ARID ZONE JOURNAL OF ENGINEERING, TECHNOLOGY & ENVIRONMENT AZOJETE, March, 2019. Vol. 15(1):77-96 Published by the Faculty of Engineering, University of Maiduguri, Maiduguri, Nigeria. Print ISSN: 1596-2490, Electronic ISSN: 2545-5818 www.azojete.com.ng 77 ORIGINAL RESEARCH ARTICLE TRANSMISSION EXPANSION PROGRAMME FOR ELECTRIC NETWORK REINFORCEMENT P. O. Oluseyi*, T. O. Ajekigbe and T. J. Akintunde (Department of Electrical and Electronics Engineering, University of Lagos, Akoka, Lagos, Nigeria) *Corresponding Author: poluseyi@unilag.edu.ng; drpeteroluseyi@gmail.com ARTICLE INFORMATION Submitted 29 March, 2018 Revised 05 September, 2018 Accepted 10 September, 2018 Keywords: Electricity transmission expansion power grid evolutionary algorithm voltage collapse power flow ABSTRACT Due to the increase in electricity demand, transmission sector has become overstressed since it can only be built at vast cost. In many developing economies, the network is highly susceptible to outages, collapse as well as partial or total failures, since the existing transmission capacity limit is often closely approached. To overcome this challenge better transmission expansion needs to be considered. This paper identified the implementation of transmission expansion with a number of creative approaches for overcoming network collapse in poor economy. The study deployed the application of improved Strength Pareto Evolution Algorithm (SPEA-2) optimization approach for solving the transmission expansion problem based on a simple power flow model. This model was deployed for running the Nigeria- 31-bus system; to serve as the benchmark hence the standard IEEE 30- bus system was also considered. Using the traditional approach, the results obtained from the power flow analysis revealed that there are four major buses that recorded very high severity of violation. These were Jos, Kaduna, Kano and Birnin-Kebbi buses. In furtherance to this, additional effort was made to establish these findings by adapting the contingency analysis tests which provided more information on the earlier results so as to establish that these buses made the adjoining transmission lines connecting them to be identified as weak. Thus this serves as the contributory factor to the violation experienced by the entire the power network. For a more creative vivid display of the results; the Powerworld software was engaged for the analysis of the existing Nigeria-31 bus system while the violated buses that require more energy flow were provided with double circuit. This, thus, resulted in improved power outflow and inflow to the buses which led to the reduction of losses in the network. In conclusion, this study established that the transmission line connecting the geographical northern and southern parts of Nigeria dissipated quantifiably large value of losses which is mainly due to the nature and length of the line linking the source of electricity supply to a number of the load centres in the farther part of the country. Hence, it is suggested that the transmission expansion programme should be adopted for the improvement of power flow quantity which will, on the long run, reduce the power loss suffer by the existing network. © 2019 Faculty of Engineering, University of Maiduguri, Nigeria. All rights reserved. mailto:poluseyi@unilag.edu.ng mailto:drpeteroluseyi@gmail.com http://www.azojete.com.ng Oluseyi, et al. Transmission expansion programme for electric network reinforcement. AZOJETE, 15(1):77-96. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng 78 1.0 Introduction Electric power transmission is the long-distance transfer of electrical energy from where it was generated to where it is consumed. Electricity is successively delivered to consumers through the distribution networks. The transmission grid is therefore the basic infrastructure that permits large physical power flow in a power system operation. Therefore, Transmission Expansion Programme (TEP), which decides which new lines will enable the system to satisfy future loads with the required degree of reliability is one of the main strategic decisions in power systems operation (Levi and Calovic, 1993). The problem of inadequate power supply can be tackled by generation upgrade and/or expansion. This means that more generating units are added to the existing power plants or new power plants are built at new locations in a nation’s power grid. Further generation always results in increased power flow on transmission lines connecting the grid. If the present transmission network is not capable of transferring this added generation, then an improvement or expansion of the transmission system is needed (Levi and Calovic, 1993). In respect of Nigeria, the electric power system is continually undergoing metamorphosis due to steady increase in installation/commission of new power generating projects with little no improvement in the power grid. So, in most cases, the system fails to maintain its stability when there is a sudden outage of one of its components. This always affects the power quality delivered by the system. In a typical power system, the supply of electricity to load centres is as a result of the system operation that involves three stages namely: : the generated power at the generating stations which is thus transferred to the distribution centres through the high voltage transmission network. At the distribution station, the electrical power is derated to a lower voltage level to serve low voltage consumers. Due to the rising electricity consumption and expected renewable energy integration, transmission network expansion planning is required to help provide alternative paths for power transfer from power plants to load centres during emergencies. For improved power