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

0

01

unsatisfy

ii

i

unsatisfy use

ii

surplus use

iii

ijiikk

jNi k

surplus

ij i

jNi

ij ji

ik

kP

st PPP

PPP

PPxC

PP

PP

xor

i

3.2. The Explanation of the Variables

unsatisfy

i

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

urplus

i

P：The residual power of Node i

use

i

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

0e

lse

ik

x

3.3. The Explanation of the Objective Function

The objective function unsatisfy

ii indicates

i

kP

minimizing the total loss cost caused by the unsatisfied

demand

3.4. The Explanation of the Constraints

max ,0

unsatisfy use

ii

PP

i

P: If the total power that

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