Metaheuristic and probabilistic techniques for optimal allocation and size of biomass distributed generation in unbalanced radial systems
2015; Institution of Engineering and Technology; Volume: 9; Issue: 6 Linguagem: Inglês
10.1049/iet-rpg.2014.0336
ISSN1752-1424
AutoresM. Gómez-González, F.J. Ruíz-Rodríguez, Francisco Jurado,
Tópico(s)Smart Grid Energy Management
ResumoIET Renewable Power GenerationVolume 9, Issue 6 p. 653-659 Research ArticlesFree Access Metaheuristic and probabilistic techniques for optimal allocation and size of biomass distributed generation in unbalanced radial systems Manuel Gómez-González, Manuel Gómez-González Department of Electrical Engineering, University of Jaén, EPS Linares, Jaén, 23700 SpainSearch for more papers by this authorFrancisco Javier Ruiz-Rodriguez, Francisco Javier Ruiz-Rodriguez Department of Electrical Engineering, University of Jaén, EPS Linares, Jaén, 23700 SpainSearch for more papers by this authorFrancisco Jurado, Corresponding Author Francisco Jurado fjurado@ujaen.es Department of Electrical Engineering, University of Jaén, EPS Linares, Jaén, 23700 SpainSearch for more papers by this author Manuel Gómez-González, Manuel Gómez-González Department of Electrical Engineering, University of Jaén, EPS Linares, Jaén, 23700 SpainSearch for more papers by this authorFrancisco Javier Ruiz-Rodriguez, Francisco Javier Ruiz-Rodriguez Department of Electrical Engineering, University of Jaén, EPS Linares, Jaén, 23700 SpainSearch for more papers by this authorFrancisco Jurado, Corresponding Author Francisco Jurado fjurado@ujaen.es Department of Electrical Engineering, University of Jaén, EPS Linares, Jaén, 23700 SpainSearch for more papers by this author First published: 01 August 2015 https://doi.org/10.1049/iet-rpg.2014.0336Citations: 15AboutSectionsPDF 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 In this study, a method for solving a probabilistic three-phase power flow in radial distribution networks and taking into account the technical constraints of the system is presented. Regulation of voltage is one of the main problems to be taken into account in networks with distributed generation. The present study introduces a probabilistic model to determine the performance of the distribution system. This study considers the random nature of lower heating value of biomass and loads. This study presents a new hybrid technique combining the shuffled frog leaping algorithm with probabilistic three-phase power flow that is solved by Monte Carlo method. Feasible results are achieved in a few iterations. The results show that the proposed technique can be applied to keep the voltages within the limits specified at each node of a distribution network with biomass power plants. The outcomes are attained using the unbalanced distribution system IEEE-13 node and connecting biomass power plants at some nodes. This study shows that the power losses and voltage unbalance are reduced as a result of the inclusion of distributed generation. 1 Introduction The profits of distributed resources can be significant. Nevertheless, these distributed benefits are site specific [1-3]. Moreover, distributed generation (DG) with renewable energy offers environmental benefits. Optimal sizing of a wind energy storage plant based on hydrogen technology has been analysed in [4]. A study proposes an optimal sizing methodology for a solar photovoltaic system considering lifetime cost requirements [5]. A suitable procedure for optimal sizing and location of single photovoltaic distributed generation (PVDGs) on radial distribution feeders has been developed in [6]. In this article, the preferred DG system is biomass power plants (BPPs). To evaluate the performance of the DG system, this paper has developed a probabilistic model that takes into account the random nature of lower heating value of biomass and load. A hybrid technique intends to look for a wide range of combinations for the placement and size of BPPs. This method combines a binary shuffled frog leaping algorithm (BSFLA) with a probabilistic three-phase power flow. For the purpose of assessing the voltage unbalances of an electrical distribution system, the uncertainties must be considered and modelled. Therefore a proper assessment of the influence of renewable energies in modern distribution networks must be addressed through a probabilistic view point [7], which takes into account the unbalanced voltages in the systems, as well. Furthermore, the probabilistic approach seems particularly helpful to investigate the performance of unbalanced voltages in the operation of electric devices in steady state, with the aim of establishing recommendations for their operation [8]. The probabilistic power flow was presented in [9, 10] and later implemented in [11]. In [12, 13], a study of probabilistic power flow was expanded to three-phase systems to take into account the uncertainties affecting the conditions of