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Electrical Power and Energy Systems 27 (2005) 398–408 www.elsevier.com/locate/ijepes

Placement of distributed generators and reclosers for distribution network security and reliability D.H. Popovic´a,*,1, J.A. Greatbanksb,1, M. Begovic´c, A. Pregeljd,2 a

Energy Networks Association (ENA), 1 Stanhope Place, London W2 2HH, UK b AEA Technology, London WC1H 0JN, UK c School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332 0250, USA d Georgia Transmission Company, Atlanta, GA, USA Received 19 August 2003; revised 25 November 2004; accepted 2 February 2005

Abstract Electricity market restructuring, advances in energy generation technology and agreements on the reduction of global greenhouse gas emissions have paved the way for an increase in the use of distributed generation. This paper formulates and discusses a methodology for the optimal siting of distributed generators and reclosers a security and reliability constrained distribution network can accept. Optimal siting is determined by sensitivity analysis of the power flow equations. The sizing method for a set of loading conditions, generation penetration level and power factor is formulated as a security constrained optimization problem. The information on optimal generation sites is used further to optimize system reliability assessed via reliability indices calculation. A genetic algorithm is designed to solve for optimal recloser positions when distributed generators are deployed in a securely optimal manner. q 2005 Elsevier Ltd. All rights reserved. Keywords: Distributed generation; Genetic algorithm; Optimization; Protection; Reliability; Static security

1. Introduction Recent years have seen a trend towards the development and deployment of distributed generation (DG) due to government policy changes and increased availability of small capacity generation technologies. The nature of distributed generation is smaller plant (less than 100 MW) with little or limited central control, connected to the distribution system. Distribution systems have been traditionally designed to operate with unidirectional power flow, from the source (transmission system) to the loads. Adding DG to a distribution system imposes a different set of operating conditions on the network, such as reverse power flow, voltage rise, increased fault levels, reduced power losses, harmonic distortion and stability problems. * Corresponding author. E-mail address: [email protected] (D.H. Popovic´). 1 Work done while at Imperial College London. 2 Work done while at Georgia Institute of Technology.

0142-0615/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijepes.2005.02.002

The presence of additional generation on a feeder may also allow for stand-alone, island mode operation where DGs are supplying portions of the feeder load after a fault has been isolated. Islanded operation, however, requires significant coordination of distributed generators with feeder protection devices in order to create possible self-supporting islands. Extensive operations planning system analysis is needed for distributed generation integration to be successful from both system security and reliability point of view. This paper will address the issue of coordinated and optimal placement of distributed generators and reclosers into a security constrained distribution system. Connecting a DG source to the distribution system must be done so as operating conditions are kept within given limits. Clearly, the effect of adding DG on network security and reliability will vary depending on its type and position and (forecast) load at the connection point. Consequently, one or more sites on a given network may be optimal. Despite relatively few generators being connected to the network at present, development of distributed generation is not envisiged to be centrally planned or operated. With this in mind, DG should be introduced for overall system benefit, especially if the grid exists to provide backup capacity. If an

