CHAPTER 6 ANFIS-RQPF FOR UNBALANCED THREE-PHASE SYSTEMS

Transcription

1 92 CHAPTER 6 ANFIS-RQPF FOR UNBALANCED THREE-PHASE SYSTEMS 6.1 POWER FACTOR IN UNBALANCED THREE-PHASE SYSTEMS In sinusoidal situations, there is a unique power factor definition for single-phase and balanced three-phase systems. However, in non-sinusoidal situations and/or unbalanced three-phase systems, different power factor definitions have been reported in the literature (Czarnecki 1995, Emanuel 1993, Emanuel 1999, Filipski 1991, Filipski 1994, Ghassemi 2000, IEEE 1996, IEEE 2000, Lev-Ari 2006, Morsi 2007, Morsi 2008a, Morsi 2008b, Morsi 2009, Morsi 2009a, Sankaran 2002, Sharon 1996, Willems 2004, Willems 2005). Among these definitions, three power factors are recommended. The IEEE Working Group on Non-sinusoidal Situations (IEEE 1996) recommended the displacement power factor in order to measure the transmission efficiency at fundamental frequency. The displacement power factor indicates how much active power is being transmitted out of the maximum power or the delivered power when considering the fundamental frequency component only. In order to be applicable for three-phase systems, the fundamental positive-sequence power factor (FPSPF) is developed in the IEEE Standard , which has the same meaning as the displacement power factor in a single-phase system. It is also recommended to use the TEPF using the

2 93 concept of effective apparent power in order to measure the overall transmission efficiency at the fundamental plus the non-fundamental frequency components. The transmission efficiency power factor indicates how much active power, including the fundamental plus the non-fundamental components, is being transmitted from the source to the load. The following example shows that neither the fundamental positivesequence power factor nor the transmission efficiency power factor that are contained in the IEEE Standard are adequate enough to describe the system utilization including the amount and quality of the transmitted power. Figure 6.1 Three Phase Linear Load supplied from Sinusoidal Balanced Source Figure 6.1 shows a three-phase system consisting of a linear load supplied from a sinusoidal balanced source. The source voltages are V 1200, V , V R S T. (6.1)

3 94 Consider two loading cases: 1. Balanced such that R R = R S =R T = 20, and L R = L S = L T = H 2. Unbalanced such that R R = 20, R S = 0.05, R T = 100, and L R = L S = L T = 0 H. According to IEEE Standard , the TEPF at the PCC for the first and second case will be 0.58 although the waveforms of the transmitted power in the two cases have different shapes. In the first case, there is no oscillation so the transmitted power will have a dc value, while in the second case; there will be some oscillation that is superimposed on the dc value. These oscillations stem from the unbalance that exists in the threephase system; therefore, summing up the unbalanced three-phase power will result in oscillation; however, in the balanced systems, the sum of balanced three-phase power will be a constant value. Furthermore, if we consider case 2, and letting the inductances in case 1, be equal to zero, then according to IEEE Standard , the FPSPF will be equal to 1 in both cases although one case is balanced and the other is unbalanced. Thus, the FPSPF is also unable to differentiate between the two cases. In order to measure the quality of the transmitted power, Willems (2004) proposed the use of the oscillation power factor (OSCPF) which is an indication of how much oscillation is being superimposed on the transmitted power. Low OSCPF values indicate high oscillations while high OSCPF values indicate low oscillations in the power received by the load. For example, when considering the two cases mentioned before, according to Willems (2004), the oscillation power factor gives 1 for the balanced case while giving for the unbalanced case.

