cired an integrated tool for optimal active network planning

CIRED

17th International Conference on Electricity Distribution

Barcelona, 12-15 May 2003

AN INTEGRATED TOOL FOR OPTIMAL ACTIVE NETWORK PLANNING Fabrizio PILO*, Vittorio ALLEGRANZA+, Gianni CELLI*, Rocco CICORIA+, Susanna MOCCI* * University of Cagliari – Italy; +CESI – Italy [email protected], [email protected], [email protected], [email protected], [email protected]

SUMMARY Distributed Generation (DG) offers an alternative that utility planners should consider. In order to provide useful tools for the medium term planning of distribution networks, efficient software packages were developed in latter years, based on heuristic optimisation techniques, able to take into consideration the presence of DG units. In the paper, a novel software package for the optimal network planning based on probabilistic techniques is presented. The package (SPREAD) allows planning the development of distribution networks, making use of heuristic techniques developed by the authors, and optimal siting and sizing of DG in a given network, by resorting to genetic algorithms. Furthermore, SPREAD resorts to the Decision Theory techniques so that planners can make their decisions by examining, in an objective manner, different solutions suitable for different scenarios. INTRODUCTION The restructuring of the electricity supply market, with the accompanying set of drivers for distribution companies, along with increasing levels of uncertainty faced by utility companies, have raised requirements for new planning methodologies. In particular, new planning tools should have the following characteristics [1-3]: deal with uncertainty and explicitly with risks; deal with multiple criteria; consider multiple and diverse solutions; be decision focused and use mathematical decision techniques; making use of appropriate graphical tools; use appropriate time schedules and planning horizons; enable reuse of model, data and solutions. Undeniably, the evolution of electric power system has determined many new challenges in distribution network planning so that there is the need of further development of techniques based on heuristics, cases and tacit knowledge. Furthermore, it is very important that new planning methodologies can incorporate the multiple drivers in present-day electricity distribution planning (e. g. reliability, DG, load, and constraints), consider simultaneously other energy or utility service and, finally, take into account the customer needs. In particular, the predicted massive penetration of DG in the distribution network requires the development of new planning techniques, which overcome the traditional

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Session 5 Paper No 64

deterministic approach to planning, and make use of new planning paradigms able to take into consideration uncertainties related to power production, to the cost of fuel, to the price of energy and to load energy demand. Moreover, new planning tools have to consider aspects that are very important for the strategic planning of distribution networks, like environmental constraints, the willingness to reduce emissions and pollution, the quality of power, which requires not only a prefixed level of continuity, but also that power quality disturbances, like flicker, harmonics, voltage dips, unbalance, etc. remain within prefixed tolerable level. The impact of DG on a distribution network is very time and location specific [4,5]. In fact, if DG units are correctly placed in a MV distribution network, they can reduce power losses cost and defer utility investment for enforcing its own electrical system but, if they are misplaced, network costs can dramatically increase as well as power quality and service reliability can sensibly make worse. For these reasons, the efficient algorithms and software packages developed in latter years are not suited for high levels of DG penetration, that imply a change from passive distribution network to active ones. These packages use deterministic procedures to find the optimal network configuration, starting from specific data (annual average power requested by load and generated by DG, power demand growth rate, etc.) [6-11]. But, disregarding uncertainties and probabilistic behaviour of loads and generators can easily lead to uneconomical or unreliable solutions. To overcome these drawbacks more recently new probabilistic planning tools have been proposed, able to find the optimal network arrangement and the optimal siting and sizing of DG [12-13]. Furthermore, Decision Theory (DT) has been successfully used for distribution network planning in different scenarios [14-17]. In the paper, a novel software package, SPREAD (System for optimal PRobabilistic Expansion of Active Distribution networks), for optimal network planning based on probabilistic techniques is presented. SPREAD is constituted by three modules that allow planning the optimal expansion of distribution networks, the optimal siting and sizing of DG in a given network and to deal with uncertainties related, for instance, to DG power production or to load demand. Suitable objective functions have been developed to take into consideration building, maintenance and upgrading costs and the cost of losses and disruptions as well as energy rates. The main novelty of SPREAD is that it allows the decision maker to perform integrated planning studies, e.g. the planner can find the optimal DG arrangement for an existing network and use this result to plan the medium term optimal network development. By iterating this procedure, it is possible to find the optimal network

