# Optimal Operation of the Hybrid Electricity Generation System Using Multiverse Optimization Algorithm

Authors: Muhammad Sulaiman; Sohail Ahmad; Javed Iqbal; Asfandyar Khan; Rahim Khan
Journal: Computational Intelligence and Neuroscience
 (2019)

---

## Abstract

The ongoing load-shedding and energy crises due to mismanagement of energy produced by different sources in Pakistan and increasing dependency on those sources which produce energy using expensive fuels have contributed to rise in load shedding and price of energy per kilo watt hour. In this paper, we have presented the linear programming model of 95 energy production systems in Pakistan. An improved multiverse optimizer is implemented to generate a dataset of 100000 different solutions, which are suggesting to fulfill the overall demand of energy in the country ranging from 9587 MW to 27208 MW. We found that, if some of the power-generating systems are down due to some technical problems, still we can get our demand by following another solution from the dataset, which is partially utilizing the particular faulty power system. According to different case studies, taken in the present study, based on the reports about the electricity short falls been published in news from time to time, we have presented our solutions, respectively, for each case. It is interesting to note that it is easy to reduce the load shedding in the country, by following the solutions presented in our dataset. Graphical analysis is presented to further elaborate our findings. By comparing our results with state-of-the-art algorithms, it is interesting to note that an improved multiverse optimizer is better in getting solutions with lower power generation costs.


