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For Review Only
A Hybrid Genetic Algorithm applied to the Transmission 
Network Expansion Planning Considering Non-Conventional 
Solution Candidates
Journal: Journal of Applied Science and Engineering
Manuscript ID JASE-2019-0040.R1
Manuscript Type: Original Article
Date Submitted by the 
Author: 04-Apr-2019
Complete List of Authors: López Lopez , Jaime; XM S.A. E.S.P.
López-Lezama, Jesús María; Universidad de Antioquia, Electrical 
Engineering
Muñoz-Galeano, Nicolas; Universidad de Antioquia, Electrical Engineering
Keywords: Transmission network expansion planning, Genetic algorithm, non-conventional solution candidates
 
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Journal of Applied Science and Engineering
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1 A Hybrid Genetic Algorithm applied Metaheuristic Approach to the 
2 Transmission Network Expansion Planning Considering 
3 Non-Conventional Solution Candidates
4 Jaime Andrés López López, XM S.A. E.S.P., Calle 12 Sur No. 18 – 168, Medellín, 
5 Colombia.
6 Jesús María López-Lezama, Grupo de Investigación en Manejo Eficiente de la Energía 
7 (GIMEL), Departamento de Ingeniería Eléctrica, Facultad de Ingeniería, Universidad de 
8 Antioquia, Calle 67 No 53-108, Medellín, Colombia.
9 Nicolás Muñoz-Galeano, Grupo de Investigación en Manejo Eficiente de la Energía 
10 (GIMEL), Departamento de Ingeniería Eléctrica, Facultad de Ingeniería, Universidad de 
11 Antioquia, Calle 67 No 53-108, Medellín, Colombia.
12 Abstract
13 This paper presents a metaheuristic approach to solve the transmission network 
14 expansion planning (TNEP) problem considering non-conventional solution candidates. The 
15 TNEP consists on finding the set of new elements required in a power system to meet a given 
16 future demand at a minimum cost. The TNEP traditionally considers as candidate solutions 
17 the addition of new lines and transformers. The main contribution of this work is the 
18 inclusion of non-conventional solution candidates. Such non-conventional solution 
19 candidates are namely: repowering of existing circuits and reactive shunt compensation. 
20 Also, an AC modeling of the network that allows obtaining more realistic results than the 
21 traditional DC model has been considered. The TNEP is represented by means of a nonlinear 
22 mixed integer programming problem which is solved through a hybrid genetic algorithm 
23 (HGA). Several tests were performed on two benchmark power systems to show the 
24 applicability and effectiveness of the proposed approach.
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26 Keywords: Transmission network expansion planning, non-conventional solution candidates, 
27 genetic algorithms, greedy randomized search procedure.
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29 1. Introduction
30 Transmission network expansion planning (TNEP) consists on determining the new 
31 circuits that must be added to a power systems in order to meet a forecasted demand at the 
32 minimum possible cost [1], [2]. In its classical version, the TNEP only considers the 
33 addition of new lines and transformers. However, new environmental constraints have made 
34 more difficult and costly the acquisition of rights of ways to expand the transmission 
35 network. In this context, the implementation of non-conventional solution candidates to the 
36 TNEP such as repowering, reconfiguration and allocation of reactive power devices has gain 
37 major attention of researchers and system planners [3]. 
38 The most approximate representation of the TNEP problem corresponds to a mixed 
39 integer nonlinear programming (MINLP) problem. Such representation involves nonlinear 
40 constraints such as power flows in lines and power balance equations, as well as a mix of 
41 integer and real variables such as the number of lines to be added in a corridor or the power 
42 flow on a circuit, respectively [1]. The TNEP has proven to be a challenging problem since it 
43 is non-convex and multi-modal (it might have several optimal and quasi-optimal solutions); 
44 therefore, linearized versions of the TNEP have been proposed, turning the original MINLP 
45 into a mixed integer linear programming (MILP) problem which can be solvable by 
46 commercially available software [3].
