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48-50 Basic Formula of Simulation for Components of Photovoltaic System

Author: Source: Datetime: 2016-12-26 09:46:48
Solar panels

The solar panel simulations studied here are for square arrays of the same characteristic solar cell modules. The equivalent circuit of the solar cell is shown in Figure 3-5, the basic formula of its analytical formula (3-35)

I=Iph=I0{exp[q(V+RsI)/nkT]-1}-(V+RsI)/Rsh                             (3-35)

I                          Solar cell output current (operating current)
V                         Solar cell output voltage (operating voltage)
Iph                       Photogenerated current
I0                         Diode saturation current
q                          Electron charge (1.6x10-19C)
Rs                        Series resistance of solar cells
n                          Diode characteristic factor
k                          Boltzmann constant
T                         Solar cell temperature, K;
Rsh                      The parallel resistance of solar cells.


Figure 3-5 Equivalent circuit of the solar cell

In general, Rsh is negligible for monocrystalline or polycrystalline silicon solar cells.

The working voltage and operating current of the solar panels are obtained from the parallel and series solar cells which constitute the solar cells. The parallel and serial numbers of the solar cells are denoted by Ncp and Ncs respectively.

IA = NcsI                                                        (3-36)
VA = NcsV                                                       (3-37)

As shown in Fig. 3-5, the equivalent circuit of the solar cell is a current source in proportion to the intensity of sunlight and a diode connected in parallel with it, including a parallel impedance and a series impedance. In the figure, the terminal voltage Vd of the diode and the current Id flowing to the diode are given by:
 relationship of the terminal voltage Vd of the diode and the current Id flowing
This current is the diode forward current. And the current flowing to the parallel resistor is Vd / Rsh. Furthermore, Vd is given by the terminal voltage V of the solar cell and the output circuit I, i.e., Equation (3-39)

Vd = V + RsI                                                     (3-39)

Therefore, formula (3-35) gives the solar cell output current is deducted from the photovoltaic current of each cell's internal resistance loss current value obtained.

There are several methods for temperature correction of the output of solar cells, here are two methods. One is to consider the temperature characteristics of the diode method. The ideal diode characteristics are to a large extent related to the temperature characteristic of the saturation current I0. Equation (3-40) gives the temperature dependence of the saturation current.

the temperature dependence of the saturation current

Where, C1 is a constant, T is temperature; Eg0 is absolute zero (-373.15 ℃) extrapolation of the forbidden band width.

Under normal circumstances, another approach is generally used, that is measured under actual conditions converted to standard test conditions under the conditions of value, and by correction factor to make the temperature correction, but on the contrary the standard experimental conditions (3-41) and (3-42) according to the temperature at any temperature

IA=[IST+ISC(HA/HST-1)+α(T-TST)]Nmp                                  (3-41)

VA=[VST+β(T-TST)-Rsm(I-IST)-KIA/Nmp(T-TST)]Nms                 (3-42)

IST                             Output current of the solar cell module under standard test conditions;
ISC                             Short circuit current of solar cell module under standard experimental conditions;
HA                             The amount of solar radiation (1h value);
HST                            Standard solar cell surface under the experimental conditions of solar radiation (1h value);
α                                The variation value of the short circuit current ISC of the module when the temperature changes by 1 ℃;
TST                             Component temperature for standard test conditions;
Nmp                            The number of components constituting the solar panel in parallel connection;
VST                             The output voltage of the module under standard test conditions;
β                                 The variation value of the module open-circuit voltage Voc for every 1 ° C change in temperature,
Rsm                              Component series resistance;
K                                 Curve correction coefficient;
Nms                             The number of components that make up the solar panel's serial link.

The solar cell temperature is determined by meteorological conditions, it is often shown with the standard conditions of different characteristics. The temperature of the solar cell is higher than the ambient temperature. The sun rises and the wind blows down the temperature. The temperature of the solar cell typically varies in proportion to these factors. The proportion coefficient directly affected by the structure of the module, the method of setting the battery plate, so it is necessary to determine the coefficient according to technical data or experiment.

