Voltage Stability Assessment of the Nigerian 330kv Transmission Network Using Artificial Neural Networks

References

[1] ” reference [6]” proposed online monitoring, evaluation and improvement of steady state voltage stability for electric power system using artificial neural networks techniques. The training data was three sets of data obtained by performing load flow and voltage stability analysis for different load factors such as 0.8, 1.0 and 1.2. The ANN was tested with data corresponding to load factors of 0.75 and 1.3 to determine the effectiveness of the proposed method. The selected objective function gave minimum deviation of the reactive power control variables, which lend to the maximization of minimum Eigen value of load flow jacobian. The considered reactive power control variables were switchable VAR compensators, OLTC transformers and excitation of generators. The method was modified on IEEE 30 bus test system. The result obtained clearly shows that the voltage profile increased from 0.86 to 0.968 at bus 26 as minimum Eigen value increased from 0.194 to 0.214 and the power loss reduced from 24.27MW to 20.46MW.

[2] ” reference [5]” proposed power system voltage stability assessment through artificial neural network. A voltage stability index with respect to a load bus was formulated from the voltage equation derived from a two bus network and computed using thevenin equivalent circuit of the power system referred to a load bus. Buses with values of voltage stability factors close to 1.0 are identified as the critical buses. ANN was developed for voltage stability monitoring.

[3] ” reference [9]” proposed power system voltage stability analysis and assessment using artificial neural network. Artificial neural network model was used along with continuation power flow methods to assess the voltage stability of a power system. The modal analysis method was first implemented to identify the most vulnerable load buses of the system. Hundreds of loading patterns were generated by varying the real and reactive power. With the help of input patterns and the target outputs, the neural network with the back propagation error architecture was developed using MATLAB and was applied to 14 bus system. It was observed that the selected neural network was efficient in calculating the voltage stability of L-INDEX for the vulnerable load buses. And the L-index value from the ANN was very close to the actual L-index from the analytical method.

[4] ” reference [8]” proposed artificial neural networks for on line assessment of voltage stability using FVSI in power transmission systems. The ANN model of the system was developed via on line checking of the load of the weak bus, then calculated the fast voltage stability index (FVSI) and line stability factor (LQF). The developed ANN technique was tested in IEEE 30 bus test system and on-line monitoring of 2 bus Indian southern power grid parameters found out the stability limit for the system without any classical calculation. ANN model was trained with a number of input training vector set to meet convergence criterion.

[5] MATERIALS AND METHOD

[6] Nigerian 48 Bus 330kv Network

[7] NEPLAN software simulation result of the modeled 330kv transmission network of a 48 bus system presented in figure 3.1 below and refers to as Pre-upgrade network. The 5 buses with red color show the unstable state of the system.

[8] Figure 3.1: Pre-Upgrade Network Simulation in NEPLAN Software

[9] Bus Operating Voltage for Nigerian 48 Bus 330kv Network

[10] Table 3.1 below shows the nominal and operating voltage of the 330kv transmission network of a 48 bus system.

[11] Table 3.1: Bus Operating Voltage for Pre-Upgrade Network Condition

[12] No

[13] Bus

[14] Name

[15] Nominal

[16] (kV)

[17] Operating Voltage

[18] (KV)

[19] Operating Voltage

[20] (P.U.)

[21] Operating Voltage

[22] (%)