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optimal siting strategy is sought, incentive programs may be considered in order to facilitate implementation of DG in the desirable location(s). Alternatively, additional charges may be imposed for DG placed so to cause problems and/or lower system performance. Preliminary studies have already shown that unless backup capacity is provided, stand-alone distributed generation may lower system reliability [1,2]. Similarly, it could harm system reliability if it is not properly coordinated, located and designed to work with existing network protection. In a radial feeder, protection devices are only expected to detect unidirectional flow of current. In a majority of cases, only one device operates per fault. The control logic for protection devices therefore is simple—the nearest recloser upstream from the fault location detects the fault current, trips, and goes into a predefined reclosing sequence in order to restore service, in case the fault was of a temporary nature. If more reclosers are present on the radial feeder, they are coordinated, usually via time lags, such that the recloser closest to the fault operates. In a DG-enhanced feeder, power flow is not unidirectional and conventional protection logic must be altered in order for the fault-detecting devices to successfully perform their function [3]. A faulted branch may be energized from both sides and several protection devices may need to operate in order to completely interrupt the fault current. Several control control strategies, using only local or SCADA measurements, may be utilized. Distributed generation and storage units, located on the feeder, may be power and/or energy limited, and may include renewable DG, whose output is dependent on the meteorological conditions. Those sources may reduce the number of faults and/or fault durations for customers within their protection zones, thus increasing the reliability of service. This paper develops a methodology for systematic and rational placement of distributed resources and reclosers in distribution networks. The following related optimization tasks may be investigated: (a) optimize recloser placement for a given DG allocation, (b) optimize DG placement for a given recloser allocation, and (c) optimize both recloser and DG placement. In this paper, the optimal recloser placement problem is solved for a previously determined optimal position of the DGs. Both voltage sensitivity analysis and loss sensitivity analysis of the power flow equations are used to determine the optimal sites for placement of distributed generators. It is followed by a security constrained optimization method which calculates the quantity of DG that can be connected to specified points with the system remaining secure. The assessment takes into account the distributed resource power factor characteristics and load profiles for various operating conditions. The information on optimal generation sites is used further to optimize system reliability assessed via calculation of reliability indices which include the DG units. A genetic algorithm is designed to solve for optimal recloser positions when distributed generators are deployed in a securely optimal

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manner. A 114-bus mixed urban and rural 11 kV feeder in the UK is used to verify and demonstrate the methodology.

2. Operation and feeder design optimization for distributed generation The introduction of generating sources into the distribution system can significantly impact the operating state and dynamics of both the transmission and distribution systems. While at low/modest levels of DG penetration, the impacts on the high voltage transmission system may not be significant, impacts at the lower voltage distribution level could be much larger especially with respect to fault current levels, the magnitude and direction of real and reactive power flow, the system voltage (both steady-state and transient) and the system stability under various small and large signal transient conditions. The impacts and interactions can be both positive and negative depending on the distribution network operating characteristics and the distributed generation characteristic, placement and size. A proper placement plays a very important role since power flows at the interface substations and throughout the networks depend on geographic distribution of all generation sources with respect to demand irrespective of the voltage at the connection point. For distributed generation to have a positive effect, it must be at least suitably integrated and coordinated with the distribution system operating practices and feeder design [4]. In order to further the positive effect and enhance network capacity limits while contributing to system security and quality of supply, local optimization would be required accompanied with taking advantage of any inherent regulation capability of dispersed generation. In short, the addition of DG will usually cause changes in voltage magnitudes and power flows. These changes will affect system losses. There are obvious implications for the current rating of lines resulting from modified power flows, and voltage changes could see voltages rise to undesirable levels. Generators operating with a leading power factor may compound the latter. In addition, DG injected power may result in voltage that is within limits at the DG site but could be out of limits further downstream. The addition of extra power sources to a network also impacts on system fault levels and may fault currents increase beyond the rating of circuit breakers. The essence is that adding generators to a passive distribution system makes it an active distribution system, akin to a mini transmission system, and extra thought must be given to its operation and control. More specifically, in voltage profile and regulation studies, available transmission capacity studies, as well as cost studies, the connection point, type, size and location of DG, the voltage regulator settings and independence characteristics of the line must all be considered for various load and load density levels. Similar considerations must be given to islanding response during upstream operation of protection and faults

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on the system. In a conventional (radial) feeder, protection device placement is designed to maximize network reliability, and therefore minimize the reliability indices assuming energy source(s) located only at substation(s). As a brief reminder, the standard reliability performance indices, such as SAIFI, SAIDI and MAIFIe, and the composite index obtained as a combination of all three will be considered. The system average interruption duration index (SAIDI) and the system average interruption frequency index (SAIFI) are typically used to measure average accumulated duration and frequency of sustained interruptions per customer. The momentary average interruption event frequency index (MAIFIe) measures the number of momentary interruptions per customer. The recloser placement can be optimized with respect to any of these three, or some other, indices. In order to include the effects of both sustained and momentary interruptions, a composite index may be used, as defined below CRI Z WSAIFI

