223 Optimal Location of Dispersed Generators

for Reliability Improvement of Distribution Networks

Ion Tristiu*, Mircea Eremia, Constantin Bulac, Lucian Toma “Politehnica” University of Bucharest

(Romania)

Abstract: This paper presents a method for optimum placement of the dispersed generators into an electrical distribution network in order to improve the reliability of supply to consumers. The objective function is a single-criteria and consists in minimisation of the total interruption cost for the consumers. The optimisation constraints are related to generators size and number, voltage level and thermal limits of the network branches. The interruption costs are evaluated on the basis of the reliability indices calculated for every load bus by means of an analytic method that consists in successive reduction of the reliability bloc diagram. The optimisation method is an exhaustive one consisting in systematic searching into the solution space. The proposed method is tested on a simple radial distribution network.

Keywords: Distribution Network – Dispersed Generation – Reliability.

1. Introduction The major changes the power industry undergone in the last years set up a favourable framework for dispersed sources. The main differences with respect to the large power plants consist in the placement location and generation capacity. Usually, dispersed sources are characterized by rated powers smaller than 100 MW, being connected in low or medium voltage distribution networks. The introduction and development of dispersed generation increases the specialists’ attention in the electrical power industry concerning the operation and their influence on the electrical networks. The aspects aimed in studies can be different such as: power flow and losses allocation [1], losses reduction [2], placement of dispersed generator [3], etc. Dispersed generators (DGs) could improve, in some conditions, the supply reliability indices into distribution networks. This aspect is strongly conditioned by the primary energy form and the conversion installation type. Dispersed generators could constitute a reserve and even a replacement of supply, of some consumers, from the centralized system. Reliability evaluation of consumers supplying paths from the electrical distribution networks is approached in different manners [4-9].

* E-mail: ion_tristiu@yahoo.com

The reliability improvement of consumers supply has been approached also by reconfiguration methods that can be applied as a necessity after the reorganizing of distribution networks. Paper [10] proposes the improvement of equivalent indices of the consumption nodes with respect to the source node. Paper [9] proposes the improvement of networks reliability and service quality by feeder-switch relocation. The evaluation of influence of the dispersed sources on the safe of consumers supply is an important aspect in planning studies of electrical distribution networks. At the same time, this task is intricate because of the distribution systems complexity. The main purpose of this analysis consists in determination of the effects due to the interruption of consumers supply. The criterion used in this regard is the Consumer Interruption Cost (CIC) [9].

2. Evaluation of the consumer interruption cost The main objective of the optimal placement of dispersed generation considered in this paper consists in consumer interruption cost minimisation. In order to evaluate this cost it is necessary to calculate some reliability indices for every consumption node. In this regard, the radial distribution electrical network presented in figure 1 is considered, which consists of an injection node A (medium voltage node of a supplying substation) and consumption nodes. n

Fig. 1. Simple radial electrical network.

Next, the evaluation of reliability indices of the consumption nodes from the electrical distribution networks, with and without dispersed generators, is presented.

2.1. Distribution network without dispersed generators A branch, between two nodes, consists of an electrical line (overhead or cable) and their Switching Equipments (SE) at the nodes (circuit breakers or sectionalisers). Each branch is characterized by two reliability indices (fig. 2):

– failure rate, expressed in failures per year (f/yr); ijλ

– failure duration, expressed in hours (h). ijr

SEi SEji j λij rij

Fig. 2. Equivalent reliability parameters for a branch.

The failure rate of each branch is calculated in terms of the failure rates of the component elements, considered as being series connected. The fault occurrence on a branch affects differently the consumption nodes. During the fault clearance, generally, four steps are distinguished [9]. Depending on the steps necessary to be followed, the restoration of the supply of any consumption node from the network, after a fault on the branch i , can be determined in terms of:

j−

– fault repairing on the branch i j− ; – fault isolation, by opening a normal closed switching equipment; – load transfer to another feeder, by closing a normal open switching equipment.

Based on the previous observations, the reliability parameters of the branch i are: j−

0 0 0; ; ijij SEi ij ij SEj ij SEi SEi ij ij ij SEj SEj ij

ij

Ul U r l r r rλ = λ + λ + λ = λ + λ + λ =

λ (1)

where is the failure rate of electrical line, expressed in failure per kilometer and year (f/km-yr), and are the failure rates of the switching equipment at nodes i and j, respectively, expressed in failure per year (f/yr), U is the unavailability of the branch i j

0ijλ

SEiλ SEjλ

ij − , while , and are the restore times of supplying paths of a consumption node from the network, expressed in hours (h), for a fault on the line of the branch i , respectively for a fault at the switching equipment from the nodes i and j.