[23] 1

[24] Adiabor

[25] 330

[26] 324.786

[27] 0.9842

[28] 98.42

[29] 2

[30] Afam

[31] 330

[32] 325.149

[33] 0.9853

[34] 98.53

[35] 3

[36] Aja

[37] 330

[38] 329.967

[39] 0.9999

[40] 99.99

[41] 4

[42] Ajakuta

[43] 330

[44] 328.317

[45] 0.9949

[46] 99.49

[47] 5

[48] Akangba

[49] 330

[50] 328.944

[51] 0.9968

[52] 99.68

[53] 6

[54] Aladja

[55] 330

[56] 329.934

[57] 0.9998

[58] 99.98

[59] 7

[60] Alagbon

[61] 330

[62] 329.868

[63] 0.9996

[64] 99.96

[65] 8

[66] Alaoji

[67] 330

[68] 325.116

[69] 0.9852

[70] 98.52

[71] 9

[72] Alaoji TS

[73] 330

[74] 325.116

[75] 0.9852

[76] 98.52

[77] 10

[78] Asaba

[79] 330

[80] 329.538

[81] 0.9986

[82] 99.86

[83] 11

[84] Ayede

[85] 330

[86] 328.812

[87] 0.9964

[88] 99.64

[89] 12

[90] Benin

[91] 330

[92] 329.868

[93] 0.9996

[94] 99.96

[95] 13

[96] B-Kebbi

[97] 330

[98] 320.463

[99] 0.9711

[100] 97.11

[101] 14

[102] Damaturu

[103] 330

[104] 292.149

[105] 0.8853

[106] 88.53

[107] 15

[108] Delta

[109] 330

[110] 330

[111] 1.00

[112] 100.00

[113] 16

[114] Egbin

[115] 330

[116] 330

[117] 1.00

[118] 100.00

[119] 17

[120] Ganmo

[121] 330

[122] 328.977

[123] 0.9969

[124] 99.69

[125] 18

[126] Geregu

[127] 330

[128] 328.317

[129] 0.9949

[130] 99.49

[131] 19

[132] Gombe

[133] 330

[134] 297.66

[135] 0.902

[136] 90.20

[137] 20

[138] Gwagalada

[139] 330

[140] 328.383

[141] 0.9951

[142] 99.51

[143] 21

[144] Ihovbor

[145] 330

[146] 329.868

[147] 0.9996

[148] 99.96

[149] 22

[150] Ikeja West

[151] 330

[152] 328.977

[153] 0.9969

[154] 99.69

[155] 23

[156] Ikot Ekpene

[157] 330

[158] 324.72

[159] 0.984

[160] 98.40

[161] 24

[162] Jalingo

[163] 330

[164] 292.314

[165] 0.8858

[166] 88.58

[167] 25

[168] Jebba

[169] 330

[170] 330

[171] 1.00

[172] 100.00

[173] 26

[174] Jebba TS

[175] 330

[176] 330

[177] 1.00

[178] 100.00

[179] 27

[180] Jos

[181] 330

[182] 313.566

[183] 0.9502

[184] 95.02

[185] 28

[186] Kainji

[187] 330

[188] 330

[189] 1.00

[190] 100.00

[191] 29

[192] Katampe

[193] 330

[194] 328.383

[195] 0.9951

[196] 99.51

[197] 30

[198] Kumbotso

[199] 330

[200] 323.07

[201] 0.979

[202] 97.90

[203] 31

[204] Lekki

[205] 330

[206] 329.967

[207] 0.9999

[208] 99.99

[209] 32

[210] Lokoja

[211] 330

[212] 328.218

[213] 0.9946

[214] 99.46

[215] 33

[216] Maiduguri

[217] 330

[218] 287.562

[219] 0.8714

[220] 87.14

[221] 34

[222] Mando

[223] 330

[224] 327.591

[225] 0.9927

[226] 99.27

[227] 35

[228] Markudi

[229] 330

[230] 321.057

[231] 0.9729

[232] 97.29

[233] 36

[234] New Heaven

[235] 330

[236] 323.697

[237] 0.9809

[238] 98.09

[239] 37

[240] Odukpani

[241] 330

[242] 324.786

[243] 0.9842

[244] 98.42

[245] 38

[246] OkeAro

[247] 330

[248] 329.142

[249] 0.9974

[250] 99.74

[251] 39

[252] Okpai

[253] 330

[254] 330

[255] 1.00

[256] 100.00

[257] 40

[258] Olorunsogo

[259] 330

[260] 329.604

[261] 0.9988

[262] 99.88

[263] 41

[264] Omotosho

[265] 330

[266] 330

[267] 1.00

[268] 100.00

[269] 42

[270] Onitsha

[271] 330

[272] 329.505

[273] 0.9985