ðSAIFI K SAIFIT Þ SAIFIT

C WSAIDI

SAIDI K SAIDIT SAIDIT

C WMAIFIe

MAIFIe K MAIFIeT MAIFIeT

(1)

where Wx indicates appropriate reliability index weights, and the subscript T indicates the target value. (Note that these target values indicate satisfactory level of reliability for a conventional feeder, and may be exceeded in a DGenhanced feeder yielding negative values for the composite index CRI.) The weights are determined by the characteristics of the feeder, customer mix and utility’s perception of the importance of momentary and sustained outages for the feeder under study. The conventional logic suggests placing a recloser at the half-way point of a radial feeder with uniformly distributed load, which, in theory, would yield a 25% feeder-wide reliability improvement. Similarly, locations at 1/3 and 2/3 of feeder length should be considered for placement of two reclosers. In reality, in the presence of critical loads and non-uniform load distributions, utilities often resort to engineering judgment to place reclosers. As an example, Fig. 1 shows a typical rural feeder, with substation breaker and two reclosers. Assuming there is no DG at the end of the feeder, a fault anywhere on the line will lead to the opening of the first recloser upstream from the fault. For example,

Fig. 1. Strategically placed reclosers increase reliability of the system by reducing the number of customers affected by the fault.

after a fault between reclosers 1 and 2, recloser 1 operates, leaving all customers downstream without service. If DG is present, recloser 2 would also operate, allowing the portion of the feeder downstream from it to operate as an island. In order to operate in island mode, DG(s) have to be able to satisfy the islanded load, and therefore keep both the voltage and frequency within acceptable ranges. Islanded operation requires significant coordination of distributed generators with feeder protection devices. The sequence of events after the fault should be as follows: † DG is tripped, and fault detected and isolated by one or more protection devices. † DG reconnects if not within the faulted zone. † After the fault is cleared, recloser synchronizes its reclosing operation with DG. The positions of protection devices and distributed generators are therefore strongly dependent. Incorrect recloser placement may lead to islands with not enough generation and would not yield additional reliability benefits. On the other side, by strategically placing reclosers, one may be able to significantly increase the reliability of service to customers in such islands. Typically, there will be a momentary interruption to the customers in the island, due to the need for the DG to disconnect after the fault in order not to interfere with protection devices’ operation. If, however, reclosers are able to disconnect immediately, there may not be even a momentary interruption, and thus MAIFIe index may also be reduced.

3. Optimal placement and size of distributed generators Optimal placement of distributed generators for enhanced reliability, reduced transmission and distribution costs and reduced emissions can be realized only by considering all factors, including the loss reduction achieved system wide and on the feeders, security limits and cost/benefit analysis. It is a very complex problem considering a high number of options in terms of sites and units available and a need to account for a 8760 h load profile and generation profile and associated uncertainties [5–7]. In [8], the OPF-based optimal placement is proposed addressing the effect of DGs on the spot prices and stability limits. Reference [9] investigates locational aspects of DG with respect to transmission and distribution losses. Other studies have tackled the optimal placement problem using genetic algorithm techniques [10,11] or tabu/parallel tabu searches [12]. These techniques vary in complexity and computation time, to implement and require some degree of cost data. The tabu search in particular is computationally intensive. In this study, costs related to adding the DG and transmission/distribution upgrades and/or savings are not taken into account and the network capacity limits

