- freely available
Energies 2013, 6(1), 128-144; doi:10.3390/en6010128
- Being a basic tool for researchers to predict the output characteristics of the photovoltaic systems in both normal and partial shading conditions.
- Having a reliable and robust model is the first requirement for designers who want to analyze the performance and efficiency of different configurations of PV systems before installation.
- It is the first step to study and define the effectiveness of Maximum Power point tracking methods applied in different configuration of a PV system under variable environmental conditions.
- It is an aid for users who want to build actual PV systems without going into the intricate details such as semiconductor physics.
2. Modeling of Photovoltaic System Parameters
2.1. PV Cell Model
2.2. PV Module Model
|Electrical Characteristic||BP SX 150s|
|Open circuit voltage||43.5 V|
|Short circuit current||4.75 A|
|Maximum power voltage||34.5 V|
|Maximum power current||4.35 A|
|Maximum power||150 W|
|Temperature coefficient of ISC||(0.065 ± 0.015)%/°C|
|Temperature coefficient of VOC||−(160 ± 20) mV/°C|
3. Characteristics of the PV System under Partial Shading
3.1. Effect of Bypass and Blocking Diodes on PV Characteristics
3.2. Partially Shaded Module
3.3. Partially Shaded Array
- Calculate the solar irradiance received by each individual PV module and determine the irradiance matrix. This point must be mentioned that in accordance with assuming a single bypass diode for each PV module, if the partial shading occurs in the PV module, the lowest irradiance level will be considered.
- Compute the Iph and Ns of each module using Equation (11) and define the Iph, Ns matrix respective to their solar irradiances.
- Rearrange Iph matrix from the highest toward the lowest value.
- Calculate the output current of array (Ipva) using Equation (13) in which the Ipvm(i) is the output current of ith module.
- Calculate the output PV voltage (Vpva) using Equation (13) in which the Vpvm(i) is the output voltage of ith module:
4. Numerical Examples
4.1. Partially Shaded Module Series with Fully Illuminated Module
4.2. Multidimensional PV System
- The lower number of sensors and transducers which significantly reduces the overall system cost.
- The lower space required for the control unit, even in a large scale PV system.
- High flexibility of this configuration helps the designers to develop the system without increasing the control units. Only some amendments in programming are required.
- Region 1 = Contribution of PV arrays in Zone2A2 + Zone1A1
- Region 2 = Contribution of PV arrays in Zone2A2 + Zone2A1
- Region 3 = Contribution of PV arrays in Zone1A2 + Zone1A1
- Region 4 = Contribution of PV arrays in Zone2A2 + Zone2A1
Diode ideality factor
Short-circuit temperature/current coefficient
Electron charge constant
Operating irradiance level (W/m2)
Nominal irradiance level (W/m2)
Number of series connected cells
Operating temperature (K)
Solar generated current
Reference cell temperature(K)
Short circuit current
PV output voltage
Diode saturation current
PV module output voltage
PV output current
PV array output voltage
PV module output current
Series connected resistance
PV array output current
Parallel connected resistance
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