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PENETRATION LEVEL ASSESSMENT OF DISTRIBUTED GENERATION BY MEANS OF GENETIC ALGORITHMS G. CELLI F. PILO Department of Electrical and Electronic Engineering University of Cagliari Italy ABSTRACT The large amount of Distributed Generation (DG), that will be installed in the near future, drastically changes the behaviour of the typical passive MV distribution network. If it is not correctly applied, it can cause degradation of power quality, reliability and control of the power system, vanishing the advantages it can introduce. This context determines the need of new tools that help the planner to correctly evaluate the DG impact on the distribution network and to find the best size and location of the DG for feeder voltage support and loss reduction. For these reasons, the paper proposes a software procedure, based on a Genetic Algorithm, able to establish the optimal distributed generation allocation on an existing MV distribution network, considering all technical constraints like feeder capacity limits, feeder voltage profile and three-phase short circuit current. The objective function implemented includes among its terms the costs of buying energy from the transmission system and from the DG units. This allows assessing the more convenient penetration level of DG in a distribution network. Application examples are presented to illustrate the algorithm effectiveness. KEYWORDS MV Distribution Networks, Distributed Generation, Genetic Algorithms, Distributed Generation Planning. INTRODUCTION The need for more flexible electric systems, changing regulatory and economic scenarios, energy savings and environmental impact are providing impetus to the development of Distributed Generation (DG), that is predicted to play an increasing role in the electric power system of the near future. Studies have calculated that DG may account for up to 20% of all new generation going online by the year 2010 [1]. DG offers an alternative that utility planners should explore in their search for the best solution to electric supply problems. In fact, if DG units are properly placed in a MV distribution network, they can reduce power losses cost and defer utility investment for enforcing its system. But, if it is not correctly applied, it can cause degradation of power quality, reliability and control of the power system, vanishing the advantages it can introduce [2-4]. For these reasons, it is essential to provide useful tools for the MV distribution networks planning task, able to take into consideration the presence of DG units. Undeniably, one of the goal of the planner is to find the optimal number and position of DG generators to install in a given network. Independent power producers, seeking interconnection under open access rules, may dictate the location, and the utility planner may not have much choice. However, a planning methodology able to solve the siting DG problem may be used to evaluate any additional credits the utility might offer if the DG is in an appropriate location to have real benefits for the network [5]. Besides, with the liberalization of electricity market, many public administration in different countries have to arrange their regional energy development plans and, consequently, decide how much distributed generation to authorize on their grid and where to locate it. Therefore, the paper proposes a new software procedure, based on a Genetic Algorithm, able to establish the optimal distributed generation allocation on an existing MV distribution network, considering all technical constraints like feeder capacity limits, feeder voltage profile and three-phase short circuit current. In previous works, this goal has been reached minimizing the typical objective function used in planning studies, that is the total cost of the network: building, maintenance, losses and costs of disruptions [6, 7]. To allow assessing the more convenient penetration level of DG in a distribution network, in this paper the costs of buying energy from the transmission system and from the DG units have been added to the objective function implemented. In fact, by acting in this way, the advantages introduced by the distributed generators are balanced by the higher cost of the energy produced, and the optimal equilibrium can be found. OPTIMAL ALLOCATION PROCEDURE GAs are a family of computational models that rely on the concepts of evolutionary processes [8]. It is a well known fact that according to the laws of natural selection, in the course of several generations, only those individuals better adapted to the environment will manage to survive and to pass on their genes to succeeding generations. Correspondingly, GAs operate on a set (population) of possible solutions (individuals) of a generic problem, applying selection and reproduction criteria whereby new solutions (offspring) are generated containing the information enclosed in the solutions from which they originated (parents). Clearly, the better the solution, the more possibilities there are of reproducing and passing on genes to the offspring. The first step to be taken in implementing these algorithms is to encode a potential solution in a simple data structure of the chromosomal type (generally a vector) in which each element is represented by means of a specific alphabet (usually binary). Once the initial population has been randomly generated, every solution is evaluated by means of the objective function. The strategy followed by GAs is very simple. To ensure an amelioration in the population, in each generation a selection operator sees that the solutions with higher fitness have greater possibilities of reproducing. At this point some individuals are coupled and cross-bred, with a generally high probability, by means of a crossover operator, which recombines the salient information brought by the parent structures in a significantly nondestructive way. The crossover operator produces