DC Array Behavior

DC Field Behavior

This collection of functions computes the I(V) characteristics of an individual module given the module temperature and irradiance. The tool uses the 1-diode model. At this point in the simulation process, the irradiance seen by the PV module has been corrected for all optical losses.

Module Temperature

Two models for estimating module temperature are supported by PlantPredict and selectable by the user in the Simulation Settings: the Sandia method and the static heat-balance model.

Sandia Module Temperature

This routine empirically computes the module temperature from the air temperature, the wind speed, and the in-plane irradiation. This model uses two empirically-determined coefficients: at establishes the upper limit for module temperature at low wind speeds and high solar irradiance, bt establishes the rate at which module temperature drops as wind speed increases.

Soiling Figure 14
 

Figure 34. Empirical Module Temperature Coefficients

 

 

Inputs

Sandia Module Temperature Inputs

Outputs

Sandia Module Temperature Outputs

 

1.) Compute the module temperature as a function of the available insolation, wind speed, and air temperature:

Sandia Module Temperature Algo86
2.) Compute the cell temperature. This temperature difference is typically 2 to 3 °C for flat-plate modules in an open-rack mount at a reference irradiance GRef of 1000 W/m2.

Sandia Module Temperature Algo87

Reference

King, D. L., Kratochvil, J.A., Boyson, W.L., Photovoltaic Array Performance Model, Report SAND2004-3535, Sandia National Laboratories, Albuquerque, NM, September 1997.

Heat Balance Temperature Model

The thermal behavior of the field, which strongly influences the electrical performances, is determined by a thermal balance between the ambient temperature and the cell’s temperature, which is elevated by incident irradiation. In this simple model, αT is the absorption coefficient of solar irradiation, and ηm is the PV efficiency (related to the Module area), i.e. the removed energy from the module.

Inputs

Outputs

Heat Balance Temperature Outputs

Algorithm

1.) Compute the module temperature as a function of the available insolation, wind speed, and air temperature:

Heat Balance Temperature Algo88

The usual value of the absorption coefficient α is 0.9. The PV efficiency is taken from the Module File.

The thermal behavior is characterized by a thermal loss factor designated here by k, which can be split into a constant component kc and a factor proportional to the wind velocity kv. These factors depend on the mounting mode of the modules (sheds, roofing, facade, etc.).

 

2.) Convert the cell temperature to a module surface temperature.

Heat Balance Temperature Algo89

Reference

Mermoud, A., Conception et dimensionnement de systèmes photovoltaïques : Introduction des modules PV en couches minces dans le Logiciel PVsyst. Université de Genève, 2005.

Module I(V) Curve

A complete module I(V) curve is computed under ambient conditions for the current time step. The “One-Diode” parameters are defined in the module file. The one-diode model uses an equivalent electrical circuit model and the governing diode equation to generate an explicit, continuous current vs. voltage function.

One-Diode Model

Given the 1-diode model parameters for the module, this routine computes the module’s current-voltage characteristics. Figure 35 shows the equivalent circuit of a PV cell. The following algorithm includes the recombination current, Irec, a refinement in the model that can be set to zero if the parameters required to determine the current (μ, τeff, di, Vbi) are not provided in the module definition input file.

Module Curve Figure 17
 

Figure 35. One-Diode Equivalent Electric Circuit Model of a PV Module

 

 

Inputs

Module Curve Inputs

Outputs

Module Curve Outputs

Algorithm

1.) Solve the following transcendental equation that relates the module’s output current i and output voltage υ to the photocurrent Iph, and the 1-diode parameters corrected for the temperature and irradiance level (I0, Rsh, Rs, γ).

Module Curve Algo90
 

Module Curve Algo91
 

Module Curve Algo92
 

Module Curve Algo93

The parameter b, given in the module parameter definition, combines the following terms:

Module Curve Algo93-1

Expanded, the transcendental function for the output current becomes:

Module Curve Algo94
 

Module Curve Algo95
 

2.) The current should be solved for diode voltages in the interval [0, νoc,g], where νoc,g is the guess for the open-circuit voltage, and can be found by setting the I to zero in the above equation (neglecting Irec):

Module Curve Algo96
3.) The limits of the I(V) curve in the first quadrant are defined by the open-circuit voltage and short-circuit current, which can be found by setting i and ν to 0, respectively.

