Multi-Mode Control of a Hybrid Transformer for the Coordinated Regulation of Voltage and Reverse Power in Active Distribution Network

Abstract

The unprecedented growth of distributed renewable generation is changing the distribution network from passive to active, resulting in issues like reverse power flow, voltage violations, malfunction of protection relays, etc. To ensure the reliable and flawless operation of active distribution networks, an electrical device enabling active network management is necessary, and a hybrid distribution transformer offers a promising solution. This study introduces a novel hybrid transformer topology and multi-mode control strategy to achieve coordinated voltage and reverse power regulation in active distribution networks. The proposed hybrid transformer combines conventional transformer windings with a partially rated SiC-MOSFET-based back-to-back converter, reducing additional investment costs and enhancing system reliability. A multi-mode control strategy is proposed to facilitate the concurrent reverse power control and voltage violation mitigation of the presented hybrid transformer, allowing a smooth transition between the P–Q control mode and the V–f control mode. The control mode switching can be activated manually or autonomously in response to voltage violations or reverse power overloading. The effectiveness of the proposed hybrid transformer configuration and its control mode transition mechanism are examined through comprehensive case studies conducted in the PSCAD/EMTDC environment. The proposed HT design has been confirmed to achieve a voltage regulation range of ±20% of the nominal voltage and effectively regulate bidirectional active power flow within a range of −25% to 25% of the rated power.

1. Introduction

The widespread adoption of distributed renewable generation alters the operation conditions of distribution networks in all forms. On the one hand, distributed renewable generations have the inherent advantage of supplying power demand locally, contributing to reduced power losses due to long-distance power distribution, and alleviating dependence on fossil fuel power plants (and hence reduced carbon emissions) [1,2]. On the other hand, the uncertain and fluctuating power generation features of distributed renewables can adversely affect the normal operation of distribution networks, causing issues like voltage fluctuation, frequency oscillation, malfunction of protection relays, etc. [2]. To ensure the stability and security of the operation of active distribution networks with high-level renewable penetrations, new technologies supporting active network management become crucial. Among all those technologies, one key technology that has gained significant attention from distribution network operators (DNOs) is the smart transformer (ST) technology due to its excellent power control flexibility. A smart transformer is a type of power-electric-based transformer, and its grid controllability is enabled by fully controllable power converters. Compared to traditional distribution transformers, ST has the advantages of precise and continuous voltage regulation, four-quadrant power control, active power factor correction, harmonic suppression, compact volume size, etc., making it an ideal replacement for traditional transformers in applications like active voltage control, primary frequency regulation, and bidirectional power flow management [3,4]. Although smart transformers are promising alternatives to traditional transformers, the high investment cost, low reliability, and scalability issues restrict their large-scale practical implementations, and only limited applications can be traced from demonstration projects [5]. Depending on whether the smart transformer is fully power electronic or integrated with a traditional transformer, the smart transformer technology can be divided into two types: solid-state transformers (SSTs) and hybrid transformers (HTs). Specifically, SST is typically presented in a three-stage configuration consisting of an AC-DC rectifier, an inverter, and a DC-DC converter [6]. As the power converters are the only power-delivering components between the upstream supply grid and the downstream end-users, SST has 100% voltage and power regulation capability. However, it should be kept in mind that the cost of power electronic semiconductors is experiencing exponential growth with increasing voltage and power ratings [7]. Moreover, to ensure reliable power delivery to end-users, SST requires a dedicated protection circuit to survive any semiconductor failure. In contrast, HT incorporates partially rated power converters into the conventional transformer design, with a 5–20% voltage and power regulation capability achieved [7]. With the reduced voltage and power ratings for semiconductors, the cost of HT is greatly reduced compared to SST. Moreover, the dual-path power-delivering feature brings enhanced reliability and efficiency to HT. Therefore, HT is a remarkable candidate for replacing conventional transformers in active distribution network management. The comparative advantages and disadvantages of mainstream transformer technologies are summarized in

Table 1. Comparison of the mainstream transformer technologies in distribution power networks.

Technology	Configuration	Advantages	Disadvantages
Conventional transformer		(1) simple configuration; (2) easy to implement; (3) high reliability; (4) low O&M cost; (5) low investment cost	(1) passive voltage regulation due to a fixed voltage ratio; (2) windings may deform due to the saturation effect; (3) no power regulation capability; (4) large volume
OLTC transformer		(1) simple configuration; (2) easy to implement; (3) high reliability; (4) discrete voltage regulation capability	(1) discrete actions and slow action response; (2) reduced lifetime due to contact wear; (3) additional investment costs for OLTC (4) windings may deform due to the saturation effect; (5) no power regulation capability; (6) large volume
SST		(1) no bulky low-frequency windings; (2) continuous voltage regulation capability; (3) bidirectional power flow capability; (4) small volume	(1) complex circuit design; (2) require a dedicated protection circuit; (3) high investment costs (4) high O&M costs; (5) reduced reliability when compared with conventional transformers and OLTC transformers
HT		(1) continuous voltage regulation capability; (2) bidirectional power flow capability; (3) improved reliability compared to SST; (4) reduced investment cost compared to SST	(1) complex circuit design; (2) require a dedicated protection circuit; (3) windings may deform due to the saturation effect

.

Up to now, a significant amount of research has been conducted regarding the designs, topologies, controls, and applications of HT. Ref. [8] presents a HT topology to address the voltage fluctuation issue due to renewable integration. By combining the traditional distribution transformer windings with a series converter, the dynamic voltage regulation capability is achieved by the proposed HT topology. Ref. [9] tailors the control circuit of HT and creates a virtual impedance for harmonic damping. With the enabled harmonic isolation capability, the proposed HT is ideal for delivering power to harmonic-sensitive loads like data centers. Ref. [10] proposes a single-phase HT configuration consisting of a three-legged power converter and the traditional low-frequency transformer windings. With the voltage vector-based control, the presented HT is immune to voltage sags, swells, and harmonics. Ref. [11] presents a novel HT architecture based on a mixture of a traditional transformer and a matrix converter. The proposed HT architecture is capable of maintaining a stable supply voltage in the transmission networks. A detailed review of the recently updated HT design can be found in [7,12,13].