offspring, that will then replace some of the old individuals of the population. Lastly, the strings can undergo mutation, which involves selecting, with little probability, a string element and changing the symbol contained therein with another symbol of the alphabet being used. Once the procedures performed by the three operators have been completed, the offspring produced are evaluated, by using a fitness function, and compared with their parents. If the GA is generational, then the offspring will replace all their parents, creating a new population. On the other hand, if the GA is steady state then the offspring will replace their parents only if they are better. Several parameters normally influence the search for the optimum solution by GAs: population size, the probability of mutation, the maximum number of generations to be explored, etc.. These parameters should be accurately calibrated, adapting them to the size of the problem in question. In this paper, a GA optimization technique has been developed for finding the optimal sizing and location of DG in a given MV distribution network; it is briefly described in the following sections. Coding of the solution The first important aspect of a correct implementation of the GA is the coding of the potential solution. Considering that the network structure is fixed, all the branches between nodes are known, and the evaluation of the objective function depends only on size and location of the DG units. For this reason each solution can be coded by using a vector, whose size is equal to the number of nodes, in which each element contains the information on the presence or not of a DG unit. In order to perform not only the siting but also the sizing of DG, a prefixed number (NDG) of generator sizes have been assumed and classified (e.g. size number 1 corresponds to a 100 kVA DG unit, size number 2 corresponds to a 200 kVA DG unit, etc.). Therefore, each element of the vector solution is represented by means of the following alphabet: 0 no DG located on the node; 1, … , NDG size index of the DG installed in the node. Of course, the vector elements corresponding to the HV/MV primary substations are fixed to 0. The type of code used is suitable for every kind of network structure (radial, meshed, etc.), that influences only the assessment of the usual technical constraints (voltage profile and thermal feeder capacity) considered during the evaluation of the objective function, but does not affect the optimal allocation procedure. In the paper the algorithm has been applied to “open loop” distribution networks, that are commonly used in Italy. GA Implementation The implementation of an optimization problem of GA is realized within the evolutionary process of a fitness function. The fitness function adopted is given as: Objectivei Penaltyi Fitnessi log Objectivemax (1) where the objective function (OF) is the total cost of the network. For each solution, all technical constraints are checked: if one of them is not verified, a penalty term is added to the OF value. The genetic algorithm procedure to solve the optimal DG units allocation problem is described below. In the first phase, an initial population of possible solutions is randomly generated by means of the following procedure: for each solution a value of DG penetration is selected between 0 and 100% of the total amount of power requested by loads; a number of DG units of different sizes is randomly chosen until the DG penetration level assigned is reached; the DG units are randomly located among the nodes of the network; the fitness for each solution is evaluated and scaled by using the fitness function. Regarding the population size, the best results have been found assuming it equal to the dimension of the problem, i.e. the number of nodes in the network. In the second phase, the genetic operators are applied in order to produce the new solutions. In this paper the following implementation details for the operators have been considered: Selection: the “remainder stochastic sampling without replacement” scheme has been adopted, whereby the number of selections of each individual is calculated in the following way: expected individual count values are calculated as a fraction between the OF value of the individual and the average of OF value of the whole population. Then integer parts of the expected numbers are assigned, and fractional parts are treated as probabilities. Crossover: the “uniform crossover” is adopted, by which each allele is swapped with probability 0.5. The probability of crossover between two individuals has been kept high (about 0.95). Mutation: all the vector elements are mutated, according to a small mutation probability (0.01), choosing a different value in the defined alphabet. Scaled the fitness of each offspring using the fitness function, the new population is generated as follow: a portion of the new individuals consists of the best solutions between parents and offspring (Steady State model); the remaining individuals to complete the new population are chosen only among the offspring, independently they are or not better than their parents (Generational model). The procedure terminates when a maximum number of generations has been explored. COSTING OF DG SITING SOLUTIONS The goodness of the solutions provided by an optimization procedure strictly depends on the definition of an objective function that correctly represents the problem to solve. Therefore great attention must be paid on modelling the main aspects that can influence the DG units allocation in an existing distribution network. Traditional Objective Function The main goal of planning studies is finding the optimal network structure that allows supplying loads minimizing the generalized cost. Thus, the objective function to be optimized within the technical constraints generally refers to the total cost of the network which considers [9, 10]: site of the substations and loads