**TYPE 70:
PHOTOVOLTAIC-cell/module/array **

**General Description**

TYPE 70 models a single solar cell or a PV module or an array consisting of a number of modules. It uses the one-diode model. The cell/module is described by cell parameters. No partial shading effects are taken into account by this component. The user may specify, if a voltage is forced upon the cell/module (e.g. by a battery) or if maximum power point tracking (MPPT) is performed. The MPPT is part of the TYPE 70 component. For the treatment of the cell temperature 4 modes can be chosen (see documentation for details):

- tcmod mode for calculation of cell temperature
- 0: cell temperature tc is input
- 1: tc calculated with simple energy balance
- 2: tc calculated with more accurate energy balance according to /1/,/2/
- 3: like 2, but with phase change material (PCM)attached to the back side of the cell

The sky temperature in tcmod 2 and 3 is calculated using the model of /3/ for the clear sky and a constant temperature difference between ambient and sky for an overcast sky.

The first input to the component is a switch (a control signal). This is useful for PV systems that may require to turn the array off, e.g. in order to protect a battery from being overcharged.

**Nomenclature**

- ab - solar radiation absorption of module
- "
_{b}- combined heat transfer coefficient back side - "
_{f}- combined heat transfer coefficient front side - A
_{m}- module area (total) - A
_{z}- cell area (per cell or total per module) - $ - array tilt angle
- boltz - Boltzmann constant
- C
_{dist}- factor for distance cell - roof (0 = no distance, 1 = huge distance) - cl - specific heat capacity of liquid phase change material (PCM)
- cs - specific heat capacity of solid PCM
- c1 - ik0*temp.coefficient
- c2 - Standard Temperature
- deltt - time step
- diod - diode quality factor
- dPCM - thickness of PCM (solid)
- e
_{chg}- electron charge - e
_{gap}- Band Gap Energy - , - glass emisivity
- eps - relative tolerance for Newton's and secant method
- err - relative error in iteration
- eta - efficiency
- fc - function for secant method iteration
- ( - factor for sky overcast (0 = no overcast, 1 = total overcast)
- g
_{tot}- radiation transformed into heat - hPCM - latent heat of melting (PCM)
- h
_{f}- convectiv heat transfer coefficient (front), based on /2/ - h
_{b}- convectiv heat transfer coefficient (backside) - I
_{cell}- current through photovoltaic cell - I
_{k}- approximation of short circuit current - I
_{k0}- Standard Short Circuit Current/Standard Irradiation - info - TRNSYS info array
- I
_{s}- dark current - I
_{sc}- short circuit current - I
_{s0}- Dark Current Factor [A/K3] - I
_{T}- Total incident radiation on a flat surface per unit area - kapalt - old portion of liquid PCM (0 = all solid, 1 = all liquid)
- mode - >0:array,<0:no array, |mode|=1:cell-, =2:module-par.
- mp - number of module series in parallel in the array
- mpp - MPPT flag
- ms - number of modules in series in the array
- np - number of cell series in parallel (per module)
- ns - number of cells in series (per module)
- out - TRNSYS output vector
- par - TRNSYS parameter vector
- P
_{el}- electric power - pelo - power of last iteration step
- f
_{min}- minimal incident radiation for which calculation is made [W/m2] - qmalt - heat used for melting exclusive this time step
- q
_{rad}- heat loss by radiation - D
_{PCM}- density of PCM (solid) - r
_{par}- parallel resistance for model - r
_{ser}- series resistance of model - F - Stefan-Boltzmann constant
- T
_{amb}- ambient temperature - tau - relative tolerance for successive substitution
- T
_{cell}- cell temperature - T
_{old}- old cell temperature - T
_{melt}- melting temperature of PCM - T
_{room}- room temperature (backside of cell) - T
_{sky}- sky temperature - U
_{cell}- voltage - Ucc - voltage for one cell saved for iterations
- U
_{oc}- open circuit voltage - U
_{roof}- u-value (roof) - U
_{0g}- first guess for open circuit voltage - V
_{wind}- wind speed - xin - TRNSYS input vector

**Mathematical Description**

Approximation of short circuit current:

Dark current:

I-U equation:

For the temperature calculation of the photovoltaic cells there are three modes. It is also possible to give the temperature as input (for example if measurements have been done and the model is verified) in mode 0.

**mode 1**

** **

**mode 2**

The total radiation on the solar cell that is turned into heat:

The sky temperature is calculated:

Heat loss by radiation:

Heat loss from the front side of the photovoltaic cell:

Heat loss from the back side of the photovoltaic cell:

or if the modules are very close to the surface under (the roof):

The cell temperature is calculated from the heat balance:

**mode 3**

The heat losses and gains are calculated as in mode 2. In addition the melting of the phase change material (PCM) is taken into account. The calculations are based on the heating capacities for the PCM as solid and as liquid. The calculations will also keep track of how much of the PCM that are melted. This is based on the melting energy for the PCM.

