Optimal metaheuristic-based sliding mode control of VSC-HVDC transmission systems

Highlights

• Nonlinear feedback control scheme for VSC-HVDC transmission system.

• Sliding Mode Control for system dynamic performance and stability improvement.

• Metaheuristic techniques for optimizing the Sliding Mode Control gains.

• Comparative study between the conventional SMC and the optimized-SMCs.

Abstract

The design of classical controllers for Voltage Source Converter High Voltage Direct Current (VSC-HVDC) transmission systems, is load-dependent and has to be adjusted for each operating condition. Thus, the robustness of such controllers becomes necessary to cope with operating condition continuous variations. Therefore, the design of hybrid optimal Artificial Intelligence Based-Sliding Mode Controllers (AI-SMCs) for VSCHVDC transmission systems is crucial research interest. These AI based controllers are proved to improve the system’s dynamic stability over a wide range of operating conditions considering different parameter variations and disturbances. For this purpose, a comprehensive state of the art of the VSC-HVDC stabilization dilemma is discussed. The nonlinear VSC-HVDC model is developed. The problem of designing a nonlinear feedback control scheme via two control strategies is addressed seeking a better performance. For ensuring robustness and chattering free behavior, the conventional SMC (C-SMC) scheme is realized using a boundary layer hyperbolic tangent function for the sliding surface. Then, the Modified Genetic Algorithm (MGA) and Particle Swarm Optimization technique (PSO) are employed for determining the optimal gains for such SMC methodology forming a modified nonlinear MGA-SMC and PSO-SMC control in order to conveniently stabilize the system and enhance its performance. The simulation results verify the enhanced performance of the VSC-HVDC transmission system controlled by both MGA-SMC and PSO-SMC compared to the C-SMC. The comparative dynamic behavior analysis for both the conventional SMC and the two meta-heuristic optimization based SMC control schemes are presented. Through simulation results, the effectiveness of the proposed metaheuristic optimization approaches and their applicability to VSC-HVDC system global stabilization and dynamic behavior enhancement are validated.

Introduction

Recently, the HVDC transmission systems play an ever-increasing role nowadays because of the wide expansion of generating electricity from Renewable Energy Sources (RESs) and the increasing demand for the interconnection of neighboring electricity markets. These challenges pave the way for more crucial research on HVDC transmission systems [2], [37].

The first commercial HVDC system, based on mercury valves, went into service in 1954 between the island of Gotland and Sweden. From that moment, HVDC technology has shown major evolutions, particularly regarding electronic devices and control systems. The modern advances in the power electronics field pave the way to thyristors and lately to Insulated Gate Bipolar Transistors (IGBTs) instead of mercury valves. Currently, HVDC can be considered as a mature technology with numerous installations spread all over the world as shown in Table 1 [20], [35].

As depicted in Fig. 1, there are two major HVDC technologies: Line Commutated Converter (LCC) Technology and Voltage Source Converter (VSC) Technology [9].

LCC systems are based on thyristors that offer a high-power transmission capacity. One of the main disadvantages of LCC technology is the commutation failure risk. These failures are usually caused by AC faults and can produce lack of power transmission for several cycles. For example, the parameter of biggest HVDC installation up to now using LCC, Changji-Guquan (China), is: 12 GW, $\pm$1100 kV Ultra High Voltage (UHV) and 3293 km [1]. Castro et al. (2015), have studied the Root Mean Square (RMS) model of the VSC-HVDC link. The model is useful for evaluating the steady state and dynamic responses of large power systems with embedded back-to-back and point to point VSC-HVDC links  [9].

VSC technology is based on IGBTs which can control both turn-on and turn-off. Accordingly, it is possible to control independently active and reactive power. IGBTs exhibit a high commutation frequency, in the kHz range. For that reason, low order harmonics are reduced and the filters size is relatively small compared to LCC. Other advantages are: the lack of commutation failure risk, black-start capability, no need for short-circuits ratio and smaller converter station size. VSC is also the most appropriate technology to implement multi-terminal systems, because of their control capabilities. The power flow can be reversed, with no need of reversing voltage polarity, as in LCC technology  [20].