0ijr SEir SEjrj−

For every consumption node, three primary reliability indices are calculated. In order to perform these calculations we start from the observation that the only switching devices capable to clear short-circuit currents are the circuit breakers. Usually, these are placed at the feeder’s connections to the medium voltage side of substation. Under these conditions, a short-circuit occurring on any of the network branches in figure 1 leads to opening of the circuit breaker 1B , so that the supply of all the consumption nodes will be interrupted. Reliability speaking, the branches are series connected (fig. 3).

Fig. 3. Reliability bloc diagram.

The equivalencing of the reliability bloc diagram to a single element relative to each consumption node is performed by taking into account the restoring manner of the supply of the respective node, that is, by considering one successive fault on each branch of the network. The restoring of supply of the consumption node i, for a fault at one of the branches between nodes A and i is performed after the fault repair. These branches form the set called Rep. For a fault at one of the branches between nodes i and n the restoring of supply of node i is performed after the fault isolation. These branches form the set called Isol. Because the network is considered radial, there is no possibility to restore the supply of the node by transferring it on others feeders.

i

The equivalent reliability indices of the consumption node i are given by:

, ,; eiei j j ei j j rep j j isol ei

j Rep j Isol j Rep j Isol ei

UU r r r∈ ∈ ∈ ∈

λ = λ + λ = λ + λ =λ∑ ∑ ∑ ∑ ;

iL

(2)

where is the equivalent failure rate, U is the equivalent unavailability at the consumption node i, and is the equivalent interruption duration of supply.

eiλ ei

eir

The quantitative evaluation of the electrical distribution network reliability can be performed by calculating the energy not supplied to the consumers and therefore the consumer interruption cost. Energy not supplied to the consumption node i can be evaluated by: i ei eiL r= λ ∆ (3)

where is the interrupted power at the consumer i. iL∆

For the evaluation of the consumer interruption cost it must be taken into account the interruption duration ( ), the per kilowatt cost of the interrupted power (eir Pc ) and the per kilowatt-hour cost of the energy not supplied ( ) [7]: Wc

( ) ( )i ei P ei W ei ei iIC c r c r r= λ + ∆ L (4)

The quantities Pc and c depend on the equivalent interruption duration and type of the consumption node i (residential, commercial or industrial).

W eir

2.2. Distribution network with dispersed generators The introduction of dispersed generation in electrical distribution networks can have a favourable influence on the safe of consumers’ supply, if some conditions are met:

– the operation of the dispersed sources should be reliable and should not depend on the environment conditions (presence of wind, of solar radiations, etc.);

– the existence into the electrical network of some switching equipments (circuit breakers) capable to automatic isolate the supplied area for a fault in any point from the network;

– the possibility of islanded operation of the dispersed sources (the existence of voltage and frequency regulators).

For simplicity, one considers that every dispersed source can supply only the consumer from the node to which it is connected. The separation of the area supplied by a dispersed source is performed by means of circuit breakers. The presence of the dispersed source and the afferent circuit breakers modifies the reliability indices of the connection node, as well as of others nodes from the area. For the study of these modifications, we consider the network from figure 1, where a dispersed source is connected at node i, that can cover totally or partially the consumption of this node (fig. 4).

Fig. 4. Electrical network with DG.

In the analysis of the failure type of the network with respect to the node i, two situations are emphasized: (i) The occurrence of a short-circuit upstream to node i (between nodes A and i): The circuit breaker 1B will clear the component of the short-circuit current fed from the system, and the circuit breaker 2B will clear the component fed by the . Because satisfies only the consumption at the node i, the circuit breaker

iDG iDG

3B will be opened by the system protection. Therefore, all the consumption nodes, except for the node i, will remain not supplied. (ii) The occurrence of a short-circuit downstream to node i (between nodes i and n): The short-circuit current passing through the circuit breaker 3B is composed by a component fed from the system and a component fed by the . Normally, this circuit breaker must open, isolating automatically the fault. The consumers upstream to node i will not be disconnected, so that the reliability indices will be improved.

iDG

Considering that the generator connected at the node i has the rated power and the active power consumed at the node i is , the interruption cost of this node becomes:

,G iP

iP

( ) ( ) ( ) ( ) ( ), ,' ' 'i ei P ei W ei ei i G i ei P ei W ei ei G iIC c r c r r P P c r c r r = λ + − + λ + P (5)

where is the interruption of the operations duration during the interruption duration of the supply from the system, taking into account the availability

'eir iDG

eir ,DG ip of this DG:

( ),' 1ei DG i eir p= − r (6)

3. Mathematical model The mathematical model of the dispersed generators placement problem consists of the objective function and constraints.

