At the lower left side of Figure 1 a PV-diesel (or Rankine-cycle generator) hybrid system is modelled. The use of fuel enables the photovoltaic SEGS (solar electricity generation system) to accomplish increased generation capacity, e. g., extend more hours of operation throughout the year far beyond the solar hours (say, 2000 solar hours as shown), by fuel firing the SEGS generator (33.2% net efficiency). At the lower left side of the figure three kinds or modes of such systems are noted. Mode 1 (the 2 kHrs point on the horizontal scale) indicates no use of any fuel during the solar hours (GREF = 1). Mode 2 (the full circular point), the use of 30% fuel, and mode 3 (the full triangular point), of 50% fuel.

At the point of 2000 operation hours with mode 1 the FCR will be zero, as there is no use of fuel. With mode 2, the FCR will be 0.11, and with mode 3, FCR of 0.2. The Green Energy Fraction (GREF) values will show 1,0.89 and 0.8, for the 3 modes, respectively. With full fuel firing beyond the 2000 solar hours, the steep, relatively thick, dashed lines show how fast the fuel-consumption grows. At around 6000 hours they reach the horizontal baseline standard line, which stands for the fully fuel fired CC (gas turbine combined cycle) (FCR=1). In other words, by operation for 6000 hours and beyond, the PV hybrid has consumed fuel (and produced emissions) as much as a 60% efficient fuel fired CC during a full year. At around 8000 hours, the PV hybrid will have produced emissions much more than the CC and nearly as much as a residual fuel oil fired Rankine cycle running at a 40% level conversion (which is a secondary standard). Figure 1 shows distinct, gradual differences between the 3 modes. In

terms of GREF (green energy fraction) the green energy (fuel avoidance energy) which has been produced by the PV system during the solar hours, now will largely diminish or be totally wiped out because of the extended operation hours. This green energy annihilation results from the long hours of firing fuel relatively inefficiently (33.2%) as compared to the baseline standard of 60%. It may also be nearly so with respect to the secondary standard of 40%.

In order to determine the battery parameters for the following simulation, experimental tests in laboratory have been performed on a scaled PV system constituted by: a PV module of the same manufacturer with 25 Wp peak power; one battery of the previous system (12 V — 110 Ah); a charge regulator of the same model but with nominal voltage of 12 V; an energy saving lamp (7 W). The experimental procedure can be summarised as in the following.

Firstly, starting from the receiving conditions of battery, a complete discharge has been carried out to verify the switch off by the charge regulator at 11.1 V threshold (p = 30%). Initially SOC is lower than 100% and in this case open circuit voltage Ub0 ~ 13 V. The battery voltage and the lamp current have been measured by a data logger supplied by the grid. Thus an extrapolation to 14 V has been calculated on the basis of mean values of AU variations in the first 7 h during discharge: this evaluation has provided more than 80 h before the start of discharge. Furthermore, a grid black-out has prevented to record the measurements for 30 hours and a linear interpolation has been calculated with 3 hourly mean values of AU variations before and after black-out. Finally, after more than 200 h, the charge regulator has switched off at the prescribed threshold: globally a discharge time of more than 300 h at 0.5 A corresponds to an assessed capacity of 156 Ah. Fig. 2 reports the discharge test with extrapolated and interpolated data.

The current-voltage I-U characteristics of the batteries can be obtained by the transient charge of a suitable capacitor, for battery as generator, and by the transient discharge of the same capacitor, for battery as load. In such a way, during these charge or discharge, the battery does not modify SOC. It is worth noting that the parasitic inductance of wires, at closing of switch, prevents step variation in the exponential waveform of capacitive current (fig. 3 for battery as generator); moreover, the selected value of capacitance (e. g. 6.8 mF) must prevent a L-C resonance and too much energy storage in the electric field. Hence, vanishing time variable, on DC frame it is possible to draw the corresponding I-U curves. Then, a complete charge has been performed up to equalisation and the corresponding I-U curve has been obtained by the capacitor method. These two characteristics (fig. 4 for battery as generator), determined in the limit conditions during a cycle of discharge-charge (e. g. from p = 30% to 100%), can be used for obtaining the battery parameters involved in the following simulation procedure.