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are evaluated based on the impacts of distributed generation on the system losses, security and adequacy of supply. To assess network capability to absorb available distributed resources safely, a steady-state system representation in the form of power flow equations will be used. The inverse power flow Jacobian relates changes in power injections to changes in angles and voltages, i.e. " # " vP vP #K1 " # Dd DP vd vV Z (2) vQ vQ DV DQ vd vV 3.1. Optimal DG siting In order to determine the most suitable sites for DGs, two sensitivity based approaches related to voltage control and power loss are proposed. Both a voltage sensitivity index (VSI) and loss sensitivity index (LSI) are defined and used to identify and rank the nodes within the network with respect to receiving new generation. It is assumed that generators can connect to any point in the network subject to security constraints and are not restricted in their location by generator controllers or existing protection devices. 3.1.1. Voltage sensitivity Assuming that angle-related problems are not a concern, the voltage sensitivity can be defined as     vV vV ½DV Z ½DQ C ½DP (3) vQ vP From (2), for each system node, there is an associated real power sensitivity (vV/vP) and reactive power sensitivity (vV/vQ). These values can be used to rank the overall voltage sensitivity of each node to real or reactive power injection. A Voltage Sensitivity Index (VSI) used in ranking is defined as [13]     vV vV VSI Z w C ð1 K wÞ (4) vP vQ The diagonal elements of the Jacobian matrix represent the sensitivity of one bus voltage magnitude to the injection of power at the same bus, whereas the off diagonal elements represent the sensitivity to power injected at other buses. Since the purpose of adding dispersed generation is to bring about an improvement in network performance, the effect of power injection at a single bus on the voltage sensitivities of the whole network must be considered. This is achieved by expressing the VSI for each node as an Euclidean norm normalised across all load buses. The value of the weighting factor w will depend on the X/R ratio of the network under consideration. In a typical 11 kV UK distribution system, X is approximately equal to R and so a weighting factor of 0.5 is used. The nodes are ranked according to the VSI value and the ranked set is used to define the optimum sites to accept injection of P and/or Q.

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3.1.2. Loss sensitivity The majority of power losses are ohmic in nature caused by power flow through lines and transformers, i.e. Ploss Z Pðd; VÞ;

Qloss Z Qðd; VÞ

(5)

Combining Eqs. (2) and (5) gives 2 3 2 3 vPloss vPloss h i K1 6 6 vP 7 7 T 6 7 4 vd 5 4 vPloss 5 Z J vPloss vQ

(6)

vV

The Loss Sensitivity Index (LSI) is defined as     vPloss vPloss LSI Z w C ð1 K wÞ vP vQ

(7)

3.2. Sizing of DG Determination of the optimal sites for DG placement in Section 3.1 is followed by determination of the amount of DG that can be added at these sites without loss increase and operational constraints violation. The sizing method is formulated as a constrained optimization problem adapted from a reactive power compensation sizing algorithm [14] and capacitor bank sizing algorithm [15,16]. Given information on the available distributed generation and assuming no expected load growth in the region of interest, the objective is to maximize the quantity of distributed generation connected to a system, i.e. max

n X

ðPGi C jQGi Þ

(8)

iZ1

where PGi and QGi are the real and reactive power injections at each node i, respectively. The equality constraints are the power flow equations. The inequality constraints are † voltage operational tolerance limits at all buses Vimin % Vi % Vimax

(9)

† limit on losses X X PlossG % Ploss

(10)

ij

ij

where Ploss is the power loss in the line from node i to node j without distributed generation, and PlossG with distributed generation. † limit on total power generated by DG subject to a penetration level of 20% (e.g. it must not exceed 20% feeder load). n X iZ1

PGi % 0:2

n X iZ1

PLi ;

n X iZ1

QGi % 0:2

n X iZ1

Q Li

(11)

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where PLi and QLi are the real and reactive loads at bus i. † branch flows limits (e.g. they must remain below thermal limits) Sij % Sijmax

(12)

† fault current limits (e.g. they must be less than the maximum fault current rating of the switchgear on each line) IFij % IFijmax

(13)

The figure of 20% was chosen for the DG penetration level in line with UK government targets for renewable and distributed generation. The government has pledged to connect 10 GW of cogeneration and supply 10% of power by renewables by 2010 to meet Kyoto Protocol targets [19]

