Title: Approach of hybrid PBIL control in distributed generation parameters for IEEE and real time Indian utility system
Abstract: IET Renewable Power GenerationVolume 11, Issue 2 p. 255-263 Research ArticleFree Access Approach of hybrid PBIL control in distributed generation parameters for IEEE and real time Indian utility system Chandrasekaran Nayanatara, Chandrasekaran Nayanatara Research Scholar, Sri SaiRam Engineering College, Chennai, IndiaSearch for more papers by this authorJeevarathinam Baskaran, Corresponding Author Jeevarathinam Baskaran [email protected] Adhiparasakthi Engineering College, Melmaruvathur, IndiaSearch for more papers by this authorDwarkadas Pralhaddas Kothari, Dwarkadas Pralhaddas Kothari Gaikwad Patil Group of Institutions, Nagpur, IndiaSearch for more papers by this author Chandrasekaran Nayanatara, Chandrasekaran Nayanatara Research Scholar, Sri SaiRam Engineering College, Chennai, IndiaSearch for more papers by this authorJeevarathinam Baskaran, Corresponding Author Jeevarathinam Baskaran [email protected] Adhiparasakthi Engineering College, Melmaruvathur, IndiaSearch for more papers by this authorDwarkadas Pralhaddas Kothari, Dwarkadas Pralhaddas Kothari Gaikwad Patil Group of Institutions, Nagpur, IndiaSearch for more papers by this author First published: 12 January 2017 https://doi.org/10.1049/iet-rpg.2016.0581Citations: 11AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract This study presents a method for regulation parameters of a distributed generation (DG) system by means of a hybrid optimisation algorithm. This aims in increasing the stability and reducing the losses and the cost of generation. The hybrid algorithm which includes probability based incremental learning and micro genetic algorithm are tested among other computational intelligence techniques to validate the efficiency of the method by maximising the total social welfare and minimising the network congestion. Simultaneous optimisation of DG parameters which includes DG size, location and type is explored using generation rescheduling and with load curtailment which is vindicated on a modified IEEE distribution system and in a real time Indian utility system. Results show us that the proposed method presents advantages of low computational complexity. 1 Introduction Distributed generation (DG) is a small level power station which is used to solve the demand for the local loads [1]. There are several methods used in the application of DG. DG introduces its useful advantages in photovoltaic (PV) cells, fuel cell and biogas and wind turbine. Its advantage includes, increasing system stability and reliability, improvement in voltage and reduction of losses. In a notably stifle area, the advantage of placing the DG is more important [2].The placement of DG should be based on its location and size. Number of promising techniques where followed to indicate the advantages of DG in the power system. In [3] the forecast using wind power analysis detection of bad data wind power forecasting is proposed. This paper deals with the maximum amount of wind energy which can be utilised in power sectors. The various analytical approaches for the location of DG placement to reduce power losses (PLs) is analysed in [4]. The pricing strategy in smart grid energy market by means of PI control technique is formulated in [5]. The investment planning strategy of DG devices for reducing the reactive PLs by switching off shunt capacitors is given in [6]. The losses reduction using DG by simple and efficient method is rightly shown in [7]. For a coordinated generation system synchronisation was done and the pricing method is given in [8]. Celli in his paper proposed a technique to appraise the placement of DG [9]. Moghaddas-Tafreshi and Mashhour [10] modelled DG for the study of power flows using forward backward base case algorithm. The current status and the opportunities available in DG were given in [11]. Linear weightage summation algorithm is used to solve the power flow fluctuation when the radiation changes in a PV distribution system [12]. In the analytical study [13], optimum placement of DG in radial system was evaluated to reduce the losses. The specific PL is proposed in [14] by modelling DG parameters using wind farms. The proper location of DG based on the reliability index strategy is given in [15]. Release of congestion which in turn reduces the losses is indicated in [16-18]. The optimal placement of capacitor banks in a radial distribution system was given in [19]. For optimal location of DG parameters location marginal pricing is implemented and optimal power flow calculations are done in [20]. The planning and analysis was done in [21] by modelling the DGs within their security limits. Value based method is employed in [22] for power quality improvements by placing the DG at the right location. Fuzzy