The existing literature on HT is mainly concentrated on proposing new topologies and control circuits, aiming at providing an ideal supply voltage to end-users. With the proliferation of renewable energy systems like wind turbines and solar PV systems, their accelerating grid penetrations not only result in the deterioration of supply voltage quality but also lead to reverse power flow in the distribution substations. The unrestricted reverse power flow can further lead to operational security issues like significantly increased transformer losses (and hence reduced lifetime) and the malfunction of protection relays [14,15]. Currently, there are no standard solutions for restricting the reverse power flow. The available options for addressing such a problem can be broadly divided into two types: active network management and the installation of power flow control devices. The former applies active network control techniques (e.g., demand side management and strategic power curtailment) to achieve the load following of the source [16,17]. In such a case, the renewable hosting capacity of the grid can be enhanced, bringing in alleviated reverse power flow conditions. A dedicated communication infrastructure is still required to achieve active network control. The latter relies on the installation of costly energy storage systems or FACTs devices to directly decrease the reverse power flow [18,19]. The application of smart transformer technologies in reverse power regulation is not well documented in existing literature. Although Refs. [20,21] proposes a frequency-droop-based control scheme for the low-voltage side of SST, it requires the adaptation of DGs local controller, which seriously limits its practical implementation.

Although some studies in the literature investigate the HTs power flow control capability, the power flow controller they developed for HTs focuses on delivering specific grid support functions such as harmonic mitigation and voltage regulation without addressing the revere power issue. For instance, Ref. [7] employs a reactive power controller in a storage-integrated HT to regulate terminal voltages. Although a ±5% voltage regulation capability is achieved by the proposed HT design, the addition of a battery energy storage system substantially increases the capital cost and O&M cost of HTs. Ref. [22] proposes a model predictive control (MPC)-based reactive power controller for a four-leg matrix converter-based HT to achieve dynamic voltage restoration under sags or swells. Similarly, a decentralized MPC-based controller is proposed in [23] to optimize HTs reactive power preference, thus achieving dynamic voltage regulation. The power converter described in [24] integrates a fractionally rated power converter into the primary-side winding of a traditional single-phase transformer. While the proposed power flow controller incorporates functions including DC mitigation, voltage balancing, and harmonic suppression, an adaptive modification is necessary to make it suitable for three-phase distribution systems. Based on the derived dynamic power flow process of HTs, Ref. [25] proposes a PI-filter-feedforward controller in order to address grid-side current distortion and asymmetry issues. To summarize, most of the studies in the literature utilize the power flow control capability of HTs to address power quality concerns like voltage deviation, voltage fluctuation, and harmonics, with minimal focus on reverse power limiting. The accelerating proliferation of renewables can cause reverse power flow in the substation transformer, leading to underperformance, failure of protective devices, overvoltage, etc. Therefore, both voltage regulation and reverse power management are essential functions for HTs in the context of future smart grids. To fill the above research gap, this paper proposes an adaptive design method for HT, enabling it to restrict reverse power flow and concurrently regulate supply voltages.

This paper first tailors the topology of HT, where the power and voltage control capability are enabled by an integrated SiC-MOSFET-based back-to-back converter. Once any converter fault occurs, the proposed HT enters a passive operating mode (i.e., operates as the traditional transformer) by disconnecting the power converter from the HT system. Based on the proposed HT topology, a multi-mode control strategy is introduced to provide concurrent control of supply voltage and reverse power flow. Once the reverse power flow violates the predefined security limit, the controller of HT can smoothly and stably transition from the V–f control mode to the P–Q control mode, and the reverse power flow will be decreased to the setting values. The effectiveness analysis of the proposed control strategy is evaluated by case studies on a simplified active distribution network where the distribution transformer is replaced by the HT proposed. The main contributions of the presented HT design are summarized below:

(i)

Demonstrate the reverse power limiting capability of HT;

(ii)

A novel HT configuration is proposed which is capable of switching between active and passive operation modes;

(iii)

A multi-mode control strategy is implemented on the integrated SiC-MOSFET converter of HT, aiming at providing both voltage regulation and reverse power flow limiting;

(iv)

A smooth and stable transition mechanism between the V–f control mode and the P–Q control mode is introduced to address the unrestricted reverse power flow, voltage fluctuation, and overvoltage issues.

The rest of this paper is organized as follows: Section 2 describes the proposed HT configuration, followed by introducing the designed multi-mode control strategy. Special focus is given to the transition mechanism between the V–f control mode and the P–Q control mode. Section 3 investigates the effectiveness and performance of the proposed HT design via multi-scenario case studies performed in the PSCAD/EMTDC environment. The main conclusions and future work are summarized in Section 4.

2. Materials and Methods

2.1. The Proposed Topology of HT

As illustrated in Figure 1, the proposed HT topology comprises three-phase primary windings (W_A1, W_B1, and W_C1), three-phase secondary windings (W_a1, W_b1, and W_c1), three-phase control windings (W_{a1_con}, W_{b1_con}, and W_{c1_con}), and a SiC-MOSFET-based back-to-back (BTB) power converter. The neutral point of each winding is grounded in a star configuration. The primary windings are magnetically linked to the secondary and control windings through wound iron cores. The secondary windings and the control windings are connected in parallel in a corresponding phase coil configuration with completely identical specifications. The neutral points of the BTB converter and the three-phase transformers are all connected to the substation grounding grid.

The control capability is enabled by the SiC-MOSFET-based BTB converter. Once any fault is detected or regular maintenance is required, the BTB converter can be immediately isolated from the main system by opening switches K1 and K2. The power converter is made up of two voltage converters (VSC1 and VSC2) connected in a BTB configuration, as in Figure 2. Its DC-link is formed by two series-connected capacitors with their coupling points grounded. VSC1 and VSC2 have their AC ports attached to the primary windings and the control windings, respectively, via the inductors L₁ and L₂. Each converter consists of three sets of bridge arms, which are interconnected in a full-bridge configuration. Regarding the electronic switching technologies, SiC MOSFETs are chosen as the switches for VSC1 and VSC2 due to the inherent advantages of low switching losses, high power density, and low thermal stress [26]. The high-frequency pulse signals (G_VSC1 and G_VSC2 in Figure 1) received from the multi-mode controller determine the on and off states of the six SiC MOSFETs in the BTB converter. The input signals fed to the multi-mode controller comprise the three-phase voltage and current waveforms measured at the primary and secondary side buses, the DC-link voltage, the operating states of switches K1 and K2, and the control mode selection signal S_TM.

