Search NASA⌕ Search

SEARCH · Search NASA

Results for “solar stringing”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Optimal interconnection of three-terminal tandem solar cells

Three-terminal (3T) tandem solar cells require an adapted module integration scheme in order to explore their full efficiency potential. The three terminals allow to extract the power of the top and bottom cell separately. In a cell string, the wide bandgap top cells are interconnected in parallel to multiple bottom cells resulting in a parallel/series interconnection. This interconnection scheme affects the operation of the subcells, the resulting current path between the subcells, the layout of the cell interconnects, and the system level. Here, we analyze by simulations and experiments the aspects of the module integration of series- and reverse-connected 3T cells with their practical impact on module processes and performance as well as the effect of varying voltage ratios on the string-end losses. If the subcells are connected in series, the module integration requires insulation layers and significantly longer interconnects compared to devices with reverse-connected subcells. Tandem devices with a reverse connection and a voltage ratio between top and bottom cell of 2:1 allow a lean interconnection design and low integration losses. Here, we present an approach for the integration of bypass diodes for the protection against shading effects that allow to minimize string-end and shading losses for a system of modules featuring 3T cells.

14 SOLAR ENERGY↗
DOE OSTI2021

Ganged-PV System Evaluation

The following report contains data and data summaries collected for the SkySun LLC elevated Ganged PV arrays. These arrays were fabricated as a series of PV panels in various orientations, suspended by cables, at the National Solar Thermal Test Facility (NSTTF) at Sandia National Laboratories (SNL). Starting in February of 2021, Sandia personnel have collected power and accelerometer data for these arrays to assess design and operational efficacy of varying ganged- PV configurations. The purpose of this power data collection was to see how the various array orientations compare in power collection capability depending on the time of day, year, and the specific daily solar direct normal irradiance (DNI). The power data was collected as a measurement of the power output from the various series strings. The project team measured direct current (DC) voltage and current from the respective arrays. The accelerometer data was collected with the purpose of demonstrating potential destructive mode shapes that could take place with each of the arrays when exposed to high winds. This allowed the team to evaluate whether impacts with respect to specific array orientations using suspended cables is a safe design. All data collection was performed during calendar year 2021.

14 SOLAR ENERGY↗
DOE OSTI2020

Conductive Adhesives for Metallization of Interdigitated Back Contact Solar Cells

The metallization and interconnection of Si solar cells to form a module is usually a multi-step process: cells are metallized individually, soldered into strings, and subsequently assembled into a module. Furthermore, the metallization process for individual cells must be compatible with the doped surfaces being contacted, which creates additional challenges when moving from diffused junctions to heterojunctions and/or passivated contact structures. To mitigate these problems and streamline module manufacturing for the case of interdigitated back contact (IBC) cell modules, we developed an approach wherein unmetallized IBC cells are bonded directly to a circuitized backsheet using a conductive adhesive (CA) that only conducts out-of-plane. The metal/CA/silicon stack is bonded by hot-pressing at 100-200 degrees C.For a CA consisting of ethylene vinyl acetate (EVA) filled with Ag-coated spheres or indium powder we find that contact resistivities in the range of 1-10 Wcm 2 are obtained, regardless of which conductive filler and which hot pressing parameters are used. XPS revealed that about 1-2 nm EVA residue bonds to the Si in these samples, suggesting the formation of an insulating barrier that is responsible for the high contact resistance. Using indium powder alone, improved contact resistivities <0.6 Wcm 2 , high shunt resistances, and an implied open-circuit voltage loss below 10 mV were obtained. Furthermore, a cost estimate is presented, indicating that substantial cost savings of up to $10/m 2 , or about $0.05/W DC , are possible through CA-based IBC module manufacturing.