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## Body

## 1. Introduction

Proper management and finding out optimal solutions to utilize the available power production sources is an important optimization problem in Pakistan, which is the main theme of this paper [1–11]. According to the reports in [12, 13], the demand of the power is increasing exponentially and which is causing an increase in load shedding each year [14]. The cause of this shortage is mismanagement of power production sources.According to a report published by National Electric Power Regulatory Authority (NEPRA) in 2016 [15], the total capacity of 27240 MW is installed in the country, whereas the demand rises to 22000 MW in summer [16]. These production units can produce enough energy if all are managed optimally. In [17], these production units were normally producing up to 13240 MW with 4760 MW of shortfall. In nomenclature, we have indicated all the 95 installed capacities of electricity production with majority of them depending on thermal sources [15]. In [14], it is reported that the gap between demand and production is expected to increase in the coming years. It is further reported in the literature [14, 18] that urban areas are facing a load shading in summer season as of 10–12 hours, and in rural areas, it is even worse as 16–18 hours a day. Urbanization and rapid increase in population have caused an increase in the industrial zones [19], and it is worth noting that the demand of electricity was 16000 (MW) during summer of 2012 while the short fall was 8500 (MW) [20].In this study, we have explored a scientific decision-making approach in terms of mathematical programming for providing a strategy to utilize the available production sources of Pakistan to meet the demand of energy in different seasons. However, in [21], a general mechanism was presented in terms of 5 major energy production types as X1 to X5. They have fixed the per unit price to estimate the overall mathematical model. We have extended the model and included 95 production sources, which generates electricity using different means (oil, gas, wind, hydropower, and coal). We have implemented per unit price according to the actual price of fuel used to run these sources. The production capacities of each source are given in Table 1 [22]. Our model will help to reduce the shortfall by utilizing the power production sources properly.Table 1
Electricity production constraints on each source.
Power unit
Lower limit
Upper limit
x
1
0
3478
x
2
0
1000
x
3
0
1450
x
4
0
243
x
5
0
184
x
6
0
130
x
7
0
121
x
8
0
72
x
9
0
30
x
10
0
22
x
11
0
22
x
12
0
20
x
13
0
17
x
14
0
14
x
15
0
13.5
x
16
0
4
x
17
0
1
x
18
0
1
x
19
0
1655
x
20
0
1350
x
21
0
850
x
22
0
244
x
23
0
195
x
24
0
174
x
25
0
150
x
26
0
132
x
27
0
59
x
28
0
39
x
29
0
35
x
30
0
17
x
31
0
247
x
32
0
100
x
33
0
100
x
34
0
1260
x
35
0
560
x
36
0
900
x
37
0
362
x
38
0
365
x
39
0
29
x
40
0
225
x
41
0
165
x
42
0
330
x
43
0
94
x
44
0
152.5
x
45
0
226.5
x
46
0
157
x
47
0
110
x
48
0
179
x
49
0
165
x
50
0
188
x
51
0
201.5
x
52
0
136
x
53
0
140
x
54
0
225
x
55
0
225
x
56
0
1292
x
57
0
165
x
58
0
120
x
59
0
131
x
60
0
1638
x
61
0
232
x
62
0
202
x
63
0
660
x
64
0
200
x
65
0
200
x
66
0
225
x
67
0
164
x
68
0
412
x
69
0
114
x
70
0
225
x
71
0
235
x
72
0
350
x
73
0
52
x
74
0
80
x
75
0
110
x
76
0
133.5
x
77
0
126
x
78
0
990
x
79
0
137
x
80
0
325
x
81
0
325
x
82
0
340
x
83
0
425
x
84
0
150
x
85
0
50
x
86
0
50
x
87
0
49
x
88
0
50
x
89
0
52
x
90
0
50
x
91
0
56
x
92
0
30
x
93
0
49
x
94
0
50
x
95
0
50In the last few years, evolutionary algorithms (EAs) are implemented to solve different real-world optimization problems. EAs simulate social behavior or natural procedures in order to handle optimization problems with best solution. Among the popular EAs are the Bat algorithm [23, 24], grasshopper optimization algorithm (GOA) [25], and firefly algorithm (FA) [26, 27]. The efficiency of metaheuristics is better as compared to classical optimization techniques in solving optimization problems with iterations and random search behavior. The main idea behind all EAs is the survival of the fittest, which in return increases the fitness of individuals in population. EAs are implemented with different frameworks, which includes population structure and search equations [28]. EAs with different frameworks generate random populations. Then, all solutions are evaluated according to a given objective function. The search space is explored and exploited in two phases. EAs get stuck in local optima due to their random search. Several papers are published in the literature to overcome this problem in EAs [29, 30].The multiverse optimization algorithm (MVO) is a nature-inspired optimization technique given in [31]. The key idea of MVO is inspired from the theory of multiverses. Since its invention, it is applied to solve several real-world problems. In [31], it is shown that MVO obtained very competitive results compared with other metaheuristic optimization algorithms. Also, Faris et al. [32] employed the MVO for training the multilayer perceptions in neural network. The efficiency of their techniques was evaluated on different medical datasets from UCI repository. The outcome of their experiments is then compared to different metaheuristics, namely, Particle Swarm Optimization (PSO), Genetic Algorithm (GA), Differential Evolution (DE) Algorithm, and Cuckoo Search (CS). It was observed that MVO was improved in terms of convergence and avoidance of local optima. MVO still lacks behind in accuracy of results and convergence speed. Fewer studies, like Levy-flight-based MVO [33] and a quantum version of MVO [34], are recently proposed to further enhance the capabilities of MVO. Experimental results show that they have improved the solutions to some extent.Currently, as can be seen in the former review, there are limited works on improving the performance of MVO. This work presents a new method of initialization with the MVO algorithm called improved multiverse optimization algorithm (IMVO). The experimental results on mathematical model of economic dispatch problem of electricity generation system in Pakistan and its three case studies show that IMVO is very competitive over FA, Bat algorithm, and GOA.Furthermore, we have presented solutions to five case studies for proper management and production by all the 95 energy producers in the country. Our model can be implemented to reduce the load shedding and distribute the burden of production on respective power production units.This work is organized as follows: Section2 describes the concept of multiverse optimizer and improvements in it. The mathematical model for the problem is described in Section 3. Experimental settings, results, and discussions based on numerical simulations are given in Section 4. Conclusion of our findings is presented in Section 5.