SHAPE * MERGEFORMAT

Fig. 4. The I-U characteristics of battery as generator by the capacitor method.

Fig. 4 shows also the equations of the straight lines which interpolate the experimental I-U curves: in particular the measuring uncertainties of the open circuit voltage and the internal resistances are about 2% and 8%, respectively. Thus, by these data (voltage Ubo, resistances as generator Rbd and as load Rbc) it is possible to calculate the battery parameters according to the following formulas for a 2 V element:

• Ub0 = Ubmin + ap where Ubmin is the open circuit voltage at p = 0;

• Rbd =——- where In is the nominal current corresponding to the ratio of capacity to

1n

discharge time of 10 h for battery as generator (discharge phase);

• Rbc = ^ + yp with 0.3 < p < 0.75 and Rbc = ^with 0.75 < p < 1 for battery as

In In

load (charge phase).

Finally, in table 1 the values of battery parameters, which are used in the system simulation, are reported.

The energy and environmental specialist company Cenergia has in March 2003, in co­operation with the companies Borry Henriksen ApS and the architects Thure Nielsen & Rubow, built a small 32 m2 mobile low-energy wood house with paper granulate insulation from the company Ecofiber and with a 80-85% efficient heat recovery unit from EcoVent.

A new thing is that the wood construction system has been constructed in a way to make the house completely airtight and without cold bridges. Monitoring tests of air leaks of the house have shown the leaks to be so small that they nearly cannot be measured by Cenergia’s "blower door test” equipment. Besides a thermo photography shows that there is in fact no cold bridges at all.

For the first time in Denmark there has, in connection with this project, been used a structural principle introducing a wood concrete plate / rabbet unit with a diffusion open membrane which according to Borry Henriksen makes the construction completely secure as to humidity. Built-in humidity sensors has been used to substantiate this. The paper granulate insulation of the house has been incorporated as to set the wall insulation in contact with the roof insulation, this has been done due to the settling of the insulation granulate.

The test house was built at the Ganlose Sawmill near Copenhagen where they also manufacture weekend cottages.

For the test house there has been used an improved level of insulation even comparing with the new EU-Energy Performance Directive for Buildings, EPD which is expected to be introduced in Denmark in 2005/2006, with an improvement in the level of insulation of approx. 33% as compared to the insulation level of today. Further energy windows, from the companies Velfac and Velux, have been used, and as regards ventilation a high — efficient heat recovery ventilation (HRV) unit with a width of 20 cm only, was placed in a partition wall. The electricity consumption of the HRV unit is very low with only 20-30 W, compared to building regulation demands of maximum 87 W.

The heat recovery ventilation unit requires only short channel elements in order to take air in and out of the house as well as a short air intake channel in the house. Thus the installation price of the heat recovery ventilation unit can be kept at a low level, and at the same time a balanced ventilation can be obtained with a good indoor climate.

On the metallic roof facing south PV modules are installed. This system has been developed by the Finnish manufacturer Rannilla, in such a way that the intake air is directed into a gap under the total roof so a solar heating of the ventilation air is possible. At the same time the idea is that the PV modules (about 13 m2) produce electricity which on a yearly basis makes the house CO2 neutral as regards heating and ventilation.

With the chosen level of insulation and other qualities mentioned the low-energy wooden house can simulate the function of a somewhat larger house according to the "house without heating system” concept which has been used with considerable success for example in Gothenburg in Sweden.

This means that we do not require a usual heating system but require only a very small heating supplement to the house via the ventilation air (max. 900 W for a 100 m2 housing unit). This can for example be achieved by help of a small “mikro” heat pump which together with a solar DHW system can supply the domestic hot water.