4 95 Since these three power factors are essential to describe the system utilization, including both the amount and quality of the transmitted power, therefore, there is a need to represent these power factors with a single value for applications, such as customer billing, setting tariffs, and evaluating the service quality especially in deregulated environment. The electric power system contains many sources of uncertainties and imprecision due to: Voltage and current transducer inaccuracies Measurement errors Changes in power system operating conditions Imprecise information caused by human involvement in the operation management and control of power systems Also, the nonexistence of a single accepted definition for the power factor in non-sinusoidal situations or unbalanced three phase systems can be considered as a source of uncertainties and imprecision when evaluating power quality in electric power systems. 6.2 FUZZY LOGIC BASED RQPF FOR THREE-PHASE SYSTEMS Morsi (2008b) extended the FRQPF index to be suitable for the three-phase systems; therefore, a single value that represents the three power factors can be obtained. Thus a fuzzy-logic-based approach is proposed by Morsi (2008b) to calculate the RQPF for three phase unbalanced systems in non-sinusoidal situations, using Mamdani s FIM.

5 96 Figure 6.2 shows a schematic diagram of the FRQPF module. This module can be built using the Fuzzy Logic Toolbox (Matlab 2008) available in MATLAB. The design procedure is as follows: Input and Output Fuzzification The inputs to the FRQPF module are the FPSPF, TEPF, and OSCPF. The value of each of these three power factors ranges from 0 to 1. A value close to 0 indicates the minimum power factor value, while a value close to 1 indicates a high power factor. Fundamental Positive Sequence Power Factor Transmission Efficiency Power Factor Fuzzy Logic based RQPF Module Fuzzy Logic based Representative Quality Power Factor Oscillation Power Factor Figure 6.2 Schematic Diagram of the FRQPF Module for Three-Phase System The triangular form can be used for the membership functions due to its simplicity to represent input variables. Thus, three linguistic variables, Low (L), Medium (M), and High (H) are used. The output is the FRQPF which is represented by seven linguistic variables; Low (L), Moderately Low (ML), Somewhat Low (SL), Medium (M), Somewhat High (SH), Moderately High (MH), and High (H).

6 Fuzzy If-Then Rules The FRQPF module has three inputs and each input is represented by three linguistic variables. Therefore there are 27 rules in the FRQPF module. The fuzzy inference rules are stated below. 1) If (FPSPF is L) and (TEPF is L) and (OSCPF is L) then (RQPF is L) 2) If (FPSPF is L) and (TEPF is L) and (OSCPF is M), then (RQPF is ML) 3) If (FPSPF is L) and (TEPF is L) and (OSCPF is H), then (RQPF is SL) 4) If (FPSPF is L) and (TEPF is M) and (OSCPF is L), then (RQPF is ML) 5) If (FPSPF is L) and (TEPF is M) and (OSCPF is M) then (RQPF is SL) 6) If (FPSPF is L) and (TEPF is M) and (OSCPF is H), then (RQPF is M) 7) If (FPSPF is L) and (TEPF is H) and (OSCPF is L), then (RQPF is SL) 8) If (FPSPF is L) and (TEPF is H) and (OSCPF is M), then (RQPF is M) 9) If (FPSPF is L) and (TEPF is H) and (OSCPF is H) then (RQPF is SH) 10) If (FPSPF is M) and (TEPF is L) and (OSCPF is L), then (RQPF is ML)

7 98 11) If (FPSPF is M) and (TEPF is L) and (OSCPF is M), then (RQPF is SL) 12) If (FPSPF is M) and (TEPF is L) and (OSCPF is H), then (RQPF is M) 13) If (FPSPF is M) and (TEPF is M) and (OSCPF is L) then (RQPF is SL) 14) If (FPSPF is M) and (TEPF is M) and (OSCPF is M), then (RQPF is M) 15) If (FPSPF is M) and (TEPF is M) and (OSCPF is H), then (RQPF is SH) 16) If (FPSPF is M) and (TEPF is H) and (OSCPF is L), then (RQPF is M) 17) If (FPSPF is M) and (TEPF is H) and (OSCPF is M) then (RQPF is SH) 18) If (FPSPF is M) and (TEPF is H) and (OSCPF is H), then (RQPF is MH) 19) If (FPSPF is H) and (TEPF is L) and (OSCPF is L), then (RQPF is SL) 20) If (FPSPF is H) and (TEPF is L) and (OSCPF is M), then (RQPF is M) 21) If (FPSPF is H) and (TEPF is L) and (OSCPF is H) then (RQPF is SH) 22) If (FPSPF is H) and (TEPF is M) and (OSCPF is L), then (RQPF is M) 23) If (FPSPF is H) and (TEPF is M) and (OSCPF is M), then (RQPF is SH)

