Robust control of electrical power systems using PSSs and Bilinear Matrix Inequalities

This work presents the application of Bilinear Matrix Inequalities to the robust adjustment of Power System Stabilizers with pre-defined structure. Results of some tests show that gain and zeros adjustments are sufficient to guarantee robust stability and performance with respect to various operating points. Making use of the flexible structure of BMIs, we propose an algorithm that guarantees a minimum damping factor specified for the closed loop system, always using a controller with flexible structure. The technique used here is the pole placement, whose objective is to place the poles of the closed loop system in a specific region of the complex plane. The BMIs are linearized using the homotopic method. Results of tests with a nine-machine system are presented and discussed, in order to validate the algorithm proposed.     

Robust excitation control design using sliding-mode technique for multimachine power systems

An output feedback controller is proposed to enhance the transient stability of nonlinear multimachine power systems considered as a classical model with flux decay dynamics. Combining high-order sliding-mode techniques with a robust high-order sliding-mode differentiator, a robust decentralized controller is obtained. Numerical results are presented to illustrate the performance of the proposed control scheme and its robustness properties.     

Robust gain-scheduled control for vibration suppression

Limited control authority is a key issue in the field of structural control and is a major research area since most of the practical control problems are dominated by constraints on the control signal. The paper presents a simple and practical gain-scheduled controller design procedure for active vibration suppression of a three-storey flexible structure. First, system identification experiments are performed and the plants uncertainty is derived. Next, robust controller design with constraint on the control signal is presented. For a better trade-off between control performance and control constraint a gain-scheduling approach is investigated. Stability analysis of the gain-scheduled controller is analysed using a parameter-independent Lyapunov function (quadratic stability) as well as a parameter-dependent Lyapunov function (biquadratic stability). Finally, the gain-scheduled controller is tested experimentally when the flexible structure is excited with a scaled historical earthquake record (1940 El Centro record). Successful experimental results show that the proposed robust gain-scheduled control approach offers good performance in the case of control authority limitation.Nomenclature M mass matrix - C damping matrix - K stiffness matrix - q relative displacement vector to base - m_a active mass - active mass acceleration - ground (base) acceleration - K_gap transfer gain of the displacement sensor - K_acc transfer gain of the acceleration sensor - K_AMD transfer gain of the active mass damper - _id frequency range of system identification experiments - r control reference - u control signal - d external disturbance - y control output - e control error - x state vector - p(t) time-varying parameter - N_p parameter boxs dimension - V(x) Lyapunov function - V(x,p) parameter-dependent Lyapunov function - largest parameter box where quadratic stability holds - S(s),T(s) sensitivity and complementary sensitivity transfer functions - G_n(s),G(s) transfer function of nominal and real plant - K_rate rate feedback gain - P_n(s) transfer function of nominal plant modified by rate feedback - P(s) transfer function of real plant modified by rate feedback - G_red transfer function of the reduced-order plant - _m(s) multiplicative uncertainty - W_S(s),W_T(s) performance and robustness weighting functions - G_c(s) controllers transfer function - G_c1(s),G_c2(s) transfer function of robust controller for vertex 1 and vertex 2 - G_cs(p,s) transfer function of the gain-scheduled controller - u_A amplitude of the control signal - K_min,K_max minimum and maximum controller gain - K(p) scheduled controller gain - J₁,J₂,J₃,J₄,J₅ performance evaluation parameters     

Interaction between phase shifting transformers installed in the tie-lines of interconnected power systems and automatic frequency controllers

FACTS devices like TCPAR can be used to regulate the power flow in tie-lines of interconnected power system. The transient state power flow occurring after power disturbances can be influenced by using TCPAR equipped with power regulator and frequency-based stabilizer. The analysis of a simple interconnected power system consisting of two power systems has shown that the control of TCPAR can force a good damping of both power swings and oscillations of local frequency. In the case of a larger interconnected power system consisting of more than two power systems, the influence of the control of TCPAR on damping can be more complicated. Strong damping of local frequency oscillations and power swings in one tie-line may cause larger oscillations in remote tie-lines and other systems. Hence the use of devices like TCPAR as tools for damping power swings and frequency oscillations in a large interconnected power system must be justified by detailed analysis of power system dynamics. In this paper, some results of time-domain simulations of a three-system area are presented. These results have proven that it is possible to obtain a good damping of tie-line power and frequency swings by optimizing the main parameters of TCPAR installed in tie-lines. The results have been confirmed by an eigenvalue analysis of linearized model of interconnected system consisting of three subsystems.     