Testing of a heat pump solution for the house will be completed during 2004.

Four main types of heat losses have been studied in this article. Flue gas losses are mainly determined by the construction of the pellet burner, the area of the heat exchanger, the dimensions of the flue gas passages etc. Parameters such as combustion power and the surplus air influence strongly the flues gas losses. Flue gas losses are considered to be leakage losses when the burner and the fan have stopped, after the stop phase of combustion has been completed. In order to prevent confusion the flue gas losses are defined as the total flue gas losses minus the leakage losses.

Qfl = Qfltot — Qleak (3)

For leakage losses, the air mass flow through the burner is calculated by type 210 as follows:

T — T

ob outd

50

where m’g50 is the flue gas mass flow at 50 K temperature difference between the gas leaving the burner (Tob) and the outdoor temperature (Toutd). The total leakage losses depend strongly on the thermal mass of the stove or boiler.

The store heat losses depend on the quality and tightness of the store insulation, the store envelope area and the temperature difference between the store content and the ambient. The UA-values for the stores that have been used in the simulations can be found in table 1. The values for the hot water stores in system 1 and 2 are based on theoretical calculation, but also match well with UA-values from measurements for rather well insulated DHW-stores (Vogelsanger, 2004). The combistore of system 3 has been

tested at SERC and two mantle UA-values, one for the top part where the pellet burner is located and one for the bottom part, have been determined. Also the UA-values for the top and the bottom of the tank have been obtained from measurements and theoretical calculations. The UA-values for the combistore of system 4 are given by Bales (2003). The boiler/burner heat losses are obtained from an output of type 210 calculated based on identified heat loss coefficients.

For the necessities of radio-net of hydrometeorological service, a few tens of solar cell systems has been installed in Serbia for past fifteen years in order to supply repeaters at hardly accessible locations (mountain peaks, etc.) with solar power. It has been shown that PV systems used for these purposes are more profitable than previously used diesel aggregates. The advantages of solar cells were particularly obvious during NATO air-raids of Serbia (spring 1999.), when destroyed repeaters at more accessible locations were promptly replaced by stand-by devices with PV supply, so that power failure lasted only as one aircraft-attack. [8]

Extremely rapid development of mobile telephony utilization in past few years, promises creation of wide market for application of solar cells. According to statement of domestic officials, new providers shall refresh competition, improve quality and lower the price of services. Expansion of net of repeater points, many of which will be supplied by PV power, represents an integral part of the process.

Therefore, anticipated dynamics of future application of solar cells in the field of telecommunications is most impressive in comparison with so-far specified applications. (Table 5.).

After rapid increase of application in 2007. and 2008., annual newly installed power rating of solar cells for telecommunication transmitters will be stabilized at the level of about 0,5 MW.

2. Charging of electric vehicle batteries

To deserve the epithet of ecology-friendly vehicles, electric vehicles should charge their accu-batteries with power produced by solar cells.

For small electric vehicles (wheelchairs, bycycles and motor-scoters) solar chargers of 160 W are sufficient. During summer season, these solar chargers provide about 135 kWh of electric power making possible for motor scooter to cover a distance of about 8,500 km.

For larger electric vehicles (small cars with 2-4 seats) solar chargers of 1.6 kW are necessary. With an average annual production of 1.350 kWh, small electric cars may cover a distance of 13,500 km. [9]

In an estimate of dynamics of development of application of solar battery chargers, one should start from relatively high final price of oil derivatives at the domestic market. However, after opening of Yugoslavia to the world, and cancellation of exterior wall of economic sanctions, one can observe mild decrease of these prices and improved supply due to increased competitiveness at this so-far monopolized market.

Therefore it is not expected that in first three years solar chargers for electric vehicles will be widely introduced: 12 kW in 2006, 38 kW in 2007, and 94 kW in 2008. (Table 6.).