(The UK has approximately 100 GW installed capacity and 60 GW annual peak load). As such, it is unlikely that many distribution networks will experience more than 10–20% penetration. Current protection and voltage regulation practice does not account for high DG penetration. As such, automatic tap changing, automatic voltage regulation on long feeders and directional protection devices may not function correctly with high penetration levels, and a penetration level greater than 100% where power is exported from the system (back through grid transformer) is infeasible. The optimal placement and sizing methods are combined to add DG penetration with generators connected at optimal points. The proposed solution algorithm is shown in Fig. 2. The sizing element is an iterative process, and involves repeatedly solving load flow equations. Each iteration has a larger value of DG source connected at predetermined (optimal) points. The DG size increment is a fixed size unit, in this case 10 kW, and is applied to all optimal sites in Start

Select Data File, Max Generator Increment, Weighting Factors

Initial System Load Level

Initial Generator Type

Solve Initial Load Flow and Fault Levels Calculate VSI & LSI

Increment Generators at Viable Nodes Normalize & Rank

Solve Load Flow and Fault Levels No

Are Constraints Breached?

Yes Remove Last Generator Increment

Repeat for All Remaining Generator Types

Repeat for All Remaining Load Levels

Finish

Fig. 2. Solution algorithm for optimal placement and sizing.

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3.3. Numerical study

Fig. 3. Load profile for test feeder.

a single iteration. The solution is reached when the next iteration fails to satisfy one or more constraints. The loading of a system plays an important role in determining the type of constraint to be violated. Consequently, the methodology and solution algorithm are applied over a range of loading conditions. Fig. 3 shows typical load profiles for three representative days for a test feeder, winter evening peak demand, summer night least demand and spring daytime average demand. These three levels are approximated by the ratio 4:2:1, exploited by the algorithm.

In order to evaluate the effects of adding DG to a system, the operating characteristics of the distributed generator should be taken into account, especially with respect to the network interface, whether it is synchronous or induction machine based, directly coupled or connected via an inverter. The vast majority of distributed generation in the UK serves the single purpose of exporting power to the power system (subject to not causing malfunction of regulation or protection devices) for consumption [17]. Little if any distributed generation is either controllable or dispatchable and is not used for any ancillary support. This, coupled with the regulatory and commercial arrangements for DGs means that there is no benefit or incentive for the generator to operate at a power factor other than unity (or as close to unity as possible). This analysis considers three generator power factors of unity, 0.95 leading and 0.95 lagging to represent likely operating generator characteristics. The methodology and solution algorithm are tested on several distribution systems representing urban, rural and mixed use 11 kV networks. All networks are assessed for ‘intact’ conditions (e.g. no contingencies). The results shown here are for a 114 bus mixed urban and rural

Fig. 4. Test feeder schematic.

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Fig. 5. Normalised voltage sensitivity index (wZ0.5).

11 kV system from the UK. Fig. 4 shows a slightly modified version of the feeder obtained by aggregating many of smaller (rural) loads located at lateral ends. Consequently, the number of buses is reduced to 75. Currently, there is no DG connected anywhere within the feeder. The total maximum feeder load is 17.4 MW, with 13.8 MW concentrated down the main feeder as housing estates and small industrial units supplied via 300–1000 kVA substations. The two right hand laterals supply small housing clusters and farms via 10–100 kVA transformers and their maximum loads are 2.5 and 1.1 MW. Fig. 5 shows the VSI results of the optimal siting method with the highest ranked sites, as expected, being located towards the feeder extremities where nodal voltages are lowest. Similarly, Fig. 6 shows the nodes’ LSI values. The highest ranked nodes are again located towards the feeder extremities. Relating Figs. 5 and 6 to Fig. 4, a clustering pattern can be clearly observed whereby neighbouring nodes have very similar voltage and loss sensitivities. Hence, simply placing the DG units at the highest ranked sites would lead to an undesirable cluster of neighbouring generators. To avoid this situation and to distinguish between feasible and non-feasible sites, a cutoff value of 0.015 was chosen for both the VSI and LSI. Of all the feasible sites identified by VSI, 10 were chosen as viable generator sites with respect to their spatial distribution around the feeder as indicated in Fig. 5 and marked in Fig. 4. The loss sensitivities in Fig. 6 indicate an even stronger clustering pattern and the eight most sensitive sites identified as optimal are chosen as to coincide with the VSI-based sites. It is worth noting that within clusters buses