delivery in the nation; this expansion programme needs to be incorporated to the existing power system operation. Fundamentally, the transmission network expansion planning is defined as the problem technical approach for determining the optimal location of new transmission lines within an existing grid in order to enhance power transfer. This helps in complementing the grid rehabilitation exercise for fast-tracking power sector recovery to ensure that the growing national electricity demand is met at the lowest economic cost. This is better achieved through mathematical modelling that is based on the optimization approach. There are different forms of Optimization techniques which have been lately adopted in solving the transmission expansion planning. This includes but not limited to the following, namely: linear programming (Levi and Calovic, 1993), Bendersde composition (Pereira, et al. 1985), branch and bound (Haffner, et al. 2001), Genetic Algorithm (Jingdong and Guoqing, 1997), simulated annealing (Romero, et al. 1996), etc. The purpose of the transmission expansion planning problem programme is to propose the least economic cost transmission expansion strategy while fulfilling all the operation and security constraints of the power system operation. For the purpose of developing an effective transmission expansion network; the optimal decision on the location of the proposed new transmission lines is best obtained by modelling the system with the help of robust mathematically designed optimization technique. This procedure would involve the dynamic determination of the best combination of the conflicting goals/objectives desired for http://www.azojete.com.ng Arid Zone Journal of Engineering, Technology and Environment, March, 2019; Vol. 15(1):77-96. ISSN 1596-2490; e-ISSN 2545-5818; www.azojete.com.ng Corresponding author’s e-mail address: gbengailori@unilag.edu.ng 79 optimization in the presence of a number of trade-offs for the purpose of identifying the optimal location of the proposed new lines through adequate modelling, development and evaluation of the existing transmission network parameters. 2. Materials and Methods The materials for the analysis of transmission expansion programme were variously ranging from the data gathered from the Transmission Company of Nigeria (TCN) on the Nigeria-31 bus system as well as the data of the IEEE-30 bus test case as obtained from the e-laboratory webpage of the Department of Electrical and Computer Engineering of the University of Washington. So also, the deployment of the power flow features of the Powerworld software for pictorial display of load flow analysis, and the use of the MATLAB software for the mathematical analysis. 2.1 Implementation of the Improved Strength Pareto Evolution Algorithm (SPEA-2) With a solid inspiration from other forms of the evolutionary algorithm, two researchers Zitzler and Thiele (1999) developed the SPEA as a multi-objective optimization solution approach (Zitzler and Thiele, 1999). Few years later, this method was later improved to provide a better approach known as the improved SPEA (normally referred to as SPEA 2) approach (Zitzler, et al. 2002). The later tries to overcome the weaknesses of the later. Some of the weaknesses in the SPEA are that the fitness assignment scheme doesn’t individuals that it dominates and dominated by, so also no strict guidance of the search process and the boundary solutions are highly threatened that there is high degree of failure to account for them in the final evaluation of best solutions. Fortunately, all the aforementioned setback are addressed in the SPEA-2. In other words, the SPEA-2 uses a regular population and an archive (external set). Starting with an initial population and an empty archive the following steps are performed per iteration: First, all non-dominated population members are copied to the archive; in which case any dominated individuals or duplicates (regarding the objective values) are removed from the archive during this updated operation. However if the size of the updated archive exceeds a predefined limit, further archive members are deleted by a clustering technique which preserves the characteristics of the non-dominated front. Afterwards, fitness values are assigned to both archive and population members with the help of the following steps: Each individual i in the archive is assigned a strength value ( )S i , which at the same time represents its fitness value ( )F i . ( )S i are the numbers of population members (i.e. j) that are dominated by or equal to individuals in the archive (i.e. i ) with respect to the objective values, divided by the population size plus ‘1’. The fitness ( )F j of an individual ‘j’ in the population is calculated by summing the strength values ( )S i of all archive members ‘ i ’ that dominate or are equal to ‘j’; and adding ‘1’ at the end. The next step represents the mating selection phase where individuals from the union of population and archive are selected by means of binary tournaments. It should be noted that fitness is to be minimized here, hence each individual in the archive has a higher chance to be selected than any other population member. Finally, after recombination and mutation the old population is replaced by the resulting offspring population. To avoid the situation whereby the individuals dominated by the same archive members have identical fitness values, thus as stated file:///C:/Users/user/Downloads/azojete143/www.azojete.com.ng Oluseyi, et al. Transmission expansion programme for electric network reinforcement. AZOJETE, 15(1):77-96. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng 80 earlier on; the beauty of the SPEA-2 is that for each individual; both dominating and dominated solutions are taken into account. In detail, each individual ‘’ in the archive tP and the population tP is assigned a strength value ( )S i , representing the number of solutions it dominates; thus as earlier stated, the SPEA-2 algorithm helps in the following ways, namely: the number of individuals contained in the archive is constant over a period of time of operation, and the truncation method prevents boundary solutions being removed. During the process of environmental selection, the first step is to copy all non-dominated individuals, i.e., those which have fitness lower than unity from archive and population size to the archive of the next generation. The following should be noted in developing this algorithm (Abido, 2006): Input: N (population size), N (archive size), T (maximum number of generations), Output: A (non- dominated set). To facilitate this procedure in the work herein presented; thus the algorithm is executed in a step-by-step approach as follows: Step 1 Initialization: Generate an initial population tP and create the empty archive (external set) 0P = ( ); .Set t = 0. Step 2 Fitness assignment: Calculate fitness value of individual tP Step 3 Environmental selection: Copy all non-dominated individuals in tP to 1tP . If size of 1tP exceeds N then reduce 1tP by means of the truncation operator, otherwise if size of 1tP is less than N then fill 1tP with dominated individual in tP and tP . Step 4 Termination: If t >T or another stopping criterion is satisfied then add set A to the set of decision vectors represented by the non-dominated individuals. Step 5 Mating selection: Perform binary tournament selection with replacement on tP >1 in order to fill the mating pool. Step 6 Variation: Apply recombination and mutation operators to the mating pool and set 1tP to the resulting population. Increment generation counter (t =t + 1) and go to Step 2. In this research; the improved strength pareto evolution algorithm (SPEA-2) as a multiple objective function technique, as introduced above, is implemented. It should be noted that this approach involves solving a multi-criteria decision making complex problem moderated with the help of relevant trade-offs. In this study, the decision making involves the following objective functions namely: power loss, relevant cost (comprising reactive power support and fuel cost) and capital investment cost. This can thus the power loss and cost can be modelled as shown in equation (1) and equation (2): http://www.azojete.com.ng Arid Zone Journal of Engineering, Technology and Environment, March, 2019; Vol. 15(1):77-96. ISSN 1596-2490; e-ISSN 2545-5818; www.azojete.com.ng Corresponding author’s e-mail address: gbengailori@unilag.edu.ng 81 For the power loss,    , lossF x z min P (1) So also for the cost of fuel and reactive support;  Min cost = )( max gi S gi SMinC (2) Equation (2) is simplified as the combination of reactive power support and fuel cost as depicted in equation (3) i.e. )()()( maxmaxmaxmax gi p gigigi q gigi s gi PCQCSMinC  (3) Equations (1) and (2) are subjected to inequality constraints as shown in equations (4) and (5), i.e.: maxmin, iii VVV  (4) max,max, gigigi QQQ  (5) In the case of the investment in new transmission line; then equation (6) was adopted; thus the Capital Investment Cost (i.e. IN):      n k kgkkgkkikik r CPbPaZdfcrIN 1 21)1( (6) While the general line impedance equation is given in equation (7); ikikik jXRZ  (7) Where Rik:=Resistance of the line to be expanded Xik:=Reactance of the line to be expanded dik:=Distance between adjacent buses of the transmission lines of interest. fc:=Capital cost of building a transmission line per km($/km) To calculate the capital investment cost or value, IN, the simple interest formular for determining the rate paid on invested principal value is obtained in equation (8) r:=Interest rate, PT INr )(100  (8) T:= number of time periods P:= principal amount of money to be invested IN:= Capital Investment cost or value , ,k k ka b c := Constant coefficient of generators Thus Pgk as the active power generation of the k generating units subjected to Active power balance constraint is obtained as in equation (9); dii k gk PPP i   (9) Where :diP Active power demand at bus, i :iP Net active power injection at bus i :gkP Net active power flowing out of various buses into bus i  :ik  Total number of buses transmitting power into bus i file:///C:/Users/user/Downloads/azojete143/www.azojete.com.ng Oluseyi, et al. Transmission expansion programme for electric network reinforcement. AZOJETE, 15(1):77-96. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng 82 2.2 Power flow model The adopted modelling approach is the establishment of nonlinear relationship among the critical system parameters such as the bus power injection; as shown in equation (10), the branch power flow is as displayed in equation (11). So also, the bus voltages are as presented in equation (12) and the voltage angles which is as expressed in equation (13). So also the expression for line admittance is as shown in equation (14). . From the foregoing therefore; the power flow model which supplies information on the electrical performance of the lines with respect to the actual power flow in the various lines is thus presented as depicted in equation (15). This thus provides the needed information about the line loading capacity is as introduced in equations (16) and (17).. In developing power flow equations, it should noted that the balanced 3-phase system operation is assumed; hence per-phase analysis is utilized to obtain the relevant equations. digii SSS  (10) )sincos( 1 * 1 ** ikikikikk n k ik n k ikiiii jBGVVVYVIVS     (11) ikj iikii eVVV   (12) kiik   (13) ikikik jBGY  (14)  ikikikikk n k ii jBGVVS  sinsin 1   (15)  