With stabilization of the market condition in our country and intensification of ecological requirements, according to the regulations of European Union, conditions will be created for more extensive application of electric-vehicle chargers so that, according to our estimates, already in 2009 year, 214 kW would be installed, while during next (2010.) year another 230 kW would be added.

Dipl. Wirt.-Ing. Frank Heunemann, Berliner Energieagentur GmbH

Although the technology for solar collective systems is available, only few installations have been realised in the commercial housing sector so far. Main reasons for the lack between huge potentials and installed systems are the specificly higher heating costs (compared to conventional boiler systems) and distrust regarding reliability and yields of the technology.

In order to overcome those barriers, the Berlin Energy Agency carries out an initiative within the European SolTherm Initiative in close cooperation with major german housing associations.

The Initiative is financed by

— the European Commission and

— the German Federal Environmental Agency.

Core elements of the initiative “Solar Thermal for Multy Family Houses” are published information like articles in housing magazines, on the internet plattform www. soltherm. info and a brochure dedicated to decision makers in the housing industry.

Main arguments to convince decision makers are successful projects within the housing industry, integrated approaches for the conventional and solar heating system, available supporting instruments and a clear description of legal frameworks. Especially in housing markets with an excess supply of dwellings, solar systems can be useful for accentuation of the offered dwellings.

As an emissions-free and renewable power source that produces energy where it is consumed, solar energy has been championed as a response to looming concerns of resource depletion, air pollution, global warming, national security, and energy security (Byrne et al., 1999 and 2004; STEAB, 2002; Lovins & Lovins, 1982). While PV is not directly cost-competitive with fossil fuel generation in the bulk power service market, there is a growing recognition that PV’s true value can be better understood when evaluated in the context of the energy services market (Byrne et al., 1997, Perez et al., 1999). The PV value chain includes the technology’s value as a peak-shaving and load management tool, as a source of emergency power, as an emission-free generation technology, and as a building component in lieu of glazing or roofing (Byrne et al., 1998). In light of these service-oriented, non-commodity contributions, Byrne et al. assert that, "price comparisons that neglect these economic and social contributions are likely to be misleading on the question of market development” (2004: 293).

While taking externalities into account and evaluating PV as a service technology can dramatically improve the economics of PV, the technology has historically not enjoyed significant market penetration in the energy services industry. From a recent study of 1,500 projects from 51 ESCOs, for example, only one was found to incorporate PV (Goldman et al., 2002). Despite this record, it is conceivable that a variety of factors may prompt ESCOs to re­examine PV as a technology option. As will be discussed below, mounting environmental and security concerns are leading large institutional customers to demand that ESCOs incorporate distributed, renewable energies into their facilities. Furthermore, the rapid change and intense competition that has recently characterized the energy services industry (Vine et al., 1998; Dayton et al., 1998) could inspire ESCOs to turn to PV as a differentiation strategy to attract customers seeking PV’s specific service values (Singh, 2001). Finally, the US Federal government, through FEMP, has created conditions for PV to be evaluated as both a service technology and an energy generation technology by building managers.

While there are several different mechanisms for delivering energy service technologies (utility programs, retail distributors and installers, fee-for-service contracts, etc.), this paper uses performance contracting as the framework for examining PV’s diffusion into the energy services market. In a typical performance contract, an ESCO installs energy or water saving technologies on existing buildings. The resulting utility bill savings are then used to pay back funds borrowed to finance the installations. In this way, facility managers can correct operational inefficiencies without increasing their budgets. Because ESCOs generate their revenue from a portion of the savings, they have a significant incentive to maximize project performance. While directly funding energy projects can be less expensive than performance contracting (Hughes et al., 2003), many facilities in the institutional and private sectors lack the up-front capital necessary to pay for retrofit projects (Rufo, 2001). As a result, performance contracting may be the only way that many buildings can install energy service technologies (Hughes et al., 2003).

