A New Placement Scheme of Distributed Generation in Power Grid

doi:10.4236/epe.2013.54B143

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Energy and Power Engineering, 2013, 5, 740-745

doi:10.4236/epe.2013.54B143 Published Online July 2013 (http://www.scirp.org/journal/epe)

A New Placement Scheme of Distributed Generation in

Power Gr id *

Zhipeng Jiang1, Tiande Guo2, Wei Pei3

1Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China

2University of Chinese Academy of Sciences, Beijing, China

3Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing, China

Email: [email protected]

Received March, 2013

ABSTRACT

Smart grid gets more and more popular today. Distributed generation is one of the key technologies, and especially, the

integration problem of the distributed generation is an important issue. Especially, the location and capacity of the dis-

tributed generation play an important role for the performance of the distribution network. In this paper, an optimization

model to minimize the loss cost of the unsatisfied demand is given. Th is model is based on a reliability computing me-

thod which avoiding power flow calculation in a previous work. Then the model is used on the IEEE-123 nodes ex-

periment network and a result of five distributed generation placement is got.

Keywords: Smart Grid; Distributed Generation; Optimal Integration ; Optimization Model

1. Introduction

The smart grid being more and more popular today and

distributed generation is one of the key technologies in it.

The distributed generation device is an independent gen-

eration, small modular and compatible with the environ-

ment whose power is from several kilowatts to 50 me-

gawatt. The power of the distributed generation is owned

by the power department, users or the third party, which

is used to meet the particular demand of the power sys-

tem and users. For example, adjusts the peak, supplies

the power for remote users and residents, decreases the

cost of the power transmission and transformation and

improves the reliability of the p ower supply. The distrib-

uted generation is deployed near the users in a distributed

way and it’s a system which can independently provide

power. The distributed generation mainly includes the

internal combustion engine micro gas turbine, wind

power generation as well as photovoltaic cells which use

liquid or gas as the fuel. The distributed generation is an

important supplement of self-healing strategy, which

plays an important role in peak averting, valley filling

and load balancing. However, it also brings about new

problems. For example, some types of distributed gen-

eration are stochastic, and increase the volatility of the

system voltage.

There are many issues concerned in distributed gen-

eration problem, among which the optimal integration is

one of the important problems. It involves many aspects

of factors. It has not only to find a proper optimization

objective, but also to analyze various elements like the

location, size and type of the distributed generation.

Hence, it is a very complicated issue. The location of

distributed generation is a location prob lem in the opera-

tions research, and it’s an NP (Non-Deterministic Poly-

nomial) problem which needs an appropriate algorithm to

solve it. The constraints need to synthesize the influence

of distributed generation on power grid when connecting

the grid, the equilibrium conditions of power gird and

voltage as well as the randomness of distributed genera-

tion; while objective function requires comprehensive

consideration of operation cost and power consumption.

2. Related Work

The In recent years, a variety of methods on the optimal

integration of distributed generation have been arisen. A

main method is establishing an optimization model with

multiple indicators as objective function and some char-

acteristics and restrictions of power grid as constraints.

The location and the access capacity of the distributed

generation can be achieved by solving the optimization

model. The most important object among these indicators

is to minimize the lin e loss [1-3]. In [1], th e authors gave

a method of line loss minimization based on analytical

method. The mathematical programming method is used

in [2] and in [3] the genetic algorithm is adopted. The

*This paper is supported by the Important Knowledge Innovation Pro-

ect of Chinese Academy of Sciences No.Y225011E

Z. P. JIANG ET AL. 741

cost minimization is also an important objective consid-

ered frequently. The representation of the cost is different

in different situation. For instance, the authors in [4]

consider the minimization of the cost from the perspec-

tive of distributed generation developers while the au-

thors in [5] consider it from that of operators, both them

adopts traditional mathematical optimization methods.

What mentioned above are all single-objective function

model and algorithm. For multi-objective programming,

in [6] the genetic algorithm based on trust region is given,

which optimizes five objectives including minimizing

power loss to find the optimal location and size of dis-

tributed generation. The randomness of load and distrib-

uted generation is considered in [7]. And its objective

function is given in the form of probability load current

in [8], in which the authors suppose that there is correla-

tion between distributed generations and loads. The

method in [9] is based on the Strength Pareto Evolution-

ary Algorithm (SPEA), and the objective function con-

tains the simple stochastic simulation of the distributed

generation and load, but this method is not superior to the

weighted single-objective programming, so the authors

suggest to adopting both of the two methods to seek op-

timal solution set. Literature [10] refers to calculate the

optimal operation of distributed generation according to

the method of multi-objective programming, with con-

sidering the uncertainty of distributed generation (e.g. the

wind power) and the relevance between the wind power

generation and the weather. Besides, in the literature, the

authors represent the changing condition of wind power

as time changes by the Markov's transition matrix. The

randomness of loads is considered when planning the

distribute d generation in [1 1] .