A. Objective Function The mathematical expression of the objective function can be written under the form:

1

MINn

ii

CIC IC=

=

∑ (7)

where CIC is the customer interruption cost for all n consumption nodes of the distribution network and is the interruption cost for the consumer i. iIC

B. Constraints For this optimization problem the following constraints are considered:

1) Power Flow Equations [3]: ( ) niPF kGi ,,2,1, , K=x (8)

where is the active and reactive power balance equations for the consumption node i, is the vector of state variables for all nodes of the electrical network and is the dispersed generators control variable (active power) at the node k.

iF x

kGP ,

2) Operational constraints:

(9) min max

maxi i i

l l

V V VP P

≤ ≤≤

where V and V are the admissible limits for the voltage level V in all nodes i, is the load-transfer capability of all branches l of the network.

mini

maxi i

maxlP

3) Constraints on the size and number of DGs:

(10) min max, ,

maxG k G k G k

DG DG

P P Pn n

≤ ≤≤

,

where is available active rated power chosen between certain limits and , k

denotes the node’s number and is the maximum number of the DGs from the network. kGP ,

min,kGP max

,kGPmaxDGn

The mathematical model described by the relationships (7)÷(10) represents the formulation of the mathematical programming problem. The unknowns of the problem are: the number of the dispersed sources from the network ( DGn ) and the power generated by each source ( ). For a given configuration of the electrical network, the equivalent reliability indices of a consumption node are independent of the indices of other nodes. Under these conditions, based on relation (5), it results that the optimal active power that should be generated at the node k must be equal to consumed active power at this node. The DGs number

,G kP

opt,G kP

kP DGn and optimal placement are to be further determined. The solution manner is based on searching into the solutions space. The use of searching heuristic methods is intricate and therefore an exhaustive searching is used. Thus, consider only one that is placed by turn in every consumption node ( ), using the optimal value of the rated active power

for each generator. The optimal placement is retained, for which CIC has the lowest value.

kDG1,2,k = ,K n

,opt

G kP

Next, consider two sources and (jDG kDG , 1, 2, , ;j k n j k= ≠K ), and the previous

algorithm is repeated, retaining the optimal solution. This proceeding goes on until all maxDGn

are verified.

One possibility to separate the classes of solutions can be the ratio of the benefit resulted by reducing the CIC to the total generation capacity:

,1

DG

without DG with DGn

G kk

CIC CICper kilowatt benefit

P=

−=

∑ (11)

where CI and CI are CIC in situation without and with DGs. without DGC with DGC

4. Case study The testing of the method proposed in this paper for the optimal introduction of DGs has been made on the radial distribution network with 12 nodes from figure 5.

Fig. 5. Electrical network with 12 buses and 11 branches.

The network operates at nominal voltage of 20 kV. The resistances and reactances of branches, as well as the characteristics of the consumption nodes can be found in [3]. The maximum load transfer capability for every branch is considered 800 kVA. The lines’ lengths are given in Table I.

Table I. Lengths of the electrical network lines. Line 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12

l [km] 1.2 1.3 2.3 3.6 1.2 1.1 3.4 4.4 2.2 1.2 1.0 We consider the existence of one circuit breaker on the feeder out from the supply node (on the branch 1-2 at the node 1), and at the others nodes there exists sectionalisers. The reliability parameters used in calculations are the ones given in Table II [8].

Table II. Component reliability data. Index

Compo- nent

Failure rate [ ]f yrλ

Repair time [ ]hrepr

Isolation time [ ]hisolr

Line [1 km] 0.045 8 4 Circuit breaker 0.003 1 1 Switch 0.004 8 3

The values of interruption costs Pc and , used in calculations, are the ones given in Table III, adapted from [7].

