Abstract: The Unified Power Flow Controller (UPFC) is the one of the FACTS devices which can control power system parameters such as terminal voltage, line impedance and phase angle. The UPFC is not only power flow controller but also power system stabilizing controller. The UPFC is a combination of Static synchronous Compensator (STATCOM) and a Static Synchronous Series Compensator (SSSC) which are coupled via a common dc link to allow bi-directional flow of real power between the series output terminals of the SSSC and the shunt output terminals of the STATCOM. UPFC is the one FACTS device which can control real and reactive power flow. UPFC can control the power system parameters such as terminal voltage, line impedance and phase angle. UPFC control provides additional damping during oscillations. The dynamic models of UPFC are used to design suitable controllers for power flow, voltage and damping controls. Fuzzy logic controller based UPFC is taken in this research. The parameters of UPFC (m_B, m_E, δ_B and δ_e) can be modulated for achieving desired damping in the system. The performance of the four UPFC based damping controllers (m_B, m_E, δ_B and δ_E ) and fuzzy based controllers are investigated under wide variations of the loading conditions in this research. A Single-Machine-Infinite-Bus (SMIB) system installed with UPFC is considered. The static excitation system model type IEEE-ST1A has been considered in this study. The UPFC considered here is assumed to be based on Pulse Width Modulation (PWM) converters.

INTRODUCTION

UPFC is the one FACTS device which can control real and reactive power flow. UPFC can control the power system parameters such as terminal voltage, line impedance and phase angle. UPFC control provides additional damping during oscillations.

The dynamic models of UPFC are used to design suitable controllers for power flow, voltage and damping controls (Nabavi-Niaki and Iravani, 1996; Smith et al., 1997; Makombe and Jenkins, 1999; Papic et al., 1997; Morioka et al., 1999; Wang, 1999). Modified Linearised Heffron-Phillips model of a power system installed with UPFC is taken in this research fuzzy logic controller.

The parameters of UPFC (m_B, m_E, δ_B and δ_E) can be modulated for achieving desired damping in the system. The performance of the four UPFC based damping controllers (m_B, m_E, δ_B and δ_E) are investigated under wide variations of the loading conditions in this research.

MATERIALS AND METHODS

System investigated: A Single-Machine-Infinite-Bus (SMIB) system installed with UPFC is considered as shown in Fig. 1. The static excitation system model type IEEE-ST1A has been considered in this research.

Fig. 1:	UPFC installed in a SMIB system

The UPFC considered here is assumed to be based on Pulse Width Modulation (PWM) converters. The nominal loading condition and system parameters are given:

Generator:

Excitation system:

Transformers:

Transmission line:

Operating condition:

UPFC parameters:

DC link parameters:

Modified Heffron-Phillips small perturbation transfer function model of a SMIB system including UPFC: The small perturbation transfer function block diagram of a machine-infinite bus system including UPFC relating the pertinent variables of electric torque, speed, angle, terminal voltage, field voltage, flux linkages, UPFC control parameters and dc link voltage is used in this research as shown in Fig. 2. This model has been obtained (Wang, 1999, 2000) by modifying the basic Heffron-Phillips model including UPFC. In Fig. 2, Δu is the column vector while [K_pu], [K_qu], [K_vu] and [K_cu] are the row vectors as defined:

Fig. 2:	FLC building blocks

Fig. 3:	Structure of UPFC based damping controllers

The control parameters of UPFC are:

Design of damping controllers: The damping controllers are designed to produce an electrical torque in phase with the speed deviation. The four control parameters of the UPFC (m_B, m_E, δ_B and δ_E) can be modulated in order to produce the damping torque.

The speed deviation Δω is considered as the input to the damping controllers. The four alternative UPFC based damping controllers are examined in this research (Table 1).

The structure of UPFC based damping controller is shown in Fig. 3. It consists of gain, signalwashout and phase compensator blocks.

Table 1:	Eigen values of the closed loop system

Table 2:	Parameters of the UPFC based damping controllers

Structure of UPFC base damping controllers: The parameters of the damping controller are obtained using the phase compensation technique (Gyugyi, 1992) (Table 2). The phase compensation technique is used to find out the damping control parameters. The detailed step-by-step procedure for computing the parameters is given as:

The phase lead/lag compensator Gc is designed to provide the required degree of phase compensation. For 100% phase compensation:

Assuming one lead-lag network T₁ = aT₂; the transfer function of the phase compensator becomes:

Since, the phase angle compensated by the lead-lag network is equal to -γ, the parameters a and T₂ are computed as:

Computation of optimum gain K_dc. The required gain setting K_dc for the desired value of damping ratio ζ = 0.5 is obtained as:

where, |Gc (s)| and |GEPA (s)| are evaluated at s = jω_n.

Table 3:	Gain and phase angle of the transfer function GEPA

Fig. 4:	Transfer function of the system-relating component of Electrical power (ΔPe) produced by the damping controllers

The signal washout is the high pass filter that prevents steady changes in the speed from modifying the UPFC input parameter. The value of the washout time constant T_w should be high enough to allow signals associated with oscillations in rotor speed to pass unchanged.

From the viewpoint of the washout function, the value of T_w is not critical and may be in the range of 1-20 sec. T_w is equal to 10 sec is chosen in the present research.

Figure 4 shows the transfer function of the system relating the electrical component of the power produced by the damping controller (m_B). The time constants of the phase compensator are chosen so that the phase lag/lead of the system is fully compensated. For the nominal operating condition, the natural frequency of oscillation ω_n = 4.0974 rad sec^-1.

