An Effective Transformerless PUC7-Based Dynamic Voltage Restorer Using Model Predictive Control

Abstract

This paper investigates the performance of a seven-level Packed U Cell (PUC7) inverter-based transformerless Dynamic Voltage Restorer (DVR) topology under short-time voltage variations (voltage sags and swells). Unlike the existing multilevel inverter (MLI)-based DVR solutions, the proposed structure requires only one DC voltage source (suitable for PV-based DVR systems), one capacitor, and six switching devices to generate seven-level output voltage. Moreover, the studied topology is characterized by reduced cost and size due to the elimination of the injection transformer. The PUC7 inverter is controlled using a multi-objective (filtering current, compensating voltage, and PUC capacitor voltage controls) Model Predictive Control (MPC) strategy. Simulation and implementation tests are carried out to demonstrate the high performance of the proposed DVR at steady-state and during transient conditions, while keeping the load voltage unaffected by the disturbances in the grid voltage.

1. Introduction

Currently, renewable energy (RE) is significantly and progressively attracting attention worldwide. RE involves natural energy sources that deliver electrical power without emitting greenhouse gases. Such sources have been used to guarantee power delivery to remote locations without making changes to transmission/distribution networks (standalone applications) and/or to provide support to the utility in case of failures (grid-connected applications). Thus, RE has become a priority in the energy sector for many countries. Photovoltaic (PV) energy has recently shown the highest investment potential among RE. In this regard, the demand for PV has been growing steadily at a pace of almost 25% per year over the past two decades, particularly for grid-tied applications. This accelerating development is associated with significant and challenging requirements for power conversion such as flexibility, reliability, modularity, performance, and quality [1].

Moreover, loads connected at the point of common coupling (PCC) are subject to voltage sags/swells occurring in the utility system. These short-time voltage variations can easily halt the operation of industrial and domestic equipment causing unplanned equipment failures and shutdowns. Therefore, reliable/high-quality power delivery at the PCC is an indispensable requirement [2]. Dynamic voltage restorers (DVRs) are widely employed in series with the grid voltage to inject the needed compensation to maintain the voltage of the load at the required level during voltage sags/swells. A basic DVR consists of a DC power supply, an inverter, a filter, and a transformer [3,4,5,6,7,8,9]. Thus, the use of PV as a clean power supply appears to be an obvious choice in DVR systems to target an effective compensation and keep the load voltage unaltered from grid voltage disturbances.

Many power electronic converter configurations have already been used for DVR applications. In [10,11], the DC input voltage of the voltage source inverter (VSI) is obtained from the AC utility voltage using a controlled three-phase rectifier. Many transformerless DVR topologies were presented in [12,13,14,15] where the compensating voltage is injected using a series connected capacitor. Transformerless DVR is suitable for use in residential environments due to its reduced volume. Furthermore, multilevel inverter (MLI)-based DVR topologies with the aim of improving the load voltage quality are also widely studied [16,17,18,19,20,21,22,23,24]. The cascaded H-bridge inverter-based DVR topologies proposed in [16,17] can be connected to PCC without a transformer, but require isolated DC source for each H-bridge inverter. In addition, three H-bridge inverters are necessary to achieve a seven-level load voltage, requiring 12 bidirectional switching devices. In [18], the application of a transformer-coupled cascaded H-bridge inverter-based DVR requiring only one DC source is investigated. In [19,20], flying capacitor inverter (FCI)-based DVR topology is introduced. In general, an FCI with M levels requires M-1 pairs of switching devices and M-2 flying capacitors. Hence, for a seven-level load voltage, FCI based DVR topology requires 12 switching devices and five flying capacitors. However, the FCI topology is characterized by an easier extension for higher voltage levels compared to neutral point clamped (NPC) inverter topology [20,21]. Different from FCI and NPC, other MLI-based topologies have been studied in the literature such as stacked multicell [23] and T-type inverters [23]. The common drawback of the aforementioned topologies is the exponential increase in the number of active/passive elements for higher voltage levels.

In this paper, the feasibility of a transformerless PV-based DVR topology [25] employing a seven-level packed U cell (PUC7) inverter is investigated. PUC inverters are single-DC-source MLI topologies (SDCS-MLI) characterized by their ability to generate higher output voltage levels with a single DC supply and their control flexibility, taking advantage of the redundant switching states. PUC topology outperforms most existing SDCS-MLIs in terms of reliability, high voltage ride through capability (capacitors as storage elements), and reduced cost (less number of switching devices) [26,27,28,29]. Unlike existing MLI-based DVRs, the proposed system requires only one DC source, one capacitor, and six switching devices.

Table 1. Comparison between the existing most common MLI-based DVR solutions.

