4850 Basic Formula of Simulation for Components of Photovoltaic System
Author: Source: Datetime: 20161226 09:46:48
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 35, the basic formula of its analytical formula (335)
I=I_{ph}=I_{0}{exp[q(V+R_{s}I)/nkT]1}(V+R_{s}I)/R_{sh } (335)
I Solar cell output current (operating current)V Solar cell output voltage (operating voltage)
I_{ph} Photogenerated current
I_{0} Diode saturation current
q Electron charge (1.6x1019C)
R_{s} Series resistance of solar cells
n Diode characteristic factor
k Boltzmann constant
T Solar cell temperature, K;
R_{sh} The parallel resistance of solar cells.
Figure 35 Equivalent circuit of the solar cell
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 N_{cp} and N_{cs} respectively.
I_{A} = N_{cs}I (336)
V_{A} = N_{cs}V (337)
As shown in Fig. 35, 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 V_{d} of the diode and the current I_{d} flowing to the diode are given by:
This current is the diode forward current. And the current flowing to the parallel resistor is V_{d} / R_{sh}. Furthermore, V_{d} is given by the terminal voltage V of the solar cell and the output circuit I, i.e., Equation (339)
V_{d} = V + R_{s}I (339)
Therefore, formula (335) 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 I_{0}. Equation (340) gives the temperature dependence of the saturation current.
Where, C_{1} is a constant, T is temperature; E_{g0} 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 (341) and (342) according to the temperature at any temperature
I_{A}=[I_{ST}+I_{SC}(H_{A}/H_{ST}1)+α(TT_{ST})]N_{mp} (341)
V_{A}=[V_{ST}+β(TT_{ST})R_{sm}(II_{ST})KI_{A}/Nmp(TT_{ST})]N_{ms} (342)
WhereinI_{ST} Output current of the solar cell module under standard test conditions;
I_{SC} Short circuit current of solar cell module under standard experimental conditions;
H_{A} The amount of solar radiation (1h value);
H_{ST} Standard solar cell surface under the experimental conditions of solar radiation (1h value);
α The variation value of the short circuit current I_{SC} of the module when the temperature changes by 1 ℃;
T_{ST} Component temperature for standard test conditions;
N_{mp} The number of components constituting the solar panel in parallel connection;
V_{ST} The output voltage of the module under standard test conditions;
β The variation value of the module opencircuit voltage Voc for every 1 ° C change in temperature,
R_{sm} Component series resistance;
K Curve correction coefficient;
N_{ms} 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
Leadacid battery model, can be shown in Figure 36 shows the equivalent circuit. Lead acid battery electromotive force to insert a DC impedance, the mathematical expression is as follows:
V_{b} = E_{b}  I_{b}R_{sb }(343)
Wherein
V_{b} The terminal voltage of the battery
E_{b} The electromotive force of the battery
I_{b} Battery charge, the discharge current (usually photoelectric is positive)
R_{sb} Internal resistance of the battery unit
Figure 36 equivalent circuit of leadacid batteries
Figure 36 equivalent circuit of leadacid batteries
Usually photovoltaic power generation system is part of the energy storage battery is N_{bs} leadacid batteries in series, N_{bp} column parallel link composed of the battery, the total battery voltage V_{B} and current I_{B} should be:
V_{B} = V_{b}N_{bs }(344)
I_{B} = I_{b}N_{bp }(345)
Leadacid battery electromotive force (E_{b}) and internal resistance (R_{b}), etc., with its charge state changes, the internal resistance changes are particularly large. In the state of high charge, the open leadacid 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.
Wherein
E_{0}Fully charged state of the electromotive force
k_{e}constant
Q(t)Discharge power, A•h;
C_{T }Maximum capacity of the battery, A•h
R_{0 }constant
β constant
γ constant
ρ State of charge
R_{1} A correction coefficient that is accompanied by a gas generated at the time of charging;
t Time, h
Q(t_{0}) The discharge quantity from the discharge to the charging or from the point to the discharge switching time t0,
C(I_{m})  And the discharge capacity of the average current Im between t0 and tm
C_{R}  Discharge capacity at rated discharge current;
б constant
R_{1} is usually proportional to or proportional to the exponential function. The time R_{1} for generating the reaction gas, the amount R_{1} of the generated gas, and the time constant α_{x} are substantially inversely proportional to the charging current. The following gives the book exponential function of the combination of Figure 37 gives the gas generation function G (t) curve.
R_{1}= R_{X}G(t)
G(t)=1/2+{1exp[α_{x}(t T_{X})]}•U(t T_{X})/2+{exp[α_{x}(t T_{X})]1}•U(t T_{X})/2
In the above formula, U (t) is the stage function
Figure 37 Gas generation function
Figure 38 Equivalent circuit of the inverter
Inverters
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 38. With a mathematical formula for that;
I_{INout}=P_{INin}η_{IN}/(V_{INout}Ф_{IN})
P_{INout}=P_{INin}=R_{INin}I^{2}_{INin}R_{INout}I^{2}_{INout}
I_{INin}=P_{INin}/V_{INin}
η_{IN}=P_{INout}/P_{INin}
P_{INout}=V_{INout}/I_{INout}
V_{INin} Inverter input voltage;
I_{INin} Inverter input current;
P_{INin} Inverter input power;
V_{INout} Inverter output voltage;
_{}/I_{INout} Inverter output current;
P_{INout} Inverter output power;
Ф_{IN} Power factor;
η_{IN} Inverter efficiency;
R_{INin} Inverter equivalent input impedance;
P_{INout} 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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