Energy storage lead - acid battery

Lead-acid battery model, can be shown in Figure 3-6 shows the equivalent circuit. Lead acid battery electromotive force to insert a DC impedance, the mathematical expression is as follows:

Vb = Eb - IbRsb                                                                           (3-43)


Vb                    The terminal voltage of the battery
Eb                     The electromotive force of the battery
Ib                      Battery charge, the discharge current (usually photoelectric is positive)
Rsb                    Internal resistance of the battery unit
Figure 3-6 equivalent circuit of lead-acid batteries
Figure 3-6 equivalent circuit of lead-acid batteries

Usually photovoltaic power generation system is part of the energy storage battery is Nbs lead-acid batteries in series, Nbp column parallel link composed of the battery, the total battery voltage VB and current IB should be:

VB = VbNbs                                                                  (3-44)
IB = IbNbp                                                                    (3-45)

Lead-acid battery electromotive force (Eb) and internal resistance (Rb), etc., with its charge state changes, the internal resistance changes are particularly large. In the state of high charge, the open lead-acid batteries due to the electrolysis of water, resulting in abnormal voltage increases. In actual simulation, the voltage can be known in two ways. The first method is obtained from the technical data or through experiments and other charges corresponding to the current state of the voltage, a list of the form of data in the use of interpolation to obtain the necessary voltage. The second method is the simulation method, the relevant constant can be related to the technical information using the least squares method to determine. The following is an example.


 use of interpolation method and simulation method

E0-----------------------Fully charged state of the electromotive force
Q(t)------------------------Discharge power, Ah;
  CT -------------------------------Maximum capacity of the battery, Ah
R0 -------------------------------constant
β -------------------------------constant
γ -------------------------------constant
ρ -------------------------------State of charge
R1 -------------------------------A correction coefficient that is accompanied by a gas generated at the time of charging;
t -------------------------------Time, h
Q(t0) -------------------------------The discharge quantity from the discharge to the charging or from the point to the discharge switching time t0,
C(Im) ------------------------------- And the discharge capacity of the average current Im between t0 and tm
CR ------------------------------- Discharge capacity at rated discharge current;
б -------------------------------constant
R1 is usually proportional to or proportional to the exponential function. The time R1 for generating the reaction gas, the amount R1 of the generated gas, and the time constant αx are substantially inversely proportional to the charging current. The following gives the book exponential function of the combination of Figure 3-7 gives the gas generation function G (t) curve.

R1= RXG(t)

G(t)=1/2+{1-exp[-αx(t- TX)]}•U(t- TX)/2+{exp[αx(t- TX)]-1}•U(t- TX)/2

In the above formula, U (t) is the stage function


Figure 3-7 Gas generation function


Figure 3-8 Equivalent circuit of the inverter


The simulation of the inverter basically takes into account the input current loss and the output current loss of reactive power loss. The equivalent circuit is shown in Figure 3-8. With a mathematical formula for that;







VINin            Inverter input voltage;
IINin             Inverter input current;
PINin            Inverter input power;
VINout          Inverter output voltage;
/IINout          Inverter output current;
PINout          Inverter output power;
ФIN              Power factor;
ηIN               Inverter efficiency;
RINin            Inverter equivalent input impedance;
PINout          Inverter equivalent output impedance.

The reactive power loss (LOIN) of the inverter, regardless of the load or not, is a constant. Circuit loss is divided into the input side and output side. For the inverter with the maximum power point tracking control of the solar panel, its input voltage is consistent with the working voltage of the maximum power point of the solar panel in the working voltage range, and can be regarded as the maximum power output. In this case, the input current becomes the current at the maximum power point of the solar panel. When beyond the operating voltage range, taking into account the voltage, current balance of the operating point, the calculation becomes necessary.

In fact, the optimal power supply tracking of the inverter is often unsatisfactory, and the operating point does not agree with the maximum power point Pmax due to the responsiveness of the tracking device and the variation of the solar radiation. Simulation of the control system is still desirable, but it should be resolved in seconds or seconds. It is also not necessary to know how much it deviates from the optimum operating point for the simulations so described. For the output side, care should be taken to control the response to the load change requirements. Output voltage control, it can be regarded as a certain value to deal with.

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