Development of a fuzzy inference engine for the fault analysis

Fig 5.23 show algorithm and steps to design the FIE for the specified purpose. As per the simulation study conducted in the VSC-HVDC system for various types of fault in the previous section, a mapping analysis has been conducted between the various input parameters such as voltages and currents of VSC1 & 2, DC line voltage and current and fault index as step 1 which is shown in Fig 5.23. From the analysis, three parameters have been identified as input variables in the fuzzy inference engine to identify twenty one possible types of fault (step 2). Twenty one type of fault is represented as seven binary bits which results in a decimal equivalent of a fault index. The fault index of different faults with respect to the binary representation is discussed in the previous

0 100 200 300 400 500 600 700 800 900 1000 0 73 69 67 76 70 74 77 71 75 79 16 41 37 35 45 39 43 44 38 42 47 D C L in e C u rr en t (A ) Fault Index PT=30% PT=50% PT=80% PT=100%

122

section as given in Table 5.4. Hence seven binary bits representation of the fault index is considered as seven output parameters in the fuzzy inference engine.

Fig 5.23 Flow chart for classification algorithm

A fuzzy inference engine shown in Fig 5.24 is therefore applied to identify different faults in the HVDC system.

123

Fig 5.24 Fuzzy inference engine for fault classification

The five range of power transfer are considered in the input (100%, 80%, 65%, 50%, 30%) to cover the full range of operation possible. The range of membership functions for the FIE are identified from 110 (22x5 i.e. 100%, 80%, 65%, 50%, 30%) element data obtained through the simulation and analysis of faults on the HVDC system, as given in Table 5.6 (step 3 in Fig 5.23) (see Appendix 3 for range of membership functions and design of FIE).

Table 5.6 Fuzzy variable in the antecedent Parts

Variable Center of Triplets

VdqVSC1 VdqVSC2 Idc mf1 0 0 0 mf2 63 67 125 mf3 123 140 250 mf4 175 180 375 mf5 182 195 500 mf6 186 200 625 mf7 240 250 750 mf8 260 275 875 mf9 280 295 1000 mf10 300 320 - mf11 330 360 - mf12 380 380 -

Hence triangular membership functions of twelve, twelve, and nine has been selected for the dq axis voltage of VSC1, dq axis voltage of VSC2 and DC line current

124

respectively for fuzzification. Two membership functions of S-shape and Z-shape are selected as the defuzzification membership for all seven output parameters of the FIE to represent the two states of the output. This 12 x 12 x 9 input membership used in the Fuzzification results in 1296 rules. However 172 valid rules with respect to the input– output data have been framed from the simulation results obtained from the fault study as follows. VdqVSC1 of 374 kV and VdqS2 of 391 kV are observed during the normal

operation of HVDC system. However according to the power transfer from VSC1 to VSC2, 8 valid rules are considered during healthy condition. Ten different faults in the VSC1 side results in 80 rules for various power transfer capacity. Similarly, 10 different faults in the VSC2 side results in another 80 rules. Based on VdqVSC1 and VdqS2, 4

valid rules are considered for DC fault. Therefore the total numbers of rules are 172 (8+80+80+4). The intermediate rules are skipped and the essential rules are listed below.

1. If VdqVSC1 is mf1, VdqVSC2 is mf12 and Idc is mf5 then VSC1 is high, VSC2 is

low, DC is low, a is high, b is high, c is high and G is high.

8. If VdqVSC1 is mf5, VdqVSC2 is mf12 and Idc is mf5 then VSC1 is high, VSC2 is

low, DC is low, a is high, b is high, c is low and G is high.

32.If VdqVSC1 is mf4, VdqVSC2 is mf12 and Idc is mf7 then VSC1 is high, VSC2 is

low, DC is low, a is high, b is high, c is low and G is high.

56.If VdqVSC1 is mf8, VdqVSC2 is mf12 and Idc is mf6 then VSC1 is high, VSC2 is

low, DC is low, a is high, b is high, c is low and G is low.

80.If VdqVSC1 is mf10, VdqVSC2 is mf12 and Idc is mf6 then VSC1 is high, VSC2 is

low, DC is low, a is high, b is low, c is low and G is high.

104. If VdqVSC1 is mf12, VdqVSC2 is mf1 and Idc is mf4 then VSC1 is low, VSC2 is

125

112. If VdqVSC1 is mf12, VdqVSC2 is mf9 and Idc is mf6 then VSC1 is low, VSC2 is

high, DC is low, a is high, b is high, c is low and G is low

136. If VdqVSC1 is mf12, VdqVSC2 is mf6 and Idc is mf5 then VSC1 is low, VSC2 is

high, DC is low, a is high, b is high, c is low and G is high

160. If VdqVSC1 is mf12, VdqVSC2 is mf12 and Idc is mf1 then VSC1 is low, VSC2

is low, DC is high, a is high, b is low, c is low and G is low

164. If VdqVSC1 is mf12, VdqVSC2 is mf12 and Idc is mf9 then VSC1 is low, VSC2

is low, DC is low, a is low, b is low, c is low and G is low

172. If VdqVSC1 is mf12, VdqVSC2 is mf12 and Idc is mf2 then VSC1 is low, VSC2

is low, DC is low, a is low, b is low, c is low and G is low

Input quantities, VdqVSC1 and VdqVSC2 along with the DC line current are given as the

input to the FIE. As these quantities are crisp in nature they need to be converted to the corresponding fuzzy variables by a fuzzyfication technique. For implementing the FIE the “min” implication operator and “max” aggregation operator has been used. After fuzzyfication the fuzzified inputs are given to the decision making unit of the FIE. The decision making unit decides the fuzzy outputs based on the Mamdani’s rule [109] base (172 rules) which are developed based on the simulation study of the HVDC system under various faults. To determine the crisp value of the output parameter from the fuzzy outputs given by the decision making unit, Maximum Of the Membership (MOM) is selected as a defuzzification method in this chapter. As per the considered input and output parameters, the number of membership functions, possible rules, and a defuzzification method of FIE has been developed using the fuzzy logic toolbox in the MATLAB environment.