While performance contracting has not traditionally been used to deliver renewable energy systems, there are some who have suggested that it could serve as an effective mechanism for PV deployment (Eckhart, 1999). As stand-alone projects, PV systems can be difficult to finance because their simple payback terms extend beyond the maximum terms permitted by
institutional regulations (Stronberg & Singh, 1999). In performance contracts, technologies with longer paybacks, like PV, can be bundled with quicker payback technologies, such as lighting, to produce a blended payback term acceptable to the customer (Raman, 1998: 10). The Federal government encourages this synergy by allowing its facility managers to make investment decisions based on the "life-cycle cost-effectiveness” of an entire project, rather than on the basis of a single project component’s payback term (ORNL, 2003: 4). Without this provision, PV systems would be disallowed from Federal performance contracts since PV systems can have payback terms of 30-40 years, and the maximum Federal contract length is 25 years (FEMP, 2004a).

Ricardo Ruther

LABSOLAR — Laboratorio de Energia Solar
Universidade Federal de Santa Catarina / UFSC
Caixa Postal 476, Florianopolis — SC 88040-900 Brazil
Tel.: +55 48 331 5174 FAX: +55 48 331 7615 Email: ruther@mbox1.ufsc. br

LABSOLAR is the solar energy research laboratory at Universidade Federal de Santa Catarina (UFSC) in southern Brazil. The laboratory’s activities in the field of photovoltaics (PV) started in 1997, with solar thermal and radiometry research going on since 1989. Over the last seven years, LABSOLAR has been engaged in promoting PV in Brazil in a number of scientific and dissemination projects. Training human resources with a sound scientific and technological background in the field has also been a major activity, carried out to multiply the still small number of PV specialists in the country. This paper reviews some of the most relevant scientific, dissemination and capacity building projects.

1. The first grid-connected, building-integrated, thin-film PV system in Brazil

In September 1997 the first grid-connected, building-integrated, thin-film PV system in Brazil was installed at LABSOLAR, on the main campus at Universidade Federal de Santa Catarina. The PV installation consists of a 2kWp thin-film amorphous silicon (a-Si) array, plus DC/AC inverter, irradiance (horizontal and plane-of-array), and temperature (ambient and back-of-module) measurement instrumentation, and a dedicated data logging system. The generator is comprised of 54 opaque and 14 semitransparent, double-junction (pin-pin), glass-glass 60 x 100cm2 a-Si modules from RWE-Schott, with a total power output rated at 2078Wp at STC, and a total surface area of ~40m2. The total power is distributed in four ~500Wp sub-systems, and fed to four independent single-phase, line-commutated sinewave inverters (from Wurth Elektronik GmbH, model WE 500 NWR, each rated at 650W). The PV array uses unframed modules designed for BIPV applications, that were installed onto a simple steel structure retrofitted as an overhang to the existing building, facing true north with latitude tilt (27o). Electrical parameters as well as irradiance and temperature data are continuously measured and stored at four-minute intervals. Figure 1 shows the BIPV system; further details on PV system design and configuration have been presented elsewhere [1,2].

The project’s main objectives are twofold: (i) demonstration and dissemination of the concept of PV in buildings in Brazil; and (ii) a long-term experiment on the seasonal effect affecting the performance of thin film a-Si, with emphasis on determining its suitability for operation under the higher temperatures common in building-integrated PV systems in warm and sunny climates. Seasonal performance shifts due to both Staebler-Wronski degradation/annealing [3] mechanisms enhanced by higher operating temperatures in summer, and to seasonal shifts in the spectral content of sunlight, as well as a small temperature coefficient of power, render a-Si a relatively better PV converter in summer than in wintertime, in contrast to the performance profile of crystalline silicon PV converters, which are more efficient in winter due to lower operating temperatures.