2.2. The Multi-Mode Control Strategy for the Proposed HT Configuration

The topology analysis in Section 2.1 indicates that the bidirectional power flow control and dynamic voltage regulation capabilities of HT are attained through active control of the SiC-MOSFET-based BTB converter. Depending on the control objectives, different control strategies are applied to VSC1 and VSC2. Specifically, VSC1 is to maintain the DC-link voltage at its reference value while pursuing a unity power factor. Accordingly, the u_dc–Q control strategy is applied to VSC1. The control objective of VSC2 is to ensure a stable and secure power supply for end users and keep them away from any power quality disturbances. As voltage rise and revered power flow are the major concerns for active distribution networks [27,28], VSC2 should be capable of providing concurrent voltage control and inverse power limiting functions. Therefore, a coordinated V–f and P–Q control is proposed for VSC2. As the control strategies for VSC1 and VSC2 are two decoupled parts, their detailed implementation procedures will be described separately in the following subsections.

2.2.1. Control Strategy of VSC1

VSC1 operates as an input rectifier, aiming at providing a stable DC-link voltage for VSC2, as well as regulating the reactive power at its reference value. Therefore, the u_dc–Q control is implemented for VSC1, with its general structure shown in Figure 3. The input signals of the u_dc–Q controller comprise the DC-link voltage (u_dc), the reactive power measured at the primary side of the HT (Q₁), and the measured three-phase voltage and current waveforms at the HTs primary side (u_A1, u_B1, u_C1, i_A1, i_B1, i_C1).

The implementation process of the proposed u_dc–Q controller for VSC1 can be divided into several steps, which are described as follows:

(a) The variance between the measured u_dc and its reference value ($u_{dc}^{*}$) is computed and sent to a PI controller, and the output is then filtered using a low-pass filter (LPF). The filtered output serves as the normalized d-axis reference current for HTs primary side, as in (1).

$$i_{d1,pu}^{*}=\frac{u_{dc}^{*}-u_{dc}}{u_{dc,b}}\left(k_{pi}+\frac{k_{ii}}{s}\right)\frac{G}{1+s·T}DBlk$$

(1)

where u_dc,b denotes the nominal value of u_dc, while k_pi and k_ii stand for the proportional and integral coefficients of the PI controller. G and T are the gain coefficient and time constant of the first-order LPF. DBlk refers to the blocking signal of the BTB converter. DBlk equals 0 when the BTB converter is blocked and 1 otherwise.

(b) Similarly, the deviation between HTs primary-side reactive power ($Q_1$) and its set value ($Q_1^{*}$) is computed and sent to the PI controller. After undergoing the low-pass filtering, the normalized q-axis reference current for HTs primary side is determined, as in (2).

$$i_{q1,\mathrm{p}\mathrm{u}}^{*}=\frac{Q_1^{*}-Q_1}{S_b}\left(k_{pi}+\frac{k_{ii}}{s}\right)\frac{G}{1+s·T}DBlk$$

(2)

where: S_b denotes HTs nominal operating power.

(c) After performing the normalization of HTs primary-side voltages and currents (u_A1, u_B1, u_C1, i_A1, i_B1, and i_C1), the Park transformation is applied to obtain the normalized values on the d-q frame, as in (3) and (4).

$$\left[\begin{array}{c}{u}_{d1,\mathrm{p}\mathrm{u}}\\ u_{q1,\mathrm{p}\mathrm{u}}\end{array}\right]=\frac{\sqrt{2}}{3U_{1,b}}\left[\begin{array}{ccc}cos\left({\theta }_{u1}\right)& cos\left({\theta }_{u1}-\frac{2}{3}\pi \right)& cos\left({\theta }_{u1}+\frac{2}{3}\pi \right)\\ -sin\left({\theta }_{u1}\right)& -sin\left({\theta }_{u1}-\frac{2}{3}\pi \right)& -sin\left({\theta }_{u1}+\frac{2}{3}\pi \right)\end{array}\right]\left[\begin{array}{c}{u}_{A1}\\ u_{B1}\\ u_{C1}\end{array}\right]$$

(3)

$$\left[\begin{array}{c}{i}_{d1,\mathrm{p}\mathrm{u}}\\ i_{q1,\mathrm{p}\mathrm{u}}\end{array}\right]=\frac{\sqrt{2}}{3I_{1,b}}\left[\begin{array}{ccc}cos\left({\theta }_{i1}\right)& cos\left({\theta }_{i1}-\frac{2}{3}\pi \right)& cos\left({\theta }_{i1}+\frac{2}{3}\pi \right)\\ -sin\left({\theta }_{i1}\right)& -sin\left({\theta }_{i1}-\frac{2}{3}\pi \right)& -sin\left({\theta }_{i1}+\frac{2}{3}\pi \right)\end{array}\right]\left[\begin{array}{c}{i}_{A1}\\ i_{B1}\\ i_{C1}\end{array}\right]$$

(4)

where the RMS reference values for HTs primary-side voltage and current are denoted as U_1,b and I_1,b, respectively, and their phase angles are represented by θ_u1 and θ_i1.