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evolution in a given study period with the optimal amount of DG placed in the most convenient points. SPREAD makes use of graphical and mathematical decision techniques, considers explicitly uncertainties and risks and allows the consideration of multiple and diverse solutions. These features are extremely important for utilities, and their unfulfillment has often been an insurmountable obstacle to the diffusion of sophisticated planning tools developed by researches worldwide. For these reasons, SPREAD can be a useful aid in making decisions in present uncertain and mutable scenarios. MODULES DESCRIPTION The SPREAD package allows planning the evolution of distribution networks, making use of heuristic techniques developed by the authors, and the optimal siting and sizing of DG in a given network, by resorting to Genetic Algorithms (GA). In particular, the package can be divided into three main modules: PREDA, PROLOCOGD, TEODORA. The theory behind each module has been described in [611,13,16-17] with great detail. Thus, considering that the paper focuses on the SPREAD integrated environment and on the communication among different modules, in the following only the main characteristics of each module are briefly recalled. Network Planning Module The PREDA module performs the optimal planning of network configuration (in presence of DG), taking into account expansion over time and the usual technical constraints. The function to be minimized, the generalized cost of the network, has to take into consideration building, maintenance, upgrading costs and the cost of losses and disruptions. In fact these terms have a great impact on the choice of network configuration, both in normal and in emergency conditions [10]. The optimisation algorithm allows finding “spurious open loop” networks with trunks and laterals in scenarios with several hundreds of trunk nodes in a reasonable computing time. The main advantage of the proposed methodology is the capability of simultaneously finding both the normal state network, the position of emergency connections and the optimal allocation of Automatic Sectionalising Switching Devices (ASSDs). By so doing, the most important service quality indicators can be correctly evaluated during the optimisation phase and they can be used as constraints in order to guide the search through more reliable structures. The used heuristic algorithm can be classified as a “hillclimbing” strategy. In other words, starting from an initial structure, new network configurations are developed by means of some local perturbations. Only cheaper solutions can be accepted during the research and, for this

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reason, the algorithm will be stopped when no more improving solutions can be found. The success of such a procedure is strongly dependent from the rules employed to generate new network configurations to be evaluated during the optimisation. In fact, a combinatorial choice, that could guide the process to find the absolute optimum, is not feasible due to the exponential growth of computing time. Conversely, if too few configurations are examined there is the risk of trapping into local minima. Summing up, the choice of suitable heuristic rules that allow finding good quality solutions, possibly near to the absolute optimum, with reasonable computing time is of the greatest importance [7,10]. In order to consider the random behaviour of DG and loads, a simplified probabilistic load flow has been developed and implemented. This procedure takes into account the probability density function (pdf) of the loads and of the annual power production associated to each generating unit. Generally, in order to guarantee the correctness of the results, it is important to consider the existing correlation between DG units, between generators and loads and also between loads. In the probabilistic approach the following assumptions have been made [12,18]: − correlation between loads, if it exists, is linear; − complex correlations between generators has not been considered, due to the present absence of any dispatchment action at the distribution level; only linear correlation has been taken into account for renewable resources (e.g. wind generators); − correlation between generators and loads is modelled with linear dependence; more precisely, some local linear correlations among generators and loads can be reasonably hypothesised (e.g. the correlation between industrial loads and CHP plants installed nearby), but linear correlation cannot be widely applied, especially if DG penetration is very high and it is mainly based on renewable resources. These hypotheses allow simplifying the resolution of the probabilistic load flow. Once known the currents flowing in each branch and the voltage of each node through their corresponding pdf, it is possible to choose the correct size of each conductor and to verify all the technical constraints, taking into account the uncertainties related to these electrical variables [13]. DG Allocation Module Once identified the starting network, the module PROLOCOGD is aimed to find optimal localization and sizing of DG units. In fact, an incorrect allocation of DG units can nullify the benefits achievable from DG or even it can lead up to hard drawbacks. Once fixed the network structure and once known the loads and the eventual existing DG units, the individuation of the more convenient connecting points of new DG units becomes extremely interesting for the