8 99 24) If (FPSPF is H) and (TEPF is M) and (OSCPF is H), then (RQPF is MH) 25) If (FPSPF is H) and (TEPF is H) and (OSCPF is L) then (RQPF is SH) 26) If (FPSPF is H) and (TEPF is H) and (OSCPF is M), then (RQPF is MH) 27) If (FPSPF is H) and (TEPF is H) and (OSCPF is H), then (RQPF is H) 6.3 ANFIS BASED RQPF FOR THREE-PHASE SYSTEMS In this chapter, an ANFIS based RQPF for unbalanced three-phase system is proposed. The ANFIS based approach is used to calculate the ANFIS-RQPF which is a single value index that represents a blend of the three recommended power factors, FPSPF, TEPF and OSCPF, each having three linguistic variables assigned as inputs. The proposed ANFIS-RQPF was applied to balanced and unbalanced cases. The results obtained reveal that the ANFIS-RQPF is meaningful and accurately represents the existing power factors. 6.4 ANFIS BASED RQPF DETERMINATION This section explains the ANFIS based approach used to calculate the ANFIS-RQPF which is a single value index that represents an amalgamation of the three recommended power factors, FPSPF, TEPF and OSCPF. This module was built using the Fuzzy Logic Tool Box available in MATLAB. About 500 samples were trained to obtain the desired results. Figure 6.3 shows the Schematic Diagram of the ANFIS-RQPF Module for Three-Phase System.

9 100 The proposed ANFIS based approach has many advantages, such as simplicity, ease of application, flexibility, and being able to handle imprecise or uncertain problems. The problem formulation of defining the power factor for unbalanced systems and the proposed ANFIS based approach used to calculate the RQPF are similar to that of them, in single phase systems. Figure 6.3 Schematic Diagram of the ANFIS-RQPF Module for Three- Phase System 6.5 APPLICATIONS AND RESULTS The FRQPF and ANFIS-RQPF were applied to different test cases that include balanced and unbalanced sources. For given values of the FPSPF, TEPF and OSCPF, the FIS and ANFIS modules were used to calculate the FRQPF and ANFIS-RQPF, respectively. Table 6.1 shows the six different cases of linear loading conditions in which the FRQPF and ANFIS-RQPF have been tested. Table 6.2 shows the rule viewer input and output of FRQPF and ANFIS-RQPF for the two cases, an ideal and non ideal case. The ideal

10 101 case corresponds to the linear load supplied from balanced sinusoidal source while the non ideal case corresponds to the linear load supplied from unbalanced sinusoidal source. Table 6.1 Six Different Cases of Linear Loading Conditions Cases R L R R R S R T L R L S L T Case H 0 H 0 H Case H 0.1 H 0.1 H Case H 0.3 H 0.3 H Case H 0 H 0 H Case H 0.1 H 0.3 H Case H 0.1 H 0.3 H Table 6.2 Rule Viewer Output for Ideal and Non-Ideal Cases Category Input Output FPSPF TEPF OSCPF FRQPF ANFIS-RQPF Ideal Case Non-Ideal Case Figure 6.4 and Figure 6.5 show the Rule Viewer diagram of FRQPF and ANFIS-RQPF, respectively for the ideal case of Table 6.2. Figure 6.6 and Figure 6.7 show the Rule Viewer diagram of FRQPF and ANFIS-RQPF, respectively for the non-ideal case of Table 6.2. It is observed that the ideal case corresponds to the sinusoidal balanced linear system where all of the input power factors have a value equal to one (that is, at their maximum) and therefore, the ANFIS-RQPF gives its maximum value which is nearly equal to one, while the non-ideal case