47 Solution approaches to the TNEP problem can be broadly classified in two groups: 
48 classical mathematical programming, and metaheuristic techniques. The first group includes 
49 techniques such as linear programming [1], mixed integer linear programming [2], dynamic 
50 programing [4], Benders decomposition [5] and branch and cut methods [6]. Within the 
51 second group some of the most commonly used are: genetic algorithms [7], tabu search [8], 
52 simulated annealing [9] and differential evolution [10]. 
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53 The main feature of classical mathematical programming approaches is that, under 
54 convexity conditions, they are able to find global optimal solutions. Nevertheless, they are 
55 usually time-consuming, especially when addressing large-scale systems. To apply a classical 
56 mathematical programming approach to the TNEP problem, this one has to be converted into 
57 a set of linear equations losing information regarding the real state of the system. As regards 
58 metaheuristic techniques, these methods are easy to implement and do not require a 
59 linearization of the power system model. Furthermore, power system analysis such as power 
60 flows, optimal power flows or stability studies can be carried out using independent software 
61 and then be fed into the optimization method. Nevertheless, a common critique of 
62 metaheuristic techniques is the fact that they do not guarantee the global optimality of the 
63 solutions found, and they also depend on the settings of several parameters. A more detailed 
64 classification of models and solution techniques applied to the TNEP problem can be 
65 consulted in [11], [12] and [13]. 
66 Although there are many studies regarding the TNEP problem, the inclusion of 
67 non-conventional solution candidates has not been studied in depth. Regarding this issue, 
68 only few studies have approached separately the inclusion of series and shunt compensation 
69 as well as repowering and reconfiguration of existing circuits [3]. In this sense, the main 
70 contribution of this paper is the consideration of non-conventional solution candidates to the 
71 TNEP problem (repowering of existing circuits and optimal allocation of shunt 
72 compensations), consideringan AC modeling of the transmission network. Several tests were 
73 performed on the 6-bus Garver System and the IEEE 24 bus power test system showing the 
74 applicability of the proposed model and solution technique. Results show that the inclusion of 
75 non-conventional solution candidates allows exploring a larger search space and finding less 
76 expensive expansion plans.
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78 2. Mathematical modeling
79 A compact mathematical model of the AC TNEP is given by (1)-(9). A detailed 
80 description of this model can be consulted in [14]. In this case c and n are the vectors of cost 
81 and number of circuits to be added to the network, respectively. The objective function given 
82 by (1) consists on minimizing the total cost of the expansion plan expressed as v. Equations 
83 (2) and (3) are the active and reactive power balance constraints. and 𝑃(𝑣,𝜃,𝑛) 𝑄(𝑣,𝜃,𝑛)
84 are the net active and reactive power injections, respectively; where and are the set of 𝜃 𝑣
85 voltage angles and magnitudes, respectively. and are the active and reactive 𝑃𝐺,𝑄𝐺,𝑃𝐷, 𝑄𝐷
86 generation and demand, respectively. Equations (4) and (5) represent the limits of active and 
87 reactive power generation, respectively. Equation (6) represents the limit of voltage 
88 magnitudes. Equations (7) and (8) are the power flow limits on new and existing lines; in this 
89 case N and N0 are diagonal matrixes that contain vector n (new circuits) and the existing 
90 circuits in the base case, respectively. Finally, equation (9) stands for the limits of new 
91 circuits to be added to the network. 
𝑀𝑖𝑛 𝑣 = 𝑐𝑇𝑛 (1)
Subject to
𝑃(𝑉,𝜃,𝑛) ― 𝑃𝐺 + 𝑃𝐷 = 0 (2)
𝑄(𝑉,𝜃,𝑛) ― 𝑄𝐺 + 𝑄𝐷 = 0 (3)
𝑃𝐺 ≤ 𝑃𝐺 ≤ 𝑃𝐺 (4)
𝑄𝐺 ≤ 𝑄𝐺 ≤ 𝑄𝐺 (5)
𝑉 ≤ 𝑉 ≤ 𝑉 (6)(𝑁 + 𝑁0)𝑆𝑓𝑟𝑜𝑚 ≤ (𝑁 + 𝑁0)𝑆 (7)(𝑁 + 𝑁0)𝑆𝑡𝑜 ≤ (𝑁 + 𝑁0)𝑆 (8)0 ≤ 𝑛 ≤ 𝑛 (9)
92
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93 When using an AC representation of the network the model given by (1)-(9) corresponds 
94 to a MINLP problem. These types of problems are better handled by metaheuristic techniques 
95 than by conventional mathematical programing [15], [16]. In this case a hybrid genetic 
96 algorithm (HGA) is proposed and described in the next section. 