control methodology is proposed to solve the power management in the integrated grid [23]. The closed loop PID control for balancing the energy demand in a real time is studied in [24]. The various DG resources are considered for optimal location alone is given in [25]. From the above available literature, it is concluded that many researchers have used various DG devices with different intelligent algorithms to address the power distribution network problems. Each work has its own merits and demerits. The limitations are considered and an attempt is made to solve the problem. The main objective of this proposed work is to achieve reliability and economic distribution by the optimal utilisation of various DG resources. System performance depends on the loadability of the system within its stability and thermal power limits with minimum PLs thereby maximising the social welfare. Since all these objectives are considered together at a time hybrid optimisation [probability based incremental learning (PBIL)-micro genetic algorithm (MGA)] technique is used. At the same time, due to the inclusion of DG devices, cost of the system should not be too high. Therefore for prioritising the objective simultaneous optimisation of all DG parameters, i.e. size, type and location are done in the IEEE 30 bus distribution and in a real time Indian Utility Neyveli Thermal Power Station (NTPS) system. The paper has five additional sections: Section 2 deals with the mathematical modelling to determine the optimum location and size of DG. Section 3 gives the intent of planning of distributed generation with formulations. Section 4 gives the Hybrid methodology for optimising the location and size of DG. The simulation results in Section 5 and the foremost contributions and conclusions are given in Section 6. 2 Mathematical modelling of DG devices 2.1 DG devices The DG plays a crucial role in locating and sizing, as it leads to the decrease in losses [26]. The increase in size of DG results with the increase in loss value and overshoots the loss values in base case. The optimum location of DG is essential for minimising losses and voltage deviation index (VDI) and maximising the customer benefit (CB). Based on their power injecting characteristics Dg can be classified into three major types: Unity power factor modelling of DG (Type 1). Zero power factor modelling of DG (Type 2). Variable power factor (between 0 to 1) modelling of DG (Type 3). The power output by the DG with variable power factor is calculated by (1) where DGPF = Power factor of DG (2) The active and reactive power injected is given by, (3) 2.1.1 Modelling of PV cell The compatibility with the grid is done by converting the DC power output from PV cell into AC by means of an inverter. The DG model [27] of PV cell is based on the design of controller. This type of DG has unity power factor. (4) the above equation is minimised to have the condition for loss minimisation (5) Mjk and Njk = coefficient of losses, Pj = real power injected to bus j, Qj = reactive power injected to bus j. 2.1.2 Synchronous compensators such as gas turbines In type 2, the chemical energy in the fossil fuel is converted into heat and then into mechanical energy with the help of gas turbines. Synchronous generators can be used to convert the mechanical energy into electrical energy and then it can be directly connected to grid. Both the sides of the loss equation are differentiated with respect to Qi for determining the optimal DG placement [28]. The optimisation is done using 3 and the power factor for this type of DG is zero. (6) QDG2i = Reactive Power of DG at the ith bus; Aij and Bij = the ijth element of the impedance matrix. 2.1.3 Modelling of wind turbine In an induction generator both active and reactive powers are functions of slip 's'. (7) Assume that the dependency of Q is very low and P is constant, the expression (7) can be reduced as follows: (8) (9) (10) where the Albert Betz constant [29] is denoted as α, ρ (t) is the air density, A is the area swept by turbine rotor, and v (t) is the wind speed. For this type of DG, the power factor is a variable parameter. The maximum DG capacity for renewable DGs is calculated from the average power estimated by irradiance and wind speed. 