Download Simulation and Mathematical Modelling for Grid

Sept.3-5, 2013, China
AORC-A-6-0002
CIGRE-AORC 2013
Simulation and Mathematical Modelling for Grid-connected
Photovoltaic Power System Based on ADPSS
Xiaowei Wang 1, Xiaobo Duan 1, Xinkui Xi 2, Zhengang Shi 1，Wenping Hu 1
1 Hebei Electric Power Research Institute
2 Hebei Electric Power Corpration
China
SUMMARY
The three-phase grid-connected photovoltaic power system includes MPPT and currentcontrolled voltage source inverter. The photovoltaic arrays maximum power point tracking
is realized applying the former boost circuit. A mathematical model for photovoltaic power
system based on the three-phase grid-connected photovoltaic power system is developed.
The mathematical model for photovoltaic power system is developed applying Matlab which
includes photovoltaic array, Maximum Power Point Tracking (MPPT), DC/DC and the inverter
system applying voltage and current loop control. The simulation results show that the
mathematical model can reflect characteristics and functions of the actual photovoltaic power
system precisely. And it can be used in the simulation on grid-connected photovoltaic power
system. After the precise mathematical model is established, the UD (user defined) model of
grid-connected photovoltaic power system is established based on PSASP. A effective tool is
given for studying the interrelationship between PV system and power grid . And it can also
confirm the capacity of grid-connected PV power system. The ability of photovoltaic power
sytem connected with grid is improved. And the ability to run stably is improved also after
the photovoltaic power sytem is connected with grid. It adapt to the requirement of vigorous
development solar energy. It plays an active role to speed up the construction of smart grid.
KEYWORDS
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Grid-connected Photovoltaic Power System; MPPT; Inverter System; Mathematical Modeling;
Matlab； Simulation
I INTRODUCTION
The output of photovoltaic power is intermittent, periodic and random. A series of problems
will be brought to power system planning, operation control and management along with the
large scale photovoltaic power and large-scale building-integrated photovoltaic power are
connected to power grid. The study on the basic principle of photovoltaic power generation
and the establishment of the mathematical model of photovoltaic power are significant. They
are important for the study of the effect on the power system with penetration of photovoltaic
power system. It also adapts to the trend of vigorous development the new energy in China.
The necessary technical support is supplied for secure and stable operation while large
capacity new resource connecting into power grid. There isn’t photovoltaic power system
model in common power system analysis software package in the domestic now. Therefore,
it is very important to establish model of PV and realize its control law in the software. It will
provide important theoretical support and calculation tool for the research and planning of
PV. A simulation module of photovoltaic system is added in PSASP in this project. And it can
be called easily in the program. It has laid the foundation for digital simulation of photovoltaic
power generation in the future.
II ESTABLISHMENT OF THREE-PHASE GRID-CONNECTED PV SYSTEM MODEL
IN MATLAB
First, the basic characteristics, actual operation characteristics and control methods are
researched for each main component in PV system, and then realistic mathematical model
is established according to system’s basic structure and principle. Three-phase gridconnected PV system model is established in MATLAB and validated with simulation.
The grid-connected PV system is generally composed of four parts, which are PV array
module, inverter, AC circuit and controller. The inverter reverses the power generated by
PV cell into sinusoidal current which is connected into grid. The controller is to control the
PV cell maximum power point tracking, the grid-connected power from inverter and the
current waveform, so then it makes the power transferred to grid balance with the maximum
electrical power from PV array module. In terms of the structure of energy conversion, the
present grid-connected PV system can be divided into single-stage energy conversion and
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dual-stage energy conversion according to the number of stages. The main research in this
paper is dual-stage grid-connected system, and the structure diagram for dual-stage energy
conversion is shown in Fig.1. Dual-stage grid-connected PV system is mainly composed of
PV cell array, DC/DC converter, DC/AC PV grid-connected inverter and controller and so on.
Its working principle is to transform the DC generated by PV cell array into that in another
voltage level through DC/DC converter, which is generally a conversion with voltage boosted.
And then the DC is transformed into AC further through DC/AC PV grid- connected inverter,
and the AC is input into power grid.