97
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98 3. Solution approach
99 The solution approach to the model given by (1)-(9), including repowering and 
100 allocation of shunt compensation as non-conventional solution candidates, is described in this 
101 section. In this case a HGAhybrid genetic algorithm (GA), that includes a greedy randomized 
102 search procedure GRASP as a mutation strategy was proposed. The mutation stage of a GA is 
103 in charge of providing diversification and allows the algorithm to eventually scape from local 
104 optimal solutions. The proposed approach takes advantage of this stage to introduce a local 
105 search. Along with a heuristic to find the initial solution candidates, the GRASP mutation is 
106 the distinctive feature of the proposed HGA. 
107 3.1. Problem codification
108 Figure 1 depicts the codification of a candidate solution (or individual) for the 6 bus 
109 Garver system depicted in Figure 2. Note that an integer number is assigned in every entry of 
110 the vector. In this case the maximum number of new transmission lines in each right of way 
111 or corridor is 5; therefore, if a given entry of the vector is 6 it indicates that the corresponding 
112 line must be repowered. Note that the individual depicted in figure 1 indicates repowering in 
113 corridors 1-2 and 2-4 plus the adding of 4 lines in corridor 3-5, 1 line in corridor 2-3 and 3 
114 lines in corridor 1-4. On the other hand, the last three elements of the vector are associated 
115 with nodes N2, N4 and N5 where it is possible to install shunt compensation. A number 
116 different than zero in these entries, indicates a shunt compensation. For simplicity purposes 
117 the number indicates the steps of 20Mvars compensation. In this case 60Mvars are installed 
118 in bus N2 and 20 Mvars in bus N5.
119
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120 Fig. 1. Example of solution candidate for the Garver system.
121
122 Fig. 2. Illustration of the Garver system (base case).
123 3.2. Fitness evaluation
124 Every candidate solution has an associated cost. In the proposed hybrid HGA this cost is 
125 referred to as the fitness of the individual (or solution candidate). Once a given number of 
126 solution candidates are proposed, their associated costs (fitness) are evaluated. The fitness 
127 function must also consider the cost of non-conventional solution candidates and the cost of 
128 non-serve demand. 
129 3.3. Initial population 
130 A constructive heuristic, depicted in Figure 3, was designed to produce the initial 
131 population. Such heuristic starts introducing new elements in the allowed right of ways to 
132 form different candidate solutions though random movements. 
133
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134
135 Fig. 3. Illustration of the constructive heuristic for the initial population.
136 3.4. Tournament selection 
137 The tournament selection process consists of taking two individuals from the initial 
138 population, evaluating their fitness function and determining which of them corresponds to 
139 the least expensive expansion plan. Later this individual is admitted to a new population. The 
140 number of tournaments held is "k". This process is illustrated in Figure 4. The same 
141 individual may eventually participate in more than one tournament. However, the probability 
142 of this happening is low since only two individuals are taken per tournament, and the value of 
143 “n” (size of the initial population) is higher respect two.
144
145 Fig. 4. Tournamentselection.
146 3.5. Recombination 
147 The recombination process is carried out starting from the new population generated in 
148 the previous step. This one consists on generating two new individuals from two parents as 
149 illustrated in Figure 5. In this case, recombination is done in a single point selected at 
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150 random. Recombination is performed k/2 times, generating a new recombined population of 
151 size k.