Load modeling for wide area power system

The electrical loads have significant impacts on the dynamic performances of the wide area power system, and the dynamic behaviors of the power system can not be reproduced by the simulation system, unless the electrical load was modeled accurately. In the previous load modeling, the dynamics of the electrical load itself is of concern. Using such load models, the satisfied dynamic behaviors of the wide area power system can not be obtained by simulation. In this paper, a system-wide load modeling strategy is proposed. The electrical loads are firstly classified into a few categories using the component based load modeling method. According to the problems studied, the output variables of the power system are selected, and the objective function is constructed using the data from Wide Area Measurement System (WAMS). The trajectory sensitivities of the load model parameters with respect to the output variables are analyzed. Based on which, the key parameters playing important roles on dynamics of the power system are identified and included in further parameter estimation. The load models for the wide area power system are built simultaneously, and the system-wide load modeling method is implemented on the IEEE 39-bus system to evaluate its effectiveness.     

Saturated robust power system stabilizers

In this paper, a new saturated control design for uncertain power systems is proposed. The developed saturated control scheme is based on linear matrix inequality (LMI) optimization to achieve prescribed dynamic performance measures, e.g., settling time and damping ratio. In this design, the closed-loop poles are forced to lie within a desired region. The proposed design provides robustness against system uncertainties. The simulation results of both a single machine infinite bus and a multi-machine power systems are given to validate the effectiveness of the proposed controller.     

Robust multimachine power systems control via high order sliding modes

This article presents a formal study of the transient stabilization problem, including a stability proof. A decentralized nonlinear robust control scheme for multimachine electrical power systems is presented. The mathematical model takes into account the interconnections between electrical elements of the power system such as generators, electric networks, loads and exciters. Each generator is considered as a seventh order system that includes the mechanical and rotor electrical dynamics with static exciter dynamics. The proposed control scheme is based on the Block Control methodology and Second Order Sliding Modes technique using the Super Twisting algorithm. A nonlinear observer is designed to estimate the rotor fluxes of the synchronous machines. The designed decentralized control scheme requires the only local information for each local controller. This control scheme was tested through simulation on the well known reduced 9 buses equivalent model of the WSCC system.     

Study of a major oscillations event in northeastern area of the Iranian power network

Iranian power system encountered major oscillations in January 2008 in the northeastern area with an amplitude of about 120 MW. Since not all the events and variables had been recorded, a scenario to simulate the recorded oscillations and results of studies conducted to reproduce the oscillations by simulation are discussed in the first part. Tuning of supplementary controllers, such as PSSs, on the generating units and the use of reactive power compensators in the long transmission line to enhance stability and eliminate severe oscillations between the north and eastern areas are investigated in the second part. Eigen-value analysis and participation factors are used to appreciate the nature of oscillations and the required PSS settings. The results show that, by using the properly tuned PSSs and accurate compensation of the reactive power, transient stability and damping of oscillations are considerably improved.     

广域时滞电力系统控制器的优化算法及其应用

随着电力系统规模的不断扩大,控制信号在广域环境下产生的时滞现象会对电力系统的稳定运行产生难以忽略的负面影响。基于 Lyapunov稳定性理论,研究在时滞影响下,基于状态反馈的广域电力系统控制器的设计问题。首先,通过构造 Lyapunov-Krasovskii泛函,运用矩阵解析方法,得到了基于非线性的矩阵不等式结构;然后,将不等式中的非线性项做线性化处理,使其转化为隶属于线性矩阵不等式的锥补问题,在迭代求解时,对迭代次数进行了优化,平衡了迭代时间与时滞上界的关系。最后,通过仿真算例验证了所得控制器不仅具有较低的保守性,而且具有较快的响应速度,在工程上有较高的实用性。     