[274] 99.85

[275] 43

[276] Oshogbo

[277] 330

[278] 328.845

[279] 0.9965

[280] 99.65

[281] 44

[282] Sakete

[283] 330

[284] 327.69

[285] 0.9930

[286] 99.30

[287] 45

[288] Sapele

[289] 330

[290] 330

[291] 1.00

[292] 100.00

[293] 46

[294] Shiroro

[295] 330

[296] 330

[297] 1.00

[298] 100.00

[299] 47

[300] Ugwaji

[301] 330

[302] 323.697

[303] 0.9809

[304] 98.09

[305] 48

[306] Yola

[307] 330

[308] 293.568

[309] 0.8896

[310] 88.96

[311] Table 3.1 above is the first NEPLAN simulation result of the operating voltage of the system. The following buses (Maiduguru, Jalingo, Yola, Damaturu and Gombe), violates the bus voltage statutory limit condition of 0.95p.u - 1.05p.u (0.8714p.u, 0.8858p.u , 0.8896p.u, 0.8853p.u , 0.9020p.u) respectively.

[312] Modeling of the Static VAR Compensator (SVC)

[313] The SVC used for this work is the Thyristor Controlled Reactor-Fixed Capacitor (TCR-FC) type. The TCR-FC functional diagram and its equivalent circuit are showcased below in figure 3.2 and 3.3.

[314] Figure 3.2: Functional Diagram of a TCR-FC SVC [7].

[315] Figure 3.3: Equivalent circuit of the SVC [7].

[316] The SVC consumes no active power as one branch of the SVC is purely inductive while the other branch is purely capacitive as depicted in figure 3.2 above. The SVC performs two main purpose of consuming (inductive) reactive power to reduce the system voltage or injects reactive power to increase the system voltage. The reactors current (IL) is positive since the reactor consumes reactive power while the capacitor current (IC) is negative since it injects reactive power into the system.

[317] Hence, the SVC current (ISVC) at maximum var could be expressed as:

[318] (3.23)

[319] Where is given as

[320] (3.24)

[321] (3.25)

[322] Where

[323] : Inductive current of the SVC

[324] : Capacitive current of the SVC

[325] : Inductive reactance of the SVC

[326] : Capacitive reactance of the SVC

[327] : Fixed Capacitance of the SVC

[328] : Frequency of the system

[329] : Bus voltage magnitude

[330] Assuming that no real power is consumed by the SVC in Figure 3.5, (i.e. ) then:

[331] (3.26)

[332] Substituting equation (3.23) into (3.26) gives:

[333] (3.27)

[334] Equating equations (3.24), (3.25) and (3.27) gives (3.28)

[335] (3.29)

[336] (3.30)

[337] The design of the SVC controller is in such a way that the TCR-FC is switched ON when the bus voltage becomes lower than the reference voltage and switched OFF when the bus voltage becomes higher than the reference voltage.

[338] Hence, the FC and the TCR are in operation at maximum VAR Injection as such , therefore equation (3.29) becomes;

[339] (3.31)

[340] And at minimum VAR Injection, as such equation (3.29) becomes

[341] (3.32)

[342] 3.4 Artificial Neural Network Architecture in

[343] Matlab

[344] Artificial Neural Network is the biologically inspired computer simulation performed to confirm the basic connection in a set of data similar to the human brain. The neural network helps to modify the input so that the network gives the best result without redesigning the output.

