Nonlinear Control Design of Three-Level Neutral-Point-Clamped-Based High-Voltage Direct Current Systems for Enhanced Availability during AC Faults with Semi-Experimental Validation ^†

Abstract

This research paper addresses the issue of enhancing the operational availability of NPC three-level converter-based high-voltage direct current (HVDC) transport systems during alternating current (AC) grid fault conditions. During short-circuit faults in power transmission lines, voltage sags can occur, causing fluctuations in the DC link voltage of converter systems. These voltage sags have the potential to induce a reversed power flow and trip the VSC-HVDC transmission system. The objective of this paper is to develop a nonlinear control technique that investigates the fault ride-through (FRT) capability of VSC-HVDC transmission system characteristics during voltage sag events. To achieve this, we conduct semi-experimental investigations using Processor-in-the-Loop (PIL) simulations and analyze the results. Symmetrical and asymmetrical voltage sag events with different remaining voltages are applied to an AC grid, and their effects are observed for varying durations. The proposed nonlinear control technique aims to mitigate the impact of voltage sags on the operational availability of HVDC transport systems. By analyzing the semi-experimental results, we aim to gain insights into the FRT capability of the VSC-HVDC transmission system.

1. Introduction

In modern electrical power transmission, high-voltage direct current (HVDC) systems have emerged as vital components of the energy infrastructure, facilitating efficient long-distance electricity transmission due to their advantages such as efficient long-distance transmission and reduced transmission losses [1]. Beyond their traditional role in efficient power transfers, HVDC systems have also played a pivotal role in addressing one of the most pressing challenges of our time: the integration of renewable energy sources into the main grid [2,3].

The three-level neutral point clamped (NPC) converter, a type of VSC, plays a pivotal role in HVDC systems. It excels in providing precise voltage and frequency control, ensuring grid stability during grid disturbances and integrating renewable energy sources [4,5]. This bidirectional VSC allows for efficient power transmission in both directions, enabling the integration of renewable sources by sending excess power to the grid or balancing power flows [6]. Furthermore, the three-level NPC converter offers scalability and high-voltage ratings, making it an indispensable component for modern HVDC systems aiming for flexibility, reliability, and efficiency [7].

However, these systems face a significant challenge during alternating current (AC) grid fault conditions, particularly when voltage sags occur in power transmission lines [8]. Voltage sags, stemming from short-circuit faults, can lead to undesirable fluctuations in the DC link voltage of converter-based HVDC systems [9,10]. Such fluctuations not only endanger the system’s stability but also have the potential to induce a reversed power flow, ultimately tripping VSC-HVDC transmission systems [11,12].

Recognizing the critical importance of ensuring the uninterrupted operation of HVDC transport systems under adverse grid conditions, this research paper introduces and investigates a novel nonlinear control technique designed to enhance the fault ride-through (FRT) capability of VSC-HVDC transmission systems during voltage sags. Furthermore, we undertake a series of semi-experimental investigations employing Processor-in-the-Loop (PIL) simulations, closely examining the system’s response to both symmetrical and asymmetrical voltage sag events, each with varying remaining voltages and durations. The proposed nonlinear control technique aims to mitigate the adverse effects of voltage sags on the operational availability of HVDC transport systems, ensuring continuous and stable power transmission even in the face of AC grid faults.

The remainder of this paper is structured as follows: In Section 2, we present the features of the proposed HVDC system utilizing a three-level NPC converter, encompassing its modeling and control design. Section 3 provides an in-depth examination of the simulation results. Lastly, in Section 4, we summarize the key findings of this study and provide recommendations for future research directions.

2. Modeling and Control of the VSC-HVDC System

2.1. Mathematical Model of the Three-Level NPC HVDC System

Figure 1 presents an equivalent system model for the point-to-point HVDC system utilizing a three-level NPC converter. This system consists of two converter stations: $VS{C}_1$, which is considered as a sending station, and $VS{C}_1$ as a receiving station. Each station connects to an AC network through resistors $(R_1,R_2)$ and inductors $(L_1,L_2)$, representing the impedance of the AC lines. The DC sides of the converter stations are interlinked via an HVDC cable.

