R. Eriksson and V. Knazkins / GMSARN International Journal 2 (2008) 15 - 20 15 Abstract— There are several possibilities to improve the small-signal stability in a power system. One adequate option is to make use of available power system components that possess high controllability properties such as, for instance, high voltage direct current (HVDC) systems. This paper presents results from a study aimed at the investigation of small-signal stability enhancement achieved by proper coordinated control of multiple HVDC links. Modal analysis was used as the main tool for the theoretical investigation. The obtained results indicate that the coordinated control of several HVDC links in a power system may assist achieving in an essential increase of damping in the power system. Another important conclusion from the paper is that the possibilities of the coordination of the HVDCs to a certain extent depend on the structure of the grid, which can be investigated by examining the controllable subspace of the linearzied model of the power system. Keywords— Coordinated control, HVDC, Modal analysis, Power System Stability. 1. INTRODUCTION Modern interconnected electric power systems are characterized by large dimensions and high complexity of the structure and the dynamic phenomena associated with the power system operation and control. Power system deregulation that took place in many countries worldwide was one of the driving forces that stimulated a fuller utilization of power systems, which in some cases lead to a reduced stability margin, as the power systems became more stressed. Under these circumstances it becomes quite important to seek new possibilities of enhancement of both transient and small-signal stability of the power systems. There are several obvious ways of improving power system stability, namely, (1) building new transmission lines, (2) installing new generation capacities, (3) better utilization of the existing equipment in the power system, or (4) a combination of the above. This paper is primarily concerned with third option, since compared to the other options it is less costly and can be easily implemented in a real power system. The central idea of the study presented in this paper is the utilization of several HVDC links for small-signal stability enhancement. The central purpose of conventional HVDC transmission is to transfer a certain amount of electrical power from one node to another and to provide the fast controllability of real power transfer. If the HVDC link is operated in parallel with a critical ac line the load-flow of the ac line can be controlled directly. The presence of an HVDC can assist in improving the stability margin in the power system [1]. In case there are several HVDC R. Eriksson (corresponding author) is with the Division of Electric Power Systems at Royal Institute of Technology, (KTH), Teknikringen 33, 100 44 Stockholm, Sweden. Email: robert.eriksson@ee.kth.se . V. Knazkins is with the Division of Electric Power Systems at Royal Institute of Technology, (KTH), Teknikringen 33, 100 44 Stockholm, Sweden. Email: valerijs.knazkins@ee.kth.se . links in the system, there is also a possibility of coordinating the HVDC links to enhance the operation of the system [by, for example, altering the load-flow patterns] and to improve the system stability evermore. The power systems are known to be operated most of the time in the so-called `quasi-steady state'. That is to say, the power systems are always subject to various— often small—disturbances [2]. A change in the loading level or capacitor switching is typical examples of such small disturbances that sometimes give rise to oscillations in the power system. The oscillations are often positively damped and their magnitudes decrease after a while thus the system remains stable. In case of negative damping of the oscillations the situation is opposite and may result in loss of synchronism unless preventive measures are taken. 2. CASE STUDY The aim of this paper is to perform modal analysis using coordinated control of two conventional HVDC links in a benchmark power system. This paper also explores the possibilities brought by the controllability and coordination of the HVDC links to enhance the rotor angle stability upset by a disturbance. In the benchmark power system, as is in all realistic cases, the turbine action is very slow compared to the fast controllability of the HVDC. The theory in this paper is based on small-signal analysis by linearizing the system around the stable or unstable equilibrium point. The modal analysis provides valuable information about the inherent dynamic characteristics of the system. By controlling the current through the HVDCs and using state feedback it is possible to move the eigenvalues to pre-specified locations in the complex plane and thereby increase the damping. 3. TEST POWER SYSTEM The system in this case study consists of three generators connected to nodes A, B, and C. The HVDC links are Robert Eriksson and Valerijs Knazkins On the Coordinated Control of Multiple HVDC Links: Modal Analysis Approach