Fig. 1. The structure diagram of dual-stage grid-connected PV system
The first-stage conversion needs to realize maximum power tracking function for PV cell
array at the same time. The second-stage PV grid-connected inverter is to reverse the DC
in DC bus into AC, which is provided for local load. It feeds the excess energy into grid and
realizes the voltage stabilization function for middle DC bus.
1 PV Array Simulation Model
PV array model is composed of a large number of PV modules, and the mathematical
expression for PV array is as follows.
Where,
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PV array model is established in matlab/simulink through the derivation of formulas.
2 The simulation model of MPPT function model
Based on the PV cell simulation model above, the S-function is written with the tool of
simulink, and then the simulation model of MPPT is established. The input of S-function is
the voltage and current which is from PV cell array and the output could be the reference
voltage or current for grid-connected control method.
The strategy of MPPT detects the output power of PV array in real time, which uses certain
control algorithm to predict the maximum possible output power under the present operating
mode. And then it could meet the requirement of maximum power output by changing the
present impedance. In this paper, MPPT is realized with the disturbance observation method
and the DC/DC circuit is used for maximum power tracking. PV array is influenced by the
change of sunlight intensity and ambient temperature, so the output voltage and current
is constantly changing and the equivalent resistance is constantly changing too. DC/DC
converter is added between PV array and load. The duty cycle of power switching device in
DC/DC converter circuit is adjusted to regulate the external load, which makes the external
load equal to the equivalent resistance of PV array and the external load obtains maximum
power, so the purpose of PV array maximum power point tracking is achieved.
3 Inverter system model
The whole idea of PV inverter system is illustrated as follows. The post-circuit controls the
grid-connected current to track the command current and it also controls the voltage stability
of capacitor C2. The Pre-Boost circuit adjusts the output voltage of PV array by regulating
the duty cycle of full-controlled device S to realize MPPT. The method of three-phase gridconnected control system in this paper has inner-loop and outer-loop control. The outer-loop
control is voltage control loop, which controls DC/DC output voltage to track the specified
voltage U*dc by a PI regulator. The inner-loop control is current control loop, which uses
current-controlled voltage source inverter to decoupling control the grid-connected current
of d-q axis by two PI regulators in the synchronous rotation coordinate system. The d-axis
current adjusts the active power output of PV inverter, which makes the PV array work at the
maximum power operating point. While the q-axis current adjusts the reactive power output
of PV inverter and controls the gird-connected power factor. The diagram of control part in
grid-connected PV system is shown in Fig.2.
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4 Simulation analysis
Based on the analysis for various models and control part in the PV system above, the
dynamic model for grid-connected PV system is established with matlab/simulink, which is
shown in Fig.3.
The system takes PV array as input source and supplies power for three-phase inverter
system through Boost circuit. The grid voltage is 380V. The improved conductivity method for
MPPT controller is written by S-Function. The voltage at maximum power point is 348V and
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the maximum power is 4780W. The parameters in Boost circuit are as follows: C1=1000μF,
L=2.5mH, C2=2600μF, AC filtering inductance L=10H, equivalent resistance R=0.1Ω. The
parameters of controller Cdi(s) are that KPd=0.03, KId=0.8. The parameters of controller
Cdv(s) are that KP=0.02, KI=8.
a) Steady-state simulation
After a few cycles, the inverter system makes the gird-connected current and the system
voltage have same frequency and phase through the phase lock link. When the light intensity
is 1kW/m2, the grid A-phase voltage from 0.2s to 0.4s is shown in Fig.4-(b) and the gridconnected current whose phase is identical with the voltage is shown in Fig.4-(a).
It is known from above simulation that the pre-inverter system realizes the dynamic tracking
for PV array maximum power point voltage well through maximum power point tracking
control. The post-inverter system uses voltage and current double closed loop control
algorithm, which guarantees the grid-connected current in sync with the system voltage.
b) Transient simulation
In Fig.5, it shows that the transient changing process of PV system voltage and current when
the AC system has 0.01-second three-phase short circuit fault. The AC parameters between
PV system and three-phase short circuit point are that R1=0.1273Ω,X1=9.337mH. It is known
from the waveform that when the PV system has three-phase short circuit fault, its voltage
and current would return to steady state based on the regulation effect itself after 0.04-second
transient process.