(d) $i_{d1,\mathrm{p}\mathrm{u}}$, $i_{d1,\mathrm{p}\mathrm{u}}^{*}$, $i_{q1,\mathrm{p}\mathrm{u}}$, $i_{q1,\mathrm{p}\mathrm{u}}^{*}$, $u_{d1,\mathrm{p}\mathrm{u}}$ and $u_{q1,\mathrm{p}\mathrm{u}}$, obtained from steps a~c, are sent to the inner current control loop of the u_dc–Q controller. The output of the inner control loop is the normalized reference current of VSC1 in the d-q frame, as in (5) and (6).

$$u_{d,VSC1,\mathrm{p}\mathrm{u}}^{*}=u_{d1,pu}-\left(i_{d1,\mathrm{p}\mathrm{u}}^{*}-i_{d1,\mathrm{p}\mathrm{u}}\right)\left(k_{pi}+\frac{k_{ii}}{s}\right)DBlk+i_{q1,\mathrm{p}\mathrm{u}}{w}_1{L}_{1,\mathrm{p}\mathrm{u}}$$

(5)

$$u_{q,VSC1,\mathrm{p}\mathrm{u}}^{*}=u_{q1,\mathrm{p}\mathrm{u}}-\left(i_{q1,\mathrm{p}\mathrm{u}}^{*}-i_{q1,\mathrm{p}\mathrm{u}}\right)\left(k_{pi}+\frac{k_{ii}}{s}\right)DBlk-i_{d1,\mathrm{p}\mathrm{u}}{w}_1{L}_{1,\mathrm{p}\mathrm{u}}$$

(6)

where $w_1{L}_{1,\mathrm{p}\mathrm{u}}$ refers to the normalized reactance of the series-connected inductor L1. Its value is calculated using the formula $2\pi f_1{L}_1/\left({U_{VSC1}^{*}}^2/S_b\right)$, where f₁ and $U_{VSC1}^{*}$ refer to the reference frequency and RMS value of VSC1’s primary-side voltage.

The reference AC voltage of VSC1 can be derived by transforming $u_{d,VSC1,\mathrm{p}\mathrm{u}}^{*}$ and $u_{q,VSC1,\mathrm{p}\mathrm{u}}^{*}$ from the d–q frame to the abc domain using Park’s inverse transformation, as in (7).

$$\left[\begin{array}{c}{u}_{A,VSC1,\mathrm{p}\mathrm{u}}^{*}\\ u_{B,VSC1,\mathrm{p}\mathrm{u}}^{*}\\ u_{c,VSC1,\mathrm{p}\mathrm{u}}^{*}\end{array}\right]=\left[\begin{array}{ccc}cos\left({\theta }_{u1}\right)& -sin\left({\theta }_{u1}\right)& 1\\ cos\left({\theta }_{u1}-\frac{2}{3}\pi \right)& -sin\left({\theta }_{u1}-\frac{2}{3}\pi \right)& 1\\ cos\left({\theta }_{u1}+\frac{2}{3}\pi \right)& -sin\left({\theta }_{u1}+\frac{2}{3}\pi \right)& 1\end{array}\right]\left[\begin{array}{c}{u}_{d,VSC1,\mathrm{p}\mathrm{u}}^{*}\\ u_{q,VSC1,\mathrm{p}\mathrm{u}}^{*}\\ 0\end{array}\right]$$

(7)

(e) Finally, the pulse control signal, G_VSC1, for the six SiC MOSFETs in VSC1 is achieved through the use of sinusoidal pulse width modulation (SPWM), as shown in Figure 4. Here, $u_{A,VSC1,\mathrm{p}\mathrm{u}}^{*}$, $u_{B,VSC1,\mathrm{p}\mathrm{u}}^{*}$ and $u_{C,VSC1,\mathrm{p}\mathrm{u}}^{*}$ serve as the modulating signals and are compared with the triangular carrier wave. Specifically, at any given moment, if the modulating signal is greater than the carrier wave, the upper bridge arm switches SW_ua1, SW_ub1, and SW_uc1 of VSC1 are turned on, while the lower bridge arm switches SW_la1, SW_lb1, and SW_lc1 are turned off. Conversely, SW_ua1, SW_ub1, and SW_uc1 are turned off, while SW_la1, SW_lb1, and SW_lc1 are turned on. It is worth noting that other state-of-the-art modulation strategies such as space vector modulation (e.g., [29]) and selective harmonic elimination PWM (e.g., [30]) can be applied to substitute the conventional SPWM currently utilized, thereby enhancing the performance of VSCs (e.g., by increasing DC-link voltage utilization ratio, decreasing harmonic as well as switching losses).

2.2.2. Control Strategy of VSC2

To tackle the voltage deviation and reverse power flow issues, a coordinated V–f and P–Q control strategy is proposed for VSC2. The two control strategies can be seamlessly switched based on the value of the control mode switching control signal (S_TM). When S_TM is 0, the V–f control is activated to regulate HTs secondary-side voltage at a suitable level. When S_TM is 1, the P–Q control is activated, with the objective of regulating the HTs secondary-side active and reactive powers at their setting values. The selection of the S_TM value depends on the operating scenario of the distribution network. For example, when a voltage violation occurs, the V–f control should be activated with S_TM set to 0. When the revere power flow monitored at the substation exceeds the security limit, the P–Q control should be activated with S_TM set to 1. The main difference between the V–f control and the P–Q control is the generation mechanism of HTs secondary-side reference current. Therefore, the control strategy is further divided into the outer control loop and the inner control loop. The outer control loop is responsible for generating the reference secondary current of HT, while the inner control loop concentrates on forming the reference AC voltage of VSC2. As the V–f control and the P–Q control share the common inner control loop, special focus is given to the outer control loop. The general control structure of the outer control loop is illustrated in Figure 5, allowing proper coordination between the V–f control and the P–Q control.

Outer Control Loop of the V–f Controller

When S_TM equals 0, the V–f control takes effect, with its main implementation procedures summarized as the following steps.

