Energy and Power Engineering, 2013, 5, 1317-1323
doi:10.4236/epe.2013.54B250 Published Online July 2013 (
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
Received March, 2013
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
Copyright © 2013 SciRes. EPE
S. X. WEI, Q. J. LIU
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
Pk Pk
fP kc kckc
The parameters k, c in the equation can be figure out
by using the mean
and standard deviation
(1 )
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
We can get equation associated with reactive power, P
and V through the circuit analysis, as follows:
=V V
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
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:
Figure 1. The equivalent circuit of induction motor.
Copyright © 2013 SciRes. EPE
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
The active power of the wind turbine outpu t is derived
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].
=- 2
 
where Cm
. 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/
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
where ,
are the shape parameters of Beta distribu-
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
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
 (7)
where C
is the Photovoltaic array area and
sents efficiency. and are the parameters related
to the location and inclination of th e photovoltaic system.
Probability density function of the real power output
0.5( ')
[0,( )]
0, otherwise
tu C
cK e
if PPK
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-
Figure 2. The equivalent circuit of a single PV cell.
Copyright © 2013 SciRes. EPE
S. X. WEI, Q. J. LIU
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
 
 (9)
00 11
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:
array array
ph S
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
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
[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]:
cell losses
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
The active and reactive power generated by fuel cell
can be deri ved from Figure 3 [19, 20].
cell S
cell SS
mU V
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.
Copyright © 2013 SciRes. EPE
S. X. WEI, Q. J. LIU 1321
3.4. Micro Gas Turb
nary synchronous generator.
and excitation system.
Gas turbine works like ordi
It has a speed control system
The speed control system adjusts active power output
according to load level.
 ( 0.23)]
  (16)
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
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
X (17)
,, 1
m inm outR
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
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
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:
where X is impedance, and are t
voltage of Distribution rk anorage battery
of nd
The charge/discharge process of battery is divided into
arge battery if it detect that battery
nt violent reaction affect the
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
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.
Copyright © 2013 SciRes. EPE
S. X. WEI, Q. J. LIU
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
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
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.
[1] Mukesh Nagpal, Frank Plumtre, Richard Fulton, T. G.
Martinich, “Dispersed Generation Interconnection-Utility
Perspective,” IEEE Transactions on Industry
Applications, Vol.42, No.3, 2006,
[2] T. E. Kim, J. E. Kim, “A Method for Determining the
Introduction limit of distribution generation system in
distribution system,” 2001 IEEE, 2001.
[3] A. Losi, M. Ru
Load Flow inin Proc IEEE P
Summer Meeting, Vol. 4, Seattle, WA, July2000, pp
, Vol.17, No.3, 2002,
sso, “An Object Oriented Approach to
Distribution Systems,”
[4] Y. Zhu, K. Tomsovic, “Adaptive Power Flow Method for
Distribution System with Dispersed Generation,” IEEE
Transactions on Power Delivery
pp.822-827. doi:10.1109/TPWR
Automation of
[5] C. S. Wang, H. F. Zheng, Y. H. Xie, K. Chen,
“Probabilistic Power Flow Containing Distributed
Generation in Distribution System,”
Electric Power Systems, Vol.29, No.24, 2005, pp.39-44.
[6] A. E. Feijoo, Jose Cidras, “Modeling of Wind Farm in the
Load Flow Analysis,”IEEE transactions on power system,
Vol.15, No.1, 2000, pp. 110-115. doi:10.1109/59.852108
[7] C. S. Wang, Maliki Guindo, “Three-phase Unbalanced
Radial Distribution Power Flow Analysis with Wind
Farm Considered,” Automation of Electric Power System,
Vol.30, No.16, 2006, pp.21-26.
[8] Z. Xiang, W. Jiang, D. Xie, “Research on Stable
Operation of Grid-connected Wind Farms,” East China
Electric Power, Vol.35, No.3, 2007, pp.36-40.
[9] H. Y. Chen, J. F. Chen, X. Z. Duan, “Study on Power
Flow Calculation of Distribution System with DGs,”
Automation of Electric Power Systems, Vol. 30, No.1,
2006, pp.35-40.
[10] S. X. Wang, X. Y. Jiang, C. S. Wang, “Distribution
Power Flow Calculation with Wind Turbines,” China
International Conference on Electricity, 2006.
[11] S. Conti, S. Raiti “Probabilistic Load Flow Using Monte
Carlo Techniques for Distribution Networks with
Photovoltaic Generators,” Sol. Energy, 2007.
[12] O. Wasynczuk, “Modeling and Dynamic Performance of
a Line-commutated Photovoltaic Inverter System,”IEEE
Transactions on Power Conversion, Vol.4, No.3, 1989,
[13] L. Zhang, A. Al-Amoudi, Y. F. Bai, “Real-time
Maximum Power Point Tracking for Grid-Connected
Photovoltaic Systems,” Power Electronics and Variable
Speed Drives, 2000, pp.124-129.
[14] D. J. Zhou, Z. M. Zhao, L. B. Wu, “Analysis
Characteristics of Photovoltaic Arrays Using Simulation,”
Journal of Tsinghua University (Natural Science), Vol.47,
No.7, 2007, pp.1109-1112.
[15] J. D. Mondol, Y. G. Yohanis, Brian Norton, “Comparison
of Measured and Predicted Long Term Performance of a
Grid Connected Photovoltaic System,” Energy
Conversion and Management, Vol. 48, No. 4, 2007,
pp.1065-1080. doi:10.1016/j.enconman.2006.10.021
[16] Shigenori Naka, Takamu Genji, Yoshikazu Fukuyama,
“Practical Equipment Models for Fast Distribution Power
Flow Considering Interconnection of Distributed
Generators,” Power Engineering Society Summer Meeting,
IEEE. Vol. 2, July200 1, pp.1007-1012.
[17] J. Yao, D. Popovic, “Stability of a MV Distribution
Network with Electronically Interfaced Distributed
Generation,” Power Engineering Society General
Meeting IEEE, June2004, pp. 2162-2167.
[18] Y. H. Li, S. Rajakaruna, S. S.Choi, “Control of a Solid
Oxide Fuel Cell Power Plant in a Grid-Connected
Sys te m, ”IEEE, Transactions on Energy Conversion, Vol.
Copyright © 2013 SciRes. EPE
S. X. WEI, Q. J. LIU
Copyright © 2013 SciRes. EPE
22, No. 2, 2007, pp.405-413.
[19] M. Y. El-Sharkh, A. Rahman, M. S.Alam, “Analysis of
Activeand Reactive Power Control of a Stand-Alone
PEM Fuel Cell Power Plant,” IEEE Transactions on
Power Systems, Vol.19, No. 4, 2004, pp. 2022-2028.
[20] Rekha, T. Jagaduri, Ghadir Radman, “Modeling and
control of distributed generation systems including PEM
fuel cell and gas turbine,” Electric Power System
Research, Vol. 77, No.1, 2007, pp.83-92.
[21] J. Zeng, B. H. Zhang, C. X. Mao, et al., “Use of Battery
Energy Storage to Improve the Power Quality and
Stability of Wind Farms,” International Conference on
Power System Technology, pp.1-6.