Fig.4 The simulation waveforms of grid-connected current
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Fig.5 The simulation waveform of grid-connected current and grid voltage when the threephase short circuit fault has occurred
Based on the transient simulation analysis, it is gotten that the grid-connected PV
system should be able to return to steady state quickly after the change of light intensity.
Furthermore, when the system has short-term short circuit fault, the short-circuit current
should not have significant influence on PV system or power grid and it should return to
synchronous operation state quickly.
III ESTABLISHMENT OF THE UD MODEL OF PV SYSTEM IN PSASP
In the paper above, a complete three-phase grid-connected PV system model is established
by the tools of Matlab/Simulink and Sympowersystem. It validates the grid-connected PV
system maximum power tracking and the inversion output, and takes optimization design
for system parameters through a large number of simulations. The UD model of PV system
is established in PSASP, which makes it have some PV generation simulation ability. The
transfer function of each main part in PV system is constructed first, and the model of PV
system is added in PSASP program based on designed model framework and transfer
function. The model is taken for simulation test according to the principle of PV generation,
and then the model’s correctness is validated. Moreover, the model parameters are adjusted
in the validation process, which make the simulation results tend to accurate.
The so-called user-defined modeling is that users design various models according to their
demands of calculation and analysis and they don’t need to know the internal structure
or programming. Their designs use the concepts that engineers are familiar with and the
methods easy to grasp. These models could simulate any system component, automatic
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device and control function. When users establish the UD model of PV system, they
establish mathematical models of simulation components first, draw function block diagram,
build connection relationship between function block and specify the system input-output
relationship. And then they establish the user-defined model and balance initial values. Initial
values balance is to deal with the model, so the output values from each block of model are
reasonable. It makes the model’s initial output coincide with the initial state values of stability
calculation, which ensure the validity of stability calculation.
The UD model of PV system is integrated into PSASP program, which could be public
resources for other power grid or calculation. It is realized to call the PV system model by
filling out the model’s calling data. Calling data is that the model’s application location is
specified and the concrete buses and branches which used for model are given, so that it
is convenient to make calculation for the model. The grid-connected buses of PV station
are set in the "Basic data" and "Bus data". The PV stations are set in the "Generator and
regulator data" of "Basic data". The synchronous machine model uses PV station model
and the parameters of PV station are entered and modified by clicking the button of edit
parameters. After the entering and editing for calling data, users could make actual grid
calculation. It is needed to refresh the power flow database first, introduce the PV station
model into calculation and modify the power flow data properly, and then the power flow
could be calculated. It is turned into transient stability calculation after power flow calculation.
Users should refresh the power flow work which the transient stability work bases on, and
then they could take various transient stability calculation and analysis, such as setting grid
fault, setting node disturbance and calling other UD models and so on. When the calculation
is finished, it is realized to output the model’s variables through view mode.
IV CONCLUSION
In this paper, the three-phase grid-connected PV control system is realized by using the
Pre-Boost circuit, which combines the PV array maximum power point tracking with the
current-controlled voltage source inverter. On the base of the analysis for three-phase gridconnected PV system, the PV system dynamic simulation models are developed in matlab/
simulink, which includes PV array model, PV array MPPT model, DC/DC boost circuit and
inverter system with voltage-loop and current-loop control. The simulation results indicate
that the developed models can reflect the features and functions of PV system accurately
and they could be used for the simulation research of PV grid-connected generation. The UD
model of grid-connected system is established in PSASP based on the correct mathematical
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model. The UD model is user-defined and its correctness is validated through simulation. The
PV system simulation models are developed in PSASP and they could be called in program
conveniently. However, there is no PV system model in the domestic existing various power
system analysis software package. So the completion of this project enriches the program's
function, which is suit to the national smart grid development needs and lays the foundation
for the future PV generation digital simulation research work. Based on the PV system model
developed in this project, the security and stability of whole grid could be analyzed and
researched when the PV system is connected into grid. Then it could provide predictable
solutions for the stability problem caused by PV system grid-connected, which improves
the ability to connect PV system into power grid and the stable operation ability after gridconnected. This project suits our development needs of exploiting solar energy resources for
generation vigorously, so it has positive role to accelerate the development of smart grid.
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Short Bio-data of Main Author
Xiaowei Wang (1970---), the engineer of Hebei Electric Power Research Institute, mainly
engaged in power system simulation .
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