(a) Generate the reference amplitude ($U_{2,pk}^{*}$) and phase angle (${\theta }_{u2}$) for HTs secondary voltage and then derive the three-phase voltage waveforms $u_{a2}^{*}$, $u_{b2}^{*}$ and $u_{c2}^{*}$ along with their corresponding d-q component achieved using the Park transformation, as in (8)–(10).

$$\left\{\begin{array}{c}{U}_{2,\mathrm{p}\mathrm{u}}^{*}=\sqrt{2}{U}_{2,\mathrm{p}\mathrm{u}}^{*}{U}_{2,b}\\ {\theta }_{u2}=\frac{2\pi f_0}{s}+{\theta }_{u2}^{\prime }\end{array}\right.$$

(8)

$$\left\{\begin{array}{c}{u}_{a2}^{*}=U_{2,pk}^{*}sin\left({\theta }_{u2}\right)\\ u_{b2}^{*}=U_{2,pk}^{*}sin\left({\theta }_{u2}-2\pi /3\right)\\ u_{c2}^{*}=U_{2,pk}^{*}sin\left({\theta }_{u2}+2\pi /3\right)\end{array}\right.$$

(9)

$$\left[\begin{array}{c}{u}_{d2,\mathrm{p}\mathrm{u}}^{*}\\ u_{q2,\mathrm{p}\mathrm{u}}^{*}\end{array}\right]=\frac{\sqrt{2}}{3U_{2,b}}\left[\begin{array}{ccc}cos\left({\theta }_{u2}\right)& cos\left({\theta }_{u2}-\frac{2}{3}\pi \right)& cos\left({\theta }_{u2}+\frac{2}{3}\pi \right)\\ -sin\left({\theta }_{u2}\right)& -sin\left({\theta }_{u2}-\frac{2}{3}\pi \right)& -sin\left({\theta }_{u2}+\frac{2}{3}\pi \right)\end{array}\right]\left[\begin{array}{c}{u}_{a2,\mathrm{p}\mathrm{u}}^{*}\\ u_{b2,\mathrm{p}\mathrm{u}}^{*}\\ u_{c2,\mathrm{p}\mathrm{u}}^{*}\end{array}\right]$$

(10)

where $U_{2,\mathrm{p}\mathrm{u}}^{*}$ and $U_{2,\mathrm{b}}$ represent the normalized reference value and the base value of HTs secondary voltage; f₀ denotes the ideal utility frequency of 50 Hz.

(b) Measure the disparities between $U_{d2,\mathrm{p}\mathrm{u}}$, $U_{q2,\mathrm{p}\mathrm{u}}$ and their respective reference values $U_{d2,\mathrm{p}\mathrm{u}}^{*}$, $U_{q2,\mathrm{p}\mathrm{u}}^{*}$. Transmit their errors to the PI controller for deriving the reference d–q components of HTs secondary current waveform, as in (11).

$$\left\{\begin{array}{c}{i}_{d2,\mathrm{p}\mathrm{u}}^{*}=\left(u_{d2,\mathrm{p}\mathrm{u}}^{*}-u_{d2,\mathrm{p}\mathrm{u}}\right)\left(k_{pi}+\frac{k_{ii}}{s}\right)\left(!S\_TM\right)DBlk\\ i_{q2,\mathrm{p}\mathrm{u}}^{*}=\left(u_{q2,\mathrm{p}\mathrm{u}}^{*}-u_{q2,\mathrm{p}\mathrm{u}}\right)\left(k_{pi}+\frac{k_{ii}}{s}\right)\left(!S\_TM\right)DBlk\end{array}\right.$$

(11)

Outer Control Loop of the P–Q Controller

When S_TM makes a step change from 0 to 1, the outer control loop of VSC2 turns from the V–f control mode to the P–Q control mode. Its implementation procedures can be summarized as follows:

(a) Calculate HTs secondary active and reactive powers ($P_2$, $Q_2$), and normalize the results as ($P_{2,\mathrm{p}\mathrm{u}}$, $Q_{2,\mathrm{p}\mathrm{u}}$). Determine the difference between $P_{2,\mathrm{p}\mathrm{u}}$, $Q_{2,\mathrm{p}\mathrm{u}}$ and their respective reference values $P_{2,\mathrm{p}\mathrm{u}}^{*}$, $Q_{2,\mathrm{p}\mathrm{u}}^{*}$. Transmit the differences to low-pass filters, with the outputs transferred to PI controllers. This process facilitates the calculation of HTs secondary reference current in a d-q frame ($i_{d2,\mathrm{p}\mathrm{u}}^{*}$, $i_{q2,\mathrm{p}\mathrm{u}}^{*}$), as in (12) and (13).

$$\left\{\begin{array}{c}{P}_2=u_{a2}{i}_{a2}+u_{b2}{i}_{b2}+u_{c2}{i}_{c2}\\ Q_2=\frac{\left(u_{b2}-u_{c2}\right)i_{a2}+\left(u_{c2}-u_{a2}\right)i_{b2}+\left(u_{a2}-u_{b2}\right)i_{c2}}{\sqrt{3}}\end{array}\right.$$

(12)

$$\left\{\begin{array}{c}{i}_{d2,\mathrm{p}\mathrm{u}}^{*}=\frac{P_2^{*}-P_2}{S_b}\frac{G}{1+s·T}DBlk\left(k_{pi}+\frac{k_{ii}}{s}\right)S\_TM\\ i_{q2,\mathrm{p}\mathrm{u}}^{*}=\frac{Q_2^{*}-Q_2}{S_b}\frac{G}{1+s·T}DBlk\left(k_{pi}+\frac{k_{ii}}{s}\right)S\_TM\end{array}\right.$$

(13)

The Common Inner Control Loop

The V–f control and the P–Q control share the same inner control loop. Its general control structure is illustrated in Figure 6, with the implementation procedures summarized as follows:

(a) Measure HTs secondary AC currents, i_a2, i_b2, and i_c2. Subsequently, process their normalized values through a Park transformation to extract their d, q components, as depicted in (14).

$$\left[\begin{array}{c}{i}_{d2,\mathrm{p}\mathrm{u}}\\ i_{q2,\mathrm{p}\mathrm{u}}\end{array}\right]=\frac{\sqrt{2}}{3I_{2,b}}\left[\begin{array}{ccc}cos\left({\theta }_{i2}\right)& cos\left({\theta }_{i2}-\frac{2}{3}\pi \right)& cos\left({\theta }_{i2}+\frac{2}{3}\pi \right)\\ -sin\left({\theta }_{i2}\right)& -sin\left({\theta }_{i2}-\frac{2}{3}\pi \right)& -sin\left({\theta }_{i2}+\frac{2}{3}\pi \right)\end{array}\right]\left[\begin{array}{c}{i}_{a2}\\ i_{b2}\\ i_{c2}\end{array}\right]$$

(14)

where I_2,b and θ_i2 represent the base value and phase angle of HTs secondar current.

