Fuzzy-based Strategy for Voltage and Reactive Power Scheduling

Transcription

1 Indian Journal of Science and Technology, Vol 9(38), DOI: /ijst/2016/v9i38/95431, October 2016 ISSN (Print) : ISSN (Online) : Fuzzy-based Strategy for Voltage and Reactive Power Scheduling S. Rajasomashekar 1, A. Ananthi Christy 1*, P. U. Poornima 2, R. Brindha 2 C. Sujitha 2, H. Bharath Varma 2 and Arul Mecloy Lobo 3 1 Annamalai University, Annamalai Nagar, Chidambaram , Tamil Nadu, India; raiasomashekar@yahoo.in, jencychristy@yahoo.com 2 Department of EEE, SRM University, Kattankulathur, Chennai , Tamil Nadu, India; poornimakandati@gmail.com, brindha.apr16@gmail.com, saisuji88@gmail.com, bharathvarma8895@gmail.com 3 Bin Salim Enterprises, Sultanate of Oman; arul@binsalim.com Abstract Background / Objectives: This paper narrates a novel strategy employing fuzzy logic for voltage profile enhancement and loss imization in power systems. Linearized model is utilized and limit violations of control variables translated into fuzzy set notation. Methods/Statistical Analysis: The method adopted here for the voltage profile enhancement consists of certain number of load buses with definite VAR compensation schemes. In this work, it is mainly aimed to enhance the system voltage profile and thereby reducing power losses in it. Here, the linearization of objective functions and constraints is done about the current operating point. Findings: The equality and inequality constraints include dependent and independent variables. Later, power flow studies are used to calculate the limit violations of bus voltage magnitude and thereby a viable solution set that aims for voltage profile improvement as well as power loss reduction is finally obtained using appropriate operations of the fuzzy sets. In order to demonstrate the efficacy of this approach, IEEE 14 bus test system is implemented. Application/: Due to the application of fuzzy logic, the control of variables in the problem is global and it involves less computational time and the results can have more accuracy. Keywords: Fuzzy-based Strategy, Fuzzification and Membership Functions, Linearized Model, Reactive Power Scheduling, Voltage Profile Enhancement 1. Introduction Now-a-days, power system has grown into a very vast and complex system particularly with the development of integrated systems and interconnected grids. Further the power that is handled in the system is in short supply compared to the ever-increasing demand. It is generally accepted that the transmission loss in India is very much above the desirable limit. Thus, any effort in imizing the losses in the power system results not only in saving money but also in conserving the scarce energy. Another important aspect in power transmission is the basic requirement of delivering power to consumers without violating the statutory provision in respect of voltage and frequency change. The control of modern power systems is not as simple as there will be a continuous imbalance between active and reactive power generation and absorption. While the active power imbalance causes frequency deviation, reactive power imbalance causes voltage fluctuation problems. Considerable amount of work has been carried out in the field of active power control, that is, Load Frequency Control (LFC) and Automatic Generation Control (AGC). But, the control of reactive power has received attention only in the recent past. The real power allocations in a system are obtained from the economic load dispatch programme that imizes the production cost. The real power allocation so obtained must not be varied as the real power demands are to be fully met with. * Author for correspondence