## 2. An Improved Multiverse Optimizer

The MVO algorithm simulates the theory of multiverse, where three verses play main part in the whole algorithmic procedure: these are white holes, black holes, and wormholes. This is a population-based algorithm, where the population is searched in two phases: exploration in which the search space is visited very well and exploitation performs the search in neighborhood of a solution extensively. White hole and black hole, in the theory of multiverses, are used as exploration agents, and wormhole is acting as exploitation agent in this algorithm. In Figure1, black, yellow, green, and pink are the objects which are moving through the white/black hole, and white points represent objects which move through the wormhole. There are 5 assumptions that are applied in MVO to the population/universe [31]:(a)
The probability of having the white holes is directly proportional to the inflation rate.(b)
Individuals (universes) having higher inflation rate send objects through white holes with higher probability.(c)
Individuals (universes) having higher inflation rate send objects through white holes with higher probability.(d)
Individuals (universes) having lower rate of inflation send objects through black holes with higher probability.(e)
The objects present in all universes are moved randomly towards the current best individual (universe) through wormholes. This random process occurs without taking into account the inflation rate. A sketch of this algorithm is shown in Figure1.Figure 1
A sketch of MVO [31].The initialization phase of MVO can be written as follows:(1)U=x11⋯x1d⋮⋱⋮xn1⋯xnd,where U represents the matrix of candidate solutions, d is the dimensions of the problem, and n is the number of universes (population of solutions) which can be represented as follows:(2)xij=xkj,r1<NIUixij,r1≥NIUi,where xij is the jth parameter of ith universe, Ui denotes the ith universe, NI (Ui) is the scaled inflation rate of the ith universe, r1∈01, and xkj is the jth parameter of kth universe selected by a roulette wheel selection mechanism. The objects are changed among the universes without perturbation. To maintain the balance between exploration and exploitation during the searching process in MVO, each universe is randomly treated to have wormholes to transport its objects through space. In order to ensure the exploitation around the current best solutions, particular wormhole tunnels are always established between a universe and the best universe formed so far, which can be represented mathematically as follows:(3)xij=XJ+TDR×ubj−lbj×r4+lbj,r3<0.5,XJ−TDR×ubj−lbj×r4+lbj,r3≥0.5,r2<WEP,xij,r2≥WEP,where Xj is the jth parameter of best universe formed so far, TDR (travelling distance rate) and WEP (wormhole existence probability) are coefficients, lbj and ubj are the lower bound and upper bound of jth variable, respectively, xij is the jth parameter of ith universe and r2, r3, and r4 are random numbers between 0 and 1. WEP and TDR are treated as adaptive formula as follows:(4)WEP=Wmin+lWmax−WminL,TDR=1−l1/pL1/p,where Wmin is the minimum (in this paper, it is set to 0.2), Wmax is the maximum (in this paper, it is set to 1), l is the current iteration, L is the maximum iterations, and p is the exploitation accuracy over the iterations (in this paper, it is set to 6). Higher the value of p, the sooner and more accurate exploitation/local search is performed [31]. It is worth to highlight that the MVO algorithm depends on number of iterations, number of universes, roulette wheel mechanism, and universe sorting mechanism. The quick sort algorithm is used to sort universe at each iteration, and roulette wheel selection is run for each variable in every universe in all iterations. Detailed description of MVO can be seen in [31].


## 3. Our Proposed Initialization Strategy

According to the trend in stochastic techniques, random initialization in each generation is the frequently used method to initialize algorithms without knowing any priory information about the problem in hand. The idea of random initialization is often pushing the algorithm to explore the given domain very well, while the exploitation around best solutions is not carried out by this type of initialization. We have used an initialization strategy in which IMVO is balanced in terms of exploration and exploitation. We have designed a two-stage initialization strategy: in the first stage, the algorithm is initialized randomly for a certain number of scattered solutions in the whole search domain. In stage two, after the algorithm completes a certain number of iterations and collects best points in the search domain, we initialize the IMVO with population of these best solutions to concentrate the algorithm on exploitation around the best solutions in the space. Hence, in current studies, we have assigned the function evaluations, fixed to solve a problem, in two parts. The first part initializes with random populations and collects the best solutions of each iteration by using the following equation:(5)Ui=Lbi+Ubi−Lbi∗rand0,1.In the second phase, the algorithm is directed to search in the neighborhood of the best solutions obtained in the first part and exploits the search space around the population of these best solutions.