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planner and it allows to minimize the power losses and/or the management costs. The problem is rather complex, due to the high number of nodes that could compose the MV distribution network and the corresponding dimension of the possible solution set to investigate; in particular, this dimension grows in exponentially manner with the number of the grid nodes. Furthermore, every solution must be generated in the respect of all the environmental and technical constraints, as the voltage profile and as the short circuit current level in the network nodes. In order to maximize the total benefits coming from the presence of DG units in the network, the algorithm in addition to the best location for the connection of DG to the grid (siting problem) finds out also the optimal size of the generators to install (sizing problem). In consequence, it is necessary to lead two different optimisation studies simultaneously, increasing substantially the number of the possible configurations to examine. The PROLOCOGD module uses a GA to solve these problems: the implementation mode of these techniques easily fits to the DG units siting problem and, with suitable expediencies, allows to contextually perform the choice of the optimal size of the generators [6]. This module at first acquires the structure of an existing open loop network (pure or with lateral MV nodes) and, by saving the original network topology, returns for each DG unit the optimal site and relative size. Considering the increasing demand of connection to the grid by private productions, the planning choices of the next years are really interesting, due to the fact that it is predictable from the utility the necessity to maximise the profits, limiting or deferring the investments on the network. PROLOCOGD implements an objective function, which considers not only the cost of investments and power losses, but also the costs related to the energy purchase to satisfy the demand, shared between transmission network and private generators. So it is possible to automatically identify the optimal penetration level of DG in the network (expressed as per cent of the total load). Furthermore, this module considers the connection costs of each generator, as building and maintenance costs if the electric utility is the owner of the DG unit, or as purchasing costs of the produced energy if the DG unit is private property. In both these cases, the program processes also the remaining purchase cost from the transmission network, necessary to complete the demand. As in PREDA, load flow calculations and network sizing are based on a probabilistic approach. The users can modify several parameters so as to obtain the suitable solution for the given network. These parameters include environmental constraints, different purchasing costs from DG and various kinds of sources. Regarding the environmental constraints, it is possible to avoid locating the generators in some nodes, previously fixed by the planner by means of the provided userfriendly graphical interface. The possible correlation between generators and loads connected to the same busbar can also be taken into consideration, because every dependence between the variables affects the probabilistic

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calculation. Of course, this correlation may exist only in the case that the generator typology allows it (e.g. not if renewable sources are going to be optimised) and the owner of the DG unit is also the owner of electric loads. Decision Theory Module The DT module, TEODORA, allows leading planning studies that consider different scenarios, by varying one of those affecting planning parameters (e.g. growth rate of load). By using the TEODORA module it is possible to define in a preliminary manner the various scenarios that must be analysed and to carry out in succession repeated optimisations, based on the same input file and obtained by automatic executing either the PREDA or the PROLOCOGD module. Each optimisation result is stored and at the end of the procedure all the solutions are treated by typical techniques of the DT in order to isolate the best compromise solution in an uncertain planning scenario. In the proposed application, the strategic options (network architecture, intentional islanding, use of ASSDs, etc.) have been chosen a priori, and remain fixed regardless the different scenarios considered. More general applications of DT may also involve the selection of a strategic option set for the development of power system. In general, the procedure can be resume as follows: − Definition of the set of scenarios and related probability (e.g. different DG penetration levels in a pre-determined location and/or various growth rate of loads); − Resolution of the planning problem for each hypothetical scenario in order to obtain a consistent number of planning alternatives; − Application of the DT techniques in order to find the optimal choice by different viewpoints (Expected Cost criterion, Maximum Regret criterion and/or combination of both the approaches). The Expected Cost criterion (EC) associates a probability to each scenario: an expected cost for each alternative is obtained by the weighted average of costs under the different scenarios. The choice is then made on the basis of the minimum expected cost [14-17,19] The Maximum Regret criterion (MR) consists of different steps: finding the cost of the best investment plan for scenario; in every scenario, measuring the “regret” for each alternative as difference between the cost of the given alternative and the best alternative for that scenario; identifying the maximum regret for each alternative, weighted with the probability occurrence of the relative scenario, and selecting the alternative with the minimum value. This alternative implies the lowest extra cost under the most adverse scenario. The two criteria do not necessary lead to the same conclusion: the EC takes into account all cases weighted by probability values, but may overlook the effect of an important event with low probability [14-18]. A crucial aspect of the above decision analysis criteria is