152
1-2 1-3 1-4 1-5 1-6 2-3 2-4 2-5 2-6 3-4 3-5 3-6 4-5 4-6 5-6 N2 N4 N5
4 3 3 5 1 4 4 2 3 0 2 3 4 5 0 0 2 0
3 2 5 2 0 4 1 3 0 3 1 3 4 4 2 3 1 0
4 3 3 5 1 4 4 2 3 0 2 3 4 4 2 3 1 0
3 2 5 2 0 4 1 3 0 3 1 3 4 5 0 0 2 0
153 Fig. 5. Illustration of the recombination stage.
154 3.6. GRASP mutation
155 In genetic algorithms, the mutation operator has the property of making an alteration to 
156 an individual that comes from the recombination process. In the proposed hybrid HGA, the 
157 alteration made by the mutation operator is an intensification of the search from a feasible 
158 candidate solution. Such intensification is carried out through a GRASP procedure. The 
159 mutation process consists of on performing a local search, which explores better solutions for 
160 each generation of the hybrid HGA. In this case, the value of each one of the bits from left to 
161 right is modified, the process is illustrated in Figure 6, and described in detail below.
162
1-2 1-3 1-4 1-5 1-6 2-3 2-4 2-5 2-6 3-4 3-5 3-6 4-5 4-6 5-6 N2 N4 N5
6 0 3 1 0 7 1 0 5 0 2 0 0 2 0 3 0 1
163 Fig. 6. Illustration of the GRASP stage (mutation).
164 Before starting the local search, the objective function (or fitness function) of the current 
165 vector (individual) is evaluated and this information is stored as a reference. Additionally, an 
166 operator "w" is defined which takes the values w = {1, 2, 3}. The first value indicates the 
167 reduction of a line in the corridor that is being evaluated. The second value indicates the 
168 addition of a line; finally, the third value indicates the repowering the corridor that is being 
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169 evaluated (if there are existing circuits in the base case). In each of the bits of the vector 
170 (except from those corresponding to the capacitors) the operator "w" is evaluated. In the case 
171 of shunt compensation, the value of the bit is replaced by a random integer number in the 
172 range between 0 and 5 (maximum steps of the capacitors bank).
173 3.7. General outline of the hybrid HGA
174 An illustrative diagram of the hybrid HGA is presented in Figure 7. The algorithm 
175 begins with the construction of a feasible individual by means of a constructive heuristic 
176 algorithm, followed by the generation of the initial population, starting from the 
177 aforementioned individual. Then, the selection by tournaments is made and the 
178 recombination process is executed. The best individual of the recombined population goes to 
179 the mutation operator, where a local search is performed (GRASP). The individual obtained 
180 after the mutation process is compared with the best solution found so far (incumbent). If the 
181 new individual is better, the incumbent is updated.
182
183 Fig. 7. Illustration of the GRASP stage (mutation).
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184 The process executed by the hybrid HGA ends when the number of generations that 
185 were established as an initial parameter to the algorithm is completed. To improve the quality 
186 of the initial population, after the mutation process, the individual obtained is compared with 
187 those existing in the initial population and if this one improves the population, it is replaced 
188 by the worst one.
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190 4. Tests and results
191 The proposed methodology was tested with the 6-bus Garver system and the IEEE 24 
192 bus test system. In order to calibrate the settings of the hybrid HGA several runs were made, 
193 modifying the size of the initial population, the number of tournaments and the probability of 
194 mutation. The adjusted data, through a sensitivity analysis, that yielded the best results are 
195 presented in Table 1. In this case, satisfactory results were found with the same parameters 
196 for both test systems. However, it is important to mention that the process of parametrizing 
197 metaheuristic techniques can vary from one system to another. The results obtained with the 
198 hybrid HGA were contrasted and validated with results reported in the technical literature. 
199 The first validation case was done with the original publication of Garver [17]; the second 
200 validation case was made with the same system, but adopting the network modifications 
201 proposed in [18]. 