 

4.) Find the maximum power point diode voltage using the Newton-Raphson method by iteratively solving the following equation until the difference between Vd,n+1 and νd,n is arbitrarily small.

Module Curve Algo97
5.) Find the maximum power point current by solving the 1-diode equation.

Module Curve Algo98
6.) Find the maximum power point voltage at the output terminal of the equivalent circuit by subtracting the voltage drop across the series resistance.

Module Curve Algo99
 

Reference

Mermoud, A., Conception et dimensionnement de systèmes photovoltaïques : Introduction des modules PV en couches minces dans le Logiciel PVsyst. Université de Genève, 2005.

One-Diode Model Temperature Correction

Given the 1-diode model parameters defined for the module under STC conditions (25 °C, 1000 W/m2), compute the temperature and irradiance-corrected parameters at the actual module temperature Tm and the available solar energy GT,Eff. The default temperature correction of all 1-diode parameters is linear. If a non-linear temperature correction of the diode ideality factor is desired, the then a set of additional parameters (polynomial coefficients) is available to affect this correction.

This non-linear response is illustrated in Figure 36 for a family of I(V) curves with a module temperature range of 8 °C to 75 °C. This data was measured in the laboratory using the module temperature control system and a Spire long-pulse solar simulator.

One Diode Model Figure18

Figure 36. Non-Linear Module Power Temperature Response using a Third-Order Polynomial Correction to the Diode Ideality Factor γ

 

 

Inputs

One Diode Model Inputs

Outputs

One Diode Model Outputs

Algorithm

1.) Given the effective available insolation GT,Eff and module temperature Tm, find the corrected 1-diode shunt and series resistance.

One Diode Model Algo100
One Diode Model Algo101
 

2.) If the linear correction to the diode ideality factor is desired, or all non-linear coefficients ay,by,cy,dy = 0, then correct it for the module temperature as follows:

One Diode Model Algo102
3.) If the non-linear correction to the diode ideality factor is desired, then correct it for the module temperature as follows:

One Diode Model Algo103
4.) Correct the saturation current for temperature. Note that this correction includes the previously temperature-corrected diode ideality factor.

One Diode Model Algo104
5.) Find the short-circuit current under the ambient conditions.

One Diode Model Algo105
6.) Even when a module is biased in short-circuit condition, a voltage drop occurs across Rs. As a result, the junction still experiences a voltage bias and there are currents flowing through both the recombination path and through Rsh when the terminal voltage of the device is zero, i.e. the recombination term does not go to zero in the short circuit condition. Therefore the photocurrent, Iph must be greater than Isc in order to supply parasitic currents as well as the external current which has the rated ISC,ref value. Find the actual Iph as follows:

One Diode Model Algo106

The temperature dependence on voltage is also computed, but not used elsewhere in the simulation. Note that μΙsc ≅ αIph, given in 1/°C.

One Diode Model Algo107
 

Reference

Schwieger, M., Michalksi, S., Non-Linearity of Temperature Coefficients, Equivalent Cell Temperature and Temperature Behaviour of Different PV-Module Technologies. TÜV Rheinland Energie und Umwelt, Cologne, Germany. Proceedings from the 28th EU PVSEC.

Mismatch

Compute the power lost due to module I(V) curve characteristic mismatches within one module bin. This is an empirical constant and suppresses the maximum power point on the I(V) curve. The mismatch can be applied to voltages within the vicinity of the I(V) curve’s knee, but is undefined for the array’s Isc and Voc.

Inputs

Mismatch Inputs

 

Outputs

Mismatch Outputs

 

Algorithm (Provisional)

1.) The mismatch factor is applied directly to the effective irradiance, prior to the evaluation of the 1-diode or Sandia models:

Mismatch Algo111
 

Algorithm (Future)

Mismatch may in future be embedded as part of a DC degradation algorithm. A simple solution can include the following.

 

1.) The depressed maximum power point is found as follows:

Mismatch Algo112
2.) To first order, the mismatch’s contribution to the current and voltage is weighted equally:

Mismatch Algo113
 

Mismatch Algo114

DC Field I(V) Curve

This routine aggregates the I(V) curves from individual modules, and then sums them in parallel and in series to yield an I(V) curve profile that is representative of the entire DC Field. Figure 37 shows a general schematic of such parallel-series connection.