geographical, geological and urbanistic features of the area concerned power demands of the loads and their growth versus time duration of the planning period some cost parameters such as inflation and interest rates unit cost of kWh lost due to Joule effect (cost of losses) construction and maintenance costs of feeders of different cross-sections and for different types of lines (overhead, underground). Due to the current Italian standard, that does not admit islanded portion of MV network directly supplied by DG, the most common reliability indices for long interruptions are not modified by DG units and thus no service quality improvements can be achieved by normal customers [11]. For this reason, the costs of disruptions are not considered in the objective function. Of course, each customer with DG units can use them to supply, totally or partially, its loads during grid faults or scheduled interruptions, increasing the availability of energy and reducing the number and duration of interruptions. More generally, service interruptions due to overloads should also be taken into account as well as those due to outages or scheduled interruptions. Thus, among the benefits introduced by DG, the reduction of overload costs, treated like expected unserved energy (EUE), should be considered. It is trivial to observe that by estimating overload costs with the EUE, which is much more higher than retail sales rate, investments decisions are made and timed such that they to emphasize the reliability of the system in areas where the value of service is higher [5]. In this paper, overload costs are disregarded because the power flow implemented considers only an annual growth of the load energy demand. Surely, in order to improve the proposed planning tool, individual hourly characteristics should be included in the OF, but this does not reduce the generality of the described optimization algorithm. Furthermore, it should be noticed this planning tool is suited for the standards of the Italian public distribution company about “open loop” networks that consider as emergency limit the maximum continuous current-carrying (at the time of peak load). The objective function to be minimized is thus represented by the total cost C0G of the generic network, with present value taken at the beginning of the whole planning period of N years. This cost can be expressed by using the sum: C 0G NTot NCp C0 j , (2) j 1 where NTot is the number of network nodes, NCp is the number of substations, NTot-NCp the number of branches in the network and C0j the present cost of the jth branch. The cost of every branch j is the sum of the construction, residual, management costs, and cost of losses in the subperiods, transferred to the cash value at the beginning of the planning period by using economical expressions based on the inflation rate, the interest rate and the load growth rate (all of them constant) [9] . The cost of every branch can be expressed by using: m C 0 j C 0 j ' C 0 pjk , (3) k 1 where C0j is the total cost of the branch j, C0j' the portion of cost independent of power flow, C0pjk the cost term proportional to the power flow through the branch in the kth subperiod (cost of losses) and m is the number of subperiods into which the planning period of N years has been divided. Denoting with C0cj the construction costs, R0j the residual value, C0gj the management costs and ej a binary factor (equal to 1 for a resized branch and 0 for an existing one), the cost C0j', independent of power, can be written by using: (4) C0 j ' e j (C0cj Roj ) C0 gj The cost of resizing the jth branch C0cj takes into account the year of reconstruction to transfer the cash value to the beginning of the planning period, while the residual value Roj considers the fact that the planning period does not coincide with the life duration of the component. The cost of Joule losses in the kth subperiod C0pjk can be calculated transferring, to the cash value at the beginning of the planning period, the annual cost of such losses Cpjk, evaluated by using: C pjk C kW h (3 8760 coeff r j L j ccp j I 2jk ) (5) where: CkWh is the cost of kWh, coeff is the utilization factor of energy losses under full load, different for overhead and underground, 8760 are the number of hours per year, rj is the resistance per km of line [Ω/km], Lj is the branch length [km], Ijk is the phase current in the jth branch [A] at the beginning of the kth subperiod, ccpj is a corrective coefficient of the losses due to the simultaneity of loads. New Objective Function By using the traditional objective function described in the previous paragraph, whichever optimization procedure tends to place a very large number of generators. In fact, equation (2) exalts exclusively the advantages introduced by DG (reduction of losses and deferment of investments for grid upgrade), and consequently the optimization process evolves towards configurations with DG penetration levels near 100% of the total amount of power requested by loads. For this reason, in a previous work the genetic algorithm procedure, to solve the optimal DG units allocation problem, was used to perform studies with prefixed DG penetration levels [6, 7]. In order to overcome this drawback and to allow assessing the more convenient penetration level of DG in a given distribution network, in this paper the costs of buying energy from transmission system, (CkWh)Tr, and from DG units, (CkWh)GD, have been added to the traditional objective function: is easy to calculate the terms (CkWh)Tr and (CkWh)GD, opportunely transferred to the cash value at the beginning of the planning period so that they can be comparable with the other costs of the objective function. An objective function like that expressed by (5) allows better estimating DG impact on MV distribution networks and also determining which DG penetration level is considered more convenient for the distribution company. In fact, the limit will be reached when the further