A direct control voltage is modified by using a feed-forward controller and a non-linear compensation to improve the quality of a passive network where a VSC-HVDC transmission voltage is connected. Compensating the non-linearity of the proposed inverter maximizes the performance of the feed-forward control in d-q rotating axis. Thanks to this proposed method, the voltage fluctuations caused by sudden changes in load current is reduced [32].

On the other hand, numerous commutations in VSC technology can cause higher total power losses than LCC converters. Problems may appear when a weak grid is connected. In addition, Darabian et al. (2020) have analyzed the limitations on the power flow transfer through a VSC-HVDC system connected to weak grids. An external reactive power source such as Static Synchronous Compensator (STATCOM) or Static VAR Compensator (SVC) can be used for supplying reactive power and its controller design has been depicted [11].

However, the increasing power demand, combined with structural changes in energy markets, requires the use of versatile power electronics. Therefore, VSC technology is considered the most adequate for converter stations when performing the conversions. These conversions do not involve excessive changes in the towers, so the reconstruction time is not too long. Additionally, if only the necessary changes to adapt the AC lines to DC are made, the costs are lower and the required time can be smaller.

It must be pointed out that VSC is a continuously developing technology and thus, the drawbacks of VSC converters are being progressively reduced. In the domain of stability analysis of HVDC system, the progress is still apparent [20]. Amin et al. (2015), present the stability analysis of VSC-based​ HVDC system which includes controller dynamics and the main AC grid impedance. An analytical method has been developed to calculate the DC impedance of the converter. The proposed method has been verified in simulation. The system stability as long as impedance ratio satisfies the Nyquist criteria [5].

Hahn et al. (2015), provide a generic stability model of a self-commutated multilevel VSC-HVDC and its appropriate control. In this model, the independence of the AC and DC quantities has been depicted. Furthermore, the distributed capacitors of the sub modules have been taken into consideration for the model. The model has been then compared with an EMT model using controlled voltage sources and a high correlation between the models has been found. In view of a detailed large signal model with its entire control scheme, the model can be used for detailed power system stability studies [17].

Thanks to these researches and other technologies, many problems in VSC-HVDC are progressively solved. Accordingly, typical installations are implemented based on these up to date technologies.

For instance, in March 2011, China’s first VSC-HVDC project with completely independent intellectual property rights named China-Shanghai Nanhui VSC-HVDC demonstration project, has been successfully completed and started its trial operation [33].

Most HVDC system has used point to point connection but this method is inapplicable for a great distance. There are many reasons to build a multi-terminal HVDC system instead of having several separate points to point HVDC transmission systems [34]. Then, several projects and initiatives focus on the development of a Multi-terminal HVDC (MT-HVDC) grid. Li et al. (2019), present a large-scale Renewable Energy (RE) resources integrated with MT-HVDC, the aim is to economic optimally dispatch a large amount of uncertain power output to the AC grid [21].

There are strong nonlinear characteristics for the VSC-HVDC system, and therefore many limitations have seen in linear control methods, and one of the research focuses is nonlinear control theory for VSC-HVDC [33].

Moreover, a significant expansion of Renewable Energy (RE) involves offshore renewables, which are often realized large-scale projects located far from the centers of demand. One example is illustrated by Germany’s race to build new HVDC transmission corridors. They connect expanding RE in the North with demand centers in the South (Fairley, 2013a, 2013b). Another example is the Kriegers Flak project, a large offshore wind park including a “super grid” network, which would connect into the existing (onshore) transmission grids in Denmark, Sweden and Germany (Energinet.dk, 2014) [6]. Therefore, there are several technical discussions on offshore wind turbines. Thus VSC-HVDC is suitable for transmission of long distance offshore wind energy which has become one of the current research focuses [33].

For example, Benadja et al. (2015), have proposed sensorless control strategies for an Offshore Wind Farm (OWF), which is composed of hundred fifty Variable Speed Wind Turbines (VSWT) based on Permanent Magnet Synchronous Generators (PMSGs), and VSC-HVDC stations [6]. Wu et al. (2014), have developed the power transmission problem which becomes one of the key issues for restricting the development of offshore wind farms [33].