202 Table 1. Settings of the implemented hybrid HGA.
Parameter Value
Initial population (n) 100
Number of 
tournaments (k)
100
Mutation probability 50%
Number of 
generations 2000
203
204 4.1. Results with the Garver system
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205 Initially, to reproduce the results reported in [17], the non-conventional solution 
206 candidates are penalized with a high cost (see [19] for details). Figure 8 illustrates the best 
207 solution obtained by proposed hybrid HGA. This solution coincides with the one reported in 
208 [17]. In this case the addition of 1 line in 3-5, 4 lines in 2-6 and 2 lines in 4-6 are indicated, 
209 with a cost of US $ 200. Figure 9 depicts the power system with the implemented solution.
210
1-2 1-3 1-4 1-5 1-6 2-3 2-4 2-5 2-6 3-4 3-5 3-6 4-5 4-6 5-6 N2 N4 N5
1 0 1 1 0 1 1 0 4 0 2 0 0 2 0 0 0 0
211 Fig. 8. Expansion plan considering high cost of non-conventional solution candidates 
212 (first validation case).
213
214 Fig. 9. Illustration of the expansionplan considering high cost of non-conventional 
215 solution candidates (first validation case).
216 In a second test, competitive costs are assumed for non-conventional candidates (see 
217 [19] for details). The results obtained are illustrated in Figure 10. The solution vector 
218 indicates the repowering of the existing circuit in 3-5, the addition of 4 lines in 2-6 and 2 
219 lines in 4-6, at a cost of US $ 190. Figure 11 illustrates the power system with the solution 
220 implemented. It can be seen that for this first validation case the inclusion of 
221 non-conventional solution candidates in the TNEP problem leads to a cost reduction of US $ 
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222 10. In this case, the solution does not contemplate the addition of shunt capacitors.
223
1-2 1-3 1-4 1-5 1-6 2-3 2-4 2-5 2-6 3-4 3-5 3-6 4-5 4-6 5-6 N2 N4 N5
1 0 1 1 0 1 1 0 4 0 6 0 0 2 0 0 0 0
224 Fig. 10. Expansion plan considering competitive costs of non-conventional solution 
225 candidates (first validation case).
226
227 Fig. 11. Illustration of the expansion plan considering competitive cost of 
228 non-conventional solution candidates (first validation case).
229 A second validation case was carried out adjusting system data as indicated in [18] and 
230 [20]. Initially a high cost of non-conventional solution candidates is considered, reaching the 
231 same results reported in [18] and [20]. This solution is illustrated in Figure 12. In this case it 
232 is necessary to add 2 lines in 3-5, 2 lines in 2-6 and 2 lines in 4-6, for a cost of US $ 160. 
233 Figure 13 illustrates the power system with the implemented solution.
234
1-2 1-3 1-4 1-5 1-6 2-3 2-4 2-5 2-6 3-4 3-5 3-6 4-5 4-6 5-6 N2 N4 N5
1 0 1 1 0 1 1 0 2 0 3 0 0 2 0 0 0 0
235 Fig. 12. Expansion plan considering high cost of non-conventional solution candidates 
236 (second validation case).
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237
238
239 Fig. 13. Illustration of the expansion plan considering high cost of non-conventional 
240 solution candidates (second validation case).
241 Subsequently, competitive costs are considered for non-conventional candidates (see 
242 [19] for details), obtaining the solution illustrated in Figure 14, which indicates 1 repowered 
243 circuit in 3-5, adding 2 lines in 2-6 , 1 line in 4-6, 1 bank of 2-step capacitors (40 Mvar) in 
244 node 4 and 1 bank of 1-step capacitor (20 Mvar) in node 5, for a cost of US $ 106. Figure 14 
245 illustrates the power system with the solution implemented. In this case, a cost reduction of 
246 US $ 54 is obtained due to the implementation of non-conventional solution candidates. 
247
1-2 1-3 1-4 1-5 1-6 2-3 2-4 2-5 2-6 3-4 3-5 3-6 4-5 4-6 5-6 N2 N4 N5
1 0 1 1 0 1 1 0 2 0 6 0 0 1 0 0 2 1
248 Fig. 14. Expansion plan considering competitive cost of non-conventional solution 
249 candidates (second validation case).
