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DIgSILENT PowerFactory Technical Reference Documentation

PV System ElmPvsys

DIgSILENT GmbH Heinrich-Hertz-Str. 9 72810 - Gomaringen Germany T: +49 7072 9168 00 F: +49 7072 9168 88 http://www.digsilent.de [email protected] r1341

Copyright ©2014, DIgSILENT GmbH. Copyright of this document belongs to DIgSILENT GmbH. No part of this document may be reproduced, copied, or transmitted in any form, by any means electronic or mechanical, without the prior written permission of DIgSILENT GmbH. PV System (ElmPvsys)

1

Contents

Contents 1 General Description

4

1.1 Basic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

1.1.1 Model for Active Power Calculation . . . . . . . . . . . . . . . . . . . . . .

4

1.1.2 Number of Parallel Inverters . . . . . . . . . . . . . . . . . . . . . . . . . .

5

1.1.3 Number of Panels Per Inverter . . . . . . . . . . . . . . . . . . . . . . . .

5

1.2 Load Flow Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

1.2.1 Local Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

2 Solar Calculation

6

2.1 Angle of Incidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

2.2 Tilt and Orientation Angle for Tracking Systems . . . . . . . . . . . . . . . . . . .

8

2.2.1 Dual Axis Tracking System . . . . . . . . . . . . . . . . . . . . . . . . . .

8

2.2.2 Horizontal Single Axis Tracking System . . . . . . . . . . . . . . . . . . .

9

2.2.3 Vertical Single Axis Tracking System . . . . . . . . . . . . . . . . . . . . .

9

2.3 Extraterrestrial Irradiance on the Horizontal Plane

. . . . . . . . . . . . . . . . .

9

2.4 Global Irradiance on the Horizontal Plane . . . . . . . . . . . . . . . . . . . . . .

9

2.4.1 Estimation of Global Irradiance on the Horizontal Plane . . . . . . . . . .

10

2.4.2 Estimation of Diffuse Irradiance on the Horizontal Plane . . . . . . . . . .

11

2.4.3 Direct (Beam) Irradiance on Horizontal Plane . . . . . . . . . . . . . . . .

12

2.5 Global Irradiance on Inclined Surface . . . . . . . . . . . . . . . . . . . . . . . . .

13

2.5.1 Direct (Beam) Irradiance on Inclined Surface . . . . . . . . . . . . . . . .

13

2.5.2 Sky Diffuse Irradiance on Inclined Surface . . . . . . . . . . . . . . . . . .

14

2.5.3 Ground Reflect Irradiance on Inclined Surface

. . . . . . . . . . . . . . .

14

2.6 Relative Efficiency of Solar Panel . . . . . . . . . . . . . . . . . . . . . . . . . . .

14

2.6.1 Average Module Temperature . . . . . . . . . . . . . . . . . . . . . . . . .

15

2.6.2 Efficiency Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15

2.6.3 Effective Irradiance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

2.7 Required Input Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

2.7.1 In Basic Data Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

2.7.2 In Load Flow Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

PV System (ElmPvsys)

2

Contents

2.7.3 In TypPvpanel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18

2.7.4 In SetTime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18

3 References

19

List of Figures

20

List of Tables

21

PV System (ElmPvsys)

3

1

General Description

1

General Description

The Photovoltaic System element (ElmPvsys) is an easy-to-use model based on the Static Generator element (ElmGenstat). The PV System element models an array of photovoltaic panels, connected to the grid through a single inverter. The main difference with the static generator, is that the PV System provides an option to automatically estimate the active power setpoint, given the geographical location, date and time. The description of the following functions supported by PowerFactory can be found in the Technical Reference of the Static Generator: - Load Flow Analysis - Short Circuit Analysis - Optimal Power Flow - Harmonics Analysis - Stability/Electromagnetic Transients Analysis

1.1 1.1.1

Basic Data Model for Active Power Calculation

The active power value can be specified directly by the user through the option Active Power Input, or it can be automatically calculated, given the data of the solar panel type, the arrangement of the solar array, the local time and date, and optionally irradiance data, with the option Solar Calculation. When the option Solar Calculation is used, the active power is calculated according to the Section 2.

Figure 1.1: Photovoltaic System

PV System (ElmPvsys)

4

1

General Description

1.1.2

Number of Parallel Inverters

The number of parallel inverters can be entered, as well as the MVA rating of a single inverter. In general, the total MW and Mvar outputs of the PV System will be the rating of a single PV Array multiplied by the number of parallel inverters specified.

