Performance Comparison of PI and Fuzzy Logic Based IPFC on Damping of Power System Oscillations

This paper presents a new approach for determining the effective control signals for damping of oscillations by using fuzzy logic based Interline Power Flow Controller [IPFC]. The IPFC performance is tested with PI controllers in comparison with fuzzy logic based controller on Modified Phllips-Heffron Model of Single Machine Infinite Bus System to achieve improved damping performance by selecting effective control signals such as deviation in pulse width modulation index of voltage series converter 1 in line 1, pulse width modulation index of voltage series converter 2 in line 2, deviation in phase angle of the injected voltage of convertor 1, injected voltage phase angle deviation of convertor 2. Investigations reveal that coordinated tuning of Interline Power Flow Controller with Fuzzy Logic Controller provides the robust dynamic performance. The Fuzzy Logic Based Interline Power Flow Controller [IPFC] is designed with simple fuzzy rules to coordinate the additional damping signal. The proposed controllers for IPFC are able to achieve improved designed performance of the power system. Validity of effective control signals has been done by eigen value analysis.


Introduction
When a power system is subjected to a disturbance, the system variables undergo oscillations.Some low frequency electromechanical oscillations of small magnitude exist in the power system for long periods of time, and in some cases they might impose limitations on the transmission line functionality.With low damping, power system is subjected to prolonged large oscillations.Several devices and control methods have been developed to increase damping in power systems and improve power transfer limits.In particular, the application of multifunctional FACTS controllers based on back to back dc/ac voltage source converter has greatly meet with power demand in the recent years.The high current semiconductor device based FACTS devices with proper control strategy can improve the power system stability of power system.Many researcher presented work on various nonlinear VSC based FACTS devices like STATCOM, SSSC and UPFC for transient stability improvement of the power system under various system conditions.Amongst the other developed VSC based nonlinear FACTS devices, Interline Power Flow Controller (IPFC) is most versatile FACTS device, it consists of number of SSSC are connected in each line which are connected via common dc bus, addresses the problem of compensating a number of transmission lines.The special feature of IPFC is not only to perform an independently controllable reactive series compensation of each individual line but also to deliver real power between the compensated lines.This capability of IPFC makes it possible to: equalize both real and reactive power flow between the lines; hence avoid the burden of overloaded; making compensation for resistive line voltage drops and the associated reactive power demand and increase the efficacy of the overall compensating system for dynamic disturbances [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18].Shan Jiang et al [17] discusses the behavior of two FACTS devices; the combined series-series controller and the combined series-shunt controller in a benchmark system and proved that the IPFC has more series branches than the UPFC, it provides more opportunities for network segmentation and, hence, has the potential for greater damping improvement.Gopinath et al [18] introduces the model of state estimation embedded with IPFC.A power injection model that shows the influence of IPFC on the power flow between the interconnected lines is presented.Segundo et al [15] have examined the efficacy of VSC-based FACTS controllers in contributing to system-wide damping.The strategy is tested on a practical 45-machine Mexican system that includes number of static VAR compensators.
Fuzzy Logic Controller is robust and easily modified.It can use multiple input and output sources.Advantageous feature of Fuzzy logic is to provide solution to the problem can be cast in terms that human operators can apply their experiences for the design of the controller to achieve maximum performance of the IPFC controller.
Dhurvey et al [23] have examined the relative effectiveness of IPFC control signals on linearized power system model of single machine infinite bus system (SMIB) system for analyzing performance comparison of IPFC in coordination with Power Oscillation Damping Controller [POD] and Power System Stabilizer [PSS].However, results has been not presented with the consideration of various damping factor D and Kp and Ki is not properly tuned.Hence, the aim of this paper is to present the modified version of reference [23].Kazemi et al [9] proved the effective damping control function of an IPFC installed in a power system.Parimi,et al [4] implement the Fuzzy logic control for IPFC for damping low frequency oscillations.Alivelu M. Parimi [6] develop the nonlinear model of power system incorporated with Interline Power Flow Controller (IPFC).The oscillation modes with low damping ratio are obtained from the eigen value analysis of the linearized Phillips-Heffron model Parimi [11] has proved that IPFC control signal m2 is the most effective.M.R.Banaei et al [13] has proved that signals m1, m2 based controllers have more effect on damping of oscillation and signal δ1, δ2 based controllers have less effect on damping of oscillation.Veeramalla, J. et al [14] investigated the effectiveness of the IPFC based damping controller.Dynamic simulations results have emphasized that the damping controller which modulates the control signal m2 provides satisfactory dynamic performance under wide variations in loading condition and system parameters.However, they have not presented an approach for obtaining the simultaneous coordination of IPFC with each control signal and Fuzzy Logic Controller In view of the available work presented by the researchers, the main objective of this paper is to study effectiveness of various control signals [m i1 ,m i2 ,α 1 , α 2 ]of IPFC for damping of power system oscillations.The comparative performance of PI based controller and fuzzy logic based IPFC for improved power system performance is demonstrated.The results are validated in MATLAB environment.