Robust decentralized PID-based power system stabilizer design using an ILMI approach

Thanks to its essential functionality and structure simplicity, proportional-integral-derivative (PID) controllers are commonly used by industrial utilities. A robust PID-based power system stabilizer (PSS) is proposed to properly function over a wide range of operating conditions. Uncertainties in plant parameters, due to variation in generation and load patterns, are expressed in the form of a polytopic model. The PID control problem is firstly reduced to a generalized static output feedback (SOF) synthesis. The derivative action is designed and implemented as a high-pass filter based on a low-pass block to reduce its sensitivity to sensor noise. The proposed design algorithm adopts a quadratic Lyapunov approach to guarantee α-decay rate for the entire polytope. A constrained structure of Lyapunov function and SOF gain matrix is considered to enforce a decentralized scheme. Setting of controller parameters is carried out via an iterative linear matrix inequality (ILMI). Simulation results, based on a benchmark model of a two-area four-machine test system, are presented to compare the proposed design to a well-tuned conventional PSS and to the standard IEEE-PSS4B stabilizer.     

Robust PID based power system stabiliser: Design and real-time implementation

This paper addresses a new robust control strategy to synthesis of robust proportional-integral-derivative (PID) based power system stabilisers (PSS). The PID based PSS design problem is reduced to find an optimal gain vector via an H∞ static output feedback control (H∞-SOF) technique, and the solution is easily carried out using a developed iterative linear matrix inequalities algorithm. To illustrate the developed approach, a real-time experiment has been performed for a longitudinal four-machine infinite-bus system using the Analog Power System Simulator at the Research Laboratory of the Kyushu Electric Power Company. The results of the proposed control strategy are compared with full-order H∞ and conventional PSS designs. The robust PSS is shown to maintain the robust performance and minimise the effect of disturbances properly.     

A robust SMES controller design for stabilization of inter-area oscillations based on wide area synchronized phasor measurements

This paper proposes a robust power controller design of superconducting magnetic energy storage (SMES) based on wide area synchronized phasor measurement units (PMUs) for stabilization of inter-area oscillation. The structure of active and reactive power controllers of SMES is the first-order lead/lag compensator. Assuming multiple PMUs are located in an interconnected power system, the steady state phasor data are obtained by applying the small load perturbation. Using the phasor data, the simplified oscillation model (SOM) included with SMES power controllers can be identified and applied to estimate the dominant inter-area oscillation modes. In the robust control design, unstructured system uncertainties such as various operating conditions, system parameters variation, etc., are represented by the inverse additive perturbation and included in the SOM. To enhance the system robust stability margin, the optimization of SMES control parameters is solved by genetic algorithm in the SOM. Simulation studies in the West Japan 6-machine power system confirm that the robustness of the proposed SMES is much superior to the conventional SMES against various operating conditions and fault locations.     

Stabilizing control of power system using fuzzy control

This paper presents an application of fuzzy control to enhance power system stability. The proposed control consists of the controller for large disturbance (FU 1), the fuzzy controller for small disturbance (FU 2), and the fuzzy judgment mechanism (FU 3). FU 1 is determined based on the fuzzy controller [FU 1(F)] is determined according to the control rules and its input signals, i.e., speed deviation and acceleration at every sampling time of the machine. FU 2 consists of two controllers, namely, FU 2-ω and FU 2-P; FU 2-ω has the same mechanism as FU 1, while the output signal of FU 2-P is determined according to the rules together with the change of error of electrical power and terminal voltage. To obtain the optimal desired control signal during both the large and the small disturbances, the operations of FU 1 and FU 2 are judged by FU 3, where the magnitude of speed deviation is chosen as its input signal. The determined control signal is fed to AVR of the machine. The implementation of the proposed control is simple due to the small amount of calculations and required data. The effectiveness of the proposed control is demonstrated by the one-machine infinite-bus system model and very good system performance is obtained throughout all the simulations.     