steady-state operation of a power system unbalanced can be seen. In [14], several algorithms for power flow in distribution systems, founded on iterative methods of sweep, and its convergence are studied for several load states. In [15], an analytical proposal is shown to model and resolve the probabilistic power flow that displays the profiles of voltage of the system, incorporating the uncertainties in the energy injected and loads. A three-phase power flow for on-line studies of distribution networks was introduced in [16]. Asymmetrical three-phase load flows were studied in [17], these studies were founded on symmetrical component theory, the node admittance matrix and the decoupling compensation technique. Artificial intelligence-based algorithms do not assure the optimum solution at all times, nonetheless they offer close solutions to the optimum with low computation cost [1-3, 18]. Shuffled frog leaping algorithm (SFLA), initially established by Eusuff et al. [19], is a memetic metaheuristic that is intended to find a global optimal solution by executing an informed heuristic search. In this paper, the hybrid method proposed determines a large range of combinations for location and size of biomass fuelled gas engines that minimises the unbalance among phases. 2 Probabilistic model of BPP and probabilistic load model It is estimated that olive pruning, very profuse in Spain, presents a higher heating value (HHV) of about 3.90 MWh/ton [20-22]. This approximate value for HHV is due to several variables, such as harvest area, moisture and nutrients in the soil and so on. It is estimated that the calorific value varies from 3.69 to 4.11 MWh/ton. That uncertainty is expressed by a normal random variable, as presented in [23]. Therefore the next equations can be derived (1) (2)where the values µG and σG correspond to the mean and standard deviation of a normal distribution which represents the electrical power generated. µHHV and σHHV are the mean and standard deviation of HHV. k is a coefficient which can be computed as seen in [24]. System loads are also represented as normal random variables. Probabilistic load model is presented in [25]. All loads are single phase, also the biomass generators are single-phase machines. 3 Probabilistic radial three-phase power flow (PR3PPF) 3.1 Radial three-phase power flow Three-phase probabilistic power flow suggested for distribution systems combines three-phase power flow presented in [26] and the Monte Carlo simulation [27]. This practice chooses input values from the distribution functions of random variables, and using those values resolves a radial three-phase power flow. Later, a determined number of samples, the probabilistic solution for the problem is rebuilt from deterministic data derived in each sample. The samples estimated as acceptable is 10 000. This number of samples was utilised in other articles to resolve probabilistic power flow [28, 29]. 4 Shuffled frog leaping algorithm 4.1 Classical approach SFLA was established by Eusuff et al. [19]. SFLA presents a memetic metaheuristic that is intended to pursue a global optimal solution by accomplishment of a heuristic search. It is founded on evolution of memes supported by interactive individuals and a global interchange of data among the population. SFLA advances by translating 'frogs' in a memetic evolution. Therefore frogs are perceived as hosts for memes and labelled as a memetic vector. Each meme contains a number of memotypes. The memotypes characterise an idea in a way analogous to a gene on behalf of an attribute within a chromosome of a genetic algorithm (GA). SFLA does not modify the physical features of the individuals, on the contrary it gradually amends the ideas kept by each frog in a simulated population. The frogs interconnect with each other, and make better the memes by tainting (communicating information) each other. Enhancement of memes outcomes in altering an individual frog's position by adapting the leaping step size. Considering this model of virtual frogs, SFLA depicts on particle swarm optimisation [30] as a local search instrument and the view of fight and mixing information from parallel local explores to a global solution. Hence, each position of the frog i or potential solution, xi = [xi,1, xi,2,. .., xi, Z], is collected by a set of variables Z. The algorithm works as indicated below: (1) Generate an original population of P frogs originated arbitrarily. The frogs must be classified in descendent order regarding to their fitness. (2) Distribute the frogs into mp memeplexes each keeping nf frogs in every memeplex such that P = mp × nf. The separation is made with the first frog moving to the first memeplex, second one going to the second memeplex, the ith frog moves to the ith memeplex and the i + 1th frog back to the first memeplex. (3) Therefore in each memeplex k, the frogs showing the best fitness and worst fitness are recognised as xbest,k and