[345] Plate 3.1: Artificial Neural Network Architecture

[346] Plate 3.1 shows a typical neural network architecture containing artificial neurons (units) arranged in a series of layers namely;

[347] (i) Input layer: is made up of nodes that transmit input data (signals) only. They do not calculate the weighted sum and do not use activation function.

[348] (ii) Hidden layer: is the layer between input and output of the neural network. It contains units of artificial neurons that transform the input data (signals) into something the output can use by multiplying the signal by the weight of the signals

[349] (iii) Output layer: is the rightmost layer of the neural network. They contain units of artificial neurons that respond to the information about how the network learned any task and uses activation function to determine the behavior of the layer.

[350] 3.4.1 Training in Artificial Neural Network The objective of the training is to obtain an anticipated output for all input values fed into the network and minimize the error. In neural network, information is stored in terms of weights of neurons. The ANN learns through an iterative process and modifies weights of input to be trained accordingly. A systematic way of modifying the weight of the neuron is known as learning rule. For this thesis, supervised learning rule was used because the target for training is already known.

[351] Supervised learning describes a class of problem where input variables (X) and an output variable (Y) use back propagation algorithm to learn the mapping function from the input to output.

[352] Y = f(X)(3.62)

[353] In this learning procedure, a back propagation algorithm model is used to learn a mapping between input examples and the target variables.

[354] The three layered ANN structure shown in plate 3.1 is known as feed forward artificial neural network. In this network, the information or signal propagates in only one direction forward starting from the input neurons through the hidden layers and to the output neuron without forming a cycle or loops. The feed forward neural networks are primarily used for supervision learning where the data to be learned is neither sequential nor time dependent. In training of the feed forward, back propagation algorithm was used in training of the feed-forward neural networks. In this algorithm, there is propagation from each input pattern of the training dataset through network to input layer and to the output layer. The error is computed when the network generated output is compared with the target output as given below [4]:

[355] (3.63)

[356] Where:

[357] yi : is the ANN generated output

[358] ti : is the component of the desired output/target T

[359] n : is the number of output neurons

[360] p : is the number of training patterns

[361] Through each neuron, this error will be propagated backward and correspondingly the connection weights will be updated.

[362] The back propagation happens when the error signals (inputs) are propagated backward through the network from the output layer to the hidden layer, assigning blames for the error and updating weights as they go. The error for a neuron in the hidden layer is calculated as the weighted error of each neuron in the output layer. Then, the back propagated error signal is accumulated and then used to determine the error for the neuron in the hidden layer.

[363] 3.4.2 Determination of Data for Training in

[364] ANN

[365] The Nigeria 330kv modeled operating voltages result is used as the input data while the improved result Nigeria 330kv modeled operating voltages is used as the target data for neural network simulation. The quantities used are operating voltage, active power respectively

[366] 3.4.3 Algorithm for ANN Training

[367] Step 1. Input training data formatted as [input, target]. For the research work, 3x36 input signals were used. The input signal is giving by

[368] Input (x)=x1ix2ix3i (3.64)

[369] Where

[370] x1i : Voltage magnitude (p.u)

[371] x2i : Active power loading (MW)

[372] x3i : Current loading (A)

[373] i=1,2,3,4,5+…….36

[374] Step 2. Initialize the weights and bias

[375] w=w1 w2 w3, b (3.65)

[376] The weighted sum of the output node i is giving by

[377] vi=w1 w2 w3*x1ix2ix3i+b (3.65)

[378] vi=w1*x1i+w2*x2i+w3*x3i+b (3.66)

[379] Where

[380] x1i : Voltage magnitude (p.u)

[381] x2i : Real power loading (MW)

[382] x3i : Current loading (A)

[383] w1 : Weight of x1i

[384] w2: Weight of x2i

[385] w3: Weight of x3i

[386] b= bias which is associated with the storage of information

[387] Step 3. Calculate output

[388] Ouput (yi)=∅(vi) (3.67) =∅(w1*x1i+w2*x2i+w3*x3i+b (3.68)