Wc

Table III. Values of interruption costs Pc and . Wc

[ ]hr Pc [€/kW] Wc [€/kWh]0 ÷ 0.2 5 5 0.2 ÷ 1 10 5 1 ÷ 10 20 5 > 10 40 5

The optimal rated value for active power of the DGs, corresponding to the consumed active power in each node, is chosen between and . The availability of each DG is considered . The maximum number of DGs has been considered

. In Table IV, the results for equivalent reliability indices and interruption costs for all consumption nodes are given for two cases: without DGs and with one DG at the node 7.

min 15 kWGP = max 60 kWGP =6.0=DGp

max 2DGn =

Table IV. Results for reliability indices and interruption cost for consumption nodes. No DGs 7DG ( ,7 55kWGP = )

Node eλ [f/yr] eU er [h] IC [€] eλ [f/yr] eU er [h] IC [€]

2 1.1175 4.63 4.15 2730.90 0.5275 2.31 4.38 1325.40 3 1.1175 4.91 4.39 1875.40 0.5275 2.58 4.90 938.40 4 1.1175 5.36 4.80 2703.53 0.5275 3.04 5.76 1415.15 5 1.1175 6.05 5.41 1577.85 0.5275 3.72 7.06 875.10 6 1.1175 6.31 5.64 1077.50 0.5275 3.98 7.55 609.00 7 1.1175 6.54 5.86 3028.58 0.5305 4.18 7.88 1043.46 8 1.1175 7.20 6.44 2624.63 1.1155 7.14 6.40 2609.78 9 1.1175 8.03 7.18 2499.40 1.1155 7.97 7.14 2486.20

10 1.1175 8.46 7.57 2263.27 1.1155 8.41 7.54 2251.73 11 1.1175 8.72 7.80 2637.80 1.1155 8.66 7.76 2624.60 12 1.1175 8.92 7.98 1004.17 1.1155 8.86 7.94 999.23

The variation of CIC to the introduction of one DG in each load node is shown in figure 6, and the variation of the benefit defined by relation (11) for the same situation is shown in figure 6. The optimal placement for the absolute variation of CIC has resulted for the node 7, while the node 6 has resulted for the per kilowatt variation.

0

5000

10000

15000

20000

25000

30000

No

DG

s

Nod

e 2

Nod

e 3

Nod

e 4

Nod

e 5

Nod

e 6

Nod

e 7

Nod

e 8

Nod

e 9

Nod

e 10

Nod

e 11

Nod

e 12

Fig. 6. CIC variation (in Euros) for one DG.

0

50

100

150

200

250

300

Fig. 7. Generated active power benefit (in

Euros per kilowatt) for one DG. The CIC variation to simultaneous introduction of two DGs into the electrical network is shown in figure 8, in increasing order for the first 10 combinations. The optimal placement is obtained for nodes 4 and 8. The generated per kilowatt benefit is shown in figure 9. It can be seen that the optimal placement, from this point of view, is obtained for nodes 6 and 12.

1440014600148001500015200

15400156001580016000

Nod

es 4

, 8

Nod

es 4

, 7

Nod

es 3

, 7

Nod

es 7

, 9

Nod

es 3

, 8

Nod

es 5

, 8

Nod

es 7

, 8

Nod

es 4

, 9

Nod

es 7

, 10

Nod

es 7

, 11

Fig. 8. CIC variation (in Euros) for two DGs.

020406080

100120140160180

Nod

es 6

, 12

Nod

es 5

, 12

Nod

es 6

, 10

Nod

es 6

, 9

Nod

es 5

, 6

Nod

es 6

, 8

Nod

es 3

, 6

Nod

es 6

, 11

Nod

es 5

, 10

Nod

es 5

, 9

Fig. 9. Generated active power benefit (in Euros per kilowatt) for two DGs.

5. Conclusions The introduction of dispersed generators, under the conditions specified in this paper, leads to the improvement of the consumers supply safe. This fact is found by the reduction of the interruption duration and their number for a part or all of the consumption nodes and implicitly the reduction of the consumer interruption cost. It is obvious that the many the dispersed sources are in the network, the total consumer interruptions cost is smaller. Per kilowatt benefit is better for one DG than for two simultaneous DGs in electrical network. Under the hypothesis that every dispersed source covers totally or partially the consumption of the node where it is connected, the voltage drops and the branches loading are smaller than in the situation without dispersed sources. A more complex analysis of the optimal placement of dispersed sources and their rated capacity should also take into consideration in the objective function more aspects such as: power losses, investments, etc. The employment of circuit breakers to separate the network area fed by a dispersed source contributes to the improvement of the consumers supply safe situated upstream to the circuit breaker location (between this place and the supplying node).

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