2 Fuzzy-based Strategy for Voltage and Reactive Power Scheduling The reactive power allocation, on the other hand can be varied independently without affecting the real power allocation. In a power system, if the bus voltages are maintained within the acceptable levels, then the power quality and its reliability can be ensured to its best. The change in power demands can bring out changes to the configuration of the system to lead to under and/or over voltages of system. In order to enhance the voltage profile of the system, there happens to be lots and lots of voltage controlling devices that are installed in the power systems like tap changing transformers, shunt capacitors, generators, synchronous condensers, static VAR compensators etc. In a real-time control, it is therefore understandable that with such voltage controlling devices, the perturbations can be easily alleviated by either varying the loads and / or through incorporating the changes into the configurations of the network. Thus, in modern complex interconnected power systems, it is always preferable that there should be a well organized strategy needed to be coordinating the control voltage and reactive power flow, by which the transmission losses can be deemed to be imized. Reactive power control can be understood as a process of controlling the voltages of generator, tap settings of variable transformers, switchable shunt capacitors and banks of reactors, in such a way that they all aim for accomplishing the best reduction in terms of losses in the system and / or controlling the voltage levels. Optimization is the process of maximizing the total effectiveness with a set of certain operating constraints of equalities and inequalities. The most common means of analyzing the voltage and reactive power flow problem for system planning is the standard load flows. Based on this, the system planner must analyze the violation of constraints on the system. In the past, a number of papers were published in the area of control of voltage and reactive power and the necessary compensation techniques were developed, with a view to reduce the losses in the power system. Some of the important works in this field pertaining to the proposed approach includes a new approach for imizing power losses and improving voltage profile 1 out of a defined system by varying the control variables, i.e., by injecting reactive power through VAR sources and changing the tap positions of the transformers. For a realtime problem, the practice of reactive power dispatch is not acceptable, when it has a wide deviation of voltages 2 that requires by how effectively the voltage violations can be solved using what sort of control variables. In practical cases, the efficiency of the system is usually measurable through the existing voltage profile, sensitivities and reserve margin of the control variables. In the area of optimal reactive power control problem, the problem formulation employing fuzzy set theory 3 focuses on how to imize the real power loss and on the other hand to improve the voltage profile for the given network. A centralized optimizing computational procedure for the on-line control of voltage and reactive power provided an optimization procedure for the real time computation of voltage and reactive power control based on the linearized equation that describes the relation between the operations of regulating devices and the corresponding changes in control variables. The method adopted here for the voltage profile enhancement consists of a certain number of load buses with definite VAR compensation schemes. The objective function of this work lies in enhancing the profile of voltage of the system and thereby reducing power losses. The objective function and the constraints are formulated from power flow equations. So they will be linear. Hence linearization of the objective function and constraints is done about the current operating point. The operating point is estimated using Newton Raphson Load flow. From the LF studies, the violations are checked and the necessary compensation requirements are implemented by the sensitivity coefficients. 2. System Modelling In this paper, a method of enhancing the voltage profile of the system by correction of PQ bus voltages is implemented. This method uses the voltage profile improvement as the foremost objective function subject to the constraints of bus voltage violation limits and the adjustable quantities of controlling devices. A sensitivity technique is employed for the analysis of voltage profile enhancement. To apply this technique in practical systems, the current system state must be detered by state estimation, which is done by a load flow model and the required system data are obtained by applying the Newton-Raphson load flow algorithm. As far as the NR method is concerned, very high accuracy can be possible over a fewer iterations, owing to its quadratic convergence of bus voltages, besides the fact that the total number of 2 Vol 9 (38) October Indian Journal of Science and Technology

3 S. Rajasomashekar, A. Ananthi Christy, P. U. Poornima, R. Brindha C. Sujitha, H. Bharath Varma and Arul Mecloy Lobo iterations is almost a constant, irrespective of the size of the system. Thus, for any complex power systems, the NR method may need only 3 to 5 iterations in providing an optimal solution. The sensitivity technique is then applied to detere the optimized PQ bus voltages. The loss in the system is imized at an operating point. This imization is achieved by the PQ bus voltage correction by suitable VAR compensating devices. This technique deteres the optimized voltage levels within the permissible limits. Due to the application of the fuzzy logic, the control of variables in the problem is global and it involves less computational time and the results have more accuracy. 3. Problem Formulation As we have discussed earlier, the goal of this work is to improve the voltage profile at busses, besides accomplishing a reduced power loss in the system that takes into account of the lower and upper bounds of bus voltage magnitude as well as the maximum and imum adjustable quantities of controlling devices. A linearized model is explored in this approach and solved by the application of fuzzy logic. 3.1 Objective Functions The Linearized Model for Bus Voltage Let us consider a system, where there is an N-bus system, wherein 1 to L being the load buses and the generator buses be L+1 to N-1, keeping N as the slack bus. Once if the voltage limits of bus i are hit, then the control action is needed to be taken and the impact upon its control of voltage depends upon the sensitivity, which is obtained by conducting the load flow studies. It is noteworthy that the voltage of bus i can be seemed to be improved, just because of adjusting the controlling device on bus j and whose quantity of improvement can mathematically be as; V i = S ij U j, i = 1, 2,..., L; j = 1, 2,..., N-1 (1) 2. The Expressions for Power Loss Evaluation As a matter of fact, the power loss is a nonlinear function of bus voltages and phase angles, given as: nl 2 2 g V + V 2V V cos( d d ) (2) P = [ ] L k i j i j i j k = 1 B. CONSTRAINTS 1. Limits on Controlling Device The adjustment of the controlling device is constrained as: U j U j U j max (3) 2. Limits on Control Variable Here, the voltage deviation of load bus should be controllable over± 5% of the noal voltage V nom, which is given as below: V i V i V i max (4) 4. Fuzzy based Solution Technique 4.1 Fuzzified Computational Modeling The objective of these computational methodologies is to obtain the feasible solution towards the bus voltage improvement and reducing the power loss, achieved through fuzzy logic Fuzzification and Membership Functions The process of conveying the crisp control variables to their equivalent fuzzy variables is referred to as Fuzzification. However, the system s nature and its expected output may play a significant role on the selection of the control variables. The input and output signals of the Fuzzy Logic Controller (FLC) are usually to be interpreted into a number of linguistic variables that may vary based on the problem and its application. The fuzzy rule base is detered by the number of linguistic variables and hence if there are more such linguistic variables, there happens to be more number of rules, by default; and equally each of the linguistic variables can have its own fuzzy membership function. The crisp values are mapped into their corresponding fuzzy variables through the membership functions. A fuzzy set A in X is defined as A={(x,µ A (x))/x X} where µ A (x) is called membership function (MF). The membership grade of each element of X is in the range Some of the one-dimensional membership functions commonly used is: Triangular membership functions. Gaussian membership functions. Trapezoidal membership functions. Vol 9 (38) October Indian Journal of Science and Technology 3