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the assignment of the subjective probabilities to the different scenarios, since both the expected costs and the weighted regrets depend on them. Moreover, when it is not clearly foreseeable “a priori” which of the two above described procedures will give the most reliable results that is to say which is the most valuable for the problem being studied - it can be of great help for the Decision Maker to have the results of both procedures at disposal [17]. Consequently, in order to overcome the probability assignment problem and to make decisions based on the results of both above procedures, it can be very interesting to introduce the "stability areas" concept proposed in [14] to solve the whole problem of the expansion of a distribution electrical system; this approach assumes the scenario probabilities as variables. THE STRUCTURE OF “SPREAD” The package SPREAD is made up of the three described modules: PREDA, PROLOCOGD and TEODORA. All they interact themselves and work under the same graphic interface. The operating scheme of the proposed procedure is shown in figure 1. Input data, e.g. geographical position of nodes and substations, feeder routes, characteristics of existing buried and overhead lines, type of DG used, electrical power absorbed or produced (expected value and variance), etc. can be acquired by special databases or can be directly obtained by GIS. In particular, the PREDA and PROLOCOGD modules are able to communicate together and generating output files, which reciprocally can be employed as input files (see Fig. 1). Different types of cross-study can be carried out: PREDA can find the optimal network evolution during a prefixed study period in given scenario. PREDA output can be used by PROLOCOGD so that the optimal arrangement of DG can be found in the optimal network; PROLOCOGD can find the optimal DG arrangement in a fixed network structure. PROLOCOGD can be also used to verify if the proposed optimal amount of DG could be tolerated by the actual distribution system or any modifications could be necessary. Finally, an iterative procedure can be activated with the aim of finding simultaneously the optimal network evolution as well as the optimal siting and sizing of DG. The iterative procedure starts with the PREDA module, which has to find the optimal network planning in the study period with no new DG added. In this optimal network, PROLOCOGD can be used to solve the problem of the optimal DG siting and sizing. Probably the former optimal network will not be perfectly suited for the amount of DG proposed, and thus it could be necessary to once again run PREDA, in order to carry out a new optimal network arrangement taking into consideration the optimal DG. This new PREDA solution can be used as base for a new run of PROLOCOGD in order to find the optimal arrangement of DG. If any modifications

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DATABASE MVdati Network reti diDataBase distribuzione MT

S.P.RE.A.D.

tool SistemaIntegrated integrato per gli studi di Pianificazione delleREti Attive diplanning Distribuzione for MV active network P.RE.D.A.

PRO.LOC.O.

output

output TEO.D.O.R.A. output

Fig. 1 - Operating scheme of the proposed procedure

appear, a new run of PREDA is required otherwise the iterative procedure ends. Thus, the ability of interaction between PREDA and PROLOCOGD allows the DG allocation optimisation in a distribution network, which is able to evolve and to modify its topology during the whole testing period. Both PREDA and PROLOCOGD produce outputs, which can be used by the third module TEODORA in order to perform studies taking into account uncertainties in the knowledge of some parameters and different scenarios, characterized by subjective probabilities. Finally, SPREAD is provided with a user friendly graphic interface that allows representing solutions, giving information about edges and nodes (i.e. feeder section, year of construction of new elements, energy demand or production, etc.), adding new primary or secondary substations and choosing preferred routes, etc.. SPREAD can load maps of the territory where the network is. The simultaneous visualization of both maps and network layout allows a more accurate planning, highlighting, for instance, unacceptable routes or solutions. RESULTS AND DISCUSSIONS In order to show the capabilities of the proposed methodology a case derived from a real distribution network is presented. As shown in Fig.2, a distribution network constituted by 71 MV/LV nodes and 2 primary substations has been considered. The period taken into consideration for the planning study is 20 years long, with all nodes existing at the beginning of the period. For each MV/LV node, a constant power demand growth rate of 3% per year has been assumed. The majority of the branches are of the overhead type, but some buried cables exist. The annual medium active power delivered to MV nodes is, at the beginning of the planning period, 3.4 MW. The iterative procedure presented starts with the PREDA module: the optimal network planning in the study period with no new DG added is obtained, and the structure of the optimal network is shown in Fig. 2. The total related cost amounts to 3557.5 k€ and it is constituted by the cost of building, cost of power losses and cost of interruptions (Step 1), as shown in Table 1. According to the iterative procedure described in the previous section,