(b) Pass the quantities $i_{d2,\mathrm{p}\mathrm{u}}^{*}$, $i_{q2,\mathrm{p}\mathrm{u}}^{*}$, $i_{d2,pu}$, $i_{q2,pu}$, $u_{d2,pu}$ and $u_{q2,pu}$ to the inner control loop, and calculate the normalized reference values ($u_{d,VSC2,\mathrm{p}\mathrm{u}}^{*}$, $u_{q,VSC2,\mathrm{p}\mathrm{u}}^{*}$) of the AC voltage of VSC2 in a d–q frame. Then, apply a Park inverse transformation to convert $u_{d,VSC2,pu}^{*}$, $u_{q,VSC2,\mathrm{p}\mathrm{u}}^{*}$ to their corresponding values in an abc frame, as in (15) and (16).

$$u_{d,VSC2,\mathrm{p}\mathrm{u}}^{*}=u_{d2,\mathrm{p}\mathrm{u}}-kdq\left(i_{d2,\mathrm{p}\mathrm{u}}^{*}-i_{d2,\mathrm{p}\mathrm{u}}\right)\left(k_{pi}+\frac{k_{ii}}{s}\right)DBlk-i_{q2,\mathrm{p}\mathrm{u}}{w}_2{L}_{2,\mathrm{p}\mathrm{u}}$$

(15)

$$u_{q,VSC2,\mathrm{p}\mathrm{u}}^{*}=u_{q2,\mathrm{p}\mathrm{u}}-kdq\left(i_{q2,\mathrm{p}\mathrm{u}}^{*}-i_{q2,\mathrm{p}\mathrm{u}}\right)\left(k_{pi}+\frac{k_{ii}}{s}\right)DBlk+i_{d2,\mathrm{p}\mathrm{u}}{w}_2{L}_{2,\mathrm{p}\mathrm{u}}$$

(16)

where the direction coefficient, kdq, varies based on the value of S_TM. If S_TM is 0, kdq is −1, and if S_TM is 1, kdq becomes 1. $w_2{L}_{2,\mathrm{p}\mathrm{u}}$ represents the normalized reactance of the series-connected filter inductor L2. Its value is calculated by $2\pi f_2{L}_2/\left({U_{VSC2}^{*}}^2/S_b\right)$, where f₂ and $U_{VSC2}^{*}$ refer to the reference frequency and RMS value of the AC voltage for VSC2.

(c) Use $u_{a,VSC2,\mathrm{p}\mathrm{u}}^{\mathrm{*}}$, $u_{b,VSC2,\mathrm{p}\mathrm{u}}^{\mathrm{*}}$, and $u_{c,VSC2,\mathrm{p}\mathrm{u}}^{\mathrm{*}}$ as the modulation signal and then obtain the pulse control signal for VSC2 using the SPWM modulation strategy.

3. Performance Evaluation via Case Studies

To assess the applicability of HT in active distribution networks, the performance of HT in addressing voltage fluctuation and unrestricted reverse power flow issues is evaluated via three diversified case studies. Specifically, Case A is to investigate the performance of HTs reverse power flow limiting function and the smoothness of the control mode transition between the V–f control and the P–Q control. Case B is to evaluate the dynamic voltage regulation capability at HTs secondary side. Case C focuses on testing HTs immunity to the upstream voltage fluctuation. All three case studies are performed on an HT-integrated active distribution network model developed in a PSCAD/EMTDC simulation environment.

3.1. Simulation Setup

The simulation setup involves a HT-integrated active distribution network model, with its single-line diagram illustrated in Figure 7. HT has its primary and secondary terminals connected to the 11 kV and 400 kV busbars, respectively. The 11 kV busbar is connected to the upstream grid, which is modeled as a controllable voltage source with adjustable voltage magnitudes. The end-users are connected to the 400 V busbar via distribution lines. As the performance evaluation is conducted at the substation section, the end-users are represented by aggregate demand and a renewable energy system. Furthermore, two breakers are included in the simulation setup. Breaker BRK1 is being used to bypass the BTB converter from its coupled windings, allowing HT to function as a traditional distribution transformer. Its default setting is 0 (i.e., the open state). A breaker PCC is used to disconnect the renewable energy system from the main grid, thereby converting the active distribution network to a passive one. In terms of the fundamental power flow configurations, the total power requirement is designated as 150 kW, while the rated operational power of the simulated HT is set at 400 kW. The renewable generation system utilizes a simplified model that is based on the controllable voltage source module.

The basic circuit parameters of the developed HT model are as follows: the rated line voltages for the primary, secondary, and control windings are set at 11 kV, 400 V, and 400 V, respectively. In order to provide a suitable voltage level for the AC side of VSC1, taps are installed on the three phases of the primary windings with a corresponding turn ratio set at 4:11. This allows VSC1 to have a rated primary voltage of 400 V. VSC2 is directly connected to the control windings, with its output voltage also rated at 400 V. The filter inductances L₁ and L₂ of the BTB converter in Figure 2 are both 0.4 mH. The reference DC-link voltage, $u_{dc}^{*}$, is set at 800 V, and the switching frequency of the SiC MOSFETs is 16 kHz.

When an external supply or load disturbance occurs, a power mismatch between VSC1 and VSC2 arises. The DC-link capacitor plays a crucial role in mitigating this mismatch through charging or discharging. For a certain DC-link voltage fluctuation $∆u_{dc}$, the capacitance can be estimated using (17) [31]. Assuming the maximum power mismatch is 10 kW and the maximum allowed DC-link voltage fluctuation is 0.3 pu, the minimum required capacitance is 906 uF. In the test case, two identical capacitors are connected in series to form the DC link, each with a capacitance of 2000 uF (i.e., C_dc1 and C_dc2 in Figure 2).

$$C_{dc}\ge \frac{2P_{mis}{t}_r}{(2u_{dc,b}+∆u_{dc})∆u_{dc}}$$

(17)

where $P_{mis}$ represents the power mismatch between VSC1 and VSC2; $∆u_{dc}$ stands for the DC-link voltage fluctuation; the recovery time $t_r$, is set at 0.02 s in this case.