System Model
Single-Machine Infinite Bus power system incorporated with Interline Power Flow Controller in one of the two transmission lines is considered for analysis which consists of an excitation transformer, a boosting transformer, a pair of voltage source converters and a DC link capacitor is shown in Fig 1 .Δmi1 is the deviation in pulse width modulation index mi1 of voltage series converter 1 in line 1.By controlling mi1, the magnitude of series injected voltage in line 1 can be controlled.Δmi2 is the deviation in modulation index mi2 of series converter 2 in line 2. By controlling mi2, the magnitude of series injected voltage in line 2 can be controlled.Δα1 is the deviation in phase angle of the injected voltage Vse1.Δα2 is the deviation in phase angle of the injected voltage Vse2.The nominal loading condition and system parameters are given in Appendix-A.
Fig. 1: A single machine infinite bus power system installed with an IPFC in one of the lines

Interline Power Flow Controller
Interline Power Flow Controller (IPFC) is VSC based FACTS controller, consists of two voltagesourced converters (VSCs) inserted in series with transmission lines, whose DC capacitors are linked such that active power can be transferred between the two VSCs.Each VSC provides series compensation for the selected transmission line and is capable of exchanging reactive power with its own transmission system.Basic function is to control power flow among transmission lines and damping of oscillations.A non-linear dynamic model of the system is derived by omitting the resistances of all the components of the system and the transients of the transmission lines and transformers of the IPFC.
A linear dynamic model of IPFC is obtained by linearizing at operating point [13].


 Fig 2 shows the modified Phillips-Heffron model of the SMIB system with IPFC installed [3].The constants of the modified Phillips-Heffron model are functions of the value of system parameters and the initial operating condition as shown in Appendix -A.In terms of state-space representation, the power system can be modeled as

Fuzzification
In fuzzification the input and output are decomposed into one or more fuzzy sets.Here, the input variables are mapped onto fuzzy linguistic variables.The choice of membership functions influences the quality of a fuzzy logic controller.Membership function defined on the universe of discourse is the space where the fuzzy variables are defined.The membership functions designs the elements of the universe onto numerical values in  P is 0 to 7.5.Under the transient conditions, large variation in the system parameters can take place and therefore large ranges are chosen for input output mapping [20].However, for other smaller ranges of input and output fuzzy performance will not deviate.

Inference
A relation between cause and effect, or a condition and a consequence is done by reasoning.For reasoning, logical inference is used, in order to draw a conclusion.The mechanism of the inference process is the search of input/output relationship to match the input conditions.The objective of control is to influence the behaviour of a system by changing an input of that system according to a rule that model how the system operates.Therefore, an integral part of the inference process is the rule-base (a list of rules that relate the input values to the output values).Control decisions are made on the basis of fuzzified linguistic variables.We usually follow rules of inference as shown in Table 2.The rules can be specified to include various operating conditions.In fuzzy logic control, in order to minimize the complexity of the controller, it is always desirable that number of rules in a working controller should be less which makes shorter controller execution time.Hence while designing FLC more stress has been given on effective input variable and minimum rule.FLC has one rule for one input variable.The min-max inference is applied to determine the degree of membership for the output variable.The main objective of the designed fuzzy inference system is for the improvement in damping of power system oscillations.

Defuzzification
After the process of fuzzy reasoning, linguistic output variable should be translated into a crisp value.Defuzzification is such inverse transformation which designs the output from the fuzzy domain back into the crisp domain.For IPFC control, the fuzzy inference system coordinates the linguistic input variables.The universe of discourse of the input variables decides the required scaling for correct per-unit operation.The fuzzy logic operations performed (Sup-Min inference) are decided by the decision making logic, and together with the knowledge base influences the outputs of each fuzzy IF-THEN rules.Those are combined and converted to crispy values with the defuzzification block.The fuzzy Controller uses the centroid method.The general function of the fuzzy Logic controller can be expressed as- ( ) .
Where, f denotes the mapping defined by the rule base and α, β is the appropriate scaling, which depends on the scale of the X-axis and Y-axis of input and output variables.The fuzzy output is given by equation-     Nature of eigen as shown in Table 3 values lying on negative part of real axis which indicates that the system is stable.from 0.025 to 0.01 rad/sec with settling time 0.25 sec.and improvement in steady state error.Also, system is more amenable with RBFN which suppress the oscillations well and hence give the best result.Hence Fuzzy logic based IPFC significantly improves small signal stability of Single Machine Infinite Bus system.Time domain result has been verified by obtaining eigen value analysis of PI based IPFC, IPFC with POD as additional damping controller and Fuzzy based IPFC for control signal m i2 as shown in Table 4 in which the negative real part of eigen values proves that the system is stable.