ikikikikk n k ii BGVVP  sinsin 1   (16)  ikikikikk n k ii BGVVQ  sinsin 1   (17) where n:=total number of buses in the system Pi and Qi:=specified active and reactive demand at load bus i Gik:= element of line conductance Bij:= element of line susceptance θij:= phase angle between sending end voltage and receiving end voltage iV := bus voltage at bus i; jV := bus voltage at bus j; Contingency analysis The term contingencies are defined as potentially harmful disturbances that occur during the steady state operation of a power system. Load flow constitutes the most important study in a power system for planning, operation and expansion. The purpose of load flow study is to compute operating conditions of the power system under steady state. These operating conditions are normally voltage magnitudes and phase angles at different buses, line flows (MW http://www.azojete.com.ng Arid Zone Journal of Engineering, Technology and Environment, March, 2019; Vol. 15(1):77-96. ISSN 1596-2490; e-ISSN 2545-5818; www.azojete.com.ng Corresponding author’s e-mail address: gbengailori@unilag.edu.ng 83 and MVAR), real and reactive power supplied by the generators and power loss (Ezechukwu, 2013). The contingency analysis is becoming an essential task for power system planning and operation. Thus the power system security analysis forms an integral part of modern energy management system. In other words, the power system security, as a term, is used for expressing the power systems ability to meet its load without unduly stressing its apparatus or allowing variables to stray from prescribed range under the apparatus or allowing variables to stray from prescribed range under certain pre-specified credible contingencies. Hence in order to predict the effect of outages; the contingency analysis approach is widely embraced. This is predictably achieved by appealing to the contingency ranking protocol. This is best developed by determining, in descending order, the contingency ranking line severity index. This is the measurement of the effect of contingency event on the power system. The evaluation of the contingency effect is thus obtained in the off-line mode suing the earlier developed power flow model (as expressed in equations 10 to 14). The violation of the line active power index is expressed as equation 15:    n i i i p P P 1 max  (15) Where Pi := active power flow in line i Pimax:= maximum active power flow in line i So also the violation voltage violation is obtained as in equation (16);             1 1 minmax )(2mn i ii ioi v VV VV  (16) Where n-m-1:= total number of load buses m:= number of PV buses n:= total number of load buses Vi:= voltage at bus i Vio:= nominal voltage at bus, i (i.e. 1p.u.) Vimin:= minimum voltage limit (95% of Vio) Vimax:= maximum voltage limit (105% of Vio) It should be noted that this analysis is very apt in determining the state of robustness of a transmission network. In other words, the higher the value of severity indices (in equations (15) and equation (16)), the more the threats of the possibility of potential collapse of the system. Thus the value obtained has measurable tendency for predicting the necessity for the importunity of the transmission expansion programme. 3. Results and Discussion From the foregoing methodology; a set of numerical results is then obtained by implementing the Powerworld software and MATLAB software. Thus, Table 1 shows the results obtained from the power flow analysis using the Newton Raphson load flow iteration method. This is then applied to the Nigeria-31 bus system by using the bus and line data gathered from the Transmission Company of Nigeria. Thus it presents the voltage profile of the Nigeria-31 bus system in which the generation buses within the network are seven in number with one of them file:///C:/Users/user/Downloads/azojete143/www.azojete.com.ng Oluseyi, et al. Transmission expansion programme for electric network reinforcement. AZOJETE, 15(1):77-96. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng 84 serving as the slack bus for the network. To further appreciate the foregoing; the appropriate equations derived in the preceding sections were then applied on the electrical loading capacity of the various lines. Further investigation was also performed on the Nigeria-31 bus system to evaluate the single line contingency test. The summary of the contingency analysis was showcased in the succeeding graphs and tables. Whereby the voltage profile is as presented in Table 1, this vividly shows at a glance the lines and buses that need attention of the network planners. From Table 1, it is clearly evident that a number of buses violated the %5 boundary set for the operation of power system; such buses are Bus Number: 2, 10, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25 and 28. It must be noted that at the verge of violation is found Bus Number: 5. In the case of Table 2; for the Nigeria-31 bus system, the lines that are highly threatened due to the line losses is arranged in the order severity are Lines: 9-11, 29-12, 8-15, 10-15 and 18-12. Table 1: Voltage profile of the Nigeria-31 bus system Loading and generation of network including bus voltage and angle Bus No V (pu) Angle Injection Generation Load (Degree) MW MVar MW MVar MW Mvar 1 1.020 0.000 825.461 332.244 825.461 332.244 0.000 0.000 2 0.990 -2.956 200.000 -43.876 200.000 -43.876 0.000 0.000 3 1.000 -2.382 300.000 11.300 300.000 11.300 0.000 0.000 4 1.000 -8.914 250.000 138.405 250.000 138.405 0.000 0.000 5 1.030 7.076 490.000 -52.650 490.000 -52.650 0.000 0.000 6 1.040 7.387 350.000 -27.038 350.000 -27.038 0.000 0.000 7 1.030 9.587 450.000 -35.419 450.000 -35.419 0.000 0.000 8 0.995 -5.036 -156.000 -79.900 0.000 0.000 156.000 79.900 9 1.040 4.645 -8.600 -5.600 0.000 0.000 8.600 5.600 10 0.982 -5.693 -429.900 -258.400 0.000 0.000 429.900 258.400 11 1.016 -0.557 -201.000 -136.700 0.000 0.000 201.000 136.700 12 1.034 -1.170 -166.200 -97.800 0.000 0.000 166.200 97.800 13 1.063 -6.450 -58.400 -28.400 0.000 0.000 58.400 28.400 14 0.978 -11.259 -144.700 -88.400 0.000 0.000 144.700 88.400 15 0.973 -10.828 -115.200 -42.000 0.000 0.000 115.200 42.000 16 0.996 -4.827 -82.100 -44.500 0.000 0.000 82.100 44.500 17 0.958 -12.711 -112.600 -50.000 0.000 0.000 112.600 50.000 18 0.994 -8.084 -184.900 -60.000 0.000 0.000 184.900 60.000 19 1.075 -10.670 -102.900 -17.500 0.000 0.000 102.900 17.500 20 1.021 2.030 -60.300 -70.000 0.000 0.000 60.300 70.000 21 1.006 -6.017 -26.800 -10.500 0.000 0.000 26.800 10.500 22 0.978 -6.133 -292.000 -114.900 0.000 0.000 292.000 114.900 23 0.998 -3.220 -193.500 -101.200 0.000 0.000 193.500 101.200 http://www.azojete.com.ng Arid Zone Journal of Engineering, Technology and Environment, March, 2019; Vol. 15(1):77-96. ISSN 1596-2490; e-ISSN 2545-5818; www.azojete.com.ng Corresponding author’s e-mail address: gbengailori@unilag.edu.ng 85 24 0.993 -4.123 -139.400 -61.000 0.000 0.000 139.400 61.000 25 1.000 -3.005 -109.700 -64.200 0.000 0.000 109.700 64.200 26 0.996 -4.356 0.000 0.000 0.000 0.000 0.000 0.000 27 0.999 -4.675 -64.300 -44.200 0.000 0.000 64.300 44.200 28 0.981 -10.991 -119.300 -65.700 0.000 0.000 119.300 65.700 29 1.041 2.785 -61.500 -10.300 0.000 0.000 61.500 10.300 30 1.045 4.892 0.000 0.000 0.000 0.000 0.000 0.000 31 1.040 4.932 0.000 0.000 0.000 0.000 0.000 0.000 In the case of Table 2; for the Nigeria-31 bus system, the lines that are highly threatened due to the line losses is arranged in the order severity are Lines: 9-11, 29-12, 8-15, 10-15 and 18-12. Table 2: Line flow and Line loss of the Nigeria-31 bus transmission line From Bus To Bus P (MW) Q (Mvar) From Bus To Bus P (MW) Q (Mvar) Line Loss (MW) (Mvar) 25 1 -825.940 -242.193 1 25 825.940 291.920 0.000 49.727 26 2 -200.000 35.026 2 26 200.000 -30.002 0.000 5.024 27 3 -300.000 -15.482 3 27 300.000 27.581 0.000 12.099 28 4 -250.000 -129.449 4 28 250.000 141.171 0.000 11.722 29 5 -490.000 86.333 5 29 490.000 -48.893 0.000 37.440 30 6 -350.000 30.718 6 30 350.000 -15.387 0.000 15.331 31 7 -450.000 63.900 7 31 450.000 -26.891 0.000 37.009 10 8 -31.213 -54.646 8 10 31.445 56.397 0.232 1.751 11 8 109.331 14.496 8 11 -108.156 -5.665 1.175 8.831 8 15 245.872 32.086 15 8 -242.515 -6.816 3.357 25.270 21 8 -26.800 22.002 8 21 26.892 -21.313 0.092 0.689 8 26 -155.680 4.482 26 8 155.889 -2.663 0.209 1.819 8 27 -196.404 59.991 27 8 197.633 -59.109 1.229 0.882 9 11 633.489 129.221 11 9 -625.505 -69.260 7.984 59.961 9 29 95.623 -17.475 29 9 -95.202 20.634 0.421 3.159 30 9 289.242 6.360 9 30 -288.018 -5.137 1.224 1.223 31 9 450.000 -61.006 9 31 -449.694 63.263 0.306 2.257 11 10 105.643 40.585 10 11 -104.185 -29.618 1.458 10.967 10 22 292.377 112.165 22 10 -292.000 -109.378 0.377 2.787 24 10 68.176 30.731 10 24 -67.865 -28.390 0.311 2.341 10 25 -519.014 -77.597 25 10 522.604 104.548 3.590 26.951 11 24 209.531 67.682 24 11 -207.576 -52.983 1.955 14.699 12 13 164.637 -65.939 13 12 -162.356 83.129 2.281 17.190 18 12 -184.900 -22.413 12 18 188.078 46.318 3.178 23.905 29 12 523.702 4.711 12 29 -518.916 31.226 4.786 35.937 13 19 103.956 -25.158 19 13 -102.900 33.097 1.056 7.939 file:///C:/Users/user/Downloads/azojete143/www.azojete.com.ng Oluseyi, et al. Transmission expansion programme for electric network reinforcement. AZOJETE, 15(1):77-96. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng 86 15 14 14.140 -14.523 14 15 -14.113 14.722 0.027 0.199 14 28 -130.587 -70.858 28 14 130.700 71.711 0.113 0.853 15 17 113.175 39.805 17 15 -112.600 -35.475 0.575 4.330 26 16 44.111 -5.689 16 26 -44.061 6.061 0.050 0.372 27 16 38.067 36.211 16 27 -38.039 -35.998 0.028 0.213 20 30 -60.300 -16.630 30 20 60.758 20.079 0.458 3.449 25 23 193.636 97.753 23 25 -193.500 -96.744 0.136 1.009 3.1 Pareto space According to Table 3 as regards the implementation of the improved strength pareto evolutionary algorithm (SPEA-2), it can be seen that the adopted number of generation (i.e. the previous generation from which the next parent for current generation are chosen) was 200 while the size of archive (externally stored pareto solution) was 50 and the population size was 250. Whenever this is implemented; it resulted in the convergence to a pareto front as will be displayed in a number of scenarios that would later be presented in this study. Table 3: Improved Strength Pareto Evolution Algorithm parameters Generation 200 Archive Set 50 Population size 250 3.2 Optimal Solution As stated earlier, there is need in decision making to consider trade-offs due to conflicting goals that must be optimized in the application of the optimization theory. In the case of this research work, the three parameters of interest are namely; the line index, power losses and capital investment cost needed for the expansion of the network; in order to alleviate the challenges of outages that are necessitated by weak links as presented in the violated lines. In order to have a better understanding of this, using the SPEA-2 the Nigeria-31 bus system is compared with a standard benchmark as represented by IEEE-30 bus system. Thus, the outcome of this led to the results displayed in Figures 1 and 2 in which the power loss was compared with the power generation cost for both bus systems. From the available details in both diagrams; the results of the IEEE-30 bus is quite optimal in outlook while that of the Nigeria-31 bus system is highly violated hence there is need for capital-intensive investment; i.e. using the transmission expansion as a formidable option; to ensure that the power loss is reduced drastically so as to be