Review of Modeling Methods of Distributed Energy Supply System Connected to the Grid

doi:10.4236/epe.2013.54B250

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Energy and Power Engineering, 2013, 5, 1317-1323

doi:10.4236/epe.2013.54B250 Published Online July 2013 (http://www.scirp.org/journal/epe)

Review of Modeling Methods of Distributed

Energy Supply System Connected to the Grid

Shengxuan Wei, Qianjin Liu

School of Electric Power, South China University of Technology, Guangzhou, China

Email: [email protected]

Received March, 2013

ABSTRACT

At present, the development of distribution network can’t meet the requirements of rapid economic development. The

traditional single energy supply is difficult to meet the request, and distributed energy supply has a lot of advantages

compared to it, particularly it's close to the end users, and they have been developed well and applied widely in recent

years. This paper summarizes the features and current development of the distributed energy supply, and mainly

describes the grid-connection model of distributed energy supply. Base on the mathematic grid-connection model of

distributed power sources with different generation principles as well as that energy storage, the treatment of these

models in distribution network power flow analysis is also presented.

Keywords: Modeling; Distributed Energy Supply; Grid-connection

1. Introduction

Recently, centralized power generation, long-distance

transmission and grid interconn ection constitute th e main

way of electricity production, transmission and

distribution. Long-distance transmission has its

advantages, but there are also some drawbacks, including:

Cannot agilely tracking load changes, local accident easy

to expand to a major accident. In addition, centralized

power generation consume a large number of fossil fuels,

produce large amounts of greenhouse gases and

substances harmful to the environment. For the purpose

of environmental protection, it is necessary to use more

wind, solar and other renewable energy. Therefore, the

interest in using renewable energy and

small/medium-sized generators are increasing, especially

in the increasingly rapid development of wind power and

photovoltaic power generation. A lot of research and

practice in this area have been done. At the same time,

the new technology of using conventional fossil fuels,

fuel cells and microturbines is also object of the study.

They can reduce the emission of pollutants greatly. Most

experts agree that combination of large power grid and

distributed power generation, together with the

appropriate energy storage equipment, so as to save

investment, reduce energy consumption, improve power

system reliability and flexibility, and are the keys to the

development of the electric power industry.

After the penetration of distributed energy systems, the

characteristics of single-power and radial will change.

2. Research Status of Distributed Power and

Energy Storage Battery

Currently, the exact definition of distributed power

supply is not recognized. The common definition is that

generated power from 1 kW to 50 MW of small

independent power module. They are typically installed

near the user, in order to meet the specific needs of the

user or to support the economic operation of the existing

distribution netw ork [1].

At present, the widely use of distributed power supply

system mainly contain wind power, photovoltaic cells,

fuel cells, micro turbines and storage batteries. The

distribution network is generally designed to radiate, user

side does not have any power supply. Penetration of

distributed power makes the network have more than one

power supply node. This will create difficulties for the

operation of the power grid, will seriously affect the

distribution network power flow, increase short-circuit

current of the power distribution network, and make

voltage regulation beco mes difficult. In order to improve

the power quality and operational reliability, its install

location and capacity must be optimized.

Thus, in order to apply to the distributed power access,

the original method of power flow calculation applied to

traditional radial distribution network planning and

optimization must be improved [2].

[3] Proposed an object-oriented modeling method and

a reconfiguration algorithm for radial distribution

network which take into account the distributed power

S. X. WEI, Q. J. LIU

1318

access. The method has strong scalability and

applicability that it can easily connect a variety of

different interfaces of distributed power.

A power flow calculation method based on the com-

pensation method presented in [4]. The whole model

includes the three-phase unbalanced load, circuitries,

capacitors, transformers and a distributed power supply.

This model’s rapidity has been verified in case of

ensuring accuracy. At present, the research literature on

distributed power mainly concentrated in a radial

network with a single distributed power source, seldom

consider the characteristics of the distributed power itself.

Interaction between distributed power and energy storage

device may affect distribution network planning, power

quality and voltage stability. The above study of the

distribution network cannot be separated from the flow

calculation. Different distributed power and energy

storage device access to distribution networks will have

different effects on the distribution power flow.

Therefore, the establishment of mathematical models of

different types of distributed power source/energy

storage device connected to the grid, has important

significance on the topological analysis, power flow

calculation, relay protection, and the planning and

configuration distribution network.

3. The Mathematical Grid-connection Model

of the Distributed Energy Supply System

3.1. Wind power

The biggest difference between wind power and conven-

tional power generation mode is the fluctuation of output

power caused by the uncertainty of the input (wind

speed). Accordingly the accurate prediction of power

output of wind turbine is the key to establish wind gen-

erator model.