As the control mode transition is activated by the step change of S_TM, it is necessary to prepare a suitable testing sequence for each case. Figure 8 provides an example of the testing sequence for the control mode transition, facilitating the transition between the V–f control and the P–Q control.

In order to evaluate the effectiveness of the proposed HT design in dynamic voltage regulation and reverse power limiting, the simulation setup must be capable of replicating the voltage fluctuations and reverse power flow issues observed in practical distribution networks. First, reverse power flow in active distribution networks occurs when the aggregate renewable energy generation surpasses the total load demand. Thus, the reverse power flow issue can be emulated by adjusting the power output of the simulated renewable energy system to a value higher than the power demand. Consequently, Scenario A is created to test the reverse power limiting and control mode transition of the proposed HT. Second, the proposed HT should be able to regulate its downstream supply voltage to a preferred value to prevent potential voltage violations at the feeder end or engage in specific grid support functions (e.g., conservation voltage reduction). Hence, the reference value for the downstream supply voltage can be modified to assess HTs reference voltage tracking capability, corresponding to Scenario B. Third, upstream voltage fluctuations in a substation transformer can propagate to the downstream busbar, affecting the supply voltage quality to the end-users. To assess the resilience of the proposed HT against fluctuations in upstream voltage, the upstream grid is simulated as a controllable voltage source with its magnitude incrementally altered. Therefore, Scenario C is to assess HTs immunity to upstream voltage fluctuations.

3.2. Test Scenarios

Based on the simulation setup introduced in Section 3.1, three representative scenarios have been created to evaluate the performance of the proposed HT in terms of its dynamic voltage regulation and reverse power limiting capability. The detailed testing sequence for each scenario is provided in the following:

3.2.1. Scenario A: Reverse Power Limiting and Control Mode Transition Test

The reverse power flow generally occurs when the total renewable power generation is higher than the total demand, and the unrestricted reverse power flow results in the underperformance of the substation transformer and the relay protection malfunctioning [32]. To demonstrate the technical feasibility of HT in revere power limiting, Scenario A has the P–Q control activated during the simulation period of 0~2 s, with different reference power settings for HTs secondary side. The reference active power, $P_2^{*}$, for the P–Q controller is set at −100 kW for the period of 0~1 s and at 100 kW for the period of 1~2 s. Once the simulation time reaches 2 s, the breaker PCC is opened, and the renewable energy system is disconnected from the main grid, converting the active distribution network to a passive one. In such a scenario, the control objective shifts from reverse power limiting to dynamic voltage regulation, and as a result, the control mode transits from the P–Q control to the V–f control (i.e., S_TM changes from 1 to 0). When HT is operating under V–f control mode during the period of 2~4 s, the reference secondary voltage of HT is set at 1 pu, aiming at maintaining a consistent supply voltage to the end-users. Once the simulation time passes 4 s, the breaker PCC is closed once again, and HTs control mode switches back to the P–Q control.

3.2.2. Scenario B-Dynamic Voltage Regulation Test

Intermittent renewable power generation can cause voltage rise and fluctuation issues, highlighting the importance of voltage management for active distribution networks [33]. Therefore, Scenario B is used to assess the dynamic control capability of HTs secondary voltage while keeping the primary voltage constant. In this manner, the dynamic adjustment of HTs secondary voltage will not impact the normal operation of the upstream grid. The testing sequence is organized as follows: for the simulation period of 0~1 s, breaker BRK1 remains closed, and the network operating condition is set to be the same as in Scenario A. During this interval, HT is operating in the P–Q control mode (i.e., S_TM = 1). When the simulation time reaches 1 s, breaker BRK1 is opened, leading to the disconnection of the renewable energy system. As the distribution network turns into passive operating mode, the control mode of VSC2 changes from the P–Q control to the V–f control (i.e., S_TM changes from 1 to 0), with HTs secondary reference voltage, $U_{1,pu}^{*}$, set at 1 pu. For the time periods of 1~2 s, 2~3 s, and 3~4 s, the reference values of HTs secondary voltage are defined as 1 pu, 1.1 pu, and 1.2 pu, respectively.

3.2.3. Scenario C-Upstream Voltage Fluctuation Immunity Test

Scenario C is being implemented to assess the immunity of HT to the voltage fluctuations in the upstream grid. Without secondary voltage management, the voltage fluctuation issue will propagate from the upstream grid to the downstream grid, ultimately impacting the supply voltage quality for the end-users. The testing sequence for Scenario C is organized as follows: The test setting for the time period of 0~1 s is the same with Scenario A and Scenario B, with the HT operating in P–Q control mode. Once the simulation time reaches 1 s, switch BRK1 is opened, and the V–f control is activated. Subsequently, at time intervals of 1~2 s, 2~3 s, and 3~4 s, the primary voltage of HT, U_1,pu, is adjusted to 1 pu, 1.05 pu, and 1.1 pu, respectively, while maintaining a constant reference secondary voltage of 1 pu.

3.3. Case Study Results

3.3.1. Simulation Results for Scenario A

The simulated results for Scenario A are given in Figure 9, Figure 10, Figure 11, Figure 12 and Figure 13. Figure 9 demonstrates that the DC-link voltage effectively tracks the reference, despite transient voltage fluctuations (about 10% of the reference value) occurring during the control mode transition. The secondary voltage frequency of HT also shows minor fluctuation (below 0.3 Hz) either due to the varying power flow conditions or the control mode transition. Figure 10 and Figure 11 show the zoomed-out voltage and current waveforms at 11 kV and 10 kV busbars. It is observed that the control mode transition has a negligible impact on HTs terminal voltage and current waveforms. Figure 12 shows that HTs terminal voltage level slightly varies under the P–Q control mode, and its variation depends on the power flow condition. Once the control mode transits to V–f control (i.e., 2~4 s), HTs secondary voltage is maintained constant at 1 pu. Figure 13 proves that HT under P–Q control mode can dynamically adjust its active and reactive powers according to the reference power settings, implying that the proposed HT design can effectively limit the reverse power flow.