1.1.3

Number of Panels Per Inverter

For each PV System, which contains a single inverter, a number of panels can be entered. The panels can be connected either in parallel, series or in series-parallel combination. The PV System models the solar array viewed from the grid side.

1.2

Load Flow Analysis

In addition to the Load Flow parameters and analysis described in the Static Generator Technical Reference, there are additional options for the local controller, which are explained in the following sections.

1.2.1

Local Controller

The local voltage controller could be set to five different modes (Power Factor, Voltage, Droop, Q(V)-Characteristic, cosphi(P)-Characteristic). The three first modes are described in the Static Generator Technical Reference. The last two are described in the following sub chapters.

Q(V)-Characteristic The Q(V) characteristic is a reactive power control and follows a specified characteristic as shown in Figure 1.2. U min and U max correspond to the lower and upper voltage deadband limit.

Figure 1.2: Q(V)-Characteristic

The local controller acts as a reactive power controller with a variable setpoint. While the reference voltage is within the deadband, the entered reactive power setpoint is kept. If the reference voltage leaves the deadband, the reactive power setpoint is adapted according to the droop entered by the user and the voltage deviation from the respective end of the deadband.

PV System (ElmPvsys)

5

2

Solar Calculation

cosphi(P)-Characteristic The cosphi(P) characteristic is a power factor control and follows a specified characteristic as shown in Figure 1.3. The local controller acts as a power factor controller, where the power factor is determined from the characteristic for the input active power flow.

Figure 1.3: cosphi(P)-Characteristic

2

Solar Calculation

The active power output of a single PV System, i.e. an array of panels connected to the grid through a single inverter is calculated based on irradiance input data and the local time and date. The following equations for the panel and system output are proposed in [5].

Ppanel =

Eg,pv · Ppk,panel · ηrel · ηinv EST D

(1)

and

Psystem = Ppanel · numpanels

(2)

Where: • Ppanel is the active power output of the panel in kW • Psystem is the single system active power output in kW • numpanels is the number of panels per inverter • Eg,pv is the global irradiance on the plane of the array in W/m2 . See Sections 2.1 to 2.5 • EST D is the standard irradiance value of 1000W/m2 • Ppk,panel is the total rated peak power of the solar panel in kW • ηrel is the relative efficiency of the panel, unit-less. See Section 2.6 • ηinv is the efficiency factor of the inverter, unit-less PV System (ElmPvsys)

6

2

Solar Calculation

The geometrical calculation of the global irradiance on an inclined surface is proposed in [1] and [3].

2.1

Angle of Incidence

The first step in the process of calculating the irradiance on the surface of the PV panel (Eg,pv ), is to calculate the angle of incidence of the solar irradiance (ν(β, α)), which can be defined as the angle between the solar rays and the line perpendicular to the surface of the solar panel. This angle of incidence of the irradiance is calculated as follows:

0 Jrad =

J · 2π 365.25

(3)

0 Jdeg =

J · 360 365.25

(4)

0 0 δ = sin−1 0.3978 · sin[Jrad − 1400 + 0.0355 · sin(Jrad − 0.0489)]

(5)

0 0 EOT = −0.128 · sin(Jdeg − 2.8◦ ) − 0.165 · sin(2Jdeg + 19.7◦ )

(6)

tLAT = tLM T +

(λ − λR ) + EOT − c 15

(7)

ω = 15 · (tLAT − 12)

(8)

sinγs = sinφ · sinδ + cosφ · cosδ · cosω

(9)

cosαs =

sinφ · sinγs − sinδ cosφ · cosγs

(10)

cosδ · sinω cosγs

(11)

sinαs =

αs =

  −cos−1 (cosαs ) 

cos−1 (cosαs )

if sinαs < 0 (12) if sinαs > 0

αF = αs − α

(13)

ν(β, α) = cos−1 (cosγs · cosαF · sinβ + sinγs · cosβ)

(14)

Where: • αF is the Julian day number (1 to 366) PV System (ElmPvsys)