**TRNSYS Component Description**

__PARAMETER NO.__ __DESCRIPTION__

- 1 mode - +1: array (modepar=2), -1: no array (modepar=0)
- 2 aream - module area (total)
- 3 areaz - cell area (per cell or total per module)
- 4 ns - number of cells in series (per module)
- 5 np - number of cell series in parallel (per module)
*mode = 1*- 6 ms - number of modules in series in the array
- 7 mp - number of module series parallel in the array
*all modes*- 6 + modpar tcmod - mode for calculation of cell temperature;
- 0: cell temperature tc is input
- 1: tc calculated with simple energy-balance
- 2: tc calculated with accurate energy-balance
- 3: equal 2, but with phase change material
*tcmod = 1*- 7 + modpar alf - combined heat transfer coefficient front side
- 8 + modpar alb - combined heat transfer coefficient back side
*tcmod = 2,3*- 7 + modpar abfak - factor for distance cell - roof (0 = no distance, 1 = huge distance). abfak<10-8 => abfpar=1, else abfpar=0
- 8 + modpar kwert - U-value (roof)
- 8 + modpar + abfpar epsgla - glass emisivity
- 9 + modpar + abfpar T
_{start}- tc at beginning of simulation *tcmod=3*- 10 + modpar + abfpar T
_{melt}- melting temperature of PCM - 11 + modpar + abfpar c
_{s}- specific heat capacity of solid PCM - 12 + modpar + abfpar c
_{l}- specific heat capacity of liquid PCM - 13 + modpar + abfpar d
_{PCM}- thickness of PCM (solid) - 14 + modpar + abfpar h
_{PCM}- latent heat of melting (PCM) - 15 + modpar + abfpar k
_{PCM}- density of PCM (solid)

__INPUT NO.__ __DESCRIPTION__

- 1 ypv - control function (switch)
- 2 I
_{T}- incident radiation - 3 U
_{c}- voltage for one cell - 4 T
_{amb}- ambient temperature - 5 $ - array tilt angle for tcmod = 0:
- 6 T
_{c}- cell temperature for tcmod = 2,3: - 6 ( - factor for sky overcast (0 = clear sky, 1 = totally overcast)
- 7 V
_{wind}- wind speed - 8 T
_{room}- room temperature (backside of cell)

__OUTPUT NO.__ __DESCRIPTION__

- 1 U
_{c}- voltage over one cell - 2 I
_{c}- current from one cell times the fraction of cells connected to load - 3 P
_{el}- electric power from one cell times the fraction of cells connected to load - 4 T
_{c}- temperature of cell in degrees Celsius - 5 Z - efficiency of panel
- 6 U
_{oc}- Open circuit voltage of one cell - 7 I
_{sc}- Short circuit current through one cell - 8 ypv - Fraction of cells in panel connected to load

**Informational Flow Diagrams**

**Data file input**

The data for a Photovoltaic cell have to be given in a separate file. The first line in this file will give the number of photovoltaic cells given in the file. Each different cell will have two lines; the first line contains the number of the cell in the file and the name of the cell, the second line contains the data for the cell. The data file for the photovoltaic cell will be like this (the third line (P1-P9) should not be in the file, but are included here to illustrate what each data represents):

- 1,Solarcell
- 0.0078 142.59 0.002996 279986 0 0 1.12 1.47 0.80
- P1 P2 P3 P4 P5 P6 P7 P8 P9

- P1 = Rser : series resistance of model
- P2 = Rpar : parallel resistance for model
- P3 = Ik0 : Standard Short Circuit Current/Standard Irradiation
- P4 = Is0 : Dark Current Factor [A/K3]
- P5 = C1 : ik0*temp.coefficient
- P6 = C2 : Standard Temperature
- P7 = Egap : Band Gap Energy
- P8 = Diod : diode quality factor
- P9 = ab : solar radiation absorption of module

OUTPUT to file logical unit 6 will look like this:

- Parameters from file to PVcell, unit xx:
- rser = 7.8000E-03 rpar = 1.4259E+02 ik0 = 2.9960E-03
- is0 = 2.7999E+05 c1 = 0.0000E+00 c2 = 2.7315E+02
- egap = 1.1200E+00 diod = 1.4700E+00 ab = 8.0000E-01

**References**

- /1/ Sand '79-7056', report Sandia Lab
- /2/ J.W. Stultz, L.C. Wen, JPL Document No. 5105-31, 1977
- /3/ Duffie, J.A., Beckmann, W.A., Solar Engineering of Thermal Processes, John Wiley & Sons, 1980