4 Fuzzy-based Strategy for Voltage and Reactive Power Scheduling The general description of fuzzy classes of Triangular MF s is shown in Figure 1. It is specified by three parameter {a, b, c} with (a<b<c) are the x-coordinates of the three corners of the MF. In this approach, the triangular membership function is exploited for the violation of load bus voltages with five linguistic variables, being defined for better accuracy. The triangular membership functions for the bus voltage violations are as given in Figure 2. In Figure 2. V i represents the error induced because of the voltage violation at load bus i and µ V i represents the membership function of V i. controlling devices are given in Figure 3. In Figure 3 C ij represents the controlling ability of controlling device of bus j on bus i and µc ij is the max membership function of C ij, where C ij and C ij take the value of 0.2 and 0.2 respectively. The effect of adjustment of a controlling device is evaluated by the sensitivity matrix obtained from the base case load flows. Figure 3. (Section IV.A.1) The membership function of controlling ability of controlling devices. Figure 1. (Section IV.A.1) The Triangular Membership functions. Figure 2. (Section IV.A.1) The Membership function of voltage violation level. Also the corresponding crisp ranges of values for the fuzzy linguistic variables are tabulated as given in table 1. Table 1. Crisp error value ranges for fuzzy linguistic variables Fuzzy Linguistic Variables Crisp Error Value Ranges VS(Very Small) -0.2 to 0.2 S(Small) 0 to 0.4 M (Medium) 0.2 to 0.6 B (Big) 0.4 to 0.8 VB (Very Big) 0.6 to 1.0 For the controlling devices, two linguistic variables are defined and they are termed as C ij and C ij max. They max are constrained subject to U j U j U j The membership functions of the controlling ability of Fuzzy Inference and Rule Base Usually, the input fuzzy sets are mapped to their corresponding output sets through fuzzy systems. Thus, the relationships between the input and output fuzzy sets are called as Fuzzy rules. While deriving such fuzzy rules, one or more of the following may be considered; Control actions of the operator. Learning out of the training examples. Expert experience and control engineering knowledge. Hence, in this work concerned, the option of learning out of the training examples being considered for arriving at the appropriate fuzzy rules. The generalized form of the fuzzy control rules being used in this approach can be given as; IF x is A i AND y is B i THEN z =f i (x, y} (5) where x, y and z are linguistic variables representing the process, state and the control variables respectively. A i, B i are the linguistic values of the linguistic variables, f i (x, y) is a function of the process state variables x, y and the resulting fuzzy inference system is called as Sugeno Fuzzy Model (also known as the TSK fuzzy model) 5, which aims at developing a methodological approach in forg the fuzzy rules from a given data set of input-output. Thus the controlling ability of the controlling device is inferred from the rule base, as C ij = S ij. M j (6) 4 Vol 9 (38) October Indian Journal of Science and Technology

