A didactic procedure for designing power oscillation dampers of FACTS devices☆
Introduction
The benefits of Flexible AC Transmission Systems (FACTS) devices are widely recognized by power system practitioners and the T&D community for enhancing both steady-state and dynamic performances of power systems [1], [2], [3]. The advent of these devices has required additional efforts in modeling and analysis, requiring engineers to have a wider background for a complete understanding of power systems dynamic behavior.
From the students’ viewpoint, the challenge is to combine the knowledge of fields formally studied separately, such as electric machines, linear analysis, and control theory. This traditional organization allows the student focusing on each field independently, for a deeper understanding of the specific mathematical tools or the solution algorithms. Although this approach is well established, it does not facilitate merging mathematical tools and models of different areas in a wider and more complex context. As a consequence, students hardly get familiar with power system dynamics and interactions, even when having an adequate background.
Power systems analysis textbooks take the advantage of simplified test systems and models for consolidating the understanding of the “physical behavior” of power systems [4], [5], [6], [7]. Nowadays, the most popular approach consists in using research-oriented Matlab-based software tools [8], [9], [10]. Both textbook and software-based approaches usually illustrate power system behavior through the single-machine infinite bus (SMIB) system. In particular, reference [8] presents an interesting discussion about control design projects using the SMIB system at the undergraduate level.
The aim of this paper is to present a procedure to design power oscillation dampers (PODs) for FACTS devices in order to contextualize some concepts of control theory into power system stability. A variety of design methods can be used for tuning POD parameters. The most common techniques are based on frequency response [11], pole placement [12], eigenvalues sensitivities [13], [12], and residue method [14]. Recently, researchers have investigated robust control techniques for designing power system stabilizers [15], [12]. However, the classical phase compensation method is the most adequate as an educational tool. In addition, comparisons of performance have shown that controllers based on classical techniques can be as good as robust ones [15]. In this paper, the POD controller is designed using the frequency response method through Nyquist plots of a given Open Loop Transfer Function (OLTF).
The proposed procedure has been successfully used in assignments of the graduate course “Low Frequency Electromechanical Oscillations in Power Systems” at the University of Campinas (Unicamp), Brazil. Students’ feedback has shown that the simulations helped not only in learning about POD controller design, but also provided a better understanding of the dynamic behavior of power systems.
It is worth to note that the proposed procedure makes use of PSAT [16], an open source Matlab-based package. The advantage of this package lies in its flexibility and scalability. Using a simple interface, the student can set up both the conventional SMIB test system as well as more complex systems of “any” size. This is an advantage because FACTS devices and controllers perform better in meshed grids [17].
The structure of the paper is as follows. Section 2 presents a brief overview of the graduate course at Unicamp. Section 3 describes the power system model and its representation in state-space form. Section 4 presents the procedure for POD design. Sections 5 Example 1: Project with TCSC, 6 Example 2: Project with UPFC discuss two examples of assignments where students have to design PODs for different FACTS devices. Finally, Section 7 provides final remarks and draws conclusions.
Section snippets
Overview of the graduate course
The graduate course “Low Frequency Electromechanical Oscillations in Power Systems” is a semester long course offered at Unicamp. The problem of electromechanical oscillations is an issue of short-term power system angle stability [18]. The course covers the main topics in this area focusing on the concepts of synchronizing and damping torque [19]. The first part of the course covers load-frequency control and synchronous machine representation in stability studies. The second part introduces
Power system model
An electric power system can be represented by a set of non-linear differential-algebraic equations (DAE), as follows [5], [7]:where
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is the vector of the state variables;
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is the vector of algebraic variables (e.g., bus voltage magnitudes and phase angles);
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is a set of controllable parameters (e.g., controller reference signals);
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is a set of output variables (e.g., line current flows);
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is a set of differential equations that represents system and
POD design
The POD controller is designed using the frequency response method through Nyquist plots of a given OLTF. The general control diagram is depicted in Fig. 1. The Nyquist criterion allows to assess the closed-loop stability of a feedback system by checking the OLTF poles and plotting its frequency response [22], [23]. Closed-loop stability of the open-loop unstable system is obtained by ensuring an anti-clockwise encirclement of the -1 point of the complex plane in the Nyquist plot of the OLTF
Example 1: Project with TCSC
The test system for this case study is depicted in Fig. 4, and is taken from [5]. It comprises a thermal generation station consisting of four 555 MVA, 24 kV, 60 Hz units connected to an infinite bus through a step-up transformer followed by two transmission circuits. The four generators of the plant are represented by an equivalent one-axis model generator equipped with an automatic voltage regulator. The operating point corresponds to a heavy load condition in which the generators are delivering
Example 2: Project with UPFC
Fig. 10 shows a test system with an UPFC installed in series to one of the branches that connects Bus #8 to Bus #9. This two-area four-machine system is taken from [5]. The UPFC provides a series compensation of the line reactance and regulates the voltage at Bus #8. Fig. 10 also shows the POD controller. However, it has to be noted that POD should be included in the system only after the POD design procedure is completed.
The UPFC is represented by one series voltage source and by one shunt
Concluding remarks
The paper presents a didactic procedure for designing POD controllers of FACTS devices. The procedure is specially suited for solving assignments in a graduate course on power system stability and control. It can help students in learning both power system electromechanical oscillations and feedback control. For instance, a course that places emphasis on power systems behavior could approach optimal FACTS siting (the compromise between the best place for steady-state operation, and the best
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This work was supported by FAPESP and CNPq.