3.3.2. Simulation Results for Scenario B

By implementing the corresponding testing sequence in the test network model, the simulation results for Scenario B are given in Figure 14, Figure 15, Figure 16, Figure 17 and Figure 18. Specifically, Figure 14 indicates that the DC-link voltage and secondary voltage frequency exhibit minimal fluctuation (below 1%) when the reference voltage changes. Figure 15 and Figure 16 show that the dynamic voltage regulation has a negligible impact on the stability of HTs terminal voltage and current waveforms. Figure 17 shows that the secondary voltage of HT is able to accurately track its reference without impacting the primary voltage. As shown in Figure 18, the power fluctuation under the V–f control is mainly determined by the voltage sensitivity of end-user power demand [34].

3.3.3. Simulation Results for Scenario C

By applying the testing sequence indicated in Figure 19 to the test network model, the simulation results are depicted in Figure 20, Figure 21, Figure 22, Figure 23 and Figure 24. Based on the simulation results, it can be inferred that the designed HT is capable of maintaining a constant supply voltage to the downstream end-users even in the presence of voltage fluctuations in the upstream grid.

3.4. Summary

Based on the aforementioned case studies, it can be concluded that the proposed HT configuration and the multi-mode control strategy equip HT with the capability of dynamic voltage regulation and reverse power suppression, making it a promising solution for active distribution network management. The performance evaluation of the suggested HT design under three scenarios is presented in

Table 2. Performance comparison of HT operating under three scenarios.

	Scenario A	Scenario B	Scenario C
Maximum DC-link voltage fluctuation	25%	3%	0.2%
Maximum secondary frequency fluctuation	0.25%	0.25%	0.24%
Maximum primary voltage fluctuation	0.05%	0.02%	0.02%
Maximum secondary voltage fluctuation	2.5%	2.5%	2%

. The fluctuation in the DC-link voltage is primarily attributed to the transition of control modes, as seen in Scenario A, whereas the dynamic voltage regulation under V–f control has minimal effect on the variation of DC-link voltage, as observed in Scenario B and Scenario C. In all three scenarios, the primary and secondary voltages of HT closely follow their respective references.

To demonstrate the superiority of the proposed HT design, we further compare its performance to those in existing literature, with the comparison results summarized in

Table 3. Performance comparison between existing solutions and the proposed approach.

The Design of HTs	Voltage Regulation (% of HTs Terminal Voltages)	Power Flow Control (% of HT’s Rated Power)
[7]	±5%	/ 1
[22]	±20%	/
[23]	±5%	/
[24]	±15%	60~88%
[25]	±20%	/
Proposed scheme	±20%	−25~25%

¹ The “/” symbol indicates that the HT design does not have the power flow control capability.

. These HT configurations are evaluated regarding their voltage regulation capability and power flow controllability, which are crucial functions for integrating HTs in the future smart grid context. As shown in Table 3, all HT designs reviewed are capable of regulating their terminal voltages within a specific range. The proposed HT design scheme can effectively maintain its terminal voltages within the range of 80% to 120% of their nominal value, thereby complying with the security operation requirements of distribution networks. Concerning power flow controllability, the HTs introduced in [7,22,23,25] adjust their reactive power preference in response to terminal voltage fluctuations or deviations without regulating the bidirectional active power flow. By incorporating a BESS system into HTs design, Ref. [24] achieves unidirectional active power regulation within a range of 60% to 88% of its rated power. However, none of the above literature investigates the potential of HTs in reverse power limiting. With the aid of the introduced multi-mode controller, the proposed HT design scheme has been demonstrated to effectively regulate bidirectional active power flow within a range of −25% to 25% of HTs rated power (a negative sign indicates reverse power limiting).

4. Conclusions

Due to its dynamic power flow control capability, HT is envisioned as a competing alternative to the traditional distribution transformer to deal with the growing complexity of active distribution networks. Currently, voltage rise and reverse power flow are the main challenges for active distribution network management. Previous research on HT design has predominantly focused on enhancing HTs dynamic voltage regulation capability, with less emphasis on the reverse power limiting requirement. To tackle the above issues, this paper presents a novel HT topology with a SiC-MOSFET-based BTB converter integrated. A multi-mode control strategy is further applied to the proposed HT configuration, allowing a seamless transition between dynamic voltage regulation and reverse power flow limiting. Based on the monitored HTs secondary supply voltage level and the power flow condition, either the V–f control or the P–Q control is activated. To verify the performance of the proposed HT design, a HT-integrated active distribution network is modeled in a PSCAD/EMTDC environment, and three representative operating scenarios of active distribution networks are applied as the case studies. It turns out that the proposed HT design exhibits excellent immunity to upstream voltage fluctuations of up to 20% of the nominal voltage. It also exhibits good voltage tracking performance during dynamic voltage regulation, with voltage overshoots during transitions remaining below 2.5% of the nominal voltage. Moreover, the proposed HT can accurately control the revere power flow to a value below its predetermined security limit. To sum up, case study results demonstrate that the proposed multi-mode control strategy can effectively resolve the voltage fluctuation and reverse power flow issues with satisfactory performance. Moreover, the multi-mode control strategy allows for a smooth transition between the V–f control mode and the P–Q control mode. This allows for maintaining constant voltage control when the penetration rate of renewable energy sources is low and for implementing reverse power limiting when the penetration rate exceeds the maximum capacity of the local distribution network. The proposed HT design ensures the safe integration of renewable energy systems while enhancing the power quality of active distribution networks.

As noticed in the case study section, the DC-link voltage exhibits varying degrees of fluctuations when switching the control mode or adjusting the reference voltage setting. Therefore, future work will involve proposing a novel DC-link voltage controller to enhance the dynamic response of the DC-link voltage. Also, advanced modulation strategies will be implemented to mitigate the harmonic and DC components. By doing so, the grid support capability of HTs can be further improved.