xworst,k, correspondingly. Moreover, the frog that achieves the overall best fitness xgbest is known. Hence, the location of the worst frog in the memeplex k is set at iteration t as indicated below (3) (4) Being t the present iteration number in local search of SFLA for each memeplex and the change vector of the k memeplex in iteration t, being Dmin ≤ dk, j ≤ Dmax, where Dmax and Dmin are the maximum and minimum allowed changes in a frog's position, respectively. If this practice creates a better result, it substitutes the worst frog. Differently, (3) and (4) are repetitive, but now regarding the global best frog (i.e. xgbest substitutes xbest). If there is no enhancement, subsequently a new solution is randomly originated to substitute that frog. (1) Keep step 3 for a precise iteration number. (2) Reshuffle the frogs and classify again. (3) Go back to step 2, if the outcome criterion is not fulfilled, then stop. The local exploration and the shuffling processes remain until the specified convergence criteria are fulfilled, in other words, a determined iteration number. Hence, g is the number of generations for each memeplex before shuffling and TC is the number of iterations used in SFLA as termination criterion, the key parameters of SFLA are P, mp, nf, g and TC. 4.2 BSFLA proposed To optimise in discrete search spaces, the locations for the particles are categorised by discrete numbers that can be binary. Therefore in the spaces the location of a particle is characterised by S length bit strings and the motion of the particle comprises of tossing some of the bits. This article presents a binary particle swarm optimisation (BPSO) [24, 31] that is implanted in a shuffled frog-leaping algorithm. The suggested BSFLA changes the step 3 of the classical SFLA. The position vector is restructured as follows (5)where is a random Z-length binary string, where their elements are '0' or '1' with the same probability, is the frog of the memeplex k presenting the best fitness at the (t − 1)th iteration and is the best location originated for each frog within the swarm at the (t − 1)th iteration. are Z-length binary strings. A bit is computed (6)Being a random variable where its value varies between 0 and 1 and Y1 and Y2 constants such that (0 < Y1 < Y2 < 1). If this procedure is a better solution, it substitutes the worst frog. If there is no enhancement, subsequently a new solution is randomly originated to substitute that frog. Figs. 1 and 2 illustrate the diagram for the BSFLA and the diagram for the local search into each memeplex, correspondingly. As shown in Fig. 1, the termination condition of BSFLA algorithm proposed is reached when the counter of iterations, I, is equal to the number of iterations set, that is, I = TC. Fig. 1Open in figure viewerPowerPoint Diagram of the proposed BSFLA Fig. 2Open in figure viewerPowerPoint Diagram of the local search into each memeplex 5 Objective function (OF) The correct performance of the network devices and the supply quality need that voltages remain within certain limits. The values expected for the node voltages, , and the output powers generated, , are enclosed by the lower, , and upper, thresholds [32] (7) (8)The heat capacity, Strmax, each transformer or line, tr, also indicates a limit to the maximum apparent power transported, Str(9)Total power demand, , and system losses, PLOSSES, must be covered by the total generation, hence (10)The probability, p, that the unbalance factor, , is below a certain value, , represents another restriction (11)being the minimum value for that probability. Considering that the unbalance factor of voltage at all nodes, i, is determined as [26] (12)where is the average value of the voltages of the three phases at node i. Finally, another restriction states to the probability, pi, that the values for voltages, , are within the stated limits and these values are not less than a predetermined one for each node in the system, (13)DG is connected so that the previous constrains are taken into account, (7)–(11) and (13), and OF is minimised. In this case, OF considers the real power losses in the system (14)being the expected value of the power losses. 6 Hybrid technique PR3PPF-BSFLA The hybrid technique defines the nodes where BPPs are interconnected and the average output power. BSFLA produces combinations of possible sites in the distribution system and the values for mean power. A particle is formed for N-length binary string which is distributed in some sub-strings. The binary sub-strings characterise as the connection nodes as the mean output power from BPPs. A PR3PPF is developed for each particle, which originates a value for the OF designated. The technique delivers the best places and the powers from a determined number of BPPs. Agreement with limits related to technical constraints is a fundamental objective for these systems, and this needs a specific attention. The best solution can be achieved in