Optimal tuning of linear controllers for power electronics/power systems applications

This paper presents a new method for tuning various linear controllers such as Proportional-Integral (PI), Proportional-Integral-Derivative (PID) and Proportional-Resonant (PR) structures which are frequently used in power electronics and power system applications. The linear controllers maintain a general structure defined by the Internal Model Principle (IMP) of control theory. The proposed method in this paper is twofold. The first perspective uses the well-known concept of the Linear Quadratic Regulator (LQR) to address the problem as a regulation problem. The Q matrix of the LQR design is then finely adjusted in order to assure the desired transient response for the system. The second perspective redefines the LQR in order to add capability to address the optimal tracking problem and is then generalized to systems with more than two states. These methods are then applied to two specific examples, one in an uninterruptible power supply (UPS) inverter system and the other one in a distributed generation (DG) system. In these examples, the tuning of PR and PI controllers is studied in great detail. These proposed design methods provide an easy and algorithmic procedure without jeopardizing stability or robustness. These tuning methods can also be utilized for linear state-space realization of any power converters. Both examples are supported via simulation and the results, which confirm analytical derivations, are presented and discussed.     

Transient stability improvement by nonlinear controllers based on tracking

This paper deals with the control problem in multi-machine electric power systems, which represent complex great scale nonlinear systems. Thus, the controller design is a challenging problem. These systems are subjected to different perturbations, such as short circuits, connection and/or disconnection of loads, lines, or generators. Then, the utilization of controllers which guarantee good performance under those perturbations is required in order to provide electrical energy to the loads with admissible stability margins. The proposed controllers are based on a systematic strategy, which calculate nonlinear controllers for generating units in a power plant, both for voltage and velocity regulation. The formulation allows designing controllers in a multi-machine power system without intricate calculations. Results on a power system of the open research indicate the proposition’s suitability. The problem is formulated as a tracking problem. The designed controllers may be implemented in any electric power system.     

时变时滞不确定系统的鲁棒控制

基于二次稳定性理论,导出了时变时滞不确定系统鲁棒镇定的充分条件,应用ＬＭＩ方法,讨论了时变时滞不确定系统的鲁棒控制器设计问题,进而通过建立和求解不同的凸优化问题,给出了控制律满足不同指标要求的构造方法,最后给出一个算例,对该方法进行了验证。     

Decentralized nonlinear H∞ controller for large scale power systems

The aim of this paper is to design nonlinear decentralized controllers for multi-machine power systems. The design procedure is based on H_∞ control theory and consists of two parts. First, the feedback linearization technique is used. Then, a robust controller is designed using the linear matrix inequalities (LMI) approach. The controller has two blocks. One, is a nonlinear function of some local measurable signals such as the generator active and reactive powers, the rotor speed and the armature current. The other block is a PID controller. The linear H_∞ theory is used to tune the PID parameters. The method results in a controller which is easy for implementing in practice. The performance of the controller is tested on a sample multi-machine power system model. Simulation results show the effectiveness, robustness and good performance of the proposed controller.     

Robust analysis and design of load frequency controller for power systems

Robust load frequency control for power systems is discussed. A detailed robustness analysis of the existing control laws shows that parameter variation is not a critical issue but more attention should be paid to the unmodeled dynamics in robust load frequency controller design. A new robust load frequency control method is then proposed considering the unmodeled dynamics of power systems. Finally, a new configuration is proposed to overcome the effects of generation rate constraints (GRC). Simulation results show that the design method and the anti-GRC configuration are effective.     

Robust pole placement indirect adaptive control

The problem of designing a robustly stable pole placement indirect adaptive controller in the presence of output disturbances and unmodelled dynamics is addressed. The key features of such a design are the following. (1) The unknown parameters are estimated by a normalized least-squares algorithm with a dead zone to provide the stability robustness with respect to bounded disturbances and ‘small’ unmodelled dynamics. (2) The estimated model controllability is ensured by modifying the control law over a finite time. The modification involved consists of adding an internal impulse excitation and ‘freezing’ the controller parameters.     

采样控制系统鲁棒稳定性的时域方法

给出了采样控制系统鲁棒稳定性的一个充分条件。离散系统模式中的扰动是由连续系统的不确定性映象得到的,本文对特殊的指数不确定性结构,用Ｌａｐｌａｃｅ变换方法给出了等效离散系统扰动下一个谱范数估计的界。