more competitive to the IEEE-30 bus system. http://www.azojete.com.ng Arid Zone Journal of Engineering, Technology and Environment, March, 2019; Vol. 15(1):77-96. ISSN 1596-2490; e-ISSN 2545-5818; www.azojete.com.ng Corresponding author’s e-mail address: gbengailori@unilag.edu.ng 87 Figure 1: Nigeria 31-bus Pareto front for Power loss against Power generation cost Figure 2: IEEE 30-bus Pareto front for Power loss against Power generation cost 3.3 Transmission expansion philosophy With reference to previous discussion, from the output of the earlier considered graphs; it’s very essential to consider the power loss against investment cost. This would provide information on the extent to which the transmission network needs to be upgraded to avoid incessant outages (which is currently very prevalent). Thus, since a number of lines has been discovered as the weakest link in the energy flow chain of the Nigeria-31 bus system hence there is need to reinforce the network to overcome the influence of voltage collapse through the threats emanating from these identified buses on the network. In this vein, Figure 3 shows the investment cost as compared with the power loss. Thus if this investment well managed at critical buses then the network will experience a better power flow. In line with the multi-objective solution philosophy of transmission expansion programme, thus the Nigeria-31 bus system was subjected to a three-objective function. With the help of the SPEA-2; this results in the generation of the results that displayed in Figure 4. This thus corroborates the propensity of the well-planned transmission expansion programme as a last resort of the current energy crisisthat is bedeviling the Nigeria electricity industry. file:///C:/Users/user/Downloads/azojete143/www.azojete.com.ng Oluseyi, et al. Transmission expansion programme for electric network reinforcement. AZOJETE, 15(1):77-96. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng 88 Figure 3: Pareto front for Power loss against investment cost Figure 4: Pareto front for Investment cost, Line Index and Power loss 3.4 Results of the contingency analysis of the Nigeria-31 bus network To achieve the contingency analysis, the lines or generators were carefully chosen and then remove from service for the purpose of subjecting the network to contingency test. In this case only one line is taken out of service in each scenario as shown in Table 5. Thus, from the foregoing, this shows that when the generators were subjected to contingency test, with one of the generators shutdown, it gave rise to cascaded violation of the network. It can be seen from this table that when contingency analysis was performed on the network; the buses that the buses that suffered major violation were: the buses located at Jos (i.e. Bus 14), Gombe (i.e. Bus 17), Birnin Kebbi (i.e. Bus 28) and Kaduna (i.e. Bus 29). Obviously, this is due to a number of factors among which are the distance and source of power generation to these buses. So also lack of transmission line reinforcement using the power conditioners (such as the bank of reactors, shunt power electronics devices) at the identified buses are all contributory indices http://www.azojete.com.ng Arid Zone Journal of Engineering, Technology and Environment, March, 2019; Vol. 15(1):77-96. ISSN 1596-2490; e-ISSN 2545-5818; www.azojete.com.ng Corresponding author’s e-mail address: gbengailori@unilag.edu.ng 89 to the violation suffered by the lines during this contingency test. However, with the introduction of the new generation at Geregu and Ajaokuta, it is expected that it will relieve the buses in the network around this section of the transmission network. Table 4: Single transmission line contingency test Contigency Considered Skip Processed Solved Violations Line from 11 (Benin) to 2 (DeltaPs) C1 NO YES YES 4 Line from 2 (DeltaPs) to 21 (Aladja) C1 NO YES YES 4 Line from 15 (Onitsha) to 3 (Okpai) C1 NO YES YES 5 Line from 11 (Benin) to 4 (Sapele) C1 NO YES YES 4 Line from 4 (Sapele) to 21 (Aladja) C1 NO YES YES 4 Line from 26 (Alaoji) to 5 (Afam) C1 NO YES YES 4 Line from 10 (Oshogbo) to 6 (Jebba) C1 NO YES YES 4 Line from 27 (JebbaTS) to 6 (Jebba) C1 NO YES NO Unsolved Line from 7 (Kainji) to 27 (JebbaTS) C1 NO YES YES 4 Line from 7 (Kainji) to 27 (JebbaTS) C2 NO YES YES 4 Line from 7 (Kainji) to 28 (B. Kebbi) C1 NO YES YES 3 Line from 27 (JebbaTS) to 8 (Shiroro) C1 NO YES NO Unsolved Line from 8 (Shiroro) to 30 (ShiroroTS) C1 NO YES NO Unsolved Line from 9 (Geregu) to 24 (Ajaokuta) C1 NO YES YES 4 Line from 10 (Oshogbo) to 11 (Benin) C1 NO YES YES 4 Line from 10 (Oshogbo) to 12 (Ikeja-West) C1 NO YES YES 4 Line from 13 (Ayede) to 10 (Oshogbo) C1 NO YES YES 4 Line from 12 (Ikeja-West) to 11 (Benin) C1 NO YES YES 4 Line from 11 (Benin) to 15 (Onitsha) C1 NO YES YES 4 Line from 11 (Benin) to 24 (Ajaokuta) C1 NO YES YES 4 Line from 13 (Ayede) to 12 (Ikeja-West) C1 NO YES YES 4 Line from 16 (Akangba) to 12 (Ikeja-West) C1 NO YES YES 5 Line from 32 (EgbinTS) to 12 (Ikeja-West) C1 NO YES NO Unsolved Line from 14 (Jos) to 17 (Gombe) C1 NO YES YES 2 Line from 29 (Kaduna) to 14 (Jos) C1 NO YES YES 4 Line from 15 (Onitsha) to 25 (N. Haven) C1 NO YES YES 4 Line from 15 (Onitsha) to 26 (Alaoji) C1 NO YES YES 4 Line from 30 (Shiroro TS) to 18 (Abuja) C1 NO YES YES 5 Line from 29 (Kaduna) to 22 (Kano) NO YES NO Unsolved Line from 23 (Aja) to 32 (EgbinTS) C1 NO YES YES 4 Line from 23 (Aja) to 32 (EgbinTS) C2 NO YES YES 4 Line from 30 (ShiroroTS) to 29 (Kaduna) C1 NO YES YES 4 Line from 30 (ShiroroTS) to 29 (Kaduna) C2 NO YES YES 4 Line from 31 (EgbinPS) to 32 (EgbinTS) C1 NO YES NO Unsolved file:///C:/Users/user/Downloads/azojete143/www.azojete.com.ng Oluseyi, et al. Transmission expansion programme for electric network reinforcement. AZOJETE, 15(1):77-96. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng 90 Table 5: Summary of contingency analysis Contigency Considered Buses Violated Line from 11 (Benin) to 2 (DeltaPs) C1 Jos (14), Gombe (17), B. Kebbi (28) and Kaduna (29) Line from 2 (DeltaPs) to 21 (Aladja) C1 Jos (14), Gombe (17), B. Kebbi (28) and Kaduna (29) Line from 15 (Onitsha) to 3 (Okpai) C1 Jos (14), Gombe (17), B. Kebbi (28), Kaduna (29) and N. Haven (25) Line from 11 (Benin) to 4 (Sapele) C1 Jos (14), Gombe (17), B. Kebbi (28) and Kaduna (29) Line from 4 (Sapele) to 21 (Aladja) C1 Jos (14), Gombe (17), B. Kebbi (28) and Kaduna (29) Line from 26 (Alaoji) to 5 (Afam) C1 Jos (14), Gombe (17), B. Kebbi (28) and Kaduna (29) Line from 10 (Oshogbo) to 6 (Jebba) C1 Jos (14), Gombe (17), B. Kebbi (28) and Kaduna (29) Line from 7 (Kainji) to 27 (Jebba TS) C1 Jos (14), Gombe (17), B. Kebbi (28) and Kaduna (29) Line from 7 (Kainji) to 27 (JebbaTS) C2 Jos (14), Gombe (17), B. Kebbi (28) and Kaduna (29) Line from 7 (Kainji) to 28 (B. Kebbi) C1 Jos (14), Gombe (17) and Kaduna (29) Line from 9 (Geregu) to 24 (Ajaokuta) C1 Jos (14), Gombe (17), B. Kebbi (28) and Kaduna (29) Line from 10 (Oshogbo) to 11 (Benin) C1 Jos (14), Gombe (17), B. Kebbi (28) and Kaduna (29) Line from 10 (Oshogbo) to 12 (Ikeja-West) C1 Jos (14), Gombe (17), B. Kebbi (28) and Kaduna (29) Line from 13 (Ayede) to 10 (Oshogbo) C1 Jos (14), Gombe (17), B. Kebbi (28) and Kaduna (29) Line from 12 (Ikeja-West) to 11 (Benin) C1 Jos (14), Gombe (17), B. Kebbi (28) and Kaduna (29) Line from 11 (Benin) to 15 (Onitsha) C1 Jos (14), Gombe (17), B. Kebbi (28) and Kaduna (29) Line from 11 (Benin) to 24 (Ajaokuta) C1 Jos (14), Gombe (17), B. Kebbi (28) and Kaduna (29) Line from 13 (Ayede) to 12 (Ikeja-West) C1 Jos (14), Gombe (17), B. Kebbi (28) and Kaduna (29) Line from 16 (Akangba) to 12 (Ikeja-West) C1 Jos (14), Gombe (17), B. Kebbi (28), Kaduna (29) and Oshogbo (10) Line from 14 (Jos) to 17 (Gombe) C1 Kano (22) and B. Kebbi (28) Line from 29 (Kaduna) to 14 (Jos) C1 Abuja (18), Kano (22) B. Kebbi (28) and Kaduna (29) Line from 15 (Onitsha) to 26 (Alaoji) C1 Jos (14), Gombe (17), B. Kebbi (28) and Kaduna (29) Line from 15 (Onitsha) to 26 (Alaoji) C1 Jos (14), Gombe (17), B. Kebbi (28) and Kaduna (29) Line from 30 (Shiroro TS) to 18 (Abuja) C1 Jos (14), Gombe (17), B. Kebbi (28), Kaduna (29) and ShiroroTS (30) Line from 23 (Aja) to 32 (EgbinTS) C1 Jos (14), Gombe (17), B. Kebbi (28) and Kaduna (29) Line from 23 (Aja) to 32 (EgbinTS) C2 Jos (14), Gombe (17), B. Kebbi (28) and Kaduna (29) Line from 30 (ShiroroTS) to 29 (Kaduna) C1 Jos (14), Gombe (17), B. Kebbi (28) and Kaduna (29) Line from 30 (ShiroroTS) to 29 (Kaduna) C2 Jos (14), Gombe (17), B. Kebbi (28) and Kaduna (29) Generator 2 (DeltaPs) U1 Jos (14), Gombe (17), B. Kebbi (28) and Kaduna (29) Generator 3 (Okpai) U1 Jos (14), Gombe (17), B. Kebbi (28) and Kaduna (29) Generator 4 (Sapele) U1 Jos (14), Gombe (17), B. Kebbi (28) and Kaduna (29) Generator 5 (Afam) U1 Jos (14), Gombe (17), B. Kebbi (28) and Kaduna (29) 3.5 Power Flow analysis with Powerworld software Furthermore, the same network data were subjected to the implementation of the the powerworld software to display the pictorial situation of the existing transmission network in the Nigeria-31 bus system so as to identify the area of improvement needed for the healthy http://www.azojete.com.ng Arid Zone Journal of Engineering, Technology and Environment, March, 2019; Vol. 15(1):77-96. ISSN 1596-2490; e-ISSN 2545-5818; www.azojete.com.ng Corresponding author’s e-mail address: gbengailori@unilag.edu.ng 91 operation of the network. The investigation is as displayed in Figure 5 whereby the existing power network of the Nigeria-31 bus system data were deployed for giving information on the existing state of the Nigeria’s transmission network. Just as earlier declared by the traditional analysis approach that identified a number of buses are the weak links in the Nigeria’s transmission network, the pictorial software further displays vividly the precarious state of power system operation in the Nigeria-31 bus system. This results further validate the earlier pronounced findings which identified the most violated buses as those situated at Kaduna, Gombe, Jos and Birnin Kebbi. In anticipation of the solution, as a correction step, extra single line was introduced between Kanji bus and Birnin-Kebbi transmission bus while another line was introduced Shiroro and Abuja buses as well as an extra line along Kaduna to Jos bus; this leads to immense improvement in the power flow in the network, especially with regard to the identified weak buses, the power flow in them increased considerably as shown in Figure 6. Thus it can be summarized that the existing Nigeria’s transmission network needs the assistance of the double line as introduced in Figure 6. This is expected to bring about great improvement in the voltage profile which has a direct and constructive influence on the reliability of electricity supply within the Nigeria-31 bus system. Figure 5: Existing Nigeria-31-bus Network file:///C:/Users/user/Downloads/azojete143/www.azojete.com.ng Oluseyi, et al. Transmission expansion programme for electric network reinforcement. AZOJETE, 15(1):77-96. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng 92 Figure 6: Improved Nigeria-31-bus transmission network 4. Conclusion This study addressed the transmission system expansion planning using an optimization approach known as the improved Strength Pareto Evolution Algorithm (SPEA-2) while also using the contingency analysis to isolate the most threatened lines and buses in the Nigeria’s transmission network. It was discovered that four major buses were violated which were located at Jos, Kaduna, Kano and Birnin-Kebbi respectively. Suggestively, it was also observed during this research work that transmission lines linking the geographical northern and southern parts of Nigeria experienced more power losses than any others. This is believed to be due to the length of transmission lines which remained uncompensated by neither traditional bank of reactors nor the modern power electronics devices. . further to this, it was observed that when contingency test was applied to the same network; the Kano, Birnin-Kebbi, Kaduna and Gombe buses had the highest number of violation when transmission line were opened as well as while one of the generators was shutdown. This thus suggests that, with the addition of double circuit on each transmission line connected to the weak buses in the Nigeria-31 bus system, thus the violation was drastically reduced. Furthermore, with the implementation of the improved strength Pareto evolution http://www.azojete.com.ng Arid Zone Journal of Engineering, Technology and Environment, March, 2019; Vol. 15(1):77-96. ISSN 1596-2490; e-ISSN 2545-5818; www.azojete.com.ng Corresponding author’s e-mail address: gbengailori@unilag.edu.ng 93 algorithm (SPEA-2); it was possible to determine the optimal and best solution in terms of line index function, Investment cost analysis and the power loss protocol. Thus the transmission expansion philosophy has shown a great potential for overcoming the identified congestion created by the weak transmission lines in the various locations. . APPENDIX Figure 7: One line diagram of the Nigerian Transmission Network Table 6: Generator Data of Nigerian 330 kV Grid System Bus No Pg (MW) Qg (MVAr) Qmax (MVAr) Qmin (MVAr) Base MVA Vg (p.u.) 1 830.23 0 450 -255 100 1.00 2 200 0 450 -250 100 0.99 3 300 0 450 -250 100 1.00 4 250 0 450 -250 100 1.00 5 490 0 450 -250 100 1.03 6 350 0 450 -250 100 1.04 7 450 0 450 -250 100 1.03 file:///C:/Users/user/Downloads/azojete143/www.azojete.com.ng Oluseyi, et al. Transmission expansion programme for electric network reinforcement. AZOJETE, 15(1):77-96. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng 94 Table 7: Line Data of Nigerian 330 kV Grid System From Bus To Bus R (p.u.) X (p.u.) 0.5B (p.u.) 25 1 0 0.00648 0 26 2 0 0.01204 0 27 3 0 0.01333 0 28 4 0 0.01422 0 29 5 0 0.01638 0 30 6 0 0.01351 0 31 7 0 0.01932 0 10 8 0.0055 0.04139 0.9425 11 8 0.00987 0.07419 0.41575 8 15 0.00538 0.0405 0.2269 21 8 0.00766 0.05764 0.323 8 26 0.0003098 0.00739 0.16565 8 27 0. 00287 0.02158 0.1209 9 11 0.00206 0.01547 0.78 9 29 0.0048 0.03606 0.80825 30 9 0.00159 0.01197 0.2683 31 9 0.00016 0.00118 0.0265 11 10 0.01163 0.0875 0.49025 10 22 0.00036 0.00266 0.0595 24 10 0.00538 0.0405 0.227 10 25 0.00122 0.00916 0.2054 11 24 0.00412 0.03098 0.1736 12 13 0.00774 0.05832 0.3263 18 12 0.00904 0.06799 0.38095 29 12 0.00189 0.01419 0.318 13 19 0.01042 0.07833 0.4398 15 14 0.00605 0.04552 0.25505 14 28 0.00049 0.00369 0.0828 15 17 0.00377 0.02838 0.159 26 16 0.00248 0.01862 0.10435 27 16 0.00102 0.00769 0.043065 20 30 0.01218 0.09163 0.51345 25 23 0.00028 0.00207 0.0464 http://www.azojete.com.ng Arid Zone Journal of Engineering, Technology and Environment, March, 2019; Vol. 15(1):77-96. ISSN 1596-2490; e-ISSN 2545-5818; www.azojete.com.ng Corresponding author’s e-mail address: gbengailori@unilag.edu.ng 95 Table 8: Bus Data of Nigerian 330 kV Grid System Bus No Type Pd (MW) Qd (MVAr) Base kV Vmax (p.u.) Vmin (p.u.) 1 1 0 0 16 1.1 0.9 2 2 0 0 16 1.1 0.9 3 2 0 0 16 1.1 0.9 4 2 0 0 16 1.1 0.9 5 2 0 0 16 1.1 0.9 6 2 0 0 16 1.1 0.9 7 2 0 0 16 1.1 0.9 8 0 156.8 79.9 330 1.1 0.9 9 0 8.6 5.6 330 1.1 0.9 10 0 429.9 58.4 330 1.1 0.9 11 0 201 136.7 330 1.1 0.9 12 0 166.2 97.8 330 1.1 0.9 13 0 58.4 28.4 330 1.1 0.9 14 0 144.7 88.4 330 1.1 0.9 15 0 155.2 42 330 1.1 0.9 16 0 82.1 44.5 330 1.1 0.9 17 0 112.6 50 330 1.1 0.9 18 0 184.9 60 330 1.1 0.9 19 0 102.9 17.5 330 1.1 0.9 20 0 60.3 70 330 1.1 0.9 21 0 26.8 10.5 330 1.1 0.9 22 0 292 114.9 330 1.1 0.9 23 0 193.5 101.2 330 1.1 0.9 24 0 139.4 61 330 1.1 0.9 25 0 109.7 64.2 330 1.1 0.9 26 0 0 0 330 1.1 0.9 27 0 64.3 44.2 330 1.1 0.9 28 0 119.3 65.7 330 1.1 0.9 29 0 61.5 10.3 330 1.1 0.9 30 0 0 0 330 1.1 0.9 31 0 0 0 330 1.1 0.9 Acknowledgment The authors wish to appreciate the Department of Electrical and Electronics Engineering of University of Lagos, Nigeria for the provision of software and the privilege embark on this study. file:///C:/Users/user/Downloads/azojete143/www.azojete.com.ng Oluseyi, et al. Transmission expansion programme for electric network reinforcement. AZOJETE, 15(1):77-96. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng 96 References Abido, MA. 2006. Multiobjective Evolutionary Algorithms for Electric Power Dispatch. IEEE Transactions on Evolutionary Computation, 10(3), 315-329. Ezechukwu, OA. 2013. Expansion Planning of Nigeria South East Electrical Power Transmission Network. The International Journal of Engineering and Science, 2(9), 97-107. Gupta, BR. 2008. Power system analysis and design. New Delhi: S. Chand Limited, India. . Haffner, S., Monticelli, A., Garcia, A. and Romero, R. 2001. Specialized Branch-and-Bound Algorithm for Transmission Network Expansion Planning. IEEE Proceedings - Generation, Transmission and Distribution, 148(5), 482-488. Jingdong, X. and Guoqing, T. 1997. 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SPEA2: Improving the Strength Pareto Evolutionary Algorithm for Multiobjective Optimization. In: Giannakoglou, KC. (Eds.) Proceedings of the EUROGEN2001 Conference, Barcelona, Spain, CIMNE, Pp. 95–100. Zitzler, T. and Thiele, L. 1999. Multiobjective Evolutionary Algorithms: A Comparative Case Study and the Strength Pareto Approach. IEEE Transactions on Evolutionary Computation, 3(4), 257- 271. http://www.azojete.com.ng