are more sensitive to voltages than losses, such as cluster 16–22 and 69–72. Within cluster 64–67 the ranking order reverses with bus 64 at the lateral end being more sensitive to voltage yet all four buses show similar loss sensitivities. The results shown in Figs. 7 and 8 are obtained using LSI based solution algorithm in Fig. 2 for the three load conditions (winter, summer, spring) and three generator power factors of 1, 0.95 leading and 0.95 lagging. In all cases, a solution was reached when 20% penetration was achieved, i.e. a breach of constraint (11). Fig. 7 shows a noticeable improvement in voltage profile along the feeder. Note that in Fig. 7, all voltage profiles have been normalised so that the source voltage (node 1) is equal to the winter level of 1.04 pu. Despite only a 20% penetration, there is roughly a 2% rise in voltage, even in buses on the main feeder geographically distant from the generators. A similar pattern was observed for the spring and summer load levels, although not shown. However, voltage rises are still moderate enough so as not to cause overvoltage problems in any load state. In each case, the leading generator power factor gives rise to the greatest voltage improvement and the lagging to the least. Fig. 9 compares the relative improvement in voltage profile for 20% penetration with generators placed by both LSI and VSI. Over the bulk of the feeder, i.e. the large main section, there is no difference in voltage improvement. However, on the laterals, there is generally a greater voltage lift from placement by LSI. This is due to the LSI optimal generators being placed at fewer sites and sized larger. The losses results of Fig. 8 all follow the same pattern for each load state of approximately a 40% reduction in losses with a 20%

Fig. 6. Normalised loss sensitivity index (wZ0.5).

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Fig. 7. Voltage profile for feeder with LSI placed DG and winter load.

Fig. 9. Voltage profile for unity power factor and winter load.

penetration and winter load. (Note that the efficiency is 1— the ratio of real power losses to real power input. Real power input is the sum of real power losses and real power loads.) A 40% reduction in losses gives rise to a 2.3% improvement in efficiency. With a summer load, a 39% reduction in losses translates to only a 0.5% rise in efficiency. Although results are only shown for a generator power factor of 1, similar results were seen for the other cases, with a leading power factor leading to most significant loss reduction. The network performance is also analyzed for VSI-based optimal placement. As expected, due to similarity in optimal sites, the reduction in losses and hence improvement in system efficiency were virtually identical to those shown in Fig. 8. The voltage profile comparison illustrated in Fig. 9 shows significant improvement in voltages along the feeder but no major differences arising from siting methods. Although not included, a set of results for fault levels was obtained. These indicated an average rise of 7.9% with no line experiencing more than a 20% increase. The case study yields a set of numerical results for optimally placed DG that the system can accept under particular load and generator power factor conditions. These represent a conservative estimate with DG added to the most sensitive nodes. If the same quantity of DG were added to

less sensitive nodes, the voltage rise or loss reduction will be less significant, although line flows and fault levels may become limiting factors. For system planners and operators, this conservative estimate is likely to be of much greater value than a ‘best case scenario’ value showing that more DG could be accepted, but with greater restrictions on its placement.

Fig. 8. Real power losses for unity power factor DG.

4. Genetic algorithm for recloser placement In a DG-enhanced feeder, the optimization of reclosers is not as straightforward as in the case of a conventional feeder, due to the presence of additional generators, which may be able to satisfy portions of the feeder load after fault has been isolated, as shown in the simple example presented above in Fig. 1. In a large, meshed network, the task of locating optimal recloser positions that would create possible self-supporting islands is not trivial. The optimal recloser position(s) depend on the types, locations and sizes of distributed generators deployed at the feeder. Conversely, if the reclosers are already placed on the feeder, optimal DG positions and sizes can also be determined. Finally, both the placement of reclosers and DG can be optimized concurrently during the planning stage of the feeder design. In this study, a simple genetic algorithm (GA) is proposed, based on the algorithm presented in [18], to solve for optimal recloser positions for a given DG allocation. The objective is to minimize the composite reliability index (CRI), described in (1) with default weights W (0.2, 0.4, 0.4) and targets WT (1, 2.2, 7) for SAIFI, SAIDI and MAIFIe, respectively. The target values for SAIFI, SAIDI and MAIFI of (1, 2.2, 7) indicate satisfactory level of reliability for a conventional feeder used as a numerical example, and may be exceeded in a DG-enhanced feeder yielding negative values for the composite index CRI. The weights for SAIFI, SAIDI and MAIFI of (0.2, 0.4, 0.4) reflect the importance given to the momentary outages, as well as to the durations of sustained outages. It is worth mentioning that the algorithm can be readily extended for the remaining two

