When an inter-area mode dominates a low-frequency oscillation in a stressed condition, control of the active power flow of interface lines, with compensating devices, can effectively reduce the electromechanical power oscillations. In general, interface lines in which inter-area oscillations are large are considered to be good locations for installation of compensating devices. A sensitivity analysis with respect to change in active power flow can provide an important factor in electric power system operation. This paper proposes a new methodology to calculate the damping sensitivity with respect to change in active power flow, which can be useful for accurate selection of critical lines from the viewpoint of small-signal stability. In the proposed methodology, a damping sensitivity index is used to select the critical lines to damp power system oscillations. This paper describes how to derive the damping sensitivity for the selected mode and illustrates an example applying the proposed algorithm to a simple two-area system and the New England 39-bus test system.
With the advent of deregulation and privatization in the power market and the increasing trend of interconnection of power grids, many interconnected power systems worldwide experience low-frequency oscillation phenomena [1] and [2]. The need for analyzing the eigenvalue problems of these kinds of power systems is more gaining in order to obtain the reliable and secure operation of power systems. As the system becomes more stressed, weak transmission links and unexpected events may lead to a problem related to a low-frequency inter-area oscillation of small-signal stability. This problem even can cause a major system breakdown. When subjected to a disturbance, the eigenvalues will experience some change. The causes of low-frequency oscillation phenomena in a power system are mainly correlated with system structure, excitation systems, disturbances, and operating conditions. The active power flows on transmission lines, especially, are closely related to those kinds of conditions. In recent times, the use of flexible AC transmission systems (FACTS) devices has become a common practice in order to enhance the damping of inter-area power swings by controlling the active power through an interface line [3] and [4]. In this respect, the changes in the critical eigenvalues associated with the inter-area mode will affect the selection of the best installing location.
Many authors have researched this topic and have proposed various indices as documented in the literature [5], [6], [7], [8], [9], [10], [11], [12] and [13]. These research efforts can be categorized into two methods. One is the residue technique, which is based on the modal control theory of linear time-variant systems. In [5], the location index for effective damping was proposed to find the suitable locations of compensating devices using the sensitivities of generator output power with respect to variable impedance. The other method is the damping torque analysis method, which is based on a physical understanding of the electromechanical oscillations of power systems. Application of the controllable series compensator in damping power system oscillations using the basis on the Phillips-Heffron model has been investigated in [7]. Recently, an estimation technique for on-line damping torque to provide information associated with poorly damped modes is proposed [12]. Consequently, those works have focused on the effects of general operating parameter changes on system performance. In large-scale interconnected power systems, the power flow oscillation on transmission lines affected by inter-area modes may depend on several machines and loads. It is known that the inter-area modes participated in hundreds of machines are more sensitive to the change in the power flow on critical lines [14] and [15]. Therefore, a study of the eigenvalue sensitivity analysis with respect to the change in power flow oscillation on transmission lines may provide more clear insight on the inter-area oscillations than those by general system parameters. The objective of this paper is to determine the dominant interface line associated with the inter-area oscillation.
In this paper, we propose a new damping sensitivity analysis with respect to the change in active power flow of interface lines. We first introduce the identification of the critical eigenvalues associated with inter-area oscillation modes. Then the damping sensitivity index with respect to active power flow for the identified modes is then calculated. The proposed method is available to obtain information regarding the changes in the eigenvalues associated with the inter-area mode. Finally, a procedure for determining the critical lines from the viewpoint of small-signal stability is presented. The proposed method was tested on a simple two-area system and the IEEE 39-bus New England test system. In addition, the numerical results are validated through comparative simulations with Small Signal Analysis Tool (SSAT) [16]. The test and results shows the capabilities of the proposed method.
This paper is organized as follows. Damping sensitivity method is proposed to identify the critical lines in Section 2. Formulations regarding the implementation needed for the damping sensitivity analysis are provided in Section 3. The proposed ideas are illustrated with numerical tests in Section 4. Some comments about future work and conclusions are discussed in Section 5.
This paper presents a new method for the identification of critical lines in small-signal stability. To identify critical lines, the new damping sensitivity index with respect to change in active power flow was proposed. This damping sensitivity was obtained from eigenvalue sensitivity with respect to change in active power flow and the damping ratio of the eigenvalue associated with the inter-area mode.
In addition, we proposed a procedure to identify the critical lines for determining the optimal location of compensating devices. Numerical tests showed that the proposed sensitivity method provided an indication of the qualitative change in the dynamic behavior resulting from the change in system conditions and parameters. Furthermore, the results of a comparative study using SSAT show the benefits of the proposed method that can select the best installing location of FACTS devices.