250
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251
252 Fig. 15. Illustration of the expansion plan considering competitive cost of 
253 non-conventional solution candidates (second validation case).
254 4.2. Results with the IEEE 24-bus test system
255 As previously mentioned, the data of this system can be consulted in [3]. For the 
256 repowering of lines, a relative cost is assumed equal to half the cost of installing new circuits. 
257 Additionally, in each of the corridors a maximum of 3 lines is allowed (see [19] for details).
258 Initially, high costs are assumed for non-conventional solution candidates. Figure 16 
259 illustrates the best solution obtained. In this case, the addition of 1 line is indicated in 
260 corridors 3-24, 12-13, 14-23, 15-16 and 15-24, 2 lines in corridors 6-10 and 7-8, for a total 
261 cost of US $ 362 Million. The results are consistent with those reported [17], [18]; especially 
262 with respect to the corridors in which the proposed hybrid HGA adds new transmission lines. 
263 The lack of accuracy of the results obtained for this system, with respect to the publications 
264 mentioned above, is mainly due to differences in the AC / DC model. Figure 17 illustrates the 
265 power system with the solution implemented.
266
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267
1-2 1-3 1-5 1-8 2-4 2-6 2-8 3-9 3-24 4-9 5-10 6-7 6-10 7-8 8-9 8-10 9-11 9-12 10-11 10-12 11-13 11-14 12-13
1 1 1 0 1 1 0 1 2 1 1 0 3 3 1 1 1 1 1 1 1 1 2
268
12-23 13-14 13-23 14-16 14-23 15-16 15-21 15-24 16-17 16-19 16-23 17-18 17-22 18-21 19-20 19-23 20-23 21-22
1 0 1 1 1 2 2 2 1 1 0 1 1 2 2 0 2 1
269 Fig. 16. Expansion plan considering high cost of non-conventional solution candidates.
270
271 Fig. 17. Illustration of the expansion plan considering high cost of non-conventional 
272 solution candidates.
273 Subsequently, competitive costs are assumed for non-conventional solution candidates, 
274 obtaining the result illustrated in Figure 18. This indicates the repowering of the existing 
275 circuits in 2-4, 3-24, 7-8, 9-12, 11-13, the addition of 1 line at 6-10, the location of a 5-step 
276 capacitor bank (100 Mvar) at nodes 3 and 10, and the location a 3-step capacitor bank (60 
277 Mvar) in node 8, at a cost of US $ 149.5 Million. Figure 19 illustrates the power system with 
278 the solution implemented. It can be seen that considering non-conventional solution 
279 candidates in the TNEP problem leads, in this case, to a cost reduction equivalent to US $ 
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280 212.5 Million. 
281
1-2 1-3 1-5 1-8 2-4 2-6 2-8 3-9 3-24 4-9 5-10 6-7 6-10 7-8 8-9 8-10 9-11 9-12 10-11 10-12 11-13 11-14 12-13 12-23
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282
13-14 13-23 14-16 14-23 15-16 15-21 15-24 16-17 16-19 16-23 17-18 17-22 18-21 19-20 19-23 20-23 21-22 N3 N8 N10 N14
0 1 1 0 1 2 1 1 1 0 1 1 2 2 0 2 1 5 3 5 0
283 Fig. 18. Expansion plan considering competitive cost ofnon-conventional solution 
284 candidates.
285
286 Fig. 19. Illustration of the expansion plan considering competitive cost of 
287 non-conventional solution candidates.
288 The summary of results obtained by the hybrid HGA for the 6-bus Garver system and 
289 the IEEE 24 bus test system are presented in Table 2. This shows when the expansion plan 
290 considering competitive cost of non-conventional solution candidates, the results for TNEP 
291 problem are better than the results obtained for the typical solutions (addition of new lines 
292 and transformers - high cost of non-conventional solution candidates).
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293 Table 2. Summary of results obtained by the hybrid HGA.