[389] ∅vi=11+e-vi (3.69)

[390] Ouput (y)=11+e-(w1*x1i+w2*x2i+w3*x3i+b) (3.70)

[391] Where

[392] ∅ : Activation function (Tan Sigmoid Function)

[393] vi : Weighted sum of the output node i

[394] x1i: Voltage magnitude (p.u)

[395] x2i : Active power loading (MW)

[396] x3i : Current loading (A)

[397] w1 : Weight of x1i

[398] w2 : Weight of x2i

[399] w3 : Weight of x3i

[400] B : Bias which is associated with the storage of information

[401] Step 4. Calculate the error.

[402] The difference between the output and the target of a neural network

[403] ei=di-yi(3.71)

[404] Where

[405] di : Target

[406] yi : Output

[407] Step 5. Calculate the weights

[408] wij=αeixj(3.72)

[409] Where

[410] α : Learning rate [0,1]

[411] ei : Error in node i

[412] xj : Output from node j where j=1,2,3 and so on.

[413] Step 6. Adjust the weight update using Mini Batch Method. The Mini Batch method has the speed of Stochastic gradient descent (SGD) method and the stability of Batch method.

[414] wij=wij+ αδixj (3.73)

[415] δi=∅Iviei(3.74)

[416] ∅v=11+e-v(3.75)

[417] ∅Ivi=∅(vi)(1-∅(vi)) (3.76)

[418] δi=∅(vi)(1-∅(vi))ei(3.77)

[419] wij=wij+ α∅(vi)(1-∅(vi))eixj (3.78)

[420] Where

[421] vi : Weighted sum of the output node i

[422] ei : Error in node i

[423] xj : Output from node j where j=1,2,3 and so on.

[424] ∅I : Derivative of the activation function ∅ of node i

[425] α : Learning rate [0,1]

[426] wij : Previous weight

[427] Step 7. Repeat step 4 to 6 for all training data until the error reaches an acceptable limit. From step 4 to step 6 is known as epoch

[428] Plate 3.2 Flow chat of ANN Training

[429] RESULTS AND DISCUSSION

[430] 4.1 Improved Nigerian 330kv transmission

[431] network

[432] NEPLAN software simulation result of the improved 330kv transmission network is presented in figure 4.1 below and refers to as Post-upgrade network. All the buses in green color signify stability state of the system.

[433] Figure 4.1: Post-Upgrade Networks Simulation in NEPLAN Software

[434] 4.1.1 Improved Buses Result

[435] The improved vulnerable buses NEPLAN simulation result is presented in figure 4.2 below showing the improved operating voltages as contained and declared by statutory condition. The buses displaying green color signifies stability of the system.

[436] Table 4.1: Bus Operating Voltage for Post-Upgrade Network Condition

[437] No

[438] Bus

[439] Name

[440] Nominal

[441] (kV)

[442] Post- Upgrade (KV)

[443] Post- Upgrade (P.U.)

[444] Post- Upgrade (%)