## 4. Modeling of Electricity Production Cost as a Single Objective Linear Programming Problem

In this paper, we have presented an optimal mixture of energy production system as a linear programming (LP) model consisting of different decision variables, representing different electricity production sources of Pakistan, see Nomenclature [21]. Each variable is bounded and generates electricity through different fuel types like hydro, thermal, nuclear, wind, and solar energies. The suggested LP model includes different production sources as xi,i=1,2,…,95 and ui,i=1,2,3,…,95 represent different costs per kWh for each source. The objective function represents the total cost (C) incurred to meet the demand of energy in different situations. Mathematically,(6)minimize cost=∑i=195uixi,where ui represents the cost per MWh and xi are the different sources given in nomenclature. The objective of this study is to produce a data set of solutions so that we can select the required optimal solution fulfilling the given demand with lowest cost per kWh as compared to other solutions in the data set. For more details, about the data set generated, the reader may refer to [35]. The problem is to search for best solutions among several candidate solutions and to meet the required power demand and satisfy constraints on each variable. These constraints are given in Equation (7) and Table 1 as follows.Table 2
Case Study A: demand for 15000 megawatt, whereS1−S8 represent the collection of sources operating on 8 fuel types.
Firefly
BAT
GOA
IMVO
Price in PKR
390.831986
252.289853
201.3324084
111.5048004
Variable (MW)
15017.4015
15006.4398
15002.26667
15067.46055
S
1
4035.19978
2893.04991
3513.562502
4785.656
S
2
1407.73428
1873.28453
1072.160605
1338.551
S
3
981.013264
158.209497
62.4800805
431.9034
S
4
1137.47918
567.079361
395.4767659
1476.913
S
5
5684.88097
8502.04227
8812.308041
5366.239
S
6
921.438836
523.099019
684.1945259
1180.03
S
7
393.294457
21.8122192
442.1898083
150.7902
S
8
456.360696
467.863004
19.8943367
337.3776Table 3
Case Study B: demand for 19000 megawatt, whereS1−S8 represent collection of sources operating on 8 fuel types.
Firefly
BAT
GOA
IMVO
Price in PKR
327.227212
236.951036
233.3069629
155.6167319
Variable (MW)
19076.3946
19017.236
19023.02749
19044.11301
S
1
6761.41122
4928.40531
5283.899334
3905.454
S
2
2395.21169
2006.62552
1695.397916
1655
S
3
1469.31172
204.258471
167.1485397
1674.898
S
4
1701.02742
1102.9362
1720.041194
2433.113
S
5
5583.69119
10116.7438
9981.020494
8160.88
S
6
517.009725
153.65083
28.65642935
480.2648
S
7
489.383474
93.3714342
137.4132769
394.7306
S
8
159.348169
411.244455
9.450307236
339.7717Total demand constraint:(7)∑t=195xt≥d.