DVR Topology	Advantages	Disadvantages
Two-level Inverter	Easy implementation Reduced cost	High switching frequency High switching losses Decreased efficiency
NPC Inverter	Easy implementation	Clamping diodes Extra control to deal with the unbalance of the capacitor mid-point voltage
T-type Inverter	Lack of clamping diodes Higher efficiency (NPC) Lower cost (NPC)	Extra control to deal with the unbalance of the capacitor mid-point voltage
CHB Inverter	Reduced harmonic content	Multiple DC-source High cost
FCI Inverter	Single DC-Source Easy extension for higher voltage levels	Challenging control High number of components High cost
PUC Inverter	Minimum number of components Single DC-Source Easy extension for higher voltage levels Reduced cost	Challenging control

presents a comparison between the existing most common MLI-based DVR solutions.

To inject a compensating voltage with appropriate amplitude and phase angle (comparison of the desired load voltage and the measured line voltage), a suitable control strategy should be applied to the PUC-based DVR. Therefore, a model predictive control (MPC) approach is proposed in this paper to control the compensating voltage, the filtering current, and the capacitor voltage of the PUC topology. A cost function regrouping the control objectives is minimized to select the optimal switching state at each sampling time.

The paper is structured as follows: The topology and modeling of the proposed DVR are discussed in Section 2. Section 3 details the MPC design, while Section 4 presents and discusses the simulation and implementation results. Finally, Section 5 concludes the paper.

2. PUC-Based DVR Topology and Modeling

2.1. Topology

The seven-level PUC structure is built by cascading three cells, where each of the cells is created by encompassing one capacitor/DC voltage source by two switches (controlled in a complimentary manner). It is worth noting that the voltage V₂ across the capacitor C₂ should be regulated at 1/3 of the DC input voltage V₁ (V₂^* = V₁/3). Figure 1 shows the proposed transformerless PUC-based DVR topology. The compensating voltage (V_comp) is injected to the system via series-connected capacitor C_comp. It is obvious that this topology does not require an injection transformer which reduces the cost and volume of the DVR.

The switching patterns (S_i denotes the switching state of the switch i = 1…3 while S’_i denotes the switching state of the complementary switch) and the corresponding generated levels of the output voltage are illustrated in

Table 2. Switching patterns of the PUC7 inverter.

State	VAN	S1	S2	S3
1	0	0	0	0
2	−V2	0	0	1
3	V2 − V1	0	1	0
4	−V1	0	1	1
5	V1	1	0	0
6	V1 − V2	1	0	1
7	V2	1	1	0
8	0	1	1	1

.

2.2. Modeling

The state variables are selected to be (i) the compensating voltage V_comp(t), (ii) the filtering current i_f(t), and (iii) the PUC capacitor voltage V₂(t). Applying Kirchhoff’s current and voltage laws, the first order differential equations related to the selected three state variables are given by:

$$C_{comp}\frac{d{V}_{comp}(t)}{dt}=i_f(t)+i_g(t)$$

(1)

$$C_2\frac{d{V}_2(t)}{dt}=\left(S_3-S_2\right)i_f(t)$$

(2)

$$L_f\frac{d{i}_f(t)}{dt}=V_{AN}(t)-V_{comp}(t)-r_f{i}_f(t)$$

(3)

3. MPC Design

A multi-objective finite control set MPC (FCS-MPC) is applied to the studied DVR system. The compensating voltage V_comp(k + 1), the filtering current i_f(k + 1), and the PUC capacitor voltage V₂(k + 1) are predicted for the different switching configurations. Thus, the aforementioned state equations can be approximated at each sampling time T_s using the Taylor expansion given in (4) by Equations (5)–(7).

$$x\left(k+1\right)\approx x\left(k\right)+\dot{x}\left(t\right).T_s$$

(4)

$$V_{comp}(k+1)=V_{comp}(k)+\frac{T_s}{C_{comp}}\left(i_f(k)+i_g(k)\right)$$

(5)

$$V_2(k+1)=V_2(k)+\frac{T_s}{C_2}\left(S_3-S_2\right)i_f(k)$$

(6)

$$i_f(k+1)=i_f(k)\left(1-\frac{r_f}{L_f}{T}_s\right)+\frac{T_s}{L_f}\left(V_{AN}(k)-V_{comp}(k)\right)$$

(7)

Figure 2 shows the general view of the proposed MPC approach. The tracking errors are computed from the desired values and the predicted state variables for the eight switching configurations, and then incorporated into the cost function g given by Equation (8). Next, the switching pattern that minimizes g is chosen and applied to the converter during the next sampling time. It is worth mentioning that λ_comp is used as a weighting factor to adjust the control priorities.