7

2

Solar Calculation

0 • Jrad is the day angle in radians 0 • Jdeg is the day angle in degrees

• δ is the declination angle in radians • EOT is the Equation of Time in hours • λ is the longitude of the site in degrees, with east being positive • λR is the longitude of the local time zone, in degrees, east positive • c is the correction for summer time in hours • tLM T is the Local Mean Time in hours • tLAT is the solar time in hours • ω is the hour angle in degrees • φ is the latitude of the location in degrees • γs is the solar altitude angle in degrees • α is the azimuth angle of the surface in degrees – Measured from due south in the northern hemisphere and from due north in the southern hemisphere, i.e. facing equator is always zero degrees – Directions to the west of north-south are positive, east is negative (for both hemispheres) • αs is the solar azimuth angle in degrees • αF is the wall solar azimuth angle in degrees – If αF > 180◦ , then αF = αF − 360◦ – If αF < 180◦ , then αF = αF + 360◦ • β is the surface tilt angle from the horizontal plane in degrees • ν(β, α) is the angle of incidence of the solar irradiance

2.2

Tilt and Orientation Angle for Tracking Systems

It is possible to specify whether or not the panels have a fixed mounting or a tracking system. When the panels are fixed, the user must specify the orientation and/or the tilt angles. If a tracking system is used, it is assumed that the angles are optimized. The optimization is calculated according to the sections below.

2.2.1

Dual Axis Tracking System

PV System (ElmPvsys)

β = βtracking = 90◦ − γs

(15)

α = αtracking = αs

(16)

8

2

Solar Calculation

2.2.2

Horizontal Single Axis Tracking System

β = βtracking = 90◦ − γs

2.2.3

Vertical Single Axis Tracking System

α = αtracking = αs

2.3

(17)

(18)

Extraterrestrial Irradiance on the Horizontal Plane

The extraterrestrial irradiance value incident on a horizontal surface corrected by the day of the year, E0 (J), is given by

I0 = 1367w/m2

(19)

0  = 1 + 0.03344 · cos(Jrad − 0.048869)

(20)

E0 = I0 · sin(γs )

(21)

E0 (J) = I0 ·  · sinγs

(22)

Where: • I0 is the solar constant, equal to 1367W/m2 •  is the correction of the variation of the sun-earth distance from its mean value • E0 is the extraterrestrial irradiance on the horizontal plane • E0 (J) is the extraterrestrial irradiance on the horizontal plane corrected by the day of the year

2.4

Global Irradiance on the Horizontal Plane

The global irradiance is the sum of two components: direct or beam irradiance (Eb,hor ), diffuse irradiance (Ed,hor ). Since the values of the global irradiance and its two components are necessary to calculate the global irradiance on the inclined surface of the solar panels, the value of two components will be needed as an input from the user.

Eg,hor = Eb,hor + Ed,hor

(23)

Where: PV System (ElmPvsys)

9

2

Solar Calculation

• Eg,hor is the global irradiance at the surface falling on a horizontal plane in W/m2 • Eb,hor is the direct or beam irradiance on the horizontal plane in W/m2 • Ed,hor is the diffuse irradiance on the horizontal plane in W/m2 The values of these irradiance components can be in the form of historical or forecasted data, or they can be estimated through simple or complex models. The simple ones use only geometrical methods, whereas the complex models include atmospheric factors. Implemented here are only the simple methods, which are described in Sections 2.4.1, 2.4.2 and 2.4.3.

2.4.1

Estimation of Global Irradiance on the Horizontal Plane

The following models are referenced in [3] and [4].

Kasten-Czeplak Model Eg,hor = 910 · sinγs − 30

(24)

Haurwitz Model Eg,hor = 1098 · sinγs · exp(

−0.057 ) sinγs

(25)

Berges-Duffie Model Eg,hor = I0 · 0.070 · sinγs

(26)

Adnot-Bourges-Campana-Gicquel Model Eg,hor = 951.39 · (sinγs )1.15

(27)

Eg,hor = 1159.24 · (sinγs )1.179 · exp(−0.0019 · gammas )

(28)

Robledo-Soler Model

Hourly Clearness Index Value The Hourly Clearness Index values can be entered through a characteristic object. From the clearness index, KT , the horizontal irradiance is calculated by

Eg,hor = E0 (J) · KT

(29)

Where: PV System (ElmPvsys)

10

2

Solar Calculation

• KT is the clearness index. Daily values vary around 0.68 to 0.72 under cloudless conditions, with lower values at high latitudes in winter. Inversely, the clearness index factor can be calculated from estimated or given irradiance data:

KT =

Eg,hor E0 (J)

(30)

Hourly Data, GHI Normally given as Global Horizontal Irradiance (GHI) data. In the dialog, the data can be entered with a characteristic object.