benefits introduced by adding new DG units no more compensate their relative costs. Distribution Network Structure Distribution networks always have a radial structure and are often subdivided into two different levels: trunk feeders and lateral branches. The degree of reliability obtainable with this network arrangement is limited by the fact that a fault in one part of the network results in outage in a large number of load points. To improve service reliability, emergency ties provide alternative routes for power supply in case of outages or scheduled interruptions. Emergency ties end with an open switch so that radial structure is maintained during normal conditions; furthermore trunks are subdivided in some segments by means of normally closed switches, generally positioned in MV/LV nodes. During emergencies, segments can be reswitched to isolate damaged sections and route power around faulted equipment to customers who would otherwise have to remain out of service until repairs were made [12]. An important class of such networks are the “open loop networks” which are usually employed in urban power distribution systems. If there are no laterals (“pure open loop networks”) then service restoration is ensured through the emergency tie that connects the ends of the feeder. An intermediate alternative is to install laterals (“spurious open loop networks”) in which top priority customers are supplied through the main feeder and can be completely reenergized in the event of a fault. The main characteristic of both “open loop networks” is that only two branches can converge in a trunk node (topological constraint) [13]. Automatic switching devices along trunk feeders and NTot NCp C0 G C0 j CkWh Tr CkWh GD . (5) Emergency connection j 1 In presence of a liberalized electricity market, it needs to consider different retail sales rate of the energy produced by a DG unit, that depends on the technology adopted (mini gas turbine, CHP, wind turbine, etc.), and of the energy coming from the transmission system. Assuming a constant power demand growth rate and a fixed amount of energy generated per year by DG, it is possible to evaluate the energy that an hypothetical distribution company has to buy from both the transmission system and the DG installed in its network in the whole planning study period. By resorting to an average value of the energy rate in the planning period, it A) Pure “open loop network” with no lateral MV nodes Emergency connection B) Spurious “open loop network” with lateral MV nodes Fig. 1 – “Open loop” networks emergency ties may reduce both the duration of service interruption and the number of customers affected thereby (Fig. 1) [12, 13]. Technical Constraints Each individual produced by GA operators has to comply with all technical constraints usually adopted by planning engineers, i.e. the voltage profile along the network trunks and the three-phase short circuit currents in the network nodes [1, 14]. Indeed, the presence of generation nodes in the distribution system can cause a voltage drop or an overvoltage in some points of the network. Due to the absence of any dispatch strategies and ancillary services in the MV distribution networks, the connection of a generator to a network can result in an increase in the voltage that depends only on the power supplied by the generator. For this reason, in the proposed methodology the voltage profile is checked and those DG allocations unable to maintain the voltage within prefixed ranges both in normal and emergency situations are penalized. Calculations are performed by determining the impedance matrix Z of each feeder examined and by calculating the voltage in each node of the network. The calculation of Z can be noticeable simplified considering the particular network architecture (“open loop” network). The presence of DG can change the magnitude, duration, and direction of the fault current. The fault current is modified since the connection of rotating generators modifies the characteristics (impedance) of distribution networks. In this context, one needs to verify that the alteration in magnitude, duration and direction of the fault current due to dispersed generation groups does not affect the selectivity of protection devices. In fact, the selectivity must be checked for each connection of a new generator to the distribution network. In the paper, fault currents are calculated for each DG configuration examined by using the diagonal elements of the short circuit matrix and the voltages in each node. Again a penalty is inflicted to all those situations which do not comply with this technical constraint. RESULTS AND DISCUSSION In order to show the capability of the proposed methodologies, an area of the real MV Italian network has been considered. As shown in Fig. 2, it is constituted by 148 nodes divided into 3 HV/MV substations and 145 MV/LV trunk nodes. The whole chosen area covers a surface of about 600 km2. The period taken into consideration for the planning study is 20 years long, with all nodes existing at the beginning of the period. The period of study is longer than those normally considered (5-10) in distribution planning, but this choice allows showing significant results even in a small case. For each MV/LV node, a constant power demand growth rate of 3% per year has been assumed; the size of the installed transformer ranges from 100 kVA to 630 kVA. The annual medium active power delivered to MV nodes is, at the beginning of the planning period, 6.6 GW. The majority of the branches is of the HV/MV primary substation MV/LV node MV/LV node with DG unit Fig. 2 – 148 nodes test network and DG siting results. overhead type, but some buried cables exist. The thermal capacity constraint is verified for all the branches at the beginning of the planning period, but some of them will have to be resized according to the growing energy demand. In order to test the proposed methodology, DG units have been