All the works above provide various objectives and

constrains. In most of these works heuristic algorithms

are used to solve the optimization models such as Ge-

netic Algorithm, Simulated Anneal Algorithm, and Parti-

cle Swarm Optimization Algorithm, etc. A new method

of reliability calculation of the power grid without con-

sidering the power flow calculation is proposed in [12].

However, the reliability calculation result is much con-

sistent with the actual reliability. Based on this method,

in this paper, an optimization model for minimizing the

total loss cost caused by the unsatisfied demand, and the

model is used on the IEEE-123 nodes experiment net-

work.

3. An Optimization Model Based on

Minimum Total Loss Cost Caused

by the Unsatisfied Demand

3.1. The Basic Model

Suppose there is a main power source supplying power in

the micro-grid with N load points, and the capacity of the

main power can satisfy all the load points' demand. In

order to keep the power grid stable, that is, to keep it ru n

normally when the main power source is out of order or

the power load increases suddenly at some nodes, the

distributed generation is added. Consider there is M dis-

tributed power generations will be integrated into the

power grid. Suppose each generation can directly con-

nect to only one load nodes and transport the power to

other nodes h op by hop.

For the convenience, in this problem, the capacity of

each distributed generation and the loads of each point

are supposed to be constant and only the active power is

considered. Meanwhile, according to the assumption in

[12], an important assumption in this model is that when

a node receives power from a distributed generation di-

rectly or from other nodes, it satisfies its own demand as

much as possible then transport the excess power to its

neighbor nodes. Only micro grid is studied in this paper,

so the transmission loss is not considered in the model.

The model is as follows:



()

min

..max,0

max ,0

unsatisfy

unsatisfy use

surplus use

iii

ijiikk

jNi k

surplus

ij i

jNi

ij ji

st PPP

PPP

PPxC

xor





















3.2. The Explanation of the Variables

 unsatisfy

P: The unsatisfied power demand of N o d e i



urplus

P：The residual power of Node i

 use

P：The power demand of Node i

 i

P：The total power that Node i can get

 ij

P：The transmission power from Node i to Node j

 k

C：The capacity of distributed generation k

 i

k：The weight of Node i



1distributedgenerationconnectwithnodei

lse

x





3.3. The Explanation of the Objective Function

 The objective function unsatisfy

ii indicates

kP



minimizing the total loss cost caused by the unsatisfied

demand

3.4. The Explanation of the Constraints







max ,0

unsatisfy use

PP

P: If the total power that

Z. P. JIANG ET AL.

742

Node i gets is less than the demand of node i, the unsatis-

fied demand of Node i will equal to use

PP; Else, it

will equal to 0;

nodes is adopted to carry out the simulation test, the load

and weight of the nodes are both constant and the units of

the nodes’ load and the capacity of the distributed gen-

eration are all kilowatt (kW). The network structure is

shown in Figure 1, and the parameters of the nodes are

shown in Table 1





: If the total power that



max ,0

surplus use

PPP

Node i gets is more than or equal to its demand, the re-

sidual energy of Node i will equal to ; Else, it

will equal to 0.

use

PPOn the test network of IEEE-123 nodes above, five

distributed generations are set, whose capacities are: C1

= 700, C2 = 650, C3 = 500, C4 = 350, C5 = 600 respec-

tively.

 k

C: The total received power

()

ijiik

jNik

PPx







of node i is equal to the total energy supplied by the dis-

tributed generation directly connected with node i and

the power transported from the neighbor nodes of node i.

We establish a model according to the method pro-

posed in this paper, and solve it by Lingo. The results of

the distributed generation’s placement and power trans-

mission are as follows. The place result of the distributed

generation is shown in Figure 2 and the result of the

power transmission (direction and size) between the

nodes is shown in Table 2. The final value of the objec-

tive function (that is the total loss cost) is: 6868.2. And

 ()

urplus

ij i

jNi





: The residual power of the node i

can be transported to its neighbor nodes through any way

of distribution, or keep it to itself.