A stochastic model of wind turbine has been estab-

lished, which is based on Weibull model [5]. Weibull

model is considered to be the most suitable model for

statistical description of the probability density function

of wind speed. Under normal circumstances, the wind

speed estimates range between the cut-in speed and

cut-out speed. When the request for accuracy is not rigid,

the output power of wind turbine was approximately

linear with wind sp eed. Th er efore, th e probab ility den sity

function of the wind generator output power can be

written as:

11 1

()()exp[()

Pk Pk

fP kc kckc





]

(1)

The parameters k, c in the equation can be figure out

by using the mean



and standard deviation



1.086

()k







(1 )

rci

kvv

kkv









where r is rated power of wind turbine, r and ci

are cut-in wind speed and rated wind speed respectively.

Pv v

The wind generator generally uses asynchronous

motor, which does not produce reactive power and need

to absorb reactive power from grid. Assume that the

reactive power can be compensated and power factor

keeps stable, then the wind generator can be seen as a PQ

node. The node mode l of asynchronous wi nd generator is

shown in Figure 1 [6].

The relation between the reactive power Q and P, V

was obtained through the analysis of the circuit, as

follows.

We can get equation associated with reactive power, P

and V through the circuit analysis, as follows:

=V V

XX X

 (2)

where C

, m

are the generator-side shunt capaci-

tance and excitation reactance respectively. 1

, 2

are stator leakage reactance and rotor leakage reactance

respectively. 12

XX.

Thus, the characteristic of the PQ node can be ob-

tained, by calculating relation curve of P, Q node and

input mechanical power.

[7] Put forward the positive and negative sequence

circuit of wind turbines, it consid ered the influence of th e

fan slip, and use symmetrical component method to ana-

lyze the equivalent circuit of the wind generator. The

function about the slip and the positive/negative se-

quence current of rotor can be determined, by calculation

of the input impedance in the positive and negative se-

quence circuit. Then the input DC value can be calcu-

lated according to the positive and negative sequence

voltage value. Base on neglecting the loss, linked the

output of the wind turbine with wind input curve, the odd

equation can be written as:



 (3)

Figure 1. The equivalent circuit of induction motor.

S. X. WEI, Q. J. LIU 1319

The slip s can be calculated by Newton’s method, and

then the node voltage and power distribution value which

are need in power flow calculation.

A kind of RX model of wind turbine was suggested in

[6,8].

The active power of the wind turbine outpu t is derived

as:

e(1) /

PIRs s (4)

where r

and are rotor current and rotor resistance

respectively. r

This power and mechanical power that generated by

wind turbine should be equal. When they are not equal,

we can balance the wind turbine mechanical power and

motor’s output power through the iterative correction of

slip s.

According to the equivalent circuit of the induction

motor, the expression of reactive power on the voltage

can be launched [9].

2242

=- 2

VVVPX

QXX

 

2

(5)

where Cm

PCm

. It is being used as a static volt-

age characteristic node in distribution network to deal

with in power flow calculation.

The methods described above treat the power factor of

wind turbine as a fixed value, but the actual value of

power factor may not be kept constant.

Therefore, the P-Q-U model of asynchronous genera-

tor was proposed [10].

Based on considering the slip, it derived the expres-

sions of wind turb ine ou tput power through an alyzing the

circuit diagram. The expressions of both the slip and the

power factor are also obtained. In the case of a given

wind speed, it is possible to get each moment the output

of the active and reactive absorption, and accordingly

calculate the power factor.

The power factor is confined within an allowable limit

through the shunt capacitance sets real-time turned on/

off.

3.2. Photovoltaic Cell Power Generation

Photovoltaic power generations are mainly divided into

two types: off-grid photovoltaic power generation system

and the grid-connected photovoltaic power generation

system. And grid-connected photovoltaic power genera-

tion is the mainstream of the development of photovol-

taic power generation. PV cells are connected to the grid,

electricity generated directly deliver back to the grid.

Thus, wind turbines can always run in the power factor 1,

and it avoid the problems like that energy storage and

additional facilities bring.

Similar to the modeling approaches of wind power

random characteristics, the output of PV cell is the ran-

dom output, which is proportional to the light intensity.

In a certain period of time, the light intensity can be

modeled as Beta distribution. Therefore, the output

power of the battery also satisfies the Beta distribution.

Its probability distribution function is as follows:

()

()( )(1)

()() MM

MMM

fP RR

















(6)

where ,





are the shape parameters of Beta distribu-

tion.

P is the total output power of Photovoltaic array.

R is the maximum output power of PV array.

Another model of random power flow is raised in [11].

The main factor affects the intensity of solar radiation is

clouds.

