^{1}

^{1}

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.

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 may 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 met 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 [

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. [

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_{i}_{1}, m_{i}_{2}, 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.

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 _{i}_{1} is the deviation in pulse width modulation index m_{i}_{1} of voltage series converter 1 in line 1. By controlling m_{i}_{1}, the magnitude of series

injected voltage in line 1 can be controlled. Δm_{i}_{2} is the deviation in modulation index m_{i}_{2} of series converter 2 in line 2. By controlling m_{i}_{2}, the magnitude of series injected voltage in line 2 can be controlled. Δα_{1} is the deviation in phase angle of the injected voltage Vse_{1}. Δα_{2} is the deviation in phase angle of the injected voltage Vse_{2}. The nominal loading condition and system parameters are given in Appendix A.

Interline Power Flow Controller (IPFC) is VSC based FACTS controller, consists of two voltage-sourced 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 [

where,

In this section, PI Based IPFC [_{DC}, wash out block and lag-lead compensator. The values of parameters of the lead-lag compensator are chosen so as to obtain best damping performance. Optimum parameters for the damping controllers are given in Appendix A. The IPFC controllable signals (m_{i}_{1}, α_{1}, m_{i}_{2} and α_{2}) can be modulated in order to produce a damping torque. Controllability indices for the different Interline Power Flow Controller controllable parameters are given in Appendix A. The washout circuit as shown in

Drawback of PI controller is the frequency deviation. It causes deterioration in performance during varying system conditions. Hence Fuzzy logic can be blended with conventional control techniques. Fuzzy logic is the art which makes machines more intelligent enabling them to reason in a fuzzy manner like humans. The mathematical concepts behind fuzzy reasoning are very simple. Hence fuzzy logic IPFC controller is proposed. Fuzzy logic is an innovative area of research as it does a good job of trading off between significance and precision. The main concept of fuzzy logic control (FLC) is to build a model of a human expert capable of controlling the plant without thinking in terms of a mathematical model.

logic controller. The control strategy has been prepared based on rules. The fuzzy logic approach more accurately represents the operational constraints of power systems and fuzzified constraints are softer than conventional constraints. Fuzzy logic based IPFC controller consists of three major parts. (a) Fuzzification; (b) Inference; (c) Defuzzification units.

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 the interval [0, 1]. 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 is chosen by trial and error approach so that best performance of the fuzzy controller can be achieved. However, the shape of the membership function can vary the small deviations in output of fuzzy logic controller [

The parameters of the membership function of the fuzzy logic controller, consisting of _{i}_{1} in

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 behavior 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 [

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

Variables | MF’s | α_{a} | α_{b} | α_{c} | α_{d} |
---|---|---|---|---|---|

Inputs | High | −10 | −5 | −4 | −0.05 |

P_{e} | good | −1.945 | 0 | 1.97 | − |

low | −0.005 | 4 | 5 | 7.5 | |

Output u | big | −2 | −1.02 | − | − |

Medium | −1 | −0.0582 | 0.926 | − | |

Small | 0.0159 | 1 | 2.01 | − |

S.N. | Instruction |
---|---|

1. | If input is low, then output is medium |

2. | If input is high, then output is big |

3. | If input is good, then output is small |

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:

Digital Simulation has been carried out with Modified Phillips Heffron model in MATLAB environment. Independent damping signals and Fuzzy with IPFC has been demonstrated. In small signal analysis, the simulation result of the linearized model with four different input control signals under 10% of variation in mechanical power input is considered. The proposed PI and Fuzzy controllers performances are tested in Single Machine Infinite Bus system.

_{i1}, first peak of speed deviation is reduced from 0.018 rad/sec. to 0.014 rad/sec. and settling time is reduced upto 0.43 sec. However, Fuzzy based IPFC reduces first swing from 0.018 rad/sec to 0.012 rad/sec with settling time 0.4 sec. Hence fuzzy based IPFC with damping controller m_{i1 }shows robust performance.

The eigen values as shown in

_{i2}. Result indicates that fuzzy based IPFC reduces first peak of speed deviation 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 Fuzzy which suppress the oscillations well and hence gives the best result. Hence Fuzzy logic based IPFC significantly improves small signal stability of Single Machine Infinite Bus system.