Performance results on the fully monitored BIPV installation operating continuously for over six years have indicated peculiarities in system sizing (PV array vs. inverter rated power) and have demonstrated that a-Si is a good performer at sunny sites and warm climates. Performance ratios (PR, defined as the ratio of the energy output and the rated efficiency, times the total solar radiation incident on the PV module’s surface) obtained during this period averaged 91.4% (DC) and 81.5% (AC), and annual AC energy yield was 1231kWh/kWp for a 1507kWh/m2 annual plane-of-array irradiation level at the site. While in the first year (1997 data) the a-Si modules showed a small but negative temperature coefficient of power (TcoeffPmax = -0.22%/oC), after stabilisation of the light-induced degradation inherent to the a-Si material (the Staebler-Wronski effect [3]) our most recent results show that TcoeffPmaX drops to negligible (and positive, TcoeffPmaX = +0.08%/°C) values (2003 data); i. e., in the stabilised level, the net performance of a-Si becomes somewhat independent of temperature, as shown in Figure 2.

One further peculiarity that can be shown by the analysis of the solar radiation data measurements over the period, is the issue of inverter x PV array sizing with respect to prevailing irradiation levels. Because there is a considerable amount of energy at high irradiation levels available at the site, inverter undersizing might be a considerable limitation to PV systems’ annual energy yields. As shown in Figure 3, some 15% of the total radiation reaching the PV modules is in the > 1000W/m2 range, and nearly 60% of the total available energy is in the > 700W/m2 range, while only less than 10% of the solar energy available lies in the < 200W/m2 range. Under conditions as such, and using thin-film a-Si PV modules, PV array vs. inverter rated power ratios < 1 will lead to smaller power losses. Furthermore, inverter efficiencies usually peak at power levels below maximum nominal power (i. e, highest efficiency takes place at partial loading), and high inverter loading levels lead to high inverter operating temperatures, reducing the DC to AC conversion performance even further.

Figure 3: Distribution of the plane-of-array irradiation in Florianopolis (48°W, 27°S), distributed at 100W/m2 bins, averaged for the six years of continuous operation. A considerable portion of the incident energy occurs at high (> 700W/m2) irradiation levels.

Following up on this project, two other BIPV systems have been further installed on campus to demonstrate to University students, our future decision-makers, the potential of this energy source. Figures 4 and 5 show these two most recent BIPV installations.

H. D. Stryczewska, K. Nalewaj, T. Janowski, Lublin University of Technology Faculty of Electrical Engineering and Computer Science, Institute of Electrical Engineering and Electrotechnologies

1. Introduction

Swimming pools water treatment in Poland is mainly carried out through chlorination. The better solution from the point of view of environment protection is the application of ozone, well-known sterilization and disinfection agent, commonly used nowadays for water and wastes treatment. Lublin Province has been regarded as the second in respect of the insolation conditions in Poland. In this upland region there are few rivers and natural lakes and therefore the need for open-air swimming pools in the summer season arises. The ozone generation power supply system requires AC high voltage in the range of 10 to 20 kV and frequency of 50-1000 Hz. Photovoltaic panels produce energy at the DC voltage of several tens volts and this energy should be converted to be applied as the power for the ozone generation system. The main components of the ozone water treatment system energized from photovoltaic panels are DC/AC converter and high voltage transformer. The value and the frequency of the supply voltage are important factors influencing the ozone productivity. The greater frequency and voltage means the greater ozone productivity but also the greater power losses in the HV transformer. Since the ozone generator represents a non-linear active — capacitive load while the DC/AC converter with HV transformer is of active — inductive nature, they may cooperate in resonance conditions that assures the best efficiency and productivity of the ozone installation. To ensure the optimal operation of the solar energy energized ozone installation the frequency of the supply voltage should be carefully estimated. The paper presents the results of investigations of the ozone generator laboratory model that consists of the 1100 mm long discharge tube of 50 W energized from photovoltaic system that comprises six batteries of 450 W total power. The application of photovoltaic panels to supply swimming pool water treatment ozonizers is the solution which is consistent with environment protection regulations. Since the most favorable conditions for using solar energy in Poland are during spring and summer season (80% of total annual insolation is noticed during six months, from early June until end of September) at periodic operation of the ozonizer, photovoltaic panel may completely fulfill the demand for energy. The usage of renewable energy in Poland in relation to its potential is still low. In neighboring countries of comparable solar conditions the usage of solar energy is much higher.