It presents a clearness index Kt, used to indicate the

ratio of the radiation intensity on ground plane and the

total extraterrestrial radiation intens ity. The output active

power of PV sy st em is:

(')

VCC tt

PAIATKTK





 (7)

where C

is the Photovoltaic array area and



repre-

sents efficiency. and are the parameters related

to the location and inclination of th e photovoltaic system.

T'T

Probability density function of the real power output

is:

0.5( ')

[0.5(')],

()

[0,( )]

0, otherwise

tu C

PVPV tu

cK e

KAT

fPV

if PPK























(8)

where '



, 2

 

 , tu

is the maxi-

mum value of t

, is the parameter of probability

density function. C

The time distribution of active power output of these

two random power flow model can be obtained by using

the Monte Carlo method.

Another model of photovoltaic cells was given [12-

14].

Figure 2. The equivalent circuit of a single PV cell.

S. X. WEI, Q. J. LIU

1320

The mathematical model of a single photovoltaic cell

can be derived through the circuit analysis. Its circuit

diagram is as follows:

0{exp[() /]1}

()/

ph S

SSK

IIIqVIR AkT

VIR R

 

 (9)

00 11

()exp[()]

rrr

TkAT





(10)

where T is the temperature of the battery and the

parameter is relevant to the environment. The remaining

parameters are fixed parameters associated with materi-

als and design of photovoltaic cells.

Thus, suppose the number of photovoltaic cells is n

and the number of parallel modules is m, such a PV array

output power is:

[{exp[()/]1}

()/]

array array

ph S

SSK

PV ImVnI

mn IIq VIRAkT

VIR R





(11)

The equation above can be solved by using Newton

iteration. The PV cell connected to the grid through the

inverter. The model above considers the efficiency of the

rectifier as constant for simplicity. In fact, the efficiency

of inverter will change with the input power. [15] Had

proposed the correction relation equation of input power

of the inverter.

0.015 0.980.09

inv npv npv n

PP  (12)

Variable is the P.U. value which relative to the rated

capacity.

The input variable in th e right hand side of equation is

the output power of PV array. The output variable in left

side of equation is the input power.

Generally, only the active power of photovoltaic cells

can be used in distribution network. The possible maxi-

mum power of output can be achieved through tracking

method of maximum power point. However, in the case

of part of output active power lose; it can make the grid

operating more stable and economic by controlling the

inverter.

[16] Put forward the model which limits the output of

inverter. It can be divided into a current control type and

a voltage control type. In the current control type, it can

be treat as the PI node and its output active power and

the injection curren t is constant.

The reactive power injections can be calculated from

the following formula.

222 2

()QIefP (13)

where is the constant node active power value,

the constant current value, and e, f are the vectors of

calculating voltage. If the model is of the type of a

voltage control, inverter will be treating as a PV node,

just like generator node. When the input current reaches

to the borderline value, it will change into PI node.

3.3. Fuel Cell

Fuel cell has the characteristic of small volume and high

efficiency. Its theoretical efficiency can reach to ninety

percent. Its power supply is reliable, low noise, high

power quality and more automatic. The efficiency of fuel

cell which capacity ranges within 250kW to 5MW is

similar to the efficiency of thermal power generator

which capacity rang es within 300-500MW.

These fuel cell need to have fuel such as hydrogen, but

it drive motor not by burning. In the presence of a cata-

lyst, it reacts with oxygen directly. Therefore, the fuel

cell is essentially a chemical energy generation.

With regard to the fuel cell accessing to distribution

network, the first need to consider is the characteristics

of its generating electricity.

The equation of output voltage of fuel cell power

system is as follows [17, 18]:

[ln]

cell losses

UNE E



(14)

Where N is the number of series fuel cell, 0 is the

single battery standard potential, T is the temperature and

is the corr espo nding g a s mo lar concen tratio n. Th e last

one is potential loss caused by system.

The output of fuel cell is DC, so it needs to be

converted into AC before connected to the distribution

network.

The active and reactive power generated by fuel cell

can be deri ved from Figure 3 [19, 20].

sin

cell S

cell SS

mU V

mU VV















(15)

where X is the line impedance from the fuel to grid, S

is the voltage of distribution network side. It controls the

output of active and reactive power through control the

parameters and



. This method is similar to the

principle of conventiona l generator’s power r egulator.

Therefore, fuel cells in power flow calculation can be

treating as a PV node. But the reactive power output of

inverter is limited. When reactive power limits are

exceeded, it will be transformed into PQ node.

Figure 3.

S. X. WEI, Q. J. LIU 1321

3.4. Micro Gas Turb

nary synchronous generator.

and excitation system.

ine

Gas turbine works like ordi

It has a speed control system

The speed control system adjusts active power output

according to load level.

[1.3





 ( 0.23)]

  (16)

where



into electric p

is the efficiency of turbine mecha

ower, the fuel ratio required for no-load

nical power

operatin is 0.23,

W is fuel flow, N is rotational speed.