The developed FIE has been tested in the fuzzy logic toolbox for sample inputs as shown in Fig 5.25 From Fig 5.25, it can be observed that the developed FIE produces

126

the crisp output value of 0.035 for all seven output parameters when the value of input parameters of VdqVSC1 = 374 V, VdqVSC2 = 391V and Idc = 940 A of the HVDC

system which transfer the 100% of the rated power from VSC1 to VSC2. Hence, these results proves that HVDC system does not have any fault for the given sample input data.

Fig 5.25 FIE rules produce crisp output

Similarly, a FIE has been developed based on the Sugeno method [110] for the same input and output parameter used in the Mamdani’s method. A simulation has been conducted on both Mamdani’s and Sugeno’s FIE for the fault identification of HVDC system for 100% rated power transfer from VSC1 to VSC2 and the results are given in Table 5.7. Mean Squared Error (MSE) has been calculated for the results obtained from both methods and MSE is expressed in Eqn. (5.7).

127 Mean Squared Error,

𝑀𝑆𝐸 = 1

𝑛 ∑(𝑎𝑖 𝑛

𝑖=1

− 𝑏_𝑖)2 _(5.7)

where n is the number of sample data points, 𝑎_𝑖 and 𝑏_𝑖 are expected value and measured value respectively. A performance comparison based on the MSE proves that Mamdani’s FIE gives a small value of 0.7% comparing to Sugeno’s FIE which gives the MSE of 2.7%.

Table 5.7 Simulation result of Mamdani and Sugeno methods for 100% power transfer

s.no VSC1 VSC2 DC a b c G E M S E M S E M S E M S E M S E M S E M S 0 0 0.04 0 0 0.04 0 0 0.04 0 0 0.04 0.00 0 0.04 0.00 0 0.04 0.00 0 0.04 0.00 73 1 0.97 1 0 0.03 0 0 0.03 0 1 0.97 1.00 0 0.03 0.16 0 0.03 0.00 1 0.97 0.84 69 1 0.97 1 0 0.03 0 0 0.03 0 0 0.03 0.19 1 0.97 0.81 0 0.03 0.19 1 0.97 0.81 67 1 0.97 1 0 0.04 0 0 0.04 0 0 0.04 0.25 0 0.04 0.25 1 0.97 0.75 1 0.97 1.00 76 1 0.97 1 0 0.03 0 0 0.03 0 1 0.97 0.76 1 0.97 1.00 0 0.03 0.00 0 0.03 0.24 70 1 0.98 1 0 0.03 0 0 0.03 0 0 0.03 0.05 1 0.97 0.95 1 0.98 1.00 0 0.03 0.05 74 1 0.97 1 0 0.04 0 0 0.04 0 1 0.97 0.92 0 0.04 0.00 1 0.97 1.00 0 0.04 0.08 77 1 0.97 1 0 0.03 0 0 0.03 0 1 0.97 1.00 1 0.97 1.00 0 0.03 0.00 1 0.97 1.00 71 1 0.97 1 0 0.03 0 0 0.03 0 0 0.03 0.01 1 0.97 1.00 1 0.97 1.00 1 0.97 1.00 75 1 0.97 1 0 0.03 0 0 0.03 0 1 0.97 0.98 0 0.03 0.02 1 0.97 1.00 1 0.97 1.00 79 1 0.97 1 0 0.04 0 0 0.04 0 1 0.97 1.00 1 0.97 1.00 1 0.97 1.00 1 0.97 1.00 16 0 0.03 0 0 0.03 0 1 0.97 1 0 0.03 0.00 0 0.03 0.00 0 0.03 0.00 0 0.03 0.00 41 0 0.04 0 1 0.97 1 0 0.04 0 1 0.97 1.00 0 0.04 0.00 0 0.04 0.00 1 0.97 1.00 37 0 0.03 0 1 0.97 1 0 0.03 0 0 0.03 0.05 1 0.97 1.00 0 0.03 0.00 1 0.97 0.95 35 0 0.04 0 1 0.97 1 0 0.04 0 0 0.04 0.05 0 0.04 0.05 1 0.97 0.95 1 0.97 1.00 45 0 0.03 0 1 0.98 1 0 0.03 0 1 0.98 1.00 1 0.97 0.98 0 0.03 0.02 1 0.98 0.98 39 0 0.04 0 1 0.97 1 0 0.04 0 0 0.04 0.00 1 0.97 1.00 1 0.97 1.00 1 0.97 1.00 43 0 0.04 0 1 0.97 1 0 0.04 0 1 0.97 0.93 0 0.04 0.07 1 0.97 1.00 1 0.97 1.00 44 0 0.03 0 1 0.97 1 0 0.03 0 1 0.97 1.00 1 0.97 0.86 0 0.03 0.00 0 0.03 0.14 38 0 0.04 0 1 0.97 1 0 0.04 0 0 0.04 0.01 1 0.97 1.00 1 0.97 1.00 0 0.04 0.01 42 0 0.03 0 1 0.97 1 0 0.03 0 1 0.97 0.95 0 0.03 0.06 1 0.97 0.95 0 0.03 0.06 47 0 0.04 0 1 0.97 1 0 0.04 0 1 0.97 1.00 1 0.97 1.00 1 0.97 1.00 1 0.97 1.00

Percentage Mean squared error of Madani and Sugeno respectively, 0.736 and 2.702