terms of other aims, but if this solution disrupts the technical constraints for the system, it might not be achievable. Fig. 3 depicts the flowchart of this method. Fig. 3Open in figure viewerPowerPoint Diagram of the technique PR3PPF-BSFLA 7 Results of the simulation 7.1 Case study With the aim of studying the proposed technique, the IEEE-13 node test feeder system is adapted [33], as depicted in Fig. 4. Fig. 4Open in figure viewerPowerPoint System used in case study Data for this the system can be seen in [33] and considerations in [13]. System loads are modelled as normal random variables, as seen in Table 1. Table 1. System loads Phase a Phase b Phase c Standard deviation Node kW kVAr kW kVAr kW kVAr 646 230 132 0.07 645 170 125 0.06 671 385 220 385 220 385 220 0.10 611 170 80 0.04 692 170 151 0.07 675 485 190 68 60 290 212 0.06 652 128 86 0.04 Previously in [34], the number of simulations required for the Monte Carlo method was calculated. Therefore 10 000 simulations have been selected for the Monte Carlo method. Then, the electrical distribution system is simulated without DG, in order to obtain the distribution functions for the voltage and voltage unbalance at all nodes. The input random variables are not correlated. A set of simulations are carried out to determine the optimum connection points and output powers for sets of nine BFGEs. Biomass generators are single-phase machines. Then, they can be connected in each of the phases of each node, except for the root node. Hence, the number of possible sites is 33. Assumed the 33 probable sites and the 4 potential levels of powers estimated for every BPP (400, 300, 200 and 100 kW), PGi, these characterise a search space of 5.6 × 1013combinations. Each simulation is a just a lengthy process, however the duration is rational, considering the nature of the procedure. As BSFLA is a relatively new algorithm, there is no theoretical basis for adjusting the parameters. This work has resorted to experiments. Extensive experiments need to be conducted with different adjusts of parameters to balance efficiency, exploration and exploitation. In this paper, the best values for the aforementioned parameters are obtained by running BSFLA algorithm 100 times. Thus, the selected parameters are P = 60, mp = 10, nf = 6, g = 5 and TC = 50. Then, using the proposed method, the optimal power and site of the BPPs are determined where the system losses are minimal and the limitations imposed in Section 5 are fulfilled. The constraints employed are , and . 7.2 Results This study has been executed in the MATLAB R2014 computing environment with Core i5, 2.80 GHz computer with 4.00 GB RAM. Optimum size and average real power for the generators, by proposed hybrid method, are shown in Table 2. Table 2. Optimal average power and location of connected BPPs Node Phase a, kW Phase b, kW Phase c, kW 633 200 646 300 652 200 671 400 675 400 300 684 400 692 400 300 The generator power is modelled by a normal probability density function (PDF), whose mean value and standard deviation are calculated according to Section 2. Fig. 5 shows the PDF of the active power for a generator of 300 kW average power. Fig. 5Open in figure viewerPowerPoint Generator PDF The value for the OF, that is, expected value of the active power losses, is 888.8 kW for the system without DG. When DG is connected, the value for real power losses is 116.6 kW. In Table 3, the mean of the voltages for each phase at some nodes of the system with and without DG can be seen. Table 3. System node voltages Node/phase Without DG With DG Voltage, p.u. Deviation Angle, deg Voltage, p.u. Deviation Angle, deg V650a 1.0199 6.36 × 10−7 7.07 × 10−5 1.0200 6.88 × 10−7 9.62 × 10−5 V650b 1.0199 1.00 × 10−6 −120.001 1.0199 1.30 × 10−6 −120.001 V650c 1.0199 2.21 × 10−6 120.001 1.0199 2.88 × 10−6 120.001 V646a 0.9932 0.0028 −2.1772 1.0119 0.0025 0.1485 V646b 0.9879 0.0026 −121.66 1.0067 0.0013 −119.90 V646c 0.9802 0.0031 117.72 1.0015 0.0016 120.05 V633a 0.9932 0.0028 −2.1772 1.0128 0.0024 0.0847 V633b 1.0073 0.0022 −121.40 1.0061 0.0013 −119.86 V633c 0.9754 0.0031 117.85 0.9994 0.0016 120.19 V684a 0.9698 0.0057 −5.4539 0.9936 0.0049 0.2099 V684b 1.0219 0.0041 −121.57 1.0116 0.0039 −119.89 V684c 0.9178 0.0065 115.70 1.0026 0.0023 120.16 V675a 0.9650 0.0061 −5.8028 0.9981 0.0025 −179.58 V675b 1.0255 0.0040 −121.72 1.0123 0.0039 −120.08 V675c 0.9162 0.0065 115.802 0.9442 0.3449 30.2001 Table 3 shows that the voltages at node 650 are balanced. Nevertheless, the voltages are unbalanced at the rest of nodes of the system. Unacceptable low voltages can be detected when there is no DG in the system, while these voltages enhance after introducing the BPPs. Table 4 specifies the average value in per cent and standard deviation for the voltage unbalances in all nodes, before and after DG is connected. Table 4. Voltage unbalances at all nodes Node Without DG With DG Mean value, % Deviation Mean value, % Deviation 650 