5 S. Rajasomashekar, A. Ananthi Christy, P. U. Poornima, R. Brindha C. Sujitha, H. Bharath Varma and Arul Mecloy Lobo Defuzzification Interface In FLC, the mechanism of the inference engine is the most pivotal point, whose prime function is to compute the overall value of the control output variable based on the individual contributions of each rule in the rule base, which is, on the other hand, said to be the defuzzification process. The Sugeno Fuzzy Model 5 that is used in this approach for defuzzification process is illustrated as shown in Figure 4. From the Figure. 4; By Weighted Average Method w 1 z 1 +w 2 z 2 z = w 1 + w 2 Which can be simplified: By Weighted Sum Method z = w 1 z 1 +w 2 z 2 Unlike the Mamdani model (Conventional Fuzzy Model) 4-11, this Sugeno Fuzzy Model delivers a crisp output for every corresponding rule base and produces the overall output through weighted average, which results in less time consumption on defuzzification as compared to the other. However, the Weighted Sum Operator occasionally outplays the weighted average operator, with z = w 1 z 1 +w 2 z 2, as in Figure 4, which reduces further computation, especially while training the fuzzy inference system. So, the output is a function of input and expressed as; f (x) = w 1 z 1 + w 2 z 2 (7) Or it can be written as f (x) = px + qy + r (8) Thus, the output so obtained from the defuzzification process deteres the optimal value of the capacitances at the selected load buses, to be employed for the bus voltage profile enhancement and loss reduction. Figure 5 gives the flowchart of the step-by-step flow in progress. The main steps involved in these computational procedures include the following steps; Step 1: Obtain data as the input out of the network configuration, line impedance, bus power, bus voltage limits and controlling margin of the controlling devices. Step 2: Perform a base case load flow by N-R method. Step 3: Calculate the sensitivity coefficients from the load flows. Step 4: Check the performance of the system with the increment of the loads at the load buses. If the voltages are in safe limits, stop the process. Step 5: Check if there are any bus voltage violations on load busses as against their operational limits, then go to step-6 ; otherwise stop. Step 6: Obtain the corresponding membership function values for bus voltage violation level and controlling requirement of controlling devices. Step 7: Evaluate the output controlling variable which is used to alleviate voltage violation and reduce power loss. Step 8: Perform load flow study again and go to step 5. Figure 4. (Section IV.A.2) The SUGENO Fuzzy model. Figure 5. (Page no. 6 beginning) Flow chart for the proposed approach. Vol 9 (38) October Indian Journal of Science and Technology 5

6 Fuzzy-based Strategy for Voltage and Reactive Power Scheduling 5. Test Case and Results 5.1 The Test System In order to show the efficacy of the proposed methodology, a standard test system of IEEE 14-Bus system as shown in Figure 6 is employed in this study, which consists of 14 buses and 20 lines along with 5 PV buses, 9 PQ buses. The line data of the test system is presented through Table 2 and that of the bus data by Table 3 Wherein said to the reactive power sources at the load buses 6, 9, 10 and 14that have imum and maximum adjustable reactive power of 1 and 1 P.U. respectively. Whereas the teral generator voltage regulators at the buses 1, 2, 3, 4 and 5 are having 0.95 and 1.05 P.U of lower and upper voltage limits respectively. And the adjusting step size on VAR sources is limited to 0.2 P.U. Table 2. Line data of IEEE 14 bus test system LINE NO BETWEEN BUSES LINE IMPEDENCE HALF LINE CHARGING R (P.U) X (P.U) SUSCEPTANCE (P. U) Figure 6. (Page no. 6 ending) One line Diagram of IEEE 14-Bus system. Table 3. Bus data of IEEE 14-bus test system (base case) BUS BUS VOLTAGE GENERATION LOAD NO MAGNITUDE (P.U) PHASE ANGLE (DEGREES) REAL (MW) REACTIVE (MV AR) REAL (MW) REACTIVE (MV AR) Vol 9 (38) October Indian Journal of Science and Technology