11 102 corresponds to any other case than the sinusoidal balanced linear system; therefore, the values of the three power factors, the FPSPF, the TEPF, and the OSCPF will be less than one and, as seen, the value of the ANFIS-RQPF is less than one. Figure 6.4 Rule Viewer Diagram for FRQPF in Ideal Case Figure 6.5 Rule Viewer Diagram for ANFIS-RQPF in Ideal Case

12 103 Figure 6.6 Rule Viewer Diagram for FRQPF in Non-Ideal Case Figure 6.7 Rule Viewer Diagram for ANFIS-RQPF in Non-Ideal Case Linear Load Supplied from Balanced Sinusoidal Source The linear load shown in Figure 6.1 was supplied by a balanced sinusoidal source voltage described by equation (6.2). v R ( t) 169.7sin (377t) v S ( t) sin (377t 120 ) v T ( t) 169.7sin (377t 120 ) (6.2)

13 104 The graph of Figure 6.8 shows the three-phase instantaneous balanced source voltage generated using equation (6.2). This source voltage was applied to the six different cases of linear loading conditions shown in Table 6.1. The graph of Figure 6.9 shows the three-phase instantaneous current for case 2 of Table 6.1. The graph of Figure 6.10 shows the threephase instantaneous current for case 4 of Table 6.1. Table 6.3 shows the FRQPF and ANFIS-RQPF values for linear load supplied from balanced sinusoidal source. Figure 6.8 Three-Phase Instantaneous Balanced Source Voltage Current Volts Figure 6.9 Three-Phase Instantaneous Current for Balanced Source Voltage Case 2

14 105 Current Figure 6.10 Three-Phase Instantaneous Current for Balanced source Voltage Case Linear Load Supplied from Unbalanced Sinusoidal Source The linear load shown in Figure 6.1 was supplied by an unbalanced sinusoidal source voltage described by equation (6.3). v R v S ( t) 290sin (377t ( t) 67.86sin (377t 90 ) ) v T ( t) 290sin (377t ) (6.3) The graph of Figure 6.11 shows the three-phase instantaneous balanced source voltage generated using equation (6.3). This source voltage was applied to the six different cases of linear loading conditions shown in Table 6.1. The graph of Figure 6.12 shows the three-phase instantaneous current for case 2 of Table 6.1. The graph of Figure 6.13 shows the threephase instantaneous current for case 4 of Table 6.1. Table 6.4 shows the FRQPF and ANFIS-RQPF values for linear load supplied from unbalanced sinusoidal source.

15 106 Figure 6.11 Three-Phase Instantaneous Unbalanced Source Voltage Figure 6.12 Three-Phase Instantaneous Current for Unbalanced Source Voltage Case 2 Current Current Volts Figure 6.13 Three-Phase Instantaneous Current for Unbalanced Source Voltage Case 4

16 107 Table 6.3 and Table 6.4 show the comparison of the values of FRQPF (Morsi 2008b) and the proposed ANFIS-RQPF for the same input. Table 6.3 FRQPF and ANFIS-RQPF values for Linear Load supplied from Balanced Sinusoidal Source Cases FPSPF TEPF OSCPF FRQPF ANFIS-RQPF Case Case Case Case Case Case Table 6.4 FRQPF and ANFIS-RQPF values for Linear Load supplied from Unbalanced Sinusoidal Source Cases FPSPF TEPF OSCPF FRQPF ANFIS-RQPF Case Case Case Case Case Case Observation of all cases shows that the ANFIS-RQPF represents the three recommended power factors FPSPF, TEPF and OSCPF more accurately in three-phase systems. Thus the proposed ANFIS-RQPF will be useful in many applications, such as customer billing, setting up tariffs, power

17 108 quality assessment and evaluating the power quality mitigation techniques in three-phase systems also. ANFIS enhances the performance of the existing power quality assessment systems in several ways: 1. Maximizing the knowledge gain from the huge amount of power quality data available. 2. By setting the proper boundaries of abnormal behavior, unnecessary invocation of more complex power quality analysis software will be prevented, hence the efficiency (including cost effectiveness) of the service currently offered will be increased drastically. 3. The adaptive technique used eliminates the need for any prior power quality knowledge on behalf of the customer or system engineers.