 0PP: The power can only be transported in

ij ji

one direction on each line  Distributed generation P1 is placed on the node 36;

 Distributed generation P2 is placed on the node 30;

4. Solution and Simulation  Distributed generation P3 is placed on the node

160;

In this paper, the standard testing network of IEEE-123

27 26 25

29 30 250

11 14

20 19

22 21

18 35

135

48 47 49 50

36 38 39

65 64

60 160 67

5453

52 55 56

152

92 90 88

91 89 87 86

82 83

73 74

300 111 110

108

109 107

112113 114

105

106

101

102

103 104

450

100

68 69

197

151

150

61 610

251

195

451

149

350

Figure 1. The network structure of the IEEE-123 nodes.

Z. P. JIANG ET AL. 743

Table 1. The parameters of the nodes.

idload weightidload weightidload weight

1358.4141 202.7780 409.97

2407.2542203.2681401.7

3203.8543 206.5482 354.98

7359.5544 405.2684 401.96

4201.3145 354.1683 209.66

5404.9547 208.4885 201.04

6204.4346 356.2787 407.97

8407.8948 205.9588 404.14

1235 8.164970 9.258940 8.36

9202.6850 703.5790 358.82

1340 5.415140 7.819140 1.76

1435 5.015220 7.7892354.6

3435 6.825340 4.429340 3.34

1840 7.385440 6.1194358.2

1135 7.795535 1.689540 4.88

1040 3.485720 1.4996209.2

1520 7.125635 5.789820 2.64

16356.95820 8.019940 3.37

1740 2.466020 9.4110040 2.31

1920 2.075920 2.1745040 2.22

2140 5.496120 6.1210135 8.82

2035 9.646235 5.2210235 6.22

2240 4.066340 1.1110520 5.95

2340 6.276440 4.03103352.3

2435 3.016575 2.4610440 8.68

2540 7.766670 8.15106406.6

2635 3.3 6775 3.8108404.16

2835 5.556835 5.7610735 5.62

2740 7.297220 2.4910940 4.62

3135 9.029735 6.4230040 1.68

3320 9.636935 3.3711035 3.16

2940 5.927040 6.8911135 2.11

3040 2.2571207.2 11220 2.66

25040 2.347340 7.7311320 3.16

3235 3.327640 5.0511440 4.76

35208.57741051.75 135201.45

3640 3.297540 3.0614935 9.12

4035 8.337740 9.22152359.5

3735 3.198640 2.3716035 5.42

3840 9.367820 8.43197355.4

3920 4.157935 5.85

Z. P. JIANG ET AL.

744

11 14

20 19

22 21

18 35

135

27 26 25

29 30 250

48 47 49 50 51

45 46

36 38 39

65 64

60 160 67

5453

52 55 56

152

92 90 88

91 89 87 86

82 83

73 74

300 111 110

108

109 107

112113 11

105

106

101

102

103 104

450

100

68 69

197

151

150

61 610

251

195

451

149

350

Figure 2. The placement result of the distributed generation.

Table 2. The power flow transmission result.  Distributed generation P4 is placed on the node 34;

 Distributed generation P5 is placed on the node

106;

1->2 40 29->28 570 72->76 295

1->3 80 30->29 610 76->77 100

1->149 35 34->13 260 76->86 155

3->5 60 34->1555 77->78 60

5->6 20 35->40 525 78->80 40

7->1190 35->13520 86->87 115

8->7225 36->35 565 87->8975

8->12 35 36->3735 89->90 35

8->9 90 36->3860 101->102 110

9->14 70 38->3920 101->197 35

13->839040->4120 102->103 75

14->11 35 40->42 470 103->104 40

15->16 35 42->4320 105->101 180

18->13 170 42->44430 105->108 325

18->19 55 44->4570 106->105 525

19->20 35 44->47 320 106->107 35

21->18 265 45->4635 108->109 245

21->222047->4820 108->300 40

23->21 325 47->49280 109->110 205

25->23 365 49->50210 110->111 35

25->26 130 50->5140 110->112 135

26->27 60 67->72 355 112->113 115

26->31 35 67->9735 113->114 40

27->33 20 72->7340 160->67465

28->25 535

5. Conclusion

The optimal integration problem of distributed genera-

tion is one of the key issues of the smart power grids. In

this paper we propose an optimization model of placing

the distributed generation, aiming to minimize the total

loss cost caused by the unsatisfied power of every node.

Meanwhile, we use this model to a five distributed power

generation placement problem on the network of

IEEE-123 nodes. The result of the distributed generation

placement and the power transmission is got.

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