7 S. Rajasomashekar, A. Ananthi Christy, P. U. Poornima, R. Brindha C. Sujitha, H. Bharath Varma and Arul Mecloy Lobo 6. Results and Discussion The effectiveness of the proposed methodology has been tested under two scenarios as case (i) and case (ii) vide given below; Case (i): Load of bus 7, 9 and 11 increased moderately to cause violation at the load buses, but the violation is less serious. Case (ii): Bus 9 is heavily loaded which causes larger voltage violation at the load bus 9 and also at buses 6, 10 and 14. Table 4, 5 and 6 show the controlling devices selected and their adjusting quantities, bus voltage change and power loss change respectively. Table 4. Controlling devices selected and their adjusting quantities CASE- 1 CASE - 2 Controlling Devices Quantity of Adjustment Controlling Devices Quantity of Adjustment Q Q Q Q Q Q Q In Case 1, since the voltage violations are small in buses 9, 10 and 14, the method selects Q9, Q10 and Q14 with very small values of the capacitances as compared over the Case 2, where the voltage violations are higher at buses 6, 9, 10 and 14 due to the heavy loading on bus 9, in which the method selects Q6, Q9, Q10 and Q14 with significantly higher values of capacitances. Table 6. Power Loss Change Case 1 Case 2 Real Power Loss Before Real Power Loss After Reactive Power Before Reactive Power After % Power Loss Reduction As seen from the facts and figures presented above, it is very obvious that the proposed method is reasonably well up to the expectation and more importantly violations of voltages at any load buses have been efficiently addressed to alleviate, besides reducing the and the power losses in the system. 7. Conclusion A systematic methodology has been developed for improving bus voltages and imizing real power loss and the objective functions were checked out subject to the constraints. The performance of the system has greatly been improved with the advent of the fuzzy logic approach. It is worth mentioning that scheme of control being employed over here in this work that uses linearized model in addition to fuzzy set theory for obtaining the enhancement on the voltage profile of the buses also takes care of reducing the power loss as well. Table 5. Bus Voltage Change Bus Case 1 Case 2 voltage Before After Before After V V V V V V V V V Vol 9 (38) October Indian Journal of Science and Technology 7

8 Fuzzy-based Strategy for Voltage and Reactive Power Scheduling It can also be claimed that the method so presented above, can be applied as an on-line tool, thanks to its much less burden on computational requirements and hence this voltage / reactive power scheduling model can take any system/s to the ideal conditions as much as possible, offering the flexibility of operation upon the realization of the controlling devices to the best of their controlling ability as well. 8. References 1. Qiu J, Shahidehpour S. A new approach for imizing power losses and improving voltage profile. IEEE Trans on Power Systems. 1987; 2(2): Exposito AG, Ramos JLM, Macias JLR, Sulinas YC. Sensitivity-based reactive power control for voltage profile improvement. IEEE Trans on Power Systems. 1993; 8(3): Rahman AKB, Shahidehpour SM. A fuzzy based optimal reactive power control. IEEE Trans on Power Systems. 1993; 8(2): Hano L, Tamura Y, Narita S Matsumoto K. Real time control of system voltage and reactive power. IEEE Trans on PAS. 1969; 8(5): Jang JSR. Neuro Fuzzy and Soft Computing. Prentice Hall of India Timothy J, Ross R. Fuzzy Logic with Engineering Applications. McGraw Hill Publishing Company Carson W, Taylor T. Power System Voltage Stability. Mc- Graw Hill Publishing Company. T.J.E. Miller, Reactive Power Control in Electric System. John Wile and sons.1992; Kiran SH, Dash SS, Subramani C, Pathy S, An efficient swarm optimization technique for stability analysis in IEEE 14 bus system. Indian Journal of Science and Technology. 2016; 9(13): Kanagavardhini K, Mahalakshimi TS. A review on nature based swarm intelligence optimization techniques and its current research directions. Indian Journal of Science and Technology. 2013; 9(10): Eghbalpour H, Rad MN, Hassani R. A Multi operator imperialist competitive algorithm for solving non convex economic dispatch problem. Indian Journal of Science and Technology. 2016; 9(6): Balasubramanium KP, Santhi KR. Best Compromised Schedule for Multi Objective Unit Commitment Problems. Indian Journal of Science and Technology. 2016; 9(2): Vol 9 (38) October Indian Journal of Science and Technology