## 5. Experimental Settings, Results, and Discussion

We have implemented IMVO which is coded in Matlab R2016 [31]. The main features of our computer included 8 GB RAM with Intel® Core™ i7-7500U CPU @ 2.7 GHz 2.9 GHz with a 64-bit operating system Windows 10. For a fair comparison, the population size was taken as 100 and the number of iterations was 100. We have repeated our simulations 10 times. To elaborate the efficiency of IMVO, we have considered three special cases. The experimental outcome is compared with state-of-the-art algorithms: firefly algorithm, bat algorithm, and grasshopper optimization algorithm, as in Tables 2, 3, and 4. Also, we have picked 5 solutions from overall 100000 solutions and presented these solutions as different case studies with their respective costs per MWh (Table 5), which are based on the power demand in summers as provided in [20, 36–38]. The power demands and decision variables, which represent the 95 production sources in Pakistan and cost incurred along with the total power produced, are given in Table 5. The individual variations of 20 best variables required to produce a particular solution in all case studies are furnished in Table 6, and a weighted comparison of the 95 energy sources is given in Figure 2. Looking at these graphs, the reader can deduce the importance of each production source of electricity in national grid of the country. One can deduce which solution to choose if a particular source is down due to some fault or which sources are very impotent and acting as a backbone in generating the required electricity. We have depicted five case studies graphically as shown in Figure 3. These graphs are collective representation of 95 production sources acting to produce a certain demand. It is interesting to note that the production of electricity from available sources is manageable, if proper techniques, like IMVO algorithm, are implemented to solve the problem. It is worth to note that we have pointed out the top 20 production sources of electricity in Pakistan according to the five case studies listed as in Table 5. These sources play vital part in the energy production as shown in Table 6. It is obvious that certain sources like x1 are producing higher demand which are overburdened and could be relaxed by installing or expanding alternate sources. In Table 7, prices depending on different fuel types are listed for a megawatt of electricity. The convergence plots for these three case studies are depicted in Figures 4–6. It is interesting to note that, in all cases with demands of 15000, 19000, and 23000 megawatts, IMVO produced better solutions with lowest costs in millions (Table 2–4).Table 4
Case Study C: demand for 23000 megawatt, whereS1−S8 represent collection of sources operating on 8 fuel types.
Firefly
BAT
GOA
IMVO
Price in PKR
350.831986
263.667565
276.6948704
187.660591
Variable (MW)
23061.0476
23022.7254
23044.31656
23064.1461
S
1
7331.80841
6292
7333.779792
5069.58882
S
2
2493.78785
2618
1725.823048
1670.682
S
3
1871.00046
219
56.0182213
2517.06661
S
4
1756
1756
533.408886
2467.49605
S
5
7685.67332
11612
11553.22811
9782.75386
S
6
1104.62969
0.02326828
1089.543135
696.3726
S
7
436.442721
525
462.5011979
448.716537
S
8
381.705102
0.70208538
290.0141633
411.469586Table 5
Electricity production of all 95 sources for five case studies.
Case Study 1
Case Study 2
Case Study 3
Case Study 4
Case Study 5
Price in PKR
1.12E + 08
1.51E + 08
1.84E + 08
1.97E + 08
2.16E + 08
Variables (megawatts)
15003.16
19003
23000.08
25000.3
27208.36
TD (x1)
2379.137
1566.35
2938.164
3478
3476.16
MD (x2)
818.677
1000
905.7829
763.4957
