure 10, the variables that ${\widehat{u}}_{sbh\_d}$, ${\widehat{u}}_{sbh\_q}$, ${\widehat{i}}_{bh\_d}$, ${\widehat{i}}_{bh\_q}$, $U_{sd}^{-}$, $U_{sq}^{-}$, $I_d^{-}$, and $I_q^{-}$are the sampling values of u_{sbh_d}, u_{sbh_q}, i_{bh_d}, i_{bh_q}, $u_{sd}^{-}$, $u_{sq}^{-}$, $i_d^{-}$, and $i_q^{-}$, respectively, according to the decoupling principles in Section 4. The current references in the positive-sequence dq frame can be expressed as

$$i_{bh\_d}^{*}={I_d^{+}}^{*}+i_{h\_d}^{*}, i_{bh\_q}^{*}={I_q^{+}}^{*}+i_{h\_q}^{*}$$

(46)

In general, to compensate the high-order harmonic components of grid currents, the components $i_{h\_d}^{*}$ and $i_{h\_q}^{*}$ are given by

$$i_{h\_d}^{*}=-{\widehat{i}}_{lh\_d}, i_{h\_q}^{*}=-{\widehat{i}}_{lh\_q}$$

(47)

However, if the HVAC port is operated as a harmonic source, the values of $i_{h\_d}^{*}$ and $i_{h\_q}^{*}$ can be set directly.

In addition, G_d represents the digital delay, including sampling and computation process, which is typically accounted as one sampling period that T_s. G_pwm is another time delay of approximately 0.5T_s due to the PWM processing. They can be expressed as

$$G_d\left(s\right)=e^{-s{T}_s},G_{pwm}\left(s\right)={\displaystyle \frac{1-e^{-s{T}_s}}{T_s\cdot s}}$$

(48)

6. The Overall Control Scheme

Figure 11 shows the overall control block diagram. All DC-link capacitor voltages u_dcmn (m = a, b, c and n = 1, 2, …, N) are fed back to the average value calculation block for reducing the double-line-frequency ripples and calculating the average values used for the follow-up control. The stability control for the sum of cluster average active power flows is designed to stabilize the average cluster voltage ${\overline{u}}_{dc}$ and balance the active power flows between the input and the output of the HVAC-PET. The individual control for the cluster average active power flows is considered to balance the three cluster voltages ${\overline{u}}_{dca}$, ${\overline{u}}_{dcb}$, and ${\overline{u}}_{dcc}$. The reactive power compensation control is to realize the function of STATCOM, and the functions of harmonic current injection and filtering are accomplished in the positive-sequence and harmonic currents control block. In addition, for balancing control of the individual DC-link capacitor voltage of the CHB cell in the same cluster, the sorting algorithm is adopted, and the carrier phase shifted sinusoidal pulse width modulation (CPS-SPWM) is employed to produce the switch control signals for each H-bridge.

7. Results

To verify the proposed control strategy by experiments, the HVAC-PET rated at 380 V and 50 kVA is built, circuit configuration is implemented as Figure 1 and Figure 2.

Table 1. Power circuit parameters.

Variable	Symbol	Value
Cascaded submodule number	N	3
AC filter inductor	Ls, Rs	2.8 mH, 28 mΩ
DC-link capacitor	Cdc	1 mF
HFT ratio	n1:n2	1:1
Line-to-line rms voltage of PCC	Us	380 V
Nominal DC voltage of submodule	$U_{dc}^{*}$	160 V
Switching frequency	fsw	20 kHz
Sampling frequency	fs	10 kHz

and

Table 2. Control parameters.

Variable	Symbol	Value
Coefficients of notch filter FN2	Q, ωb	250.0, 80 Hz
Coefficients of notch filter FN6	Q, ωb	250.0, 80 Hz
Coefficients of notch filter FN12	Q, ωb	250.0, 80 Hz
PI regulator for PLL	kPpll, TIpll	2.0, 0.07
PI regulator for ibh	$k_{Pi}^{+}$$, T_{Ii}^{+}$	1.5, 0.1
PI regulator for i−	$k_{Pi}^{-}$$, T_{Ii}^{-}$	1.5, 0.1
Coefficients of VPI controller $G_{VPI}^2$	kP2, kR2	0.05, 0.5
Coefficients of VPI controller $G_{VPI}^6$	kP6, kR6	0.05, 0.5
Coefficients of VPI controller $G_{VPI}^{12}$	kP12, kR12	0.05, 0.5
PI regulator for average cluster voltage	kPacv, TIacv	0.8, 0.016
PI regulator for cluster voltage	kPcv, TIcv	10.0, 0.5

show the controller parameters used in this control scheme.

7.1. Experiments for Reactive Power Injection and Cluster Voltage Balancing Control

Figure 12 shows the laboratory prototype of HVAC-PET, in which two cells and one high-frequency transformer (HFT) constitute a submodule depicted in Figure 2. The 1.2 kV/120 A CAS120M12BM2-type SiC-MOSFET is employed to implement the power switch in each H-bridge. The digital signal processor (DSP) and field programmable gate array (FPGA) based controller is designed to implement the control system. Active loads with the resistances R_a, R_b, and R_c are connected to the three separated LVDCLs of HVAC-PET, respectively. In the DAB stage of HVAC-PET, the gate control signal of each switch is always at 50% duty ratio with a square-waveform output at the primary-side H-bridge, while the switches of the secondary-side H-bridge are turned off all the time.