The mathematical model for the converter station on the AC side of the HVDC system is presented in a synchronous reference frame ($dq$) as follows [13,14,15,16]:

$$\begin{array}{}\mathrm{(1a)}& \begin{array}{cc}\hfill {\displaystyle \frac{d{i}_{d_1}}{dt}}& =-{\displaystyle \frac{R_1}{L_1}}{i}_{d_1}+{\omega }_1{i}_{q_1}+{\displaystyle \frac{e_{d_1}}{L_1}}-{\displaystyle \frac{u_{d_1}}{L_1}}\hfill \end{array}\mathrm{(1b)}& \begin{array}{cc}\hfill {\displaystyle \frac{d{i}_{q_1}}{dt}}& =-{\displaystyle \frac{R_1}{L_1}}{i}_{q_1}-{\omega }_1{i}_{d_1}+{\displaystyle \frac{e_{q_1}}{L_1}}-{\displaystyle \frac{u_{q_1}}{L_1}}\hfill \end{array}\mathrm{(1c)}& \begin{array}{cc}\hfill {\displaystyle \frac{d{i}_{d_2}}{dt}}& =-{\displaystyle \frac{R_2}{L_2}}{i}_{d_2}+{\omega }_2{i}_{q_2}-{\displaystyle \frac{e_{d_2}}{L_2}}+{\displaystyle \frac{u_{d_2}}{L_2}}\hfill \end{array}\mathrm{(1d)}& \begin{array}{cc}\hfill {\displaystyle \frac{d{i}_{q_2}}{dt}}& =-{\displaystyle \frac{R_2}{L_2}}{i}_{q_2}-{\omega }_2{i}_{q_2}-{\displaystyle \frac{e_{q_2}}{L_2}}+{\displaystyle \frac{u_{q_2}}{L_2}}\hfill \end{array}\end{array}$$

The DC side of the HVDC system is defined by the following equations [17,18]:

$$\begin{array}{}\mathrm{(2a)}& \begin{array}{cc}\hfill {\displaystyle \frac{d{V}_{dc1}}{dt}}& ={\displaystyle \frac{e_{d_1}{i}_{d_1}}{C_1{V}_{d{c}_1}}}-{\displaystyle \frac{i_c}{C_1}}\hfill \end{array}\mathrm{(2b)}& \begin{array}{cc}\hfill {\displaystyle \frac{d{V}_{dc2}}{dt}}& ={\displaystyle \frac{i_c}{C_1}}-{\displaystyle \frac{i_{inv}}{C_1}}\hfill \end{array}\mathrm{(2c)}& \begin{array}{cc}\hfill {\displaystyle \frac{d{i}_c}{dt}}& =-{\displaystyle \frac{R_c}{L_c}}{i}_c+{\displaystyle \frac{V_{d{c}_1}-V_{d{c}_2}}{L_c}}\hfill \end{array}\end{array}$$

The expressions for the active and reactive powers entering both VSC1 and VSC2 can be formulated as follows [19]:

$$\left\{\begin{array}{c}{P}_i=v_{d_i}{i}_{d_i}+v_{q_i}{i}_{q_i}=v_{d_i}{i}_{d_i}\hfill \\ Q_i=v_{d_i}{i}_{q_i}+v_{q_i}{i}_{d_i}=v_{d_i}{i}_{q_i}\hfill \end{array}\right.\mathrm{with}i=1\mathrm{or}2$$

(3)

2.2. Nonlinear Controller Design

The diagram presented in Figure 1 offers a concise overview of the VSC-HVDC system along with its corresponding control loops. Within this setup, VSC1 is assigned the crucial responsibility of regulating the DC voltage at the HVDC cable, denoted as Vdc1. On the other hand, the converter station VSC2 is dedicated to controlling the active power, thereby ensuring bidirectional active power transmission. Additionally, each converter station unit independently exercises control over the reactive power, adding an extra layer of flexibility and adaptability to the overall system operation.

The controller design was developed using the Backstepping and Lyapunov approach, as presented in [20,21]. The various control laws are derived as follows:

$$\begin{array}{}\mathrm{(4a)}& \begin{array}{cc}\hfill u_{d_1}& =L_1\left[c_1{e}_1-{\displaystyle \frac{R_1}{L_1}}{i}_{d_1}+{\omega }_1{i}_{q_1}+{\displaystyle \frac{e_{d_1}}{L_1}}-{\dot{i}}_{d_1}^{*}\right]\hfill \end{array}\mathrm{(4b)}& \begin{array}{cc}\hfill u_{q_1}& =L_1\left[c_2{e}_2-{\displaystyle \frac{R_1}{L_1}}{i}_{q_1}-{\omega }_1{i}_{d_1}+{\displaystyle \frac{e_{q_1}}{L_1}}\right]\hfill \end{array}\mathrm{(4c)}& \begin{array}{cc}\hfill u_{d_2}& =L_2\left[-c_3{e}_3+{\displaystyle \frac{R_2}{L_2}}{i}_{d_2}-{\omega }_2{i}_{q_2}+{\displaystyle \frac{e_{d_2}}{L_2}}+{\dot{i}}_{d_2}^{*}\right]\hfill \end{array}\mathrm{(4d)}& \begin{array}{cc}\hfill u_{q_2}& =L_2\left[-c_4{e}_4+{\displaystyle \frac{R_2}{L_2}}{i}_{q_2}+{\omega }_2{i}_{d_2}+{\displaystyle \frac{e_{q_2}}{L_2}}\right]\hfill \end{array}\end{array}$$

where $c_i(i=1,\dots ,4)$ are the controller gains and $e_i(i=1,\dots ,4)$ are the tracking errors between the $dq$-currents and their reference signals.