2.4.2

Estimation of Diffuse Irradiance on the Horizontal Plane

The following models are referenced in [2] and [6].

Bugler Model Ed,hor = 16 ·

√

γs − 0.4 · γs

(31)

Erbs et al. Model

Ed,hor

 Eg, hor · (1.0 − 0.09 · KT )        Eg, hor · (0.9511 − 0.1604 · KT − 4.388 · KT 2 − = 16.638 · KT 3 + 12.336 · KT 4 )        Eg, hor · (0.165)

f or KT ≤ 0.22

f or 0.22 < KT < 0.8

(32)

f or KT ≥ 0.8

Reindl et al. Model

Ed,hor

 Eg, hor · (1.02 − 0.254 · KT + 0.0123 · sinγs )      Eg, hor · (1.4 − 1.749 · KT + 0.177 · sinγs ) =      Eg, hor · (0.468 · KT − 0.182 · sinγs )

f or KT ≤ 0.3 f or 0.3 < KT < 0.78

(33)

f or KT ≥ 0.78

Liu and Jordan Model

Ed,hor =

PV System (ElmPvsys)

Eg,hor · (0.384 − 0.416 · KT ) KT

(34)

11

2

Solar Calculation

Orgill and Holands Model

Ed,hor

 Eg, hor · (1.0 − 0.249 · KT )      Eg, hor · (1.577 − 1.84 · KT ) =      Eg, hor · (0.177)

f or KT < 0.35 f or 0.35 ≤ KT ≤ 0.75

(35)

f or KT > 0.75

Spencer Model

Ed,hor

 Eg,hor · (0.94 + 0.0118 · |φ| − (0.41475 + 0.004725 · |φ|))      Eg,hor · (0.94 + 0.0118 · |φ| − (1.185 + 0.0135 · |φ|) · KT ) =      Eg,hor · (0.94 + 0.0118 · |φ| − (0.88875 + 0.010125 · |φ|))

f or 0.35 < KT f or 0.35 ≤ KT ≤ 0.75 f or KT > 0.75 (36)

Where: • φ is the latitude of the site in degrees

Lam and Liu Model

Ed,hor

 Eg, hor · (0.977)      Eg, hor · (1.237 − 1.361 · KT ) =      Eg, hor · (0.273)

f or KT ≤ 0.15 f or 0.15 < KT ≤ 0.7

(37)

f or KT > 0.7

Louche et al. Model

Ed,hor = Eg,hor (1 −

2.4.3

1 · (−10.627 · KT 5 + 15.307 · KT 4 − 5.205 · KT 3 + KT 0.994 · KT 2 − 0.059 · KT + 0.002))

(38)

Direct (Beam) Irradiance on Horizontal Plane

Hourly Data, Horizontal (DHI) In the dialog, the data can be entered with a characteristic object.

Hourly Data, Normal (DNI) In the dialog, the normal direct irradiance data can be entered with a characteristic object. PV System (ElmPvsys)

12

2

Solar Calculation

From the normal direct irradiance, the direct horizontal irradiance can be calculated by

Eb,hor = Eb,norm ∗ sinγs

(39)

Where • Eb,norm is the normal solar irradiance in W/m2

2.5

Global Irradiance on Inclined Surface

Finally, the global irradiance on an inclined surface, Eg,pv , is the sum of the direct (beam), the diffuse and the ground reflected irradiance values, all of them on the plane of the inclined surface, and affected by respective overshading factors.

Eg,pv = Eb,pv · (1 − Sdir ) + Ed,pv · (1 − Sdif f ) + Er,pv

(40)

Where: • Eg,pv is the global solar irradiance at the surface on the inclined plane in W/m2 • Eb,pv is the slope direct or beam component in W/m2 • Ed,pv is the slope sky diffuse component in W/m2 • Er,pv is the slope ground reflected component in W/m2 • Sdir is the direct Irradiance shading factor, unit-less • Sdif f is the diffuse Irradiance shading factor, unit-less

2.5.1

Direct (Beam) Irradiance on Inclined Surface

The direct or beam component Eb,pv can be calculated very easily with some of the values calculated above in the following way