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problems by adjusting the optimization function and algorithm properties. Genetic algorithms are suitable candidates for such optimization problems, due to the nature of the optimization function. The search space is spanned by mimicking the natural principles of reproductive evolution. Starting from an initial population of individuals, GAs effectively implement the ‘survival of the fittest’ strategy—fitter individuals (those with higher values of the optimization function) are more likely to reproduce and/or survive to the next generation, thus improving the overall population. The population evolves using the genetic operators, selection, mutation and crossover. For selecting the individuals chosen to continue into the next generation, a normalised geometric ranking selection procedure is used. The parameter vector X contains the positions of individual reclosers to be placed on the feeder. The composite reliability index is chosen as the optimization function and the probability of selecting each individual is given by (14) Pðxi Þ Z

qð1 K qÞrK1 1 K ð1 K qÞp

(14)

where q is the probability of selecting the best individual (given in advance), r is the rank of the individual after sorting (1 being the best),and P is the population size. Additionally, the elitist model is implemented, with the best individual always included in the next generation. In the crossover step, a combination of arithmetic and heuristic operators is employed. Arithmetic crossover provides random mixture of individuals, while the heuristic operator incorporates fitness information, resulting in individuals more likely to have higher values of the objective function. Both crossover operators are applied to 10% of individuals randomly chosen from the population in each generation. Three mutation operators are used: single uniform, single non-uniform and multi-non-uniform mutation. Single uniform mutation changes only one of the parameters resulting in a recloser being placed randomly on the feeder. Single non-uniform mutation replaces one of the parameters, xi, according to (15)

xi Z ð1 K f ðgÞÞxi C bf ðgÞ

(15)

where b is either the lower or upper bound of the parameter space, with probability of 0.5 of choosing each value, and the non-uniform operator f(g) is defined as   g t f ðgÞ Z r 1 K (16) G where r is U(0,1), g current generation number, G maximum number of iterations, and t is the tuning parameter. Multinon-uniform mutation applies the single non-uniform mutation to all parameters of the individual. All three mutation operators were applied to 5% of the population per generation. The algorithm is initialized with randomly generated started starting population. The test feeder was used to demonstrate the algorithm, with DG placed at the optimal nodes from the voltage sensitivity analysis—see Fig. 4. It is assumed that the fault incidence rate and the duration of faults (damage restoration time, DRT) are uniform over all feeder branches. Also, in the case of the fault, only the minimum number of reclosers closest to the fault should operate, and isolate the fault. The actual implementation of the control algorithm required for such operation is not the subject of this paper. For each recloser configuration, a composite index is calculated by determining the reliability zones (zones bounded by the reclosers), simulating the faults in those zones, determining the online and offline loads, and finally calculating the composite index. For each reliability zone that has a DG, after a fault in other zones, the maximum output of all zone generators is compared with the load duration curve for zone loads, and the number of faults is reduced by the percentage of time that the zone generation exceeds zone load. For example, if a zone’s generation corresponds to the 70% on the zone’s load duration curve (i.e. for 70% of the time generation is higher than load), it is assumed that 70% of the faults outside the zone will not lead to outages within the zone. The results of the algorithm are presented in Table 1, which shows the top three values for the composite index,

Table 1 The composite reliability index for DG enhanced feeder and various recloser placement strategies Number of reclosers