294
High cost of non-
conventional solution 
candidates
Competitive cost of non-
conventional solution 
candidates 
High cost of non-
conventional solution 
candidates
Competitive cost of non-
conventional solution 
candidates 
US $200 US $190 US $160 US $106
n3-5 = 1 n3-5 = Repowering n3-5 = 2 n3-5 = Repowering
n2-6 = 4 n2-6 = 4 n2-6 = 2 n2-6 = 2
n4-6 = 2 n4-6 = 2 n4-6 = 2 n4-6 = 1
N4= 40 Mvar
N5= 20 Mvar
N3= 100 Mvar
N10= 100 Mvar
N8= 60 Mvar
n7-8 = 2
Competitive cost of non-conventional solution candidates 
US $ 149.5 Million
n2-4 = Repowering
n3-24 = Repowering
n7-8 = Repowering
n9-12 = Repowering
n11-13 = Repowering
n6-10 = 1
US $ 362 Million
n3-24 = 1
n12-13 = 1
High cost of non-conventional solution candidates
n14-23 = 1
n15-16 = 1
n15-24 = 1
n6-10 = 2
Hybrid GA
First Validation Case - Garver System Second Validation Case - Garver System
IEEE 24-bus System
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296 5. Conclusions
297 This paper presented a new model and solution approach to the transmission network 
298 expansion planning problem. The main contribution of this work is the introduction of 
299 non-conventional solution candidates, namely: repowering of existing circuits and optimal 
300 allocation of shunt compensations. In addition, the use of an AC model to represent the 
301 network allows a closer look at real phenomena of electric power systems.
302 The inclusion of non-conventional solution candidates in the TNEP problem allows 
303 exploring a larger set of possible solutions and finding new alternatives for expansion plans 
304 that involve lower costs, compared with those obtained by considering only traditional 
305 solution candidates (new lines and transformers). The hybrid HGA showed satisfactory 
306 results, finding and improving the solutions for the TNEP problem that have been previously 
307 reported in the technical literature.
308 Future work will consider other aspects of the TNEP problem, such as new 
309 non-conventional solution candidates, reliability, changes in voltage levels, voltage stability, 
310 and also the use of other metaheuristic techniques.
311 Acknowledgements
312 The authors want to acknowledge the “Proyecto de sostenibilidad” of Universidad de 
313 Antioquia, and Colciencias project 2016-10306 for their support in the development of this 
314 work.
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316 References
317 [1] Leou, R. C. (2011) A multi-year transmission planning under a deregulated market. Int. J. 
318 Electr. Power Energy Syst 33(3), 708–714.
319 [2] Dominguez, A. H., L. H. Macedo., A. H. Escobar and R. Romero. (2017) Multistage 
320 Security-Constrained HVAC/HVDC Transmission Expansion Planning With a Reduced 
321 Search Space. IEEE Trans. Power Syst., 32(6), 4805–4817.
322 [3] Tejada, D. J., M. López-Lezama., M. J. Rider and G. Vinasco. (2015) Transmission 
323 network expansion planning considering repowering and reconfiguration. Int. J. Electr. 
324 Power Energy Syst. 69., 213–221.
325 [4] Wu, Z., P. L. Zeng., X. P. Zhang., H. Fu and Q. Dai. (2015) Two-stage stochastic dual 
326 dynamic programming for transmission expansion planning with significant renewable 
327 generation. IET International Conference on Resilience of Transmission and Distribution 
328 Networks (RTDN)., 1–6.
329 [5] Kim, H., S. Lee., S. Han., W. Kim., K. Ok and S. Cho. (2015) Integrated Generation and 
330 Transmission Expansion Planning Using Generalized Bender’s Decomposition Method. 
331 2015 IEEE International Conference on Computational Intelligence Communication 
332 Technology., 493–497.
333 [6] Rahmani, M., G. Vinasco., M. J. Rider., R. Romero and P. M. Pardalos. (2014) 
334 Multistage transmission expansion planning considering fixed series compensation 
335 allocation. 2014 IEEE PES General Meeting | Conference Exposition., 1–1.