3 Objectives of distributed generation planning 3.1 CB maximisation CB is the summation of Customer surplus+provider excess Customer surplus is the difference between monetary assessment of electricity to customer and the charge of obtaining electricity. Provider excess is the difference between the electricity sales profit and the charge of supply. These two parameters are indicated in monetary terms. In this paper the cost is expressed in terms of dollar. Let the customer surplus be represented as U and supplier surplus as V, then, (11) where αc is the customer utility, βc is the cost of electricity, µc is the sales revenue and γc is the cost of supply. The vital planner maximises, Since the supplier receives what the consumer pays, electricity cost and sales revenue is similar and those two parameters get cancelled and result in (9). The input–output characteristics of generating units will be different. The objective function total social welfare (TSW) is a quadratic function with the demand and the generation. Thus the function gives the total assessment of the excess, calculated in each group. (12) Thus the optimal size for maximising the objective function is given by the following sub-problem, (13) The possible maximum welfare is achieved if the size and power factor is selected to be equal to that of the additive load. The system considers the demand of ith customer and therefore, the above equation maximises the difference between total benefit and total cost. Quadratic and cubic cost functions are considered normally to model the actual response of the entire generator and load bus system. For all practical cases the cost of function can be represented as a quadratic function. The incremental fuel cost is obtained by taking the derivative of the fuel cost with the real power. The first and second order coefficients in the quadratic function gives the behaviours of the electricity market participants. The second and the first order coefficients give the capital fuel cost and the operation and maintenance cost. The cost of labour is given by the constant parameter. 3.1.1 Equality constraints Equality constraints are based on power flow equation. (14) where (15) 3.1.2 Inequality constraints Generation limits: Generating stations are assigned with maximum and minimum generation limits beyond which the generation is not feasible due to some economical and technical reasons. Real power generation limits: (16) Reactive power generation limits: (17) Line flow limit: It gives the maximum power that can be transmitted over the line. The transmission of power depends on stability and thermal considerations. It facilitates to maintain the absolute power at the sending and the receiving end of the line to be within the maximum limit of the line. (18) (19) For base case OPF, For load bus, where, N = Number of buses present in the system; PGi = Generated real power at bus i; PDi = Demand of real power at bus i; PDGi = Power supplied by DG at bus i. di, aj and gk = Cost coefficient of demand, generator and DG buses; ei, bj and hk = Supply and maintenance cost coefficients of the respective buses; fi, cj and lk = labour cost coefficients of the respective buses; Vi = voltage at bus i; δi, δj = Power angle at bus i and j; Bij & Gij = Susceptance and conductance of the line ij; QGi, QDi = reactive power at bus i for generator and load buses; and = upper and lower limit for real power generation by generator at bus i; Yij = Bus admittance value between buses i and j; θij = Admittance angle between buses i and j; and = upper and lower limit for reactive power generation by generator at bus i; and = upper and lower limits of voltage at bus i; Sij & Sji = the complex power transfer from bus i to bus j and from bus j to bus i. The total energy management indicates the loss in the system [30] can be calculated using the following equation, (20) (21) are the kjth element of [Zbus] matrix (22) Based on the sensitivity index calculation which is obtained from base case, the bus having the lowest loss sensitivity factor will be the best location for the placement of DG. 4 Hybrid approach for optimal placement and sizing of DG The motivation of this hybrid algorithm is to speed up the convergence and to get a better solution than that obtained when applying the individual method. The conventional techniques lack to solve this problem because they depend on the derivatives of the objective function. Thus the solution obtained may not give guarantee to achieve the global optimum. Further it may reach local minima and at worst it may diverge. Our aim is to concurrent optimisation [31] of DG parameters satisfying the constraints and achieving the best result. The PBIL-MGA approach used has a great potential in handling the problem of power system. The PBIL is used to find the global optimum and the MGA to search the local optimum. Therefore the solution obtained will be of merit order. 4.1 Objective function The main aim of this research is to find out the optimal size, type and the location for maximising the customer benefit which in turn reduces the congestion and real PL. The objective function is given as, (23) Subjected to the constraint (24) where Wk€ [0, 1]. The reactive power loading is gradually increased until the load flow solution fails to converge and for the loadability condition VDI and the maximum reactive power loading is calculated. The load buses are arranged in the ascending of their maximum loadability. This base case is passed on to stage 1 and consecutively to stage 2. Thus the control variables of DGs are randomly chosen to give the optimised value. The type, rating and size of the DG devices are chosen. 