Control Signal m_{i}_{1} | With POD | With Fuzzy |
---|---|---|

−11.1052 ± 26.1203i | −14.6918 ± 27.3709i | −0.7128 ± 3.7544i |

0.0000 | −19.4661 | −11.1907 ± 26.1568i |

−0.0022 | −0.7128 ± 3.7544i | −0.0047 |

−0.7128 ± 3.7544i | −0.0721 | |

−0.0025 |

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

The MATLAB result as shown in _{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. Also, system is more suitable with Fuzzy based controller which 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 _{1} respectively lies on negative part of real axis which ensures that the system is stable.

With coordinated action of IPFC and POD as additional damping controller, reduction in peak amplitude, settling time and steady error are delineated in _{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

Control Signal m_{i2} | With POD | With Fuzzy |
---|---|---|

−11.0063 ± 26.0774i | −18.6719 ± 28.1777i | −0.7128 ± 3.7544i |

0.0000 | −19.4655 | −11.1907 ± 26.1568i |

−0.0022 | −0.7128 ± 3.7544i | −0.0047 |

−0.7128 ± 3.7544i | −0.0605 | |

−0.0025 |

Control Signal α_{1} | With POD | With Fuzzy |
---|---|---|

−11.1140 ± 26.1241i | −15.6530 ± 27.4281i | −0.7128 ± 3.7544i |

0.0000 | −4.5630 | −11.1907 ± 26.1568i |

−0.0022 | −0.7128 ± 3.7544i | −0.0047 |

−0.7128 ± 3.7544i | −0.0727 | |

−0.0026 |

Control Signal α_{2} | With POD | With Fuzzy |
---|---|---|

−11.1351 ± 26.1331i | −14.4546 + 27.1546i | −0.7128 ± 3.7544i |

0.0000 | −4.618 | −11.1907 ± 26.1568i |

−0.0022 | −0.7128 + 3.7544i | −0.0047 |

−0.7128 ± 3.7544i | −0.0767 | |

−0.0025 |

The comparative performance of Figures 7-10 justified that fuzzy based IPFC with pulse width modulation index of voltage series converter 1 and 2 (m_{i}_{1} and m_{i}_{2}) 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.

In this paper, a systematic approach for determining relative effectiveness of Interline Power Flow Controller (IPFC) control signals (m_{i}_{1}, α_{1}, m_{i}_{2}, α_{2}) in damping low frequency oscillations has been presented. 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 show the significant improvement in damping of power system performance. Investigations have revealed that IPFC control signals m_{i}_{1} and m_{i}_{2} 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 in comparative performance in terms of small signal stability improvement and damping of oscillations are demonstrated. The fuzzy logic controller demonstrates the robust performance and is 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 validate the performance of various IPFC control strategy.

S. N. Dhurvey,V. K. Chandrakar, (2016) Performance Comparison of PI and Fuzzy Logic Based IPFC on Damping of Power System Oscillations. Journal of Power and Energy Engineering,04,78-90. doi: 10.4236/jpee.2016.44008

M = 2H = 0.1787, _{b} = 1 p.u

K_{a} = 50.0, T_{a} = 0.05

K_{1} = 0.3837, K_{2} = −0.1717, K_{3} = 3.6667, K_{4} = −0.7350, K_{5} = −0.0237, K_{6} = 1.0659, K_{7} = −0.0139, K_{8} = −0.6890, K_{9} = 0.0023

K_{p}_{α}_{1} = 0.0376, K_{q}_{α}_{1} = 0.0010, K_{v}_{α}_{1} = −0.0029, K_{c}_{α}_{1} = 0.0672

K_{p}_{α}_{2} = −0.0045, K_{q}_{α}_{2} = 0.0033, K_{v}_{α}_{2} = −0.0021, K_{c}_{α}_{2} = −0.01116

K_{pmi}_{1} = 0.0552, K_{qmi}_{1} = −0.0326, K_{vmi}_{1} = −0.0360, K_{cmi}_{1} = −0.000766

K_{pmi}_{2} = 0.2530, K_{qmi}_{2} = 0.0056, K_{vmi}_{2} = −0.0038, K_{cmi}_{2} = −0.0087, K_{pp} = 1, K_{pi} = 0.5