983.48
GBHPP (x3)
516.5337
1450
1023.352
1347.306
1421.054
WD (x4)
130.7975
210.4076
177.7411
106.4834
181.5488
CB (x5)
38.74718
184
75.42442
174.4151
163.8171
DKD (x6)
42.56789
116.3349
116.0204
60.36495
127.4962
AKHPP (x7)
25.02909
0.415286
119.0034
33.87101
47.99439
KKHP (x8)
6.04886
15.92544
41.72064
72
19.27703
JagHP (x9)
14.17929
30
12.85605
8.998066
21.38508
JabHP (x10)
8.375935
10.57083
18.06
9.438497
0.704657
RG (x11)
6.866051
3.330527
0.380166
4.987555
9.745063
DHP (x12)
1.428187
13.53056
12.65834
20
2.044366
GHD (x13)
6.05225
0.280779
2.219217
9.40119
15.5921
NHP (x14)
6.647023
11.40453
7.595507
6.010873
13.86329
SHP (x15)
11.55404
11.2018
8.391618
11.16708
13.093
KHP (x16)
1.869716
1.137132
1.534735
2.692804
1.023365
RKHP (x17)
0.905093
1
1
0.651626
0.854247
CHPP (x18)
0.864139
0.815802
0.815802
0.965926
0.830172
GTPP (x19)
1305.331
1655
1655
1655
1645.54
MTPP (x20)
640.0394
546.27
1350
1350
1350
JTPP (x21)
149.5429
850
850
850
849.0554
FGTPP (x22)
148.9675
181.2005
188.0609
103.1949
217.891
MGTPP (x23)
4.385999
74.8375
155.4596
145.8149
168.1718
MGTPP (x24)
127.056
65.27735
166.15
34.1201
110.9528
KGTPP (x25)
112.8329
116.059
30.98832
0.567566
149.5035
LTPP (x26)
40.37149
0.883692
24.3518
120.5104
117.4427
FSPP (x27)
39.19613
54.27258
59
56.63659
55.09061
SGTPP (x28)
0.914076
21.86785
14.66417
22.23108
31.08445
PGTPP (x29)
27.30059
14.45997
0.589928
8.484009
23.07876
PTPP (x30)
12.70353
17
6.695689
16.85053
11.95603
KGTPS (x31)
91.79519
228.2708
247
127.6751
246.8065
KPC (x32)
91.12861
100
0.076503
16.21392
1.324039
GTPS (x33)
21.39859
30.86809
0.608317
41.91513
1.135833
TPS (x34)
1019.436
852.5889
921.7966
1132.252
1260
CCPP 1 (x35)
363.8285
375.9421
485.8476
538.1132
552.4153
CCPP 2 (x36)
67.16314
359.9164
551.1955
798.5884
899.1415
AES LL (x37)
12.48976
362
330.1038
341.4665
346.4409
AES PG (x38)
87.79272
289.7815
365
244.1401
364.9033
AEL (x39)
3.047575
29
29
12.08485
19.5939
AP (x40)
146.5024
194.7207
214.9626
225
225
AGL (x41)
153.9627
107.4664
152.7011
114.3378
113.5217
CHMC PL (x42)
75.13341
265.198
273.3111
255.6046
322.7874
DHA C L (x43)
68.73455
0.476099
6.545028
62.96757
70.30826
EPC (x44)
23.40477
98.656
37.10004
141.3346
152.0636
EPQL (x45)
130.7633
214.0389
222.3562
226.5
226.2002
FKPCL (x46)
95.2459
157
151.2643
27.8556
155.6898
FTSM (x47)
56.16674
104.4668
100.8249
76.57812
107.0448
FPCDL (x48)
10.1152
164.3581
127.2432
106.039
177.7063
GHLLP (x49)
101.702
56.26072
109.8266
140.2346
157.6599
GEPtvL (x50)
162.3922
188
144.4615
179.5249
131.9891
GEL (x51)
8.193736
89.19682
201.5
84.89962
201.5
GAEL (x52)
100.5592
92.35572
57.18626
110.4825
82.02294
HCPC (x53)
111.3358
58.26757
110.9772
43.47083
111.5484
HPGC (x54)
169.7313
0.807693
192.3602
125.0309
215.355
HUBCO NPP (x55)
147.8875
225
212.279
209.5134
223.5541
HUBCOHPP (x56)
148.0634
1292
1167.515
1292
1292
Iptvl (x57)
21.53738
158.6019
141.6202
164.2585
164.9125
JPG (x58)
84.13137
120
120
65.22738
119.424
KEL (x59)
43.50688
47.52342
103.8332
30.58684
130.8207
KAPCL (x60)
811.4451
1223.218
1185.71
1638
1638
LPL (x61)
153.0046
0.52402
94.67205
196.4468
182.2104
LPTL (x62)
124.1896
68.1917
50.95543
138.8238
198.6912
LEPCL (x63)
255.6012
589.7144
578.5459
660
658.6634
NCP (x64)
158.2538
200
95.85135
200
151.3611
NPL (x65)
32.48763
200
168.4331
168.8323
199.1059
OPCL (x66)
205.2865
0.89022
132.7586
65.89102
220.0356
REPGCL (x67)
30.20849
100.2075
52.99079
164
163.4477
RP (x68)
327.1605
276.0325
302.1523
412
411.8322
SPC (x69)
72.08175
75.02883
91.21424
109.1339
112.6283
SPPQ (x70)
101.0073
225
124.0716
211.05
221.962
SESL (x71)
208.1023
26.5598
66.00281
215.5041
200.3566
SSEL (x72)
220.5401