Dynamic performance of the system with control signal α 1
The MATLAB result as shown in Fig 9 demonstrates the satisfied performance of PI based IPFC, IPFC with POD as additional damping controller and Fuzzy based IPFC for control signal α 1. Result indicates with fuzzy based IPFC, first peak of speed deviation is reduced from 0.017 to 0.012 rad/sec, settling time is reduced and steady state error has been improved.Also, system is more amenable with Fuzzy suppress the oscillations well and hence give the best result.Time domain result has been verified by obtaining eigen value analysis which are tabulated in Table 5 in which all the eigen values regarding PI based IPFC, IPFC with POD as additional damping controller and Fuzzy based IPFC for control signal α 1 respectively lies on negative part of real axis which ensures that the system is stable.

Dynamic performance of the system with control signal α 2
With coordinated action of IPFC and POD as additional damping controller, reduction in peak amplitude, settling time and steady error are delineated in Fig 10 .However, Fuzzy based IPFC shows the improvement in the response of the system for control signal α 2 in which first peak of speed deviation is reduced from 0.016 to 0.013 rad/sec with settling time 0.4 sec.This again highlights the efficacy of the Fuzzy based IPFC.
This inference has been checked by obtaining eigen value analysis of PI based IPFC, IPFC with POD as additional damping controller and Fuzzy based IPFC for control signal α 2 as shown in Table 6.The negative real part of eigen value indicates that the system is stable.
The comparative performance of Figure 7,8,9,10 justified that Fuzzy based IPFC with control signals m i1 , m i2 are more effective in damping of power system oscillations.
This inference has been checked by obtaining eigen value analysis which indicates that the system is stable.

Fig 4 :
Fig 4: Structure of Fuzzy Logic Controller

Fig 5 :
Fig 5: For Input variable Fig 7: Speed deviation response of linearized SMIB system for signal m i1 Each fuzzified variable has certain membership function.The input (P e ) is fuzzified using three fuzzy sets: high, good and low.Many types of curves can be used, Out of all the curves available, triangular or trapezoidal shaped membership functions are the most popular.These shapes are easier to represent in embedded controllers.The shape of membership function are chosen by trial and error approach so that best performance of the fuzzy controller can be achieved.

Table 1
Parameters of membership function for control signal m i1

Table 2 .
Table for Input-output mapping

Table 3 :
Comparison with POD controller and fuzzy logic controller for control signal m i1

Table 4
Comparison with POD controller and fuzzy logic

Table 5 :
Comparison with POD and fuzzy logic controller for signal 1

Table 6 :
Comparison with POD controller and fuzzy logic controller for control signal 2 The linearized power system model of Single Machine Infinite Bus system for analyzing the performance of fuzzy based IPFC for variation in system parameters has been studied.These control signals shows the significant improvement in damping of power system performance.Investigations have revealed that IPFC control signals m i1 and m i2 provide robust performance over other signals.The proposed Fuzzy Logic Controller performance is comparatively better than PI based controller.The fuzzy rules have been designed to minimize transients swing, improvement in damping of oscillations.The controllers comparative performance in terms of small signal stability improvement and damping of oscillations is demonstrated.The fuzzy logic controller demonstrates the robust performance and easy to coordinate with damping schemes.The simplicity of the design is the most attractive feature of Fuzzy based control scheme.The proposed controller fulfills the main objective of this paper.Time domain analysis and eigen value analysis results validated the performance of various IPFC control strategy.Parimi A.M., Sahoo N.C., Elamvazuthi I, Saad N., Transient stability enhancement and power flow control in a multi-machine power system using Interline Power Flow Controller, Energy, Automation, and Signal (ICEAS), 2011 International Conference , pp. 1 -6 [7]Gomathi V., Ramachandran, Kumar C.V., Simulation and state estimation of power system with Interline Power flow Controller,