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336 [7] Gallego, L. A., L. P. Garcés., M. Rahmani and R. A. Romero. (2017) High-performance 
337 hybrid genetic algorithm to solve transmission network expansion planning. Transm. 
338 Distrib. IET Gener., 11(5) 1111–1118.
339 [8] Silva, E. L. D., J. M. A. Ortiz., G. C. D. Oliveira and S. Binato. (2001) Transmission 
340 network expansion planning under a Tabu Search approach. IEEE Trans. Power Syst., 16 
341 (1) 62–68.
342 [9] Cortes-Carmona, M., R. Palma-Behnke and O. Moya. (2009) Transmission Network 
343 Expansion Planning by a Hybrid Simulated Annealing Algorithm. 2009 15th 
344 International Conference on Intelligent System Applications to Power Systems., 1–7.
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346 distributed generation and demand response programs,” IET Renew. Power Gener., 11(5) 
347 650–658.
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349 Review. IEEE Lat. Am. Trans., 8(3) 245–258.
350 [12] Hemmati, R., R. A. Hooshmand and A. Khodabakhshian. (2013) State-of-the-art of 
351 transmission expansion planning: Comprehensive review. Renew. Sustain. Energy Rev., 
352 23 312–319.
353 [13] Latorre, G., R. D. Cruz., J. M. Areiza and A. Villegas. (2003) Classification of 
354 publications and models on transmission expansion planning. IEEE Trans. Power Syst., 
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356 [14] Rider, M. J., A. V. Garcia and R. Romero. (2007) Power system transmission network 
357 expansion planning using AC model. Transm. Distrib. IETGener., 1(5) 731–742.
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358 [15] Lin, W., W, Lei, G. Tian and Y Zhang (2018). MTLBO: A multi-objective Multi-course 
359 Teaching-Learning-based Optimization Algorithm. Journal of Applied Science and 
360 Engineering, 21(3) 331–342.
361 [16] Lin, W., L. Wang, Y, Zhang and C. Zhang (2018). Full-active Scheduling in Job Shop 
362 Problems Using an Improved Genetic Algorithm. Journal of Applied Science and 
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364 [17] Garver, L. L. (1970) Transmission Network Estimation Using Linear Programming. 
365 IEEE Trans. Power Appar. Syst., 89(7) 1688–1697.
366 [18] Rider, M. J., A. V. Garcia and R. Romero (2004) A constructive heuristic algorithm to 
367 short term transmission network expansion planning. Proc. 2004 IEEE Power Eng. Soc. 
368 Gen. Meet., Denver, USA., 2 2108–2114.
369 [19] López-López, A. (2017) Planeamiento de la expansión de la red de transmisión 
370 considerando repotenciación, reconfiguración de circuitos existentes y ubicación de 
371 compensaciones en serie y en derivación., Universidad de Antioquia.
372 [20] Rider, M. J and A. V. Garcia. (2004) A constructive heuristic algorithm to short term 
373 transmission network expansion planning. IEEE Power Engineering Society General 
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We would like to thank the reviewer for his valuables comments. All suggestions have been taken 
into account in the new version of the paper. Answers to the reviewer are provided below:
Comment 1. I suggest changing the title to: "A Hybrid Genetic Algorithm to the transmission ..."
Answer 1. We agree with the reviewer. The title of the paper has been modified accordingly. 
Comment 2. Use HGA instead of GA for Hybrid Genetic Algorithm.
Answer 2. We have used HGA instead of hybrid GA throughout the document 
Comment 3. On line 106 change the word "line" for "transmission line".
Answer 3. We have made the corresponding change
Comment 4. Explain in detail the reasons why only the mutation operator was modified
Answer 4. The HGA was modified in the selection mechanism through a heuristic to choose the 
first candidate solutions and also through a GRASP within the mutation operator.
Mutation is the most suitable stage to introduce a local search since the previous solutions have 
passed through selection and crossover. Furthermore, it allows the algorithm to escape from local 
optimal solutions. 
We have state this reasoning in the first paragraph of section 3 in lines 102 to 10.
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