4.2 PBIL algorithm Since PBIL only needs tuning of two parameters the number of trial and error will be less which is the greatest merit of this algorithm. It inherits the properties of genetic algorithm (GA) and the significant feature of using the probability vector is the genetic operators [32] which take place directly on the vector rather than on individual solution vectors. The PBIL algorithm consists of the following steps (see Fig. 1): Fig. 1Open in figure viewerPowerPoint PBIL algorithm Where Mut_Shift is the amount of mutation by which the probability vector gets affected. 4.3 Micro genetic algorithm MGA gives the best result and reduces the processing time. Mutation becomes unwanted in MGAs, because after a definite number of iterations the best chromosome is maintained. The flowchart of MGA is given in Fig. 2. This method is more applicable for combinatorial optimisation algorithm. The elitism approach we use is based on the replacement of the population memory by the best solution attained when nominal convergence is achieved. Fig. 2Open in figure viewerPowerPoint Working methodology of MGA 4.3.1 Hybrid optimisation (PBIL-MGA) This hybrid method undergoes two stages. PBIL is applied at stage-1. The aim is to create a probability vector with a very high probability represents a solution in turn gives a high evaluated solution vectors. The location, size and rating of DG are optimised and the optimised values are passed to stage-2 which overcomes the situation that has non-convexity. Thus the hybrid method has the following steps (Fig. 3): Estimate the bus voltage (BV), power and line losses without accounting DG devices in a power system. Verify the BV, PL defined for each bus. Use PBIL to determine the sub-groups within the buses and to choose the location which has more credits. Randomly generate a P size population depending on the subgroup and go to step 6. Generate a population of size P-1 randomly depending on the subgroup Calculate the fitness factor for all chromosomes in the population. Perform the crossover process. Determine the fitness factor for new set of chromosomes. Repeat steps 7 and 8 till the best chromosomes are obtained; print the best chromosome and discard the others. Repeat steps (5–9) for n times; and the desirable characteristics will be obtained after m consecutive generations. Fig. 3Open in figure viewerPowerPoint Working methodology of hybrid combination Generation rescheduling is sufficient for eliminating the line overloads. To maintain the security of the system within the limits, load shedding is used in order to formulate the minimum blackout. 5 Simulation results Using VC++ software package the power flow studies are simulated. The reliability of the proposed distribution system which has 30 nodes and 32 segments are verified using the hybrid algorithm. The assumption made is that all the loads are from node1 substations and loads are of variable nature. It consists of 30 buses with real power of 4.43 MW and reactive power of 2.73 MVAR. The type is defined as follows; 1 for PV cell, 2 for wind turbine, 3 for gas turbine. To execute the effectiveness of the hybrid approach and to prove the benefits of DG four case studies were taken and simulation is carried in modified IEEE Distribution system and in a real time Indian Utility System. The optimal DG size, type and rating for each of the case is determined. The corresponding PL, generation cost and the benefit to the customers is found. To extend the study the loadability limit was also executed to its corresponding maximum limit and the convergence ability is also checked. The maximum customer benefit can be obtained only for the optimised DG size and ratings. Beyond that it will decrease and it may also reach a negative value. However summary of the result comparing with other computational techniques and the voltage deviation found, with and without DG and the achievement of the objective function are given in this section. To achieve the operational security both generation and load parameters are taken as a variable parameter. Also the power varies between 0 and 1. These parameters are taken into simulation to justify the uncertainty of PV and wind. The following computational parameters are chosen for simulation. Population size = 100 Number of generations = 200 Mutation constant = 0.01 Probability constant = 0.1 Crossover constant = 0.6 The convergence characteristics and fitness distribution are shown in Figs. 4 and 5. The convergence characteristics which converge linearly show the efficiency of the proposed algorithm. Fig. 4Open in figure viewerPowerPoint Iteration (vs.) customer benefit Fig. 5Open in figure viewerPowerPoint Iteration (vs.) fitness The buses which have extensive range of voltage ranges are tabulated in Table 1. Table 1. Voltage deviation table with and without DG S.No Voltage range, p.u. Number of buses available (bus number) Without DG With DG 1 0.49–0.63 3(6,9,14,23) NIL 2 0.63–0.72 5(1,5,8,12,16,21,24) NIL 3 0.73–0.84 4(3,13,15,20,26,29) NIL 4 0.85–0.94 7(4,11,17,19,28,30) 4(2,13) 5 0.94–1.05 9(2,10,18,22,25,27) 20(1,3,4,5,7,8,9,11,12,13,14,15,16,17,19,20,21,23,24, 28,29,30) 6 1.05–1.1 NIL 2(10,18,22) The distributed generators are used to supply some out-of-phase current combining active power with reactive power feed to improve grid quality. With the proper control variables of DGs not only minimising the PL is considered, it takes care of loadability also. The results of Figs. 6a and b show that with the combined operation of DGs optimally the loadability limit has still increased to twice from the normal loading condition. The loading capability limits reveal the success of DG and the corresponding PL is graphically represented. Fig. 6Open in figure viewerPowerPoint (a) Normal loading conditions with and without DG, (b) double the loading condition with and without DG For a 24 h load duration cycle the load has been divided into peak, medium and low load. The optimal DG size and location reduces the PLs drastically and the results showing PLs with and without are tabulated in Table 2 and represented in Fig. 7. Table 2. Optimal location and sizing of DG for a daily load cycle Load type Location of bus Optimal DG size, p.u. PL with DG, MW PL without DG, MW peak load 14 0.57 8.02 12.14 medium load 6 0.39 6.37 9.03 low load 23 0.17 2.45 5.26 Fig. 7Open in figure viewerPowerPoint Loss with DG size The simultaneous optimisations of all DG parameters are done initially by normal genetic and MGA (GA and MGA) and also by the hybrid method. The size, type and the rated value for various DGs is chosen and the optimised value is used for the maximisation in Social Welfare and in the minimisation of losses which is tabulated in Table 3. From the result we can see the hybrid method gives more selection in the number of lines. Also the maximum social welfare is seen only in the hybrid combination. Table 3. Optimisation of DG parameters (a) Individual optimisation GA MGA Line Device Rated value in MW % increase in TSW % Power loss reduction Line Device Rated value in MW % increase in TSW % Power loss reduction 1 1 4.3 0.55 3.98 1 1 3.16 2.8 1.1 2 3 0.23 3.45 8.56 2 2 2.98 3.7 5.45 4 1 2.23 9.34 5.76 4 1 3.34 17.67 56.89 6 2 1.6 14.65 0.53 16 3 1.98 12.78 11.89 8 2 3.23 16.4 2.06 18 2 2.72 25.87 6.78 12 1 1.87 10.54 19.00 22 1 3.76 9.78 2.97 13 3 0.34 14.23 21.57 17 2 1.97 22.23 36.78 22 3 2.6 12.76 32.78 23 1 3.23 7.43 32.78 (b) Proposed hybrid optimisation PBIL-MGA Line/location Device/type Power factor Rated value in MW % Increase in TSW % Power loss reduction 1 3 0.75lead 3.16 3.5 1.1 2 2 0.02lag 2.98 2.4 5.45 4 2 0.01lead 3.34 11.23 56.89 7 3 0.25lag 2.6 14.56 0.61 9 2 0.05lag 1.6 13.33 5.87 15 2 0.01lag 2.1 21.34 7.67 16 3 0.65lead 1.98 6.23 11.89 18 3 0.77lag 2.72 22.34 6.78 19 1 1.00 2.87 13.56 12.83 21 3 0.60lag 2.1 4.23 7.99 22 1 1.00 3.76 3.21 2.97 23 1 0.95 3.12 31.32 32.78 28 3 0.75lead 3.1 24.23 82.89 (c) Convergence results obtained for the IEEE and real time system Scenario F1, % F2, MW F3, $/h Min Xm1 Max Xn1 Mean value Standard deviation Min Xm2 Max Xn2 Mean Value Standard deviation Min Xm3 Max Xn3 Mean Value Standard deviation IEEE 30 bus system 102 144 123 6.2 7.2 13.6 12.53 1.3 643 1134 567 31.56 real time NTPS system 93 136 174 11.89 5.5 14.8 13.54 2.56 536 1253 732 21.45 (d) Comparison results obtained by individual optimisation of parameters Method Objective functions Average CPU time, s Cost minimisation, % Loss minimisation, % Welfare maximisation, % proposed hybrid optimisation algorithm (PBILMGA) 11.56 34.12 23.768 1.31 genetic algorithm [16] 3.78 8.56 2.67 6.14 simulated annealing optimisation [18] 5.78 9.56 12.67 5.12 micro genetic algorithm [17] 2.35 2.768 8.33 4.33 fuzzy-GA [16] 9.45 26.68 18.32 3.67 The PLs are reduced with the optimised values of DG. The four test cases simulated using IEEE distribution system and the Real time system clearly indicates the effective utilisation of DGs with minimum PL. The table given below shows the implementation of objective function with given renewable energy sources. The best solution for maximising the welfare objective is treated as maximum goal () and the worst solution is treated as the minimum goal (). The best solution for minimising the total real PL and minimising the overall cost of the system are treated as minimum goals () () and the worst solutions are treated as the maximum goal() (). Thus the Table 3c gives the best and worst solution obtained for the two test system