0.0039 0.0001 0.0041 0.0002 632 3.2447 0.5525 1.1952 0.4535 646 1.4305 0.5606 1.0401 0.4906 645 1.6824 0.5477 1.3213 0.4588 633 3.2450 0.5525 1.3385 0.5003 671 10.5264 1.090 1.3195 0.8541 611 11.0448 1.100 2.8125 0.9338 684 10.7900 1.095 1.8305 0.9302 692 10.8190 1.098 1.4360 0.4974 675 11.3386 1.116 1.4072 0.5012 652 10.8119 1.097 2.4851 0.9909 680 10.5264 1.090 2.9475 0.9475 Before connecting the BPPs, the maximum mean of voltage unbalance at each node of the system is 11.3386%, while 1.116 is the standard deviation. At nodes 652, 632, 680, 692, 675, 611, 671, 633 and 684, when there is no DG, the voltage unbalances are very large for the right function of the system. Table 4 shows how those voltage unbalances are improved at all nodes when DG is inserted. Fig. 6 displays the cumulative distribution function (CDF) for the voltage unbalance at node 646 without and with DG. The probability that the value of unbalance does not exceed a specified threshold can be determined from these CDFs. Fig. 6Open in figure viewerPowerPoint CDF of the voltage unbalance at node 646 The probability of voltage unbalance drops when DG is connected. Fig. 6 shows an example. The probability of voltage unbalance to be <1.8% without DG is 75.01%, whereas this probability with DG is 93.33%. Fig. 7 depicts the voltage unbalance profiles, obtained from their mean values, after and before inserting the DG. Fig. 7Open in figure viewerPowerPoint Profiles of the voltage unbalances Fig. 7 shows how the voltage unbalances at the nodes have reduced significantly when the DG is connected. Table 5 indicates the probability that the unbalance of each node is <2.5%, for the system with DG. Table 5. Probability of unbalanced voltages to be <2.5% Node Probability, % Node Probability, % 650 99.99 611 37.62 632 99.75 684 76.64 646 99.85 692 98.39 645 99.36 675 98.41 633 98.94 652 50.87 671 89.92 680 32.63 The outcomes were matched among the BSFLA presented, standard BPSO [35] and genetic algorithms (GAs) [36]. To achieve an impartial comparison among the selected metaheuristics, the set of evaluations of the fitness function should be comparable in all methods. Table 6 shows the results from these methods after 30 runs. Table 6. Results for BPSO, GAs and BSFLA proposed Simulation Method OF mean value, kW OF optimum value, kW Standard deviation, kW CPU time, s 9 BPPs BSFLA 119.21 106.83 6.25 6870 BPSO 144.59 122.51 16.86 6973 GAs 148.41 121.56 14.79 6887 Lastly, Fig. 8 indicates and matches the convergence curves for the OF regarding the iterations, for the employed methods. Fig. 8Open in figure viewerPowerPoint Convergence curves of BPSO, GAs and BSFLA after 30 runs The BSFLA method proposed is more strong and efficient than BPSO and GAs, as shown in Fig. 8. Moreover, BSFLA algorithm offers better outcomes than the other techniques, the trade-off between diversification and intensification is the greatest in BSFLA. BPSO and GAs methods achieve results of lower quality than that one acquired by the BFSLA suggested. This lower quality is originated since the method will not be able to explore complex search space and the intensification is quite reduced. GAs and BPSO provide good results. However, GAs and BPSO need more evaluations to achieve similar results than those from BSFLA. This means raising the particle number and/or iterations, consequently the computational effort will be greater. 8 Conclusions The study under stationary state for an unbalanced system with BPPs has been performed by a probabilistic three-phase power flow. The probabilistic study has allowed to consider the uncertainties related to the loads and HHV of biomass. The Monte Carlo simulation technique has been considered to resolve probabilistic three-phase power flow. The IEEE-13 node test system containing BPPs at some nodes has been used to develop numerical applications. The results achieved show the reduction of the power losses and the unbalance factor. A novel method using shuffled frog leaping technique and probabilistic three-phase power flow has been presented. This new hybrid method has obtained the best combination of locations and sizes to interconnect a BPPs among a great set of combinations for a specified distribution system. The outcomes have confirmed the worthy performance of the technique BSFLA suggested, regarding the results from GAs and BPSO. Satisfactory results have been achieved with a reduced number of iterations. Consequently, convergence is rapidly achieved and computational effort is short enough than that demanded by GAs, BPSO and noticeably the exhaustive search algorithms. 9 Acknowledgment This work was funded by the 'Junta of Andalusia', Spain under the grant AGR-5720-2009. 10 References 1Reche-Lopez, P., Ruiz-Reyes, N., Garcia Galan, S., Jurado, F.: 'Comparison of metaheuristic techniques to determine optimal placement of biomass power plants', Energy Convers. 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