The HVDC transmission system based on a Three-Level Neutral Point Clamped Voltage Source Converter (3L-NPC VSC) has been used for the interconnection between the OWF and onshore grid via two DC cables. Singh. (2015), has studied the controllability on DC voltage, AC voltage, frequency, active and reactive power of VSC based HVDC links over conventional HVDC. The stability analysis for the two-terminal VSC based HVDC transmission system is performed. To integrate VSC based HVDC links into the networks consisting of large wind farms and other industrial systems, transient stability, voltage stability and frequency stability of the VSC based link have been checked. Furthermore, small signal stability of the link has been studied to ensure the system stability under small disturbances [31].

At the same time, it is widely agreed that concern policies are significantly lagging behind changes in electricity supply across Europe. Thus, this lagging threatens to constrain the energy transition. Nevertheless, there are indeed several policies established in order to assist the development. One point is climate policy. The need for a new transmission infrastructure is driven by climate policy, energy security and electricity markets integration. Noticeably, power systems across Europe need more transmission shore renewables [6]. Besides, the European Commission is now developing an infrastructure policy that integrates climate and energy goals. One outcome is “Energy infrastructure priorities for 2020 and beyond”, which identifies four priority electricity corridors (EC, 2010b).

There are also some specific policies for VSC-HVDC technology given the need of standardization. As the North Sea states, all start expanding their offshore infrastructure and the related regimes, they might develop national standards. The companies are also getting more advanced with VSC-HVDC technology. It would be more efficient to agree on a common voltage level from the outset instead of having to harmonize it in a few years.

In Germany, for example, the draft for an ‘Offshore Grid Development Plan’, which identifies the location and capacity of future offshore wind farms as well as the related infrastructure, introduces a standard of 7320 kV for DC transmission systems of converter stations (BSH, 2012).

In UK, there is currently no harmonized standard for offshore transmission assets. Lines with a voltage of 132 kV and higher are classified as offshore transmission assets, but only after they have been transferred to an OFTO (DECC, 2012).

This establishment of individual national standards may not be problematic at the beginning since it only concerns radial connections. However, this would mean that offshore assets build today would probably not be integrated into a future offshore grid. The different voltage levels that are currently applied demonstrate that it would be reasonable to introduce a common standard before the coastal states develop individual standards. A common voltage level would both allow for an efficient radial connection as well as the interconnection of different assets at a later stage.

Several organizations are possible to develop a standard policy such as: the European Committee for Electrotechnical Standardization (CENE-LEC), the International Electrotechnical Commission (IEC) and the Council on Large Electric Systems (Cigré). Two organizations are responsible for developing EU network codes including the Agency for the Cooperation of Energy Regulators (ACER) and the European Network for Transmission System Operators in Electricity (ENTSO-E).

Dash et Nayak. (2014), have proposed the design of a robust nonlinear controller for a parallel AC–DC power system using a Lyapunov Function-based Sliding Mode Control (L-SMC) strategy. The proposed controller for a three-phase power system including the VSC-HVDC link in parallel with AC transmission link produces a large damping in both the inter-area and local oscillations of the generators. The PI control has been used in the most common approach in the design of controllers for the VSC-HVDC system. However, PI control is inefficient and it takes several lead–lag blocks and coordinated control strategy when multiple oscillatory modes are present [7], [8], [16], [26].

The major contributions of this paper are the novel metaheuristic optimization techniques based SMC system and the relevant detailed analysis methods such as design procedure, stability and dynamic analysis. The novel SMC is a hybrid control design based on the referential integrity of both two different metaheuristic optimization techniques together with Lyapunov theorem. This novel SMC technique holds the advantages of hybridized complementary approaches while overcoming their well-known practical performance limitations. To effectively design the robust SMC that cope with the HVDC system, the modeling/parameter uncertainties are considered upon the controller design. The robustness of the proposed SMC is assessed via applying different conventional/meta-heuristic optimization techniques. Definitely, the proposed SMC scheme can be ideally considered for: (i) guaranteeing robustness of the proposed SMC; and (ii) providing better dynamic performance and stability through selecting the gains using metaheuristic optimization techniques in comparison with conventionally tuned controllers. Therefore, such novel technique can be generally adopted for further engineering applications.

The rest of the paper is organized as follows: Section 2 provides a concise definition for the HVDC system. In Section 3, an overview of the Sliding Mode Control is presented. The Metaheuristic MGA and PSO techniques are characterized and exhibited in Section 4. Simulation results are considered in Section 5. Finally, the conclusions and the perspectives are drawn in Section 6.