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PROLOCOGD has used to find the optimal arrangement of DG (Step 2) in the starting optimal network. In Fig. 2 the optimal set of DG is depicted showing a DG penetration level equal to 39.7%. In this case, not only the generalized network cost but also the cost of acquiring energy from DG units should be considered because, according to Italian standards, distributors cannot hold generators and must buy energy at wholesale from the transmission line or private producers (see rows 6 and 7 in Tab. 1). A more economical solution can be achieved by using PREDA to calculate the optimal network suited for the amount of DG proposed (Step 3). The new PREDA solution (Fig. 3) is different from the former and shows a cost reduction due to a major exploitation of existing branches. It worth to notice that the global cost, i.e. the cost of energy plus the network cost, is decreasing (see Tab. 1, columns 2 and 3) showing a convergence of the iterative procedure. This new optimal network (Fig. 3) is used as base for a

Primary substation MV/LV trunk node with ASSD DG unit MV/LV trunk node MV/LV lateral node

Fig. 2 – The testing network optimised by PREDA (Step 1) with the first optimal allocation of DG (Step 2).


new run of PROLOCOGD, in order to find the new optimal arrangement of DG corresponding to the given network (Step 4). The new penetration level of DG is about 37% and, due to changes in DG siting and sizing, a new run of PREDA is required. This execution leads to the same costs and network structure of the former step, even with the new optimal DG, so the iterative procedure can be stopped and this solution can be accepted as the optimal one. The proposed iterative procedure allows a global optimal planning of both network and DG and it can be used to evaluate any additional credits the utility might offer to persuade DG owners to choose appropriate locations that imply real benefits for the network [4]. To illustrate the capability of the TEODORA module, another study has been performed. The same MV distribution network has been considered, and its structure (topology, brunch sections, position and number of Automatic Sectionalising Switching Devices - ASSD) has been optimised by the PREDA module, supposing three different scenarios, characterized by three different power demand growth rates, constant in the planning period: 1%, 3% and 5%. The optimal network architectures (A1, A2 and A3) for the three cases considered are depicted in Fig. 2, for the intermediate case, and in fig. 4a and 4b for the other cases, while their costs are summarized in Tab. 2. Then, at first, the EC and MR approaches have been applied. Tables 3 and 4 show, for each alternative, the expected value of the cost associated to the 3 scenarios and the maximum weighted regret, evaluated as pointed out previously; the scenario probabilities are also reported. From the analysis of Tables 3 and 4, it follows that the alternative recommended by EC and MR approaches are A1 and A3, respectively (in bold). It is important to notice that in this case the EC and MR approaches lead to different choices. Finally, Fig. 5 shows the stability areas for EC, MR and EC–MR approaches; these areas have been obtained varying randomly the values of the scenario weights, always meeting the constraint that the sum of all the weights is equal to 1, and determining for each set of probabilities the optimal solution. From the analysis of Fig. 5 it follows that all three approaches give the sizing alternative A3 as solution in the largest range of weights.

CONCLUSIONS

Fig. 3 - The final optimal network (Step 3) with final optimal DG siting and sizing (Step 4). TABLE 1 – Total Costs related to each step. Costs [k€] STEP 1 STEP 2 STEP 3 STEP 4 Building 2298.6 1598.3 1446.1 1446.1 Losses 1115.3 423.1 422.1 458.8 Disruptions 143.6 77.55 73.7 76.2 Total 3557.5 2098.9 1942.0 1981.1 Energy from Transmission 16341,5 11187.2 11187.2 11530.8 Energy from private DG -5798.6 5798.6 5412.0 TOTAL 19899.0 19084.7 18927.8 18923.9

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The restructuring of the electricity supply market, with the accompanying set of drivers for distribution companies, along with increasing levels of uncertainty faced by utility companies, have raised requirements for new planning methodologies. In the paper a novel software package, called SPREAD, able to deal with the uncertainties related to a massive penetration of DG is presented. It makes use of heuristic techniques developed by the authors and it can be a useful tool for medium and long term planning of real size distribution networks. Examples proposed have shown how planners can use the package and what kind of information can be acquired.

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AKNOWLEDGMENTS This activity has been sponsored by CESI in the context of the Italian Research Project on Power Systems.