The transfer function relating ΔP and Δm_B is denoted as GEPA. For the nominal operating condition, phase angle of GEPA, pGEPA = 9.057° lagging. The manitude of GEPA, ,GEPA, = 0.6798. To compensate the phase lag, the time constants of the lead compensator are obtained as T₁ = 0.2860 and T₂ = 0.2082 sec (Table 3).

Fuzzy logic controller: In the conventional control, the amount of control is determined in relation to a number of data inputs using a set of equations to express the entire control process. Expressing human experience in the form of a mathematical formula is a very difficult task if not an impossible one.

Fuzzy logic provides a simple tool to interpret this experience into reality. Fuzzy Logic Controllers (FLC) are rule-based controllers. The structure of the FLC resembles that of a knowledge based controller except that the FLC utilizes the principles of the fuzzy set theory in its data representation and its logic. The basic configuration of the FLC can be simply represented in four parts as shown in Fig. 2.

Fuzzification module: The functions of which are 1st to read, measure and scale the control variable (speed, acceleration) and 2nd to transform the measured numerical values to the corresponding linguistic (fuzzy variables with appropriate membership values).

Knowledge base: This includes the definitions of the fuzzy membership functions defined for each control variables and the necessary rules that specify the control goals using linguistic variables.

Inference mechanism: It should be capable of simulating human decision making and influencing the control actions based on fuzzy logic. In the inference mechanism, rules are defined by the user. On the bases of these rules, output of fuzzy controller is controlled.

Defuzzification module: Which converts the inferred decision from the linguistic variables back the numerical values.

The 1st step in designing a fuzzy controller is to decide which state variables represent of system dynamic performance must be taken as the input signal to the controller.

However, choosing the proper linguistic variables formulating, the fuzzy control rules are very important factors in the performance of the fuzzy control system. System variables which are usually used as the fuzzy controller inputs includes states error state error derivative, state error integral, etc.

In power system, based on previous experience. Generator speed deviation (Δω) and acceleration (Δω) are chosen to be the input signals of fuzzy PSS. As it was mentioned earlier if the synchronous generator automatic voltage regulator is utilized in a proper way, it is capable of damping electromechanically oscillations of the generator shaft. The input to the excitation system would be the control variable which is actually the output of fuzzy PSS.

In practice, only shaft speed deviation is ready available. Hence, the acceleration signal can be derived from speed signals measured at two sampling instant by the following expression:

where, T_s is the sampling time. Universe of discourse which is basically the range of input variable is selected from -3 to 3 for present investigation. For best result, the UOD should be minimum but greater then input of fuzzy controller. Fuzzification of crisp input signals menace conversion of numerical input signal from SMIB system into fuzzy logic form.

After choosing proper variables as input and output of fuzzy controller, it is required to decide the membership function (mfs). These variables transform the numerical values of the input of the fuzzy controller to fuzzy quantities. The number of these membership function specifies the quality of the control which can be achieved using the fuzzy controller. As the number of the membership function increases, the computational time and required memory increase.

Therefore, a compromise between the quality of control and computational time is needed to choose the number of linguistic variables. For the power system under study, five membership function for each of the input and output variables are used to describe them as in the following Table 4.

The performance of a FLC also depends upon the type of membership functions. The most commonly used membership functions are triangular, trapezoidal and Gaussian. All the investigations are carried out considering Gaussian membership functions. A Gaussian membership function is defined as:

Where:

Table 4:	Input and output membership function

Table 5:	Rule base with five membership functions

Fig. 5:	Surface view of stabilizing signal according to both inputs (speed deviation and acceleration)

For the present investigations σ = 1.75 is chosen and all the membership functions are symmetrically placed in the Universe of Discourse (UOD) from -3 to 3. Mamdani inference engine is used. The two inputs; speed deviation and acceleration, result in 25 rules for each machine.As shown in Table 5 that results of 25 rules where a positive control signal is for the deceleration control and a negative signal is for acceleration control. After it, the next step is aefuzzification in which the stabilizer output which is in fuzzy form is to be converted in numeric values. On the bases of these rules the FLC output in the form of stabilizing signal can seen on surface viewer as shown in Fig. 5.

RESULTS AND DISCUSSION

The Heffron-Philips model of a SMIB with UPFC has been simulated using Matlab-Simulink software with estimated K constant values. In this research for the improvement of the SMIB system, we have introduced a fuzzy based damping controller with the UPFC (Fig. 6 and 7). Here, response of the SMIB system are analysed with and without UPFC based damping controllers for various configurations (Fig. 8a, b). Dynamic responses for the alternative damping controllers the different values of X_e at P_e = 0.8 p.u. Q_e = 0.1670 p.u. are given:

Fig. 6:	Without UPFC based damping controller

Fig. 7:	Combined dynamic responses for Δω with and without UPFC based damping controller

Fig. 8:	An introduction of fuzzy based damping controller

Damping controller (δ_B):

Fuzzy based damping controller:

CONCLUSION

The present research has been directed towards developments of UPFC based damping controllers for power system stabilization. The modified Heffron-Phillips model of SMIB power system installed with fuzzy based damping controlled UPFC is taken in the present research. The alternative UPFC based damping controllers for damping power system oscillations also has been examined in this research.

The modified Heffron-Phillips model of SMIB power system installed with UPFC and without UPFC is simulated using Matlab-Simulink. The performance of the four alternative damping controllers (m_B, m_E, δ_B and δ_E) has been examined considering wide variations in loading conditions and line reactance X_n in this work. Investigations reveal that the damping controller (δ_B) and damping controller (δ_E) provide robust performance to wide variations in loading conditions and line reactanceX_e. The simulation results shows that the fuzzy based damping controllers on UPFC control parameters may be preferred over the existing damping controllers.

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