considered, ranging between 100-300 kVA. It is straightforward noticing that there are no limits on the size of DG units that can be treat by the optimization procedure proposed. The cost of Joule losses has been taken as 0.05 US$/kWh, the cost for section unity has been assumed 0.3 US$/mm2 for buried cables and 0.5 US$/mm2 for overhead lines (no adjunctive costs for digging or poles, considering that no new paths are built). The cost of buying energy from T&D is 4¢ while the cost of energy from DG has been varied within the range 5¢÷6¢. In Table I, the costs of investments for grid upgrade and of power losses are reported for the network in Fig. 2, without DG and with the optimal arrangement of DG units obtained with the proposed GA. Energy costs are evaluated considering 5¢ for the energy bought from DG. The DG penetration level is 22.1% of the total amount of power requested by loads. It is worth noticing that DG units allow reducing all costs considerably. In particular, the greater saving is represented by the reduction of the investments for upgrading the existing branches. This is really an important result, considering that T&D costs represent almost 30-50% of the kWh cost and the deferment of investments will produce benefits to both utilities and final customers regardless the type of distribution energy market adopted. In Fig. 3 is reported the voltage profile along the highlighted feeder for the same case, clearly showing DG benefits in voltage regulation. Without DG, despite high building investments, the feeder voltage is dangerously close to the lower bound limit (8%) and, thus, not foreseen growths in load demand can lead to poor quality of service. By using DG, voltage profile along the feeder can be drastically improved and the higher engineering margin leads to a more robust solution. Table I. Comparison between costs for the MV distribution network in Fig. 2 Without DG With DG 7953.9 kUS$ Cost of investments Cost of losses Cost of energy from T&D Cost of energy from DG Total cost 3646.3 kUS$ 626.9 kUS$ 542.0 kUS$ 45688.0 kUS$ 37670.2 kUS$ -------------- 10022.3 kUS$ 54268.8 kUS$ 51880.7 kUS$ Different simulations have been performed in the same network varying the cost of energy from DG. Obviously, when the retail sales rate increases lower levels of DG penetration have been found. Indeed, variations in the energy cost have a great impact in planning and this impact increases with the increment of the planning horizon. Anyway, nevertheless the cost of energy from DG, the optimization algorithm has detected in which feeders it is always more convenient to install generators. This is a very important information for the utility, which can use it to force independent power producers, by means of discounts or additional credits, to interconnect their generators in the more convenient locations. assessed accurately so that these DG units can be applied in a manner that avoids causing degradation of power quality, reliability, and control of the utility system. On the other hand, DG has much potential to improve distribution system performance and it should be encouraged. For this reason DG should be incorporated into distribution planning as an option along with traditional feeder and substation options. On the basis of these considerations, the paper deals with the important task of finding the optimal siting and sizing of DG units for a given network so that the cost of power losses during a prefixed period of study can be minimized and investments for grid upgrades can be deferred. Retail sales rates for energy have been also considered so that the optimal DG penetration level in a given distribution network can be automatically assessed. Since much of the value inherent in DG is its ability to hedge against uncertain load growth, a typical planning study would analyze the cost curves for a number of growth scenarios defined by the utility. Thus, further studies will deal with the application of probabilistic techniques in order to improve power flow calculations and better treat uncertainties introduced by loads and DG. ACKNOWLEDGMENT The authors wish to acknowledge CESI for funding this activity with research contracts focused on DG. REFERENCES CONCLUSIONS DG is predicted to play an increasing role in the electric power system of the near future. In fact, studies have predicted that distributed generation may account for up to 20% of all new generation going online by the year 2010. With so much new distributed generation being installed, it is critical that the power system impacts be Voltage profile with DG Voltage profile [kV] Voltage profile without DG Lower bound of voltage drop (8%) 11.6 11.4 11.2 11.0 10.8 10.6 10.4 emergency tie Fig. 3 – Effect on the feeder voltage profile of the presence of DG. [1] P. P. Barker, R. W. de Mello, Determining the Impact of Distributed Generation on Power Systems: Part 1- Radial Distribution Systems, Proc. of IEEE PES Summer Meeting, Seattle, 2000, 1645-1656. [2] CIGRE WG 37-23, Impact of increasing contribution of dispersed generation on the power system - Final Report, Electra, 1998. 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Pilo, Network planning and service reliability optimization in MV distribution systems, Proc. of ESMO'95 Conference, Columbus, USA, 1995, 36-46. [11] S. Barsali, G. Celli, et. al., Operating and Planning Issues of Distribution Grids Containing Diffuse Generation, Proc. of CIRED2001 Conference, Amsterdam, The Netherlands, 2001. [12] G. Celli, F. Pilo, Optimal Sectionalizing Switches Allocation in Distribution Networks, IEEE Trans. Power Delivery, 14(3), 1999, 11671172. [13] B. Cannas, G. Celli, F. Pilo, Optimal MV distribution networks planning with heuristic techniques, Proc. of AFRICON’99 Conference, Cape Town, South Africa, 1999, 995-1000. [14] N. Hadisaid, J. F. Canard and F. Dumas, Dispersed generation impact on distribution networks, IEEE Computer Applications in Power, 12(2), 1999, 22-28.