1

2

3

4

Without DG

With DG

Index value

Recloser positions

Index value

Recloser positions

0.1862 0.5855 0.6063 0.0672 0.0677 0.0794 K0.0397 K0.0391 K0.0276 K0.2519 K0.2494 K0.2429

15–22 14–15 14–69 15–22, 42–55 15–22, 4–55 14–15, 15–16 42–55, 14–15, 15–16 4–55, 14–15, 15–16 42–55, 15–16, 15–22 2–53, 14–15, 15–16, 46–75 2–22, 14–15, 15–16, 46–75 2–53, 14–15, 15–16, 27–58

0.1351 0.4717 0.4840 0.0037 0.0066 0.0212 K0.1648 K0.1610 K0.1534 K0.2962 K0.2923 K0.2847

15–22 14–15 14–69 12–68, 15–22 14–15, 15–16 13–69, 15–16 2–53, 15–22 46–75 2–22, 15–22, 46–75 2–53, 15–22, 27–58 2–53, 12–68, 15–22, 46–75 2–22, 12–68, 15–22, 46–75 2–53, 12–68, 15–22, 27–58

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and corresponding branches at which reclosers are placed, when up to four reclosers are strategically placed on the feeder. The branch numbering corresponds with numbering shown in Fig. 4 Two cases are considered: the feeder without DG, and with 20% DG penetration with the 10 generators sited by the VSI. In the one recloser case, the recloser placement is dominated by the ‘conventional’ benefits obtained by placing the recloser towards the middle of the feeder. The additional benefits, obtained by reducing the number and duration of outages during islanded operation, do not justify placing a recloser at a different location. In the case with two reclosers, note that the optimal recloser positions differ significantly. Without DG, reclosers are optimally placed at branches 15–22 and 42–55, isolating two portions of the feeder downstream from buses 15 and 55, and allowing the remaining customers to continue receiving service even after the fault in the isolated areas. In a DG-enhanced feeder, reclosers are concentrated closer to the DGs, creating islands of supply for customers downstream from bus 15. Similar to the one-recloser case, for a fault upstream from bus 15, the whole portion of the feeder downstream from bus 15 may operate as an island. The placement of the second recloser at the branch 12–68 creates additional possible island for customers downstream from bus 12; they may now remain on-line even after a fault between reclosers. As a result, the reliability index drops to 0.0037, as compared to the 0.0672 in the case without DG. Note that if reclosers are placed at buses 15–22 and 42–55 (optimal placement for a feeder without DG), the index in the case with DG would be 0.0247. A similar trend continues for the cases with more than two reclosers. In some cases, the composite index becomes negative, indicating the target values for reliability indices have been exceeded. This is because target values for reliability indices used in the definition of the composite index in (1) represent sufficient level of reliability for a conventional distribution network.

5. Conclusions This paper has presented a methodology for optimizing and coordinating the placement of distributed generators and reclosers in a security constrained distribution network. A systematic and rational placement of distributed generation and reclosers is shown to be able to improve both system security and reliability, by improving feeder voltage profile, reducing losses and increasing efficiency, and providing energy to some of the customers, even after the fault in the distribution system. The level of improvement depends on the type, number and size of the distributed generators, number of reclosers, and positions of both generators and reclosers on the feeder.

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Optimal sites for placing distributed generation are identified using both voltage sensitivity and loss sensitivity analysis of power flow equations. Due to potential limitations to the choice of sites, the optimal placement is not likely to be applied in practice. Instead, the paper illustrates how the information on the sensitivity pattern along the feeder expressed via clearly observed clusters of buses with similar sensitivity values can be used to define a set of viable yet practically suitable sites. With powerconstrained distributed generators placed at viable (nearoptimal) sites, the improvement in overall reliability is demonstrated by finding optimal recloser positions using a specially tailored genetic algorithm. Currently, the analysis has been carried out for a variety of load conditions and generator power factors only. Further work is planned to expand this scope to determine and quantify benefits of scenarios with energy constrained sources, variable (e.g. renewable) types of distributed generation and storage systems that will require representation of time varying load and generator characteristics along with their uncertainties, control capability and associated storage needs.

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