14.1361
321.1493
310.6587
343.2993
SNPCL (x73)
39.3573
44.14536
0.398791
20.11775
51.89066
SE (x74)
77.28166
11.07506
66.37944
23.84816
16.50386
SEPC (x75)
12.01473
71.11238
40.1338
47.43561
83.28035
SPGL (x76)
71.382
35.85756
10.86969
88.37954
113.884
TEL (x77)
110.2271
25.38428
113.5676
26.5028
94.01525
UchPL (x78)
735.2781
28.16507
990
990
989.7866
KANUPP (x79)
50.4151
92.10906
137
105.7683
134.7101
CHASNUPP-1 (x80)
282.9386
86.3647
275.8089
325
268.7866
CHASNUPP-2 (x81)
200.2746
243.2484
149.4219
325
320.8773
CHASNUPP-3 (x82)
191.8579
340
319.874
301.6324
214.0955
NPP (x83)
18.16426
173.693
374.8168
336.2965
420.7756
QezSP (x84)
49.71705
106.9033
70.03342
147.3463
126.7687
YEL (x85)
15.58682
2.334511
46.23074
24.48091
12.86986
MWPCL (x86)
41.01434
21.35616
27.94642
36.45242
45.21504
TGL (x87)
9.466357
25.20002
49
47.79046
47.90783
GAWPL (x88)
15.35919
18.91722
45.14516
15.24926
27.94244
MWEL (x89)
14.96827
21.99775
52
47.87871
46.00231
FFCEL (x90)
30.26861
42.68928
50
50
15.58795
ZEP (x91)
20.88768
14.37346
44.67045
30.45881
40.17728
TWEL (x92)
15.28468
12.1674
30
29.52479
28.65781
HCDPL (x93)
9.876255
20.00362
47.25205
31.9031
41.52962
FWEL 1 (x94)
43.69201
29.80095
45.98028
29.68556
22.61687
FWEPL 2 (x95)
6.404915
50
6.872093
21.65334
40.28912Figure 2
A weighted comparison of the 95 energy sources used in five case studies. Series 1–5 represent case studies 1–5, respectively.Figure 3
Comprehensive plots of five case studies discussed in Table4. All production sources are plotted against the electricity production in megawatts. (a) Case Study 1: demand of 15003 MW. (b) Case Study 2: demand of 19003 MW. (c) Case Study 3: demand of 23000 MW. (d) Case Study 4: demand of 25000.3 MW. (e) Case Study 5: demand of 27208.3 MW.
(a)
(b)
(c)
(d)
(e)Table 6
Top 20 electricity production sources according to the five case studies.
No. 1
No. 2
No. 3
No. 4
No. 5
No. 6
No. 7
No. 8
No. 9
No. 10
No. 11
No. 12
No. 13
No. 14
No. 15
No. 16
No. 17
No. 18
No. 19
No. 20
x
1
x
19
x
60
x
3
x
20
x
56
x
34
x
78
x
21
x
2
x
36
x
63
x
35
x
68
x
83
x
37
x
38
x
72
x
74
x
81Figure 4
IMVO convergence graph demand for 15000 megawatt.Figure 5
IMVO convergence graph demand for 19000 megawatt.Figure 6
IMVO convergence graph demand for 23000 megawatt.Table 7
Per megawatt cost of electricity for different fuel types.
Fuel type
Price in PKR per megawatt
Hydel
2500
LNG
9070
Furnace oil
11050
High-speed diesel
17960
Coal
12080
Solar
16950
Wind
16630
Nuclear
6860
Regasified liquefied natural gas
11270


## 6. Conclusions

In this paper, an improved multiverse optimization algorithm is implemented for solving a linear programming model for proper management of electricity production sources in Pakistan. To address the proper management of power production sources, several bound constraints, such as constraint for total demand, and bounds on all variables are considered. The objective function is linear with 95 decision variables and different coefficients. The IMVO algorithm is easy to implement with few parameters. We have found solutions for five different case studies and analyzed all solutions graphically. A link to the data set of 100000 different solutions is provided in this paper. In our results, we have obtained better solutions to meet the power demand in summer. It is recommended that current resources can produce the required power demand but some of the resources are required to be expanded in capacity along with installation of new sources. In future, we intend to include other factors, like power loss, in our model.



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*Source: 6192980-2019-03-11.xml*