Remark 1. 

In light of page constraints, we have condensed and focused our content to adhere to the allotted six pages. As a result, some detailed discussions and additional material have been omitted.

3. Simulation Results and Discussion

In order to validate the practicality and efficiency of the proposed nonlinear control strategy for a three-level NPC converter within an HVDC transmission system, illustrated in Figure 1, a comprehensive design and implementation process has been executed. The specifications of the implemented HVDC systems can be found in

Table 1. Electrical parameters of the system under consideration.

Parameters	Symbols	Values
AC voltage	$V_{AC}$	220 KV
Frequency	$f_{1,2}$	50 Hz
AC inductor	$L_{1,2}$	50 mH
AC resistor	$R_{1,2}$	0.62 $\Omega$
DC side capacitor	$C_{1,2}$	200 $\mathsf{\mu }$F
DC cable inductor	$L_c$	0.082 mH/Km
DC cable resistor	$R_c$	8.02 m$\Omega$/Km

, while the relevant control parameters are given as follows: $c_1=700$, $c_2=1000$, $c_3=1200$, $c_4=700$. The outputs of $V_{dc1},Q_1,P_1$ and $Q_2$ were chosen as 200 KV, 0 Mvar, 100 MW, 0 Mvar, respectively. To assess the hardware implementation of the suggested control approach, a semi-experimental simulation incorporating the PIL test was performed. In this setup, real-time control signals are generated using the eZdsp F28335 Discovery board. Figure 1 illustrates the block diagram of the PIL test employed in this study. In this configuration, the plant model was simulated within the MATLAB/Simulink environment on the host PC, while the proposed controller was executed on the eZdsp F28335 Discovery board (Figure 2).

In this study, one case study has been performed, focusing on three-phase voltage sags occurring at the point of common coupling of Grid 2, referred to as PCC2.

In Figure 3a, we can observe the voltage behavior of $V_{dc1}$, which clearly demonstrates the precise tracking of the specified constant reference value ($V_{dc1}^{*}$ = 200 KV), while Figure 3b,c illustrates the temporal changes in the measured active power ($P_2$) and the reactive power for both sides ($Q_1$ and $Q_2$), along with their corresponding signal references. It is evident that these power values are impeccably controlled to match their reference values.

In the case under investigation, a three-phase voltage sag takes place at the PCC2 point, causing a uniform decrease of $60\%$ in the magnitude of the three-phase voltages ($v_2$) within a brief time window during the voltage sag, specifically from 1 s to 1.5 s, as depicted in Figure 3g. Throughout the period of the three-phase voltage sag that appears at PCC 2, the magnitude of the three-phase voltages ($v_1$) remains constant, as illustrated in Figure 3d. During the interval time [1 s, 1.5 s], we observe a reduction in the three-phase current $i_1$, as shown in Figure 3e, while Figure 3h illustrates that the three-phase current $i_2$ remains constant. As depicted in Figure 3f,i, it is clear that throughout the duration of the voltage sag, the DC power for both converter stations (VSC1 and VSC2) experiences a decrease.

The suggested control approach for the HVDC transmission system is aimed at maintaining power supply stability throughout the entirety of the voltage sag period, encompassing the periods before, during, and after the sag event. This signifies that the VSC-HVDC transmission system remains operational for power transmission from Grid 1 to Grid 2 even following the occurrence of a three-phase voltage sag in Grid 2.

4. Conclusions

This research paper addresses the issue of enhancing the operational availability of NPC three-level converter-based high-voltage direct current (HVDC) transport systems during alternating current (AC) grid fault conditions. The objective of this paper is to develop a nonlinear control technique aimed at mitigating the impact of voltage sags on the operational availability of HVDC transport systems. To achieve this, we conducted semi-experimental investigations using Processor-in-the-Loop (PIL) simulations. Through an analysis of the semi-experimental results, our aim was to gain insights into the fault ride-through (FRT) capability of the VSC-HVDC transmission system. The semi-experimental results demonstrate the effectiveness of the proposed method.

Looking ahead, future work in this domain will focus on further strengthening the adaptability of the nonlinear control technique. Specifically, we will explore the development of an adaptive nonlinear control system capable of dynamically responding to varying grid conditions. Additionally, our research will transition from semi-experimental simulations to full-scale experimental setups to enhance the real-world practical applicability of our findings.