Figure 13 shows the transition of HVAC-PET operation from capacitive 30 kVar injection to inductive 30 kVar injection, while R_a = R_b = R_c = ∞. U_{c_ref} represents the voltage reference generated by the current controller for the cluster C of CHB, and i_a, i_b, i_c being the cluster input currents of CHB. The current i_c leads the phase voltage U_{c_ref} 90° in the capacitive operation and becomes lagging 90° in the inductive operation. In the steady state, the cluster voltages ${\overline{u}}_{dca}$, ${\overline{u}}_{dcb}$, and ${\overline{u}}_{dcc}$ are regulated at the same level of 160 V, and in the transition period of 20 ms, the max variation is about 60 V.

Figure 14a shows the system response to a reactive-power-injection sudden variation from 0 to inductive 20 kVar under a 15.36 kW three-phase-balanced active load that R_a = R_b = R_c = 5 Ω. It can be observed that the transition period is about 18 ms, and the max variation of ${\overline{u}}_{dcm}$ is about 13 V. Figure 14b shows the system response to an active-power release under inductive 20 kVar injection from three-phase-balanced 15.36 kW (i.e., R_a = R_b = R_c = 5 Ω) to 0 (i.e., R_a = R_b = R_c = ∞). The max variation of ${\overline{u}}_{dcm}$ is about 45 V in the transition period of 20 ms.

Figure 15 shows experimental results for the cluster voltage control. As illustrated in Figure 15a, with the cluster voltage balancing control scheme proposed in this paper, the cluster input currents i_a, i_b, and i_c are balanced, and the cluster voltages ${\overline{u}}_{dca}$, ${\overline{u}}_{dcb}$, and ${\overline{u}}_{dcc}$ are all equal to 160 V under the active load condition of R_a = R_b = R_c = 5 Ω. And although the amplitude of steady input current i_c is elevated by 15A while the resistance R_c changed from 5 Ω to 2.5 Ω, the cluster voltages are well controlled and stabilized at 160 V. The transition period of this scenario is about 120 ms, and the max variation of ${\overline{u}}_{dcm}$ is about 15 V. However, without cluster voltage balancing control, i.e., no negative-sequence current injection, as illustrated in Figure 15b, the cluster voltages cannot be controlled equal to each other under the active load conditions of R_a = R_b = 5 Ω, and R_c = 2.5 Ω. Namely, ${\overline{u}}_{dca}$ is equal to ${\overline{u}}_{dcb}$, they are both 10 V higher than the objective value, while ${\overline{u}}_{dcc}$ is 20 V lower than that.

7.2. Experiments for Reactive Power Compensation and Active Power Filtering

To validate the functions of reactive power compensation and active power filtering for the proposed control scheme in this paper, a two-HVAC-PETs connected in parallel based experiment bench is established as shown in Figure 16a. From the block diagram of the experiment bench depicted in Figure 16b, HVAC-PET2 is controlled as a grid load emulator generating harmonic and reactive currents, while HVAC-PET1 works as a compensator to compensate the reactive power absorbed by the emulator and the harmonic current components in i_l.

Figure 17 shows the experimental results for reactive power compensation. In Figure 17a, u_sab, u_sbc, and u_sca are the line-to-line voltages of the PCC, the cluster input-currents i_a, i_b, and i_c of HVAC-PET1 can track the reactive currents of HVAC-PET2 that i_la, i_lb, and i_lc well when the reactive power changes from inductive 20 kVar to 0 with the transition period of 6 ms, and the grid currents i_sa, i_sb, and i_sc are always about 0. Similar results can be obtained when the reactive power of HVAC-PET2 changes from 0 to capacitive 20 kVar as illustrated in Figure 17b, and the transition period is also about 6 ms.

Figure 18 shows the experimental results for harmonic current injection, where HVAC-PET2 is employed as the harmonic source. The 5th harmonic current with a peak value of 20 A is injected in Figure 18a, as well as the 7th harmonic current with a peak value of 20 A in Figure 18b, and the THD analysis results are shown in Figure 18c and Figure 18d, respectively. It should be noted that the THD in this paper, which takes the fundamental component as the reference, conforms to the standard definition of THD.

Figure 19 presents the experimental results of harmonic current injection and filtering. When the emulator injects 20 kVar of inductive reactive power along with high harmonic currents (peak value: 10 A) into the grid, HVAC-PET1 functions as a compensator to eliminate the harmonic current components introduced by the emulator. Measurement results show the emulator’s input current (i_la) exhibits 24.04% THD, which is effectively suppressed to 5.74% THD in the grid current (i_sa) after compensation.

8. Conclusions

The medium-voltage AC port of the power electronic transformer (HVAC-PET) connected to the AC grid needs to simultaneously achieve multiple functions, including active power tracking, reactive power compensation, and active filtering, while these multi-mode controls exhibit strong coupling characteristics. This paper proposes a dual-dimensional analysis approach from both power and current perspectives to achieve decoupling and control of multiple modes. From the power dimension, instantaneous active power is decomposed in the dq coordinate system to obtain three-phase active power distribution characteristics, and the control problem of three-phase active power imbalance is solved through negative-sequence current injection and three-phase active power deviation regulation. From the current dimension, a control scheme is proposed to regulate unified components composed of fundamental positive-sequence and high-order harmonics in the positive-sequence dq frame while managing fundamental negative-sequence components in the negative-sequence dq frame, achieving voltage–current decoupling and accurate extraction by incorporating notch filters in control loops, and employing PI + VPIs to control unified current components containing fundamental positive-sequence and harmonic currents, thereby realizing effective tracking of high-order harmonic currents. The effectiveness of the proposed control strategy is finally verified through a scaled-down 380 V/50 kVA experimental platform. Future research should focus on breakthroughs in: (1) AI-based control parameter design and adaptive strategies; (2) system stability analysis and comparative studies with conventional methods.