[445] 1

[446] Adiabor

[447] 330

[448] 328.581

[449] 0.9957

[450] 99.57

[451] 2

[452] Afam

[453] 330

[454] 328.779

[455] 0.9963

[456] 99.63

[457] 3

[458] Aja

[459] 330

[460] 329.967

[461] 0.9999

[462] 99.99

[463] 4

[464] Ajakuta

[465] 330

[466] 328.35

[467] 0.995

[468] 99.50

[469] 5

[470] Akangba

[471] 330

[472] 328.944

[473] 0.9968

[474] 99.68

[475] 6

[476] Aladja

[477] 330

[478] 329.934

[479] 0.9998

[480] 99.98

[481] 7

[482] Alagbon

[483] 330

[484] 329.868

[485] 0.9996

[486] 99.96

[487] 8

[488] Alaoji

[489] 330

[490] 328.746

[491] 0.9962

[492] 99.62

[493] 9

[494] Alaoji TS

[495] 330

[496] 328.746

[497] 0.9962

[498] 99.62

[499] 10

[500] Asaba

[501] 330

[502] 329.769

[503] 0.9993

[504] 99.93

[505] 11

[506] Ayede

[507] 330

[508] 328.812

[509] 0.9964

[510] 99.64

[511] 12

[512] Benin

[513] 330

[514] 329.901

[515] 0.9997

[516] 99.97

[517] 13

[518] B-Kebbi

[519] 330

[520] 320.463

[521] 0.9711

[522] 97.11

[523] 14

[524] Damaturu

[525] 330

[526] 323.862

[527] 0.9814

[528] 98.14

[529] 15

[530] Delta

[531] 330

[532] 330

[533] 1.00

[534] 100.00

[535] 16

[536] Egbin

[537] 330

[538] 330

[539] 1.00

[540] 100.00

[541] 17

[542] Ganmo

[543] 330

[544] 329.01

[545] 0.997

[546] 99.70

[547] 18

[548] Geregu

[549] 330

[550] 328.35

[551] 0.995

[552] 99.50

[553] 19

[554] Gombe

[555] 330

[556] 324.159

[557] 0.9823

[558] 98.23

[559] 20

[560] Gwagalada

[561] 330

[562] 328.416

[563] 0.9952

[564] 99.52

[565] 21

[566] Ihovbor

[567] 330

[568] 329.901

[569] 0.9997

[570] 99.97

[571] 22

[572] Ikeja West

[573] 330

[574] 328.977

[575] 0.9969

[576] 99.69

[577] 23

[578] Ikot Ekpene

[579] 330

[580] 328.515

[581] 0.9955

[582] 99.55

[583] 24

[584] Jalingo

[585] 330

[586] 322.179

[587] 0.9763

[588] 97.63

[589] 25

[590] Jebba

[591] 330

[592] 330

[593] 1.00

[594] 100.00

[595] 26

[596] Jebba TS

[597] 330

[598] 330

[599] 1.00

[600] 100.00

[601] 27

[602] Jos

[603] 330

[604] 326.667

[605] 0.9899

[606] 98.99

[607] 28

[608] Kainji

[609] 330

[610] 330

[611] 1.00

[612] 100.00

[613] 29

[614] Katampe

[615] 330

[616] 328.383

[617] 0.9951

[618] 99.51

[619] 30

[620] Kumbotso

[621] 330

[622] 324.489

[623] 0.9833

[624] 98.33

[625] 31

[626] Lekki

[627] 330

[628] 329.967

[629] 0.9999

[630] 99.99

[631] 32

[632] Lokoja

[633] 330

[634] 328.218

[635] 0.9946

[636] 99.46

[637] 33

[638] Maiduguri

[639] 330

[640] 322.839

[641] 0.9783

[642] 97.83

[643] 34

[644] Mando

[645] 330

[646] 328.911

[647] 0.9967

[648] 99.67

[649] 35

[650] Markudi

[651] 330

[652] 327.459

[653] 0.9923

[654] 99.23

[655] 36

[656] New Heaven

[657] 330

[658] 327.921

[659] 0.9937

[660] 99.37

[661] 37

[662] Odukpani

[663] 330

[664] 328.581

[665] 0.9957

[666] 99.57

[667] 38

[668] OkeAro

[669] 330

[670] 329.142

[671] 0.9974

[672] 99.74

[673] 39

[674] Okpai

[675] 330

[676] 330

[677] 1.00

[678] 100.00

[679] 40

[680] Olorunsogo

[681] 330

[682] 329.604

[683] 0.9988

[684] 99.88

[685] 41

[686] Omotosho

[687] 330

[688] 330

[689] 1.00

[690] 100.00

[691] 42

[692] Onitsha

[693] 330

[694] 329.736

[695] 0.9992

[696] 99.92

[697] 43

[698] Oshogbo

[699] 330

[700] 328.845

[701] 0.9965

[702] 99.65

[703] 44

[704] Sakete

[705] 330

[706] 327.69

[707] 0.993

[708] 99.30

[709] 45

[710] Sapele

[711] 330

[712] 330

[713] 1.00

[714] 100.00

[715] 46

[716] Shiroro

[717] 330

[718] 330

[719] 1.00

[720] 100.00

[721] 47

[722] Ugwaji

[723] 330

[724] 327.921

[725] 0.9937

[726] 99.37

[727] 48

[728] Yola

[729] 330

[730] 322.443

[731] 0.9771

[732] 97.71