Gerald Kunz, Andreas Wagner

University of Applied Sciences Dortmund
Postfach 10 50 18, 44047 Dortmund, Germany
wagner@fh-dortmund. de

1. Introduction

The principal task of photovoltaic measurement is to monitor the correct function of all components of a PV-system, to detect problems and to iniciate maintenance and repair where necessary, otherwise defects will result in losses in energy yield. As the energy yield decreases if the peak power decreases, the measurement of the peak power of the complete PV-generator is necessary on site under natural ambient conditions [1], [3]. If a decrease of the peak power is detected, an increase of the internal series resistance can be the cause for the decrease of the peak power.

For the determination of the internal series resistance out of one dark IV-curve several methods are known, e. g. [7]. The dark IV-curve can be easily measured for single cells or singele modules. For the measurement of the dark IV-curve an external DC-current source is necessary. Such strong external DC-current sources for large PV-generators (several kW) are very expensive and so hardly available.

For the measurement of the internal series resistance under illumination two IV-curves of different irradiance but of the same spectrum and at the same temperature are necessary according to IEC 60891 [6]. With a new method for the simulation of the second IV-curve, using the effective solar cell equation-method [2], now it is possible to obtain the internal series resistance out of only one IV-curve measured under illumination.

2. Effective Solar Cell Characteristic

The purpose of I-V-characteristic approximation by means of equivalent circuit diagrams lies in the explicit calculability of the I-V-curve. A calculation method for the internal series resistance Rs out of a measured I-V-curve demands the following options:

— Explicit calculation of current-voltage-characteristic equation V(I)

— Explicit calculation of the parameters of the characteristic equation from the measured parameters Isc, Voc, I

— Degree of accuracy of approximation within the range of degree of accuracy of measuring method (state-of-the-art: 1%)

— The unknown parameter Rs, which shall be the result of the calculation, must not be a parameter of the current-voltage-characteristic equation.

The "Effective Solar Cell Characteristic” [1], [2] meets all four demanded options, as it has the same approximation accuracy as the two-diodes-model [1] and does not include Rs.

The equivalent circuit diagram contains a fictitious component which presents either a positive or a negative resistance. This parameter is called Rpv (photovoltaic resistance). Important: the true internal series resistance Rs must not be confused with the photovoltaic resistance Rpv. The determination of the actual Rs will be desribed later. Follows the effective solar cell characteristic:

V +1 Rpv

I = Iph — 1o(e V -1) (1)

Explicit version

V = V ln(-^———— -1 Rpv (2)

10

With the introduction of the photovoltaic resistance the explicit calculability of matching problems between solar generators and several loads is possible with an accuracy of 1%, related to the maximum power of the solar generator.

For the determination of the 4 independent equation parameters Rpv, VT, I0, Iph there are also 4 independent measured parameters necessary. In the present case these measured parameters are Isc, Voc, Ipmax, Vpmax. If in addition the slope M at open-circuit voltage is to be considered

-K)

with the equation-constants

-5.411

6.450

3.417

-4.422

Important notice: these equation-constants are not empirical constants, they are, independent of material properties of the solar cell.

The equation parameters can be determined as follows [2]:

I V I -^

Rpv=-M+7=41 — J*4 VT=-(M +Rpv) Isc h=LerT Iph = Ic (5)

pmax p max pmax

Example 1: Monocrystalline PV-Module BP585F:

Check of approximation quality of the effective solar cell characteristic: Comparison with measured values.

Voltage (V)

Fig.2. IV-curve approximation of a
crystalline PV-module

Example 2: Amorphous PV-module Solarex MSX 40:

Check of approximation quality of the effective solar cell characteristic: Comparison with measured values.

(7)

Voltage [V]

Fig.3. IV-curve approximation of an
amorphous PV-module