Microturbine combines th e traditional gas turb ine with

the recuperator, panent magnet generator, variable erm

ower frequency current before import to

equency regulation technique and intelligent control

technology.

The current generated by microturbine need to

transform to p

stribution network. Whereas, just like centralized

generators, its active power can still be adj usted:

()

fi i

QV 



X (17)

,, 1

m inm outR

ww

PP g

 (18)

where is the engine power,

is the motor

outputr, and are tinput and output powe

of ,min ,mout

power engine respectively, w

PP he

and

w are the

angular velocity of the sen end and receiving end of

power units, M and R are the torqe and imdance of

generator respectively

Excitation device and power electronic device keep the

output voltage of gas t

ding u pe

urbine stable. For this reason, gas

atical Model of Energy

Storage Device Distributed Access grid

unthe

Battery model is the most studied storage way. Its unit

ow. [21] Put forward with a model

rbine generator can be treating as a PV node. For the

voltage deviation appear in process of iterative algorithm,

the reactive power can be adjusted by sensitivity matrix.

In the iterative process, the node type converts between

PV node and PQ node once the reactive power or voltage

exceeds the limit.

4. The Mathem

Both wind power and solar cell h ave the characteristic

stable power output. Energy storing device store

unstable energy and release energy according to demand.

Sometime power in grid is insufficient, and is surplus

in other times. If the energy storage devices connect to

stribution network, it will play an effective ro le in load

staggering management. At present, the most common

type of distributed energy storage is storage battery.

4.1. Battery Model

energy storage cost is l

of battery cell access to distribution network.

The current of battery itself is DC. Hence, it need the

converter' help to access to grid. The active and reactive

power through inverter and grid is as follow:

sin



os)

RRS















(19)

where X is impedance, and are t

voltage of Distribution rk anorage battery

of nd

The charge/discharge process of battery is divided into

oat

arge battery if it detect that battery

nt violent reaction affect the

ode

to 80 percent. After this, it

netwo U

d sthe output

respectively. The exchange active a reactive power

between battery and grid can be adjusted through

controlling the phase shift and the output amplitude of

inverter.

4.2. The Charge/Discharge Process of Battery

three stages: main charge mode (constant current), fl

charge mode (limitary-voltage) and even charge mode

(constant voltage).

4.2.1. Main Charge Mo de

The system will ch

lack of electricity. To preve

battery life, it uses constant current charging mode.

The current rating is commonly 0.1C. Where, C is the

capacity of battery pack. The battery can b e topped up in

10 hours if it has been charging in this way. For constant

current charge, the voltage of battery pack will continue

to rise. When it rises to no minal v oltage o f sin gle b attery,

float charge mode will displace main charge mode.

4.2.2. Even Charge Mode

Experiments show that charging in constant current m

need eight hours to get back

adopts to even charge mode automatically. The limit

voltage is 24n, where n represent the number of a pack.

This process takes almost 10 hours, and the charging

current reduces gradually. When the current is 0.01 C,

the battery is fully charge. At this point, the float charge

mode begins.

Figure 4.

S. X. WEI, Q. J. LIU

1322

4.2.3. Float Charge Mo d e

The float charge mode is the main way of long-running

The voltage of float charging is 235n. The system

changes it into main charge mode when the capacity is

shortage cause by outrage.

The battery can discharge with constant current. It can

keep the output power constant for a considerable time.

5. Summary and P

merous model of different

more and more attention.

se asynchronous gen-

d as accessing to

rospect

This article summarizes nu

electric-generation principle of distributed energy supply

access grid. They include distributed power supply and

distributed storage system. For the study of distributed

energy supply system attract

Distributed energy access to distribution network is the

future trend of the development of the power system.

Wind power generator mainly u

erator model, generally considere

dis-

tribution network directly. According to the needs of the

calculation accuracy, they can be handled as PQ or PQU

nodes. For photovoltaic power generation, the main con-

sideration is modeling of the relationship between the

output active power and sunshine intensity. In the case of

special requirements, it can adjust the reactive power by

using power electronic device. The modeling of the fuel

cell is that connect the battery to grid through the

switching of electric power electronic device, which con-

trol the output active and reactive power. The modeling

of microturbine is similar to the general synchronization

generator, but need to consider the effects produced by

power electronic control unit. Storage battery also need

power electronic device to access to distribution network,

and to take reasonable charge and discharge model ac-

cording to the different stages of charge and discharge.

According to the need of analysis and control of distrib-

uted energy supply system accessing to grid, we need to

build a unified mathematical model which consider dif-

ferent power generation principle. This model will pro-

vide a basis for power flow analysis, short-circuit current

calculation as well as a variety of advanced analysis

software for transmission and distribution network.

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