DC Field Curve Figure19
 

Figure 37. Array Comprised of N Series x M Parallel PV Modules

 

 

Currents add for parallel-connected modules and voltages add in series-connected modules.

Inputs

DC Field Curve Inputs

Outputs

DC Field Curve Outputs

Algorithm

1.) For combination of identical modules in series and parallel, the points on the I(V) curves or current and voltages can be scaled as follows:

a.) Compute the aggregate I(V) curve for a series string comprised of Nms identical modules. The voltages can be multiplied by the number of modules in the series string; the current remains unchanged:

DC Field Curve Algo109

b.) Compute the I(V) curve for a parallel connection of Nsp identical series strings in parallel modules. The currents can be multiplied by the number of strings in parallel; the voltage remains unchanged:

DC Field Curve Algo110
2.) For heterogeneous arrays comprised of modules that do not exhibit the same I(V) curve (i.e. a cool shaded module connected to a hot unshaded module), the individual I(V) curves must be added:

 

a.) Parallel connection: Combine heterogeneous modules or strings connected in parallel by interpolating the I(V) array at common voltage points so that the sampled currents are aligned; then sum the individual currents.

 

b.) Series connection: Combine heterogeneous modules or strings connected in series by interpolating the I(V) array at common current points so that the sampled voltages are aligned; then sum the individual voltages.

DC Wiring

This routine computes the power lost due to Joule heating losses within the DC portion of the array. The resulting current and voltage is that seen at the inverter terminals. The resistance can also be estimated if a percent Joule loss (PJL) at STC is provided instead of the equivalent bulk resistance. The resistance from a percent Joule loss is estimated as follows from the module’s rated STC current and voltage and number of series & parallel connections in the DC Field:

DC Wiring Algo115
 

Inputs

DC Wiring Inputs

Outputs

DC Wiring Outputs

Algorithm (Delta Series Resistance)

1.) Given an equivalent bulk resistance RDC, find the delta series resistance seen by one module as follows:

DC Wiring Algo116
2.) This ΔRS is then added to the series resistance in the one-diode model.

3.) An approximation of the power dissipated by the bulk resistance can be obtained from the DC Field power seen by the inverter is as follows:

DC Wiring Algo117

Degradation and Plant Construction Schedule

Large power plants are not constructed and commissioned at one point in time, but come on line on a Block-by-Block basis. Therefore, different sections of the plant will start contributing energy staggered in time as each comes on line, and accounting for energization times lasts until the last section is energized and the full capacity of the plant is realized.

In addition, the long term power plant production reduces continuously over time due to environmental exposure, component aging, and accrued module defects. Three mutually-exclusive models are supported, and can be selected by the user on simulation setup:

Degradation Figure20
 

Figure 38. List of Degradation Models

 

 

Degradation Figure21
 

Figure 39. The 3 Degradation Models at 0.5% per year Rate for 4 years. The Linear AC and DC Degradation Follow the Same Line.

 

DC Linear

Linear DC degradation function reduces the DC power input to the inverter as a linear function of time by the specified rate from the user.

 

Inputs

DC Linear Inputs

 

Outputs

DC Linear Outputs

 

Algorithm

1.) Loop for all simulation steps for each Block

a.) The continuous-time function in hours is as follows:

DC Linear Algo118

b.) Find the system power due to energization time and degradation for time t.

DC Linear Algo119

AC Linear

This function will reduce the AC power output as a linear function of time.

 

Inputs

AC Linear Inputs

 

Outputs

AC Linear Outputs

 

Algorithm

1.) Loop for all simulation steps for each Block.

a.) The continuous-time function in hours is as follows:

AC Linear Algo120

b.) Find the system power due to energization time and degradation for time t.

AC Linear Algo121

AC Stepped

This function will reduce the AC power output as a stepped function of time. The AC output of the block is reduced by the linear annual degradation rate at a discrete point in time.

 

Inputs

AC Stepped Inputs

 

Outputs

AC Stepped Outputs

 

Algorithm

1.) Loop for all simulation steps for each Block

a.) The discrete-time function in hours is as follows:

AC Stepped Algo122

b.) Find the system power due to energization time and degradation for time t.

AC Stepped Algo123