Eb,pv

 Eb,hor · cosν(β, α)    sinγs =    0

f or cos ν(β, α) > 0 (41) otherwise

Where: • Eb,hor is the direct (beam) irradiance on a horizontal plane • ν(β, α) is the angle of incidence in degrees • γs is the solar altitude in degrees PV System (ElmPvsys)

13

2

Solar Calculation

2.5.2

Sky Diffuse Irradiance on Inclined Surface

The diffuse component Ed,hor can also be computed straight forward with

Ed,P V =

   1 + cos(β)   E ·    d,hor 2     

0

f or

1 + cos(β) >0 2 (42)

otherwise

Where: • β is the surface tilt angle from the horizontal plane in degrees

2.5.3

Ground Reflect Irradiance on Inclined Surface

The ground reflected irradiance can be computed as a fraction of the global horizontal irradiance with the following

Er,pv =

   1 − cos(β)   E ·ρ ·    g,hor g 2     

0

f or

1 − cos(β) >0 2 (43)

otherwise

Where: • ρg is the ground albedo, unit-less • β is the surface tilt angle from the horizontal plane in degrees

2.6

Relative Efficiency of Solar Panel

The relative efficiency is calculated according to [5].

     Eg,pv Eg,pv ηrel = (1 + βc · (Tc − Tr )) · 1 + k1 · ln − k2 · −1 EST D EST D

(44)

Where: • ηrel is the relative efficiency of the solar panel, unit-less • βc is the temperature coefficient for module efficiency, unit-less • Tc is the average module temperature in ◦ C • Tr is the reference temperature = 25◦ C • k1 and k2 are efficiency coefficients PV System (ElmPvsys)

14

2

Solar Calculation

2.6.1

Average Module Temperature

Tc = Ta + ∆T · Eg,pv

∆T =

N OCT − 20 0.8 · EDST D

(45)

(46)

Where: • Ta is the ambient temperature in ◦ C • N OCT is the Nominal Operating Cell Temperature in ◦ C

2.6.2

Efficiency Coefficients

For the efficiency coefficients, the single-diode model is considered:

Figure 2.1: Solar Cell Model

Figure 2.2: Solar Cell Curve

The efficiency coefficients are calculated as follows:

PV System (ElmPvsys)

15

2

Solar Calculation

UT 0 Upmax0

(47)

Rpv · Ipmax0 Upmax0

(48)

k1 =

k2 =

  Ipmax · Upmax Upmax Ipmax Uoc · −5.411 · + 6.450 · + 3.417 · − 4.422 M= Isc Isc · Uoc Uoc Isc

Rpv = −M ·

Isc Ipmax

  Upmax Isc + · 1− Ipmax Ipmax

(50)

UT = −(M + Rpv ) · Isc

UT 0 = UT ·

Ipmax0 = Ipmax ·

Upmax0 =

Upmax + UT 0 · ln 1 + β · (Tc − Tr )



(51)

Tr Tc

(52)

EST D Eg,ef f

EST D Eg,ef f

(49)



(53)

 − Ipmax · Rpv ·

 EST D −1 Eg,ef f

(54)

Where: • k1 is first coefficient, unit-less • k2 is second coefficient, unit-less • Upmax is the rated voltage at maximum power point in V • Ipmax is the rated current at maximum power point in A • Uoc is the open circuit voltage in V • Isc is the short-circuit current in A • UT is the temperature voltage • UT 0 is the temperature voltage proportional to temperature • Upmax0 is the voltage at maximum power point proportional to irradiance in V • Ipmax0 is the current at maximum power point proportional to irradiance in A • M is the slope of the IV curve at I = 0 • Rpv is the photovoltaic resistance in Ohm • Eg,ef f is the effective irradiance, in W/m2 . See Section 2.6.3 below. PV System (ElmPvsys)

16

2

Solar Calculation

2.6.3

Effective Irradiance

The effective irradiance is the irradiance measured at AM 1.5-conditions. AM 1.5 applies, when for the solar altitude angle applies

sin(γs ) =

1 1 = AM 1.5

(55)

Therefore, the effective irradiance is calculated as the global horizontal irradiance (as calculated in Section 2.4 with the following conditions:

(56)

Eg,ef f = Eg,hor   1 γs = asin 1.5   sinγs − sinφ · sinδ ω = −acos cosφ · cosδ

2.7

(57) (58)

Required Input Parameters

The required parameters to calculate the active power setpoint of the solar system are shown in the following tables.