[733] Table 4.1 shows the nominal and operating voltage of the system for post-upgrade network condition. The post-upgrade network condition is the state when static var compensators are installed. Table 4.1 shows that no buses violate the statutory limit condition of 0.95p.u. (313.5kV) - 1.05p.u. (326.5kV)

[734] 4.3 Voltage Profile Comparisons of Pre-Upgrade and Post-Upgrade Network

[735] Figure 4.3 below shows voltage profile of pre-upgrade in (KV) and post-upgrade network in (KV) against bus name where the blue color represents the pre-upgrade while the red color represents the post upgrade.

[736] Figure 4.3: Voltage Profile Comparisons of Pre-Upgrade and Post-Upgrade Network

[737] Figure 4.3 depicts comparisons of pre-upgrade maximum voltage loadability and post-upgrade maximum voltage loadability and showcases the improvement achieved. of pre-upgrade maximum voltage loadability is below 300KV while the post-upgrade maximum voltage loadability is above 320KV.

[738] 4.4Voltage Improvement for the vulnerable buses

[739] Figure 4.4 depicts the voltage profile comparison of bus operating voltages without static var compensation and bus operating voltages with static var compensation in (KV). The blue color represents the buses without var compensation while red color represents bus voltages with var compensation.

[740] Figure 4.4: Voltage Improvement for the vulnerable buses

[741] The graph shows the improvement achieved after optimal placement of static var compensator on the vulnerable buses and also showcases the maximum voltage loadability of the buses without static var compensator placement being below 300KV and the maximum voltage loadability of the buses after static var compensator placement being above 320KV.

[742] 4.5 ANN Training Regression Plot

[743] Figure 4.5 shows the regression plot of the ANN output against the targets which reveals the fitness of the training result.

[744] Figure 4.5: ANN Training Regression Plot

[745] Regression (R) = 1 indicates there is an exact linear relationship between outputs and targets and Regression (R) = 0 indicates no linear relationship between the output and the target. Figure 11 shows the R value equals to 0.9992 for training, 0.99993 for validation and 0.99855 for testing. This shows that the applied ANN model, training, testing and validation are significantly acceptable and a perfect regression existed between the output and the target

[746] 4.6ANN Training Performances

[747] Figure 4.6 below shows the performance plot of the ANN training. The blue, green and red clolrs represent the training, validation and test mode respectively.

[748] Figure 4.6: ANN Training Performances

[749] During training, the performance for each iteration is calculated and the point where the three plots almost coincided is chosen to be the best performance. At that point, the training process is stopped and no further training is required else the results maybe predicted wrongly. From the performance plot the best validation performance during training process is 10.4258 at epoch 4 which indicates how much minimized errors occurred during the training.

[750] CONCLUSION

[751] Following the completion of the research, it can be observed that the research successfully addressed the objectives set out at the beginning of the research. Artificial neural network applications were able to asses and predict the voltage stability of the Nigerian 330KV transmission network using regression supervised learning that deals with prediction of numerical label.

[752] REFERENCES

[753] Anazia, A. E., Okolo, C. C., Ngene, C. C., & Ezeugbor, I. C. (2020). Artificial neural network (ANN) controlled VSC-HVDC as a means to enhance the transient stability of Benin bus in the Nigerian 330kv transmission system. International journal of scientific and engineering research, 11(6), 2229-5518.