REFERENCES [1] [2]

a)

[3] [4] [5] [6] [7] [8] [9] [10]

b) [11] Fig. 4 – Optimal network A1 (a) and A3 (b)

[12]

TABLE 2 – Costs of the three alternatives A1, A2 and A3 [k€]. A1 A2 A3

Building 1447.85 2298.60 2773.38

Losses 892.85 1115.30 952.20

Disruption 145.17 143.59 207.91

[13]

Total 2485.87 3557.48 3933.91

[14]

TABLE 3 – EC approach: Decision Matrix of Costs [k€]. (p1=0.35; p2=0.4; p3=0.25) A1 A2 A3

Scenario 1 2485.87 2758.06 3431.70

Scenario 2 3666.59 3557.48 3704.93

Scenario 3 5299.46 5518.82 3933.49

[15]

Expected Cost 3661.55 3768.02 3666.44

[16] [17]

TABLE 4 – MR approach: Decision Matrix of Weighted Regrets [k€]. (p1=0.35; p2=0.4; p3=0.25) A1 A2 A3

Scenario 1 0.0 95.27 331.04

Scenario 2 43.64 0.0 58.98

Scenario 3 341.49 396.33 0.0

[18]

Maximum Regret 341.49 396.33 331.04

p2

[19]

H. L. Willis, W. G. Scott, 2000, Distributed Power Generation, Marcel Dekker, New York. N. Jenkins, R. Allan, P. Crossley, D. Kirschen, G. Strbac, 2000, Embedded Generation, London IEE Publisher. G. Ault, et al., 2002, “Distribution System Planning in Focus”, IEEE Power Engineering Review, Vol.22, N° 1, pp. 61-64. R.C. Dugan, S.K. Price, 2002, “Issues for distributed generation in the US”, Proc. IEEE PES Winter Meeting, Vol. 1, pp. 121–126. P. P. Barker, et al., 2000, “Determining the impact of Distributed Generation on power systems: Part 1 - Radial Distribution Systems”, Proc. IEEE PES Summer Meeting, pp. 1645-1656. G. Celli, F. Pilo, 2001, “Optimal Distributed Generation Allocation in MV Distribution Networks”, Proc. PICA Conference, pp 81-86. A. Invernizzi, et al., 1995, “Planning and Design Optimization of MV Distribution”, Proc. T&D Conference, pp. 549-557. C. Muscas, F. Pilo and W. Palenzona, 1996, “Expansion of large MV networks: a methodology for the research of optimal network configuration”, Proc. CIRED Conference, vol. 4, pp. 69-74. G. Celli, F. Pilo, 1999, “Optimal Sectionalizing Switches Allocation in Distribution Networks”, IEEE Trans. on Power Delivery, Vol. 14, No. 3, pp.1167-1172. B. Cannas, G. Celli, F. Pilo, 2001, “Heuristic Optimization Algorithms for Distribution Network Planning with Reliability Criteria”, Proc. SCI Conference. G. Celli, F. Pilo, 2002, “Penetration Level Assessment of Distributed Generation by means of Genetic Algorithm”, Proc. PSC Conference. A. Dimitrovski, et al., 1996, “Probabilistic Load Flow in Radial Distribution Networks”, Proc. T&D Conference, pp. 102-107. G. Celli, R. Cicoria, S. Mocci, F. Pilo, 2002, “Probabilistic Optimization of MV Distribution Network in presence of Distributed Generation”, Proc. PSCC Conference. V. Miranda, L.M. Proenca, 1998, “Probabilistic Choice vs Risk Analysis – Conflicts and Synthesis in Power System Planning”, IEEE Trans. on Power Systems, No. 3, pp. 1038-1043. V. Miranda, L.M. Proenca, 1996, “Dynamic planning of distribution networks including dispersed generation”, Proc. CIRED Conference, vol. 4, pp. 51-56. G. Carpinelli, G. Celli, F. Pilo, A. Russo, 2001, “Distributed Generation Siting and Sizing under Uncertainty”, Proc. Powertech Conference, vol. 4, pp. 376-401. G. Carpinelli, G. Celli, F. Pilo, A. Russo, 2002, “Embedded Generation Planning under Uncertainty Including Power Quality Issues”, Proc. PMAPS Conference, pp. 525-533. R. N. Allan, M. R. G. Al-Shakarchi, 1977, “Linear dependence between nodal powers in probabilistic a. c. load flow”, Proc. IEE, vol. 124, No. 6, pp. 529-534. Working Group 37.10, 1995, “Methods For Planning Under Uncertainty - Towards Flexibility in Power System Development”, ELECTRA N°161, August 1995.

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