$$g=\left|V_2^{*}(k+1)-V_2\left(k+1\right)\right|+{\lambda }_{comp}\left|V_{comp}^{*}(k+1)-V_{comp}\left(k+1\right)\right|+\left|i_f^{*}(k+1)-i_f\left(k+1\right)\right|$$

(8)

For the sake of simplicity, the reference values of the filtering current i_f^*(k + 1) and the compensation voltage V_comp^*(k + 1) are supposed to be equal to those at (k) sampling time, which are calculated by:

$$i_f^{*}\left(k\right)=i_{comp}\left(k\right)-i_L^{*}(k)$$

(9)

$$V_{comp}^{*}\left(k\right)=V_L^{*}(k)-V_{grid}(k)$$

(10)

where the reference load current $i_L^{*}(k)$ is computed using Ohm’s law from the reference load voltage $V_L^{*}(k)$.

4. Simulation and Real-Time Implementation Results

A Matlab/Simulink environment is used in this paper to simulate the proposed DVR system. Moreover, a dSpace 1103 controller board is employed to enable the dynamic real-time simulation responses and validate the results. The system parameters used in both simulation and real-time validations are illustrated in

Table 3. Parameters used for simulation and real-time implementations.

Parameters	Values
AC grid RMS voltage (Vgrid)	230 V
Input voltage (V1)	400 V
Filter inductor (Lf)	0.7 mH
Filter internal resistor (rf)	0.5 Ω
Filter capacitor (Ccomp)	50 μF
PUC capacitors (C1, C2)	100 μF
Grid inducor (Lg)	0.1 mH
Load inductor (LL)	10 mH
Load resistor (RL)	50 Ω
Sampling time (Ts)	35 μs

, while the setup of the system’s real-time implementation is shown in Figure 3.

To verify the effectiveness of the proposed system, several tests were performed by introducing line voltage dips and swells. Figure 4 and Figure 5 show the simulation and implementation results of the line voltage, compensation voltage, and load voltage during a short period of decrease in the rms value of the line voltage (five cycles voltage dip). The produced compensating voltage remains null before the line voltage drops. When the voltage sag occurs, the required compensating voltage is generated to maintain the sensitive load voltage at the required level.

Moreover, the ability of the proposed DVR to mitigate the voltage drops when the input voltage changes (a step-down change from 400 V to 350 V) is illustrated in Figure 6 and Figure 7.

Another test was performed by emulating a grid voltage swell. The corresponding simulation and implementation results are presented in Figure 8 and Figure 9. One can notice that the proposed PUC-based DVR system injects a compensating voltage with 180° phase shift compared to the line voltage to keep the load voltage unaffected.

Figure 10 and Figure 11 show the FFT spectrums of the grid and load voltages with the respective voltage THD values. One can notice that Figure 11 confirms the effectiveness of the proposed PUC7-based DVR solution in protecting the load voltage (voltage THD around 1%) against the grid voltage disturbances (voltage grid THD around 15% during voltage sag/swell operating conditions as depicted by Figure 10). This reduced voltage THD at the load side is due to the produced multilevel output voltage (seven-level output voltage) at the inverter side.

The dynamics of the different currents flowing in the proposed DVR system (load current, compensation current, and filtering current) during line voltage sag/swell events are illustrated in Figure 12, Figure 13, Figure 14 and Figure 15. Obviously, during normal operating conditions, no current will be flowing across the compensation capacitor. As a result, the filtering current is 180° phase shifted from the load current (i_f = −i_L). At the voltage sag/swell events, a compensating sinusoidal current is produced to make i_comp = i_L + i_f.

5. Conclusions

This paper proposed a transformerless Packed U Cell (PUC)-based dynamic voltage restorer (DVR) solution for single-phase PV systems. The investigated topology is characterized by its lowered cost and size due to the exclusion of the injection transformer. The aim of the proposed system is to produce a compensation voltage during grid voltage sag/swell events to keep the load voltage unaffected. An effective finite control set model predictive control (FCS-MPC) strategy was proposed to ensure the generation of the required compensating voltage while regulating the filtering current and the PUC capacitor voltage around their references throughout the line voltage disturbances. Theoretical study, simulation, and real-time implementation results were presented, during normal and disturbed operating conditions, to demonstrate the high dynamic performance and the effectiveness of the proposed solution. However, the computational burden remains a challenge for FCS-MPC techniques due to the real-time calculation constraints. Another emerging research axis concerns the tuning of the weighting factors to sort the priorities of the control objectives in the control decision. Artificial intelligence-based algorithms could play an important role in the auto-tuning process of the weighting factors and deal with the codependency of the control objectives.