Journal of Control Science and Engineering

Volume 2016 (2016), Article ID 9537342, 13 pages

http://dx.doi.org/10.1155/2016/9537342

## An Improved Phase-Locked-Loop Control with Alternative Damping Factors for VSC Connected to Weak AC System

State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China

Received 12 October 2015; Revised 1 January 2016; Accepted 4 January 2016

Academic Editor: Ahmed M. Massoud

Copyright © 2016 Bin Yuan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The gains of phase-locked-loop (PLL) have significant impacts on the power transfer limits for the voltage source converter (VSC) connected to weak AC system. Therefore, in this paper, an improved PLL control, respectively, with alternative damping factors for rectifier and inverter is proposed. First, it is proved that the impedance angle of AC system has a great impact on the small-signal stability of the VSC system. With the same variation tendency of Thévenin equivalent resistance, the limits of power transmission are changing in opposite trends for rectifier and inverter. Second, the improved PLL with alternative damping factors is proposed based on the participation factor analysis. Third, the optimal damping factors of the improved PLL control for rectifier and inverter are calculated. Simulations and calculations validated the following three conclusions: (1) in rectifying operation, the equivalent system resistance has a negative impact on the stability of the system and this is not the case for inverting operation; (2) adding the alternative damping factors to PLL control shows similar results compared with changing the impedance angle of AC system; (3) the proposed optimal damping factors of PLL can effectively extend the power transfer limits under both rectifier and inverter modes.

#### 1. Introduction

Renewable energy resources are emerging as a future energy vector, and the voltage source converters (VSCs) are widely used to integrate such energies into power system [1–4]. The VSC-HVDC link connected to weak AC system with very low short circuit ratio (SCR < 2) will emerge quite often in the future [5–7]. However, the conventional vector-current control in - frame exhibits poor dynamic performance when applied to VSC connected to it. This brings a problem that the transmitted power cannot reach the ideal limitation for the unstable of small-signal model [8–17].

There are three possible approaches to solve this problem. The first approach is shown in [8], which proposed an advanced vector-current control to decouple the - outer-loop control completely by optimizing the control parameters. However, the provided method is quite complicated and it is not suitable for frequent and rapid power changing.

The second approach shown in [9] is adopting power synchronization control (PSC) as the main control strategy. PSC is similar with power angle control. This control strategy will not cause stable operating problems in extremely weak AC systems. However, it behaves in relatively low response speed due to the lack of the inner-loop current control and hence it cannot satisfactorily meet the requirement of the AC system.

The last approach shown in [10] is changing the parameters of phase-locked-loop (PLL), especially the proportional gain in PI controller. It has been recognized that the challenging for VSCs operating in weak AC system is caused by the PLL dynamics. The response speed and small-signal stability are contradictory characteristics of the system. With a high proportional gain, the system response becomes quicker while the power transfer limitations decrease. Further, [16] reported that PLL has negative impact on the stability of VSC connected to weak AC system with reduced order model. However, quite few literatures have attempted to optimize PLL control system to enhance the stability of VSCs connected to weak AC system.

This paper aims to propose an improved PLL control to extend the power transfer limitations. In the research of this work, it has been recognized that the impedance angle of weak AC system can also influence the power transfer limits. Meanwhile, an important observation is that for VSCs under different operation modes the equivalent resistance (related to the impedance angle directly) has opposite effects on the stability of VSCs. An advanced PLL with damping factor is proposed in this paper to enhance the power transfer limitations of grid-connected VSCs.

The rest of this paper is organized as follows. Section 2 presents the fundamental analysis of VSC connected to weak AC system. Section 3 studies the influence on power transfer limitations caused by impedance angle. Section 4 proposes an advanced PLL control system to enhance the stability of VSC connected to weak AC system. Section 5 verifies the proposed control by several case studies. And Section 6 concludes this paper.

#### 2. Small-Signal Model of VSC Connected to Weak AC System

##### 2.1. Benchmark Test Model

A two-level VSC is adopted in this paper as the topology. The test model is shown in Figure 1. The weak AC system is represented by a Thévenin equivalent circuit and the equivalent impedance is . The DC side of the converter is represented by a DC voltage source. With the consideration of the current limitation of transformer, a capacitor is shunted at PCC to provide reactive power compensation. is the leakage inductance of transformer and is the resistance between PCC and converter.