[754] Madueme, T. C., & Kalu, O. O. (2015). Application of artificial neural network for enhanced power systems protection on the Nigerian 330KV network. [Master Degree Disertation, University of Nigeria, Nsukka], 93-96. Researchgate.net.

[755] Mbamaluikem, P. O., Awelewa, A. A., Samuel, I. A. (2018). An Artificial Neural Network-Based Intelligent Fault Classification System for the 33-kv Nigeria Transmission Line. International Journal of Applied Engineering Research, 3(5), 12-18.

[756] Mohan, R., Srivastava, R., K., Dinesh C. S., Bisht, H. C., Sharma, & Anil, K. 1. (2011). Development of Artificial Neural-Network-Based Models for the Simulation of Spring Discharge. Hindawi Publishing Corporation Advances in Artificial Intelligence, 2(3), 25-28.

[757] Rahi, O. P., Amit, K. Y., Hasmat, M., Abdul, A., & Bhupesh, K. (2011). Power system voltage stability assessment through artificial neural network. International Conference on Communication Technology and System Design, 4(5), 53-60. www.sciencedirect.com

[758] Shamam, F. A. (2011). Online monitoring, evaluation and improvement of steady state voltage stability for electric power system using artificial neural networks techniques. Journal of Babylon University/pure and applied sciences, 1(19), 6-8.

[759] Simeon, M., Samuel, W. T., Isaiah, A., & Emmanuel, A. (2014). Power system’s voltage stability improvement using static var compensator. International Journal of Emerging Technology and Advanced Engineering, 4(1), 2250-2459. www.ijetae.com

[760] Vadivelu, K. R., & Marutheswar, G. V. (2012). Artificial neural network for on-line assessment of voltage stability using FVSI in power transmission systems. Journal of electrical and electronic engineering (IOSR-JEEE), 7(6), 52-58.

[761] Rohan, S. (2014). Power system voltage stability analysis and assessment using artificial neural network. [M.SC Disertation, The Californa State University, Northridge], 91-97. Researchgate.net.

@article{1703628,
      author = {Chukwuka L. Onita, Osazee E. Ogbeifun, Harmon E. Okilo, Bright Z. Ogoro},
      title = {Voltage Stability Assessment of the Nigerian 330kv Transmission Network Using Artificial Neural Networks},
      journal = {Iconic Research And Engineering Journals},
      year = {2022},
      volume = {6},
      number = {1},
      pages = {295-306},
      issn = {2456-8880},
      url = {https://www.irejournals.com/formatedpaper/1703628.pdf},
      abstract = {The study looked at Nigerian 330kv transmission network of a 48 bus system. The identified vulnerable buses in the system (Maiduguri bus, Jalingo bus, Yola bus, Damaturu bus and Gombe bus) were optimally compensated using static var compensator. In order to assess the voltage stability of the Nigerian 330KV transmission network after optimal compensation, artificial neural networks were introduced. The artificial neural network was introduced. Artificial neural network simulation showed that blue, green and red plot indicates the training, validation and test mode respectively. The performance regarding each iteration was calculated and the point where the three plots coincided was chosen to be the best performance as it became the best line of fit. The best validation performance during the training process is 10.4258 at epoch 4 which indicates how much minimized Mean-Square Error (MSE) occurred during the training. Also, the regression plot of the artificial neural network output against the targetsreveals the fitness of the training result. Regression = 1 indicates there is an exact linear relationship between outputs and targets and Regression=0 indicates no linear relationship between the output and the target. The regression plot shows the R value equals to 0.9992 for training, 0.99993 for validation, and 0.99855 for testing. This shows that the applied ANN model, training, testing and validation are significantly acceptable and a perfect regression existed between the output and the target.},
      month = {July},
  }