along with their mean value and the standard deviation. To validate the accuracy of the proposed method a comparative analysis is done among the other intelligence technique available in the literature. From Table 3d it is clear that the proposed PBIL-MGA technique predominates over the other techniques. IEEE 30 bus system and a real time Indian NTPS system are considered as test systems in this work. Case (i) Rescheduling of Generation (140 ↑). Case (ii) Rescheduling of Generation with DG Devices (150↑). Case (iii) Rescheduling of Generation with load shedding (155↑). Case (iv) Rescheduling of Generation with load shedding and DG Devices (155↑). i. IEEE30 bus system: The below simulated results indicate the cost of generation and PL in the above four test cases. The comparison is done with GA and hybrid and it is tabulated in Table 4. The maximum increase in loading without affecting the stability and convergence is also given for each case. Table 4. Generation cost and real power for four cases (IEEE 30 bus system) Case studies Load increased, % Generation cost in, $/h Real PL in MVA GA PBIL-MGA GA PBIL-MGA Case (i) 130 957.78 966.98 21.23 23.56 Case (ii) 150 945.33 974.34 17.78 16.64 Case (iii) 150 912.99 976.22 20.45 23.67 Case (iv) 155 922.35 992.23 27.56 24.45 The simulation is carried out for the four case studies which give a clear aspect on the total load, losses and the corresponding objective function. It can also be noted that the computational time taken by the hybrid method is minimal which proves to be a promising dimension in the power system (Table 5). Table 5. Evaluated functions for four cases (IEEE distribution system) Evaluated functions ò Case (i) Case (ii) Case (iii) Case (iv) GA Hybrid GA Hybrid GA Hybrid GA Hybrid total generation, MW 283.39 283.42 267.73 267.73 268.34 272.78 288.12 293.46 total load, MW 278.67 278.67 262.21 262.21 253.45 269.65 285.33 295.54 time, s 0.56 0.06 0.11 0.10 0.19 0.11 0.15 0.02 objective function, $/h 982.07 985.45 874.32 873.32 945.21 948.88 991.57 997.77 The increase in loadability limit is indicated in all the cases and the results reveal the reduction in losses and the benefit obtained by the customers which is the total social welfare and it is given by the objective function. ii. Indian utility-NTPS23 bus system: The NTPS 23 bus system is taken as the base case. A base of 100 MVA and 400 KV is chosen. All the case studies are analysed (Fig. 8). Fig. 8Open in figure viewerPowerPoint Indian utility-NTPS Single line diagram Table 6 indicates the results obtained by taking the real time NTPS system data and for the same system all the case studies with the possibility of increasing the loadability limit was performed. and tabulated. Table 6. Generation cost and real power for four cases Case studies Load increased, % Generation cost in, $/h Real PL in MVA GA HYBRID GA HYBRID Case (i) 130 556.89 932.44 13.76 20.56 Case (ii) 150 662.34 889.35 32.23 18.34 Case (iii) 150 689.44 1056.21 14.12 22.44 Case (iv) 155 644.89 1023.45 23.89 21.99 The computational time taken by the three methods while simulating the case studies is given in Fig. 9. Fig. 9Open in figure viewerPowerPoint Simulation time taken by various case studies The results reveal that hybrid combination overcomes GA and MGA in terms of all aspects. Optimisation of DG parameters places a crucial role in achieving this maximum total social welfare. The results obtained using NTPS system which is tabulated in Table 7 indicates the increase in loading capability limits with load and generation both to be a variable parameter. Generation rescheduling with load shedding can be taken as the last case for maintaining the reliability of the network. Table 7. Evaluated functions for four cases (real time NTPS system) Evaluated functions Case (i) Case (ii) Case (iii) Case (iv) GA Hybrid GA Hybrid GA Hybrid GA Hybrid total generation, MW 234.11 277.44 218.45 283.42 232.34 293.23 255.55 264.95 total load, MW 245.54 211.54 232.55 277.67 273.34 295.43 263.67 263.54 time, s 0.18 0.04 0.63 0.02 0.43 0.04 0.56 0.03 objective function, $/h 1045.32 1267.67 1329.01 1845.33 1039.87 1045.76 2016.44 2053.42 The results reveal the benefit of customers with minimised congestion in the network by concurrently optimising all the DG parameters. 6 Conclusion The proposed hybrid optimisation algorithm justifies in solving more complex problems in an efficient way. Four different case studies were simulated ranging from a basic planning to the optimal planning. The results illustrate the main benefits of DG which was tested on a sample 30 bus distribution systems and in a real time Indian utility system. 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Publication Year: 2017
Publication Date: 2017-01-12
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 19
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