2.7.1

In Basic Data Page

The parameters in the Basic Data page are shown in Table 2.1. Table 2.1: Input parameters in Basic Data Page (ElmPvsys) Parameter

Unit

typ id nnum npnum cGPSLat cGPSLon timezone mount orient tilt inveff

2.7.2

Default Value

1 1 deg deg

deg deg %

0 0 30 95

Description General Tab Type No.of Parallel Inverters No.of Panels per Inverter System Configuration Tab Latitude Longitude Local Time Zone Mounting System Orientation Angle Tilt Angle Efficiency Factor

Range

Symbol

numpanels φ λ λR α β ηinv

In Load Flow Page

The parameters in the Load Flow page are shown in Table 2.2. PV System (ElmPvsys)

17

2

Solar Calculation

Table 2.2: Input parameters in Load Flow Page (ElmPvsys) Parameter

Unit

Default

iopt rad

1

iopt glo kt ghi

W/m2

0 0.6 600

iopt dir dhi

W/m2

400

W/m2

400

◦

25 0

dni iopt dif Tamb shfdir

C

shfdif

0

albedo

0.31

2.7.3

Description Environment Factors Tab Specified Components option Global Irradiance option Clearness Index Global Horizontal Irradiance Direct Irradiance option Direct Horizontal Irradiance Direct Normal Irradiance Diffuse Irradiance option Ambient Temperature Shadowing Factor (Direct) Shadowing Factor (Diffuse) Albedo

Range

Symbol

0 ≤ KT ≤ 1

KT Eg,hor

Eb,hor Eb,norm

0 ≤ Sdir ≤ 1

Ta Sdir

0 ≤ Sdif f ≤ 1

Sdif f ρg

In TypPvpanel

The parameters in the TypPvpanel dialog are shown in Table 2.3. Table 2.3: Input parameters in Type (TypPvpanel) Parameter Ppk Umpp Impp Uoc Isc material iusetval dcT

Unit W V A V A

dnoct

◦

2.7.4

%/◦ C C

Default 500 80 6 90 7 0 1 -0.4

Description Rated Power of the Panel Rated Voltage at MPP Rated Current at MPP Open Circuit Voltage Short-Circuit Current Material Use default values Temperature coefficient

45

Nominal Operating Cell Temperature

Range

Symbol Ppk,panel Upmax Ipmax Uoc Isc

−100 ≤ βc ≤ 0

βc N OCT

In SetTime

The parameters in the object SetTime are shown in Table 2.4. Table 2.4: Input parameters in Type (TypPvpanel) Parameter cTime dayofyear

Unit

PV System (ElmPvsys)

Default

Description Local Time Day of Year

Range

Symbol tLM T J

18

3

3

References

References

[1] T. Markvart and L. Castaer. Practical Handbook of Photovoltaics: Fundamentals and Applications. Elsevier Science, 2003. [2] M. Paulescu, E. Paulescu, P. Gravila, and V. Badescu. Weather Modeling and Forecasting of PV Systems. Springer, 2013. [3] V. Quaschning. Regenerative Energiesysteme. Hanser Verlag, 2013. [4] M. J. Reno, C. W. hansen, and J. S. Stein. Global horizontal irradiance clear sky models: Implementation and analysis. Technical Report SAND2012-2389, Sandia National Laboratories, March 2012. [5] A. Wagner. Photovoltaik Engineering. Springer, 2009. [6] L. T. Wong and W. K. Chow. Solar radiation model. Applied Energy, 69(3):191–224, 2001.

PV System (ElmPvsys)

19

List of Figures

List of Figures 1.1 Photovoltaic System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

1.2 Q(V)-Characteristic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

1.3 cosphi(P)-Characteristic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

2.1 Solar Cell Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15

2.2 Solar Cell Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15

PV System (ElmPvsys)

20

List of Tables

List of Tables 2.1 Input parameters in Basic Data Page (ElmPvsys) . . . . . . . . . . . . . . . . . .

17

2.2 Input parameters in Load Flow Page (ElmPvsys) . . . . . . . . . . . . . . . . . .

18

2.3 Input parameters in Type (TypPvpanel) . . . . . . . . . . . . . . . . . . . . . . . .

18

2.4 Input parameters in Type (TypPvpanel) . . . . . . . . . . . . . . . . . . . . . . . .

18

PV System (ElmPvsys)

21