14 SOLAR ENERGY↗
DOE OSTI2020

Low Cost (CAPEX and variable): Tool design for cell and module fabrication with thin, free-standing silicon wafers

This project aimed to develop technologies that can potentially enable free-standing thin (<80 μm) wafer in today’s manufacturing lines with high production yield, and thereby reduce capex barriers of silicon photovoltaics cells and modules. One of the major benefits is that thin wafer dramatically reduces the amount of polysilicon required. As a result, it can lead to reduction in the capital expenditures associated with polysilicon refining and wafer fabrication, which together are more than half of the total capital expenditure to manufacture Si PV module. We focused our efforts on developing the tools needed to enable high yield fabrication of wafer, cell, and module with thin silicon wafers. However, as the wafer thickness reduces, the major challenge is that wafer breakage increases significantly. Three technological areas were explored in this project to improve the production yield of the silicon wafer, namely detection of edge cracks via dark-field near-infrared (NIR) scattering; (2) wafer handling using controlled temperature profiles; (3) manufacturable low-stress cell interconnection for multiwire. First, the formation of wafer cracks in submillimeter length is one of the reasons that causes wafer breakages. Crack detection tools are needed to enable us to locate and track the wafer crack during manufacturing, so that we can improve the process to reduce initialization. The state-of-the-art crack detection technique cannot fulfill the need for measuring submillimeter edge cracks detrimental for thin wafers. The prototype developed in this project demonstrates the scanning of microcracks near wafer edges. With a semi-automatic laboratory setup, the submillimeter cracks were reliably detected near the edges in multi-Si wafers. The smallest detectable crack is 200 µm in length in slow scans; and submillimeter cracks are detected in high-throughput scans at the scan speed of >0.5 m/s, which is compatible with the inline detection of a manufacturing line at least 1 sec/wafer. This detection limit is a significant advancement in comparison to the benchmarked industrial tool. Second, wafer handling with the well-controlled temperature profile was thought to be the solution to reduce crack initiation and propagation during the manufacturing. However, without crack detection being widely adopted in production line, we did not find a strong industrial pull toward this technology. We did an initial literature survey and then diverted our efforts to the other tasks. Third, the innovation on low-stress multi-wire interconnection tackles a fundamental problem in the standard interconnection scheme. The standard over-under “zig-zag” interconnection induces a significant amount of stress into the soldering point on the cell whenever PV module is under stress, e.g., thermal cycling, transportation, and installation. Therefore, the interconnection process was re-designed in this project to allow for significant movement between adjacent solar cells, e.g., due to thermal expansion, without building up stresses on the solar cells or solder joints. The new interconnection method with the cross-connect wire also simplifies the tabbing and stringing process by replacing the standard over-under method with an off-cell interconnect from top to bottom. A manual tabbing and stringing tool for this new process was prototyped in the lab to demonstrate the fabrication of this new interconnection design. During the test with brass sheets as our “testing cells”, it was found that the mechanical cycling test only broke the interconnection after more than 50,000 cycles, which is equivalent to more than 130 years of the day-and-night thermal cycles. Lastly, throughout the project, we continuously analyzed the PV market with techno-economic analysis to identify the opportunity for thin Si adoption. Even though the drastic cost reduction has already happened in the past five years, our analysis results indicated that we can still save quite significantly in both manufacturing cost and factory capex, Particularly, in order to grow the PV manufacturing capacity to multi-terawatt level, reducing the thickness of silicon wafer is one of the most effective ways to quickly reduce factory capex, and sustain the high growth rate. The technologies developed in this project are readily available to provide some assistances in tackling the production yield problem.

14 SOLAR ENERGY↗
NASA NTRS2005

Experimental Study of Arcing on High-voltage Solar Arrays

The main obstacle to the implementation of a high-voltage solar array in space is arcing on the conductor-dielectric junctions exposed to the surrounding plasma. One obvious solution to this problem would be the installation of fully encapsulated solar arrays which were not having exposed conductors at all. However, there are many technological difficulties that must be overcome before the employment of fully encapsulated arrays will turn into reality. An alternative solution to raise arc threshold by modifications of conventionally designed solar arrays looks more appealing, at least in the nearest future. A comprehensive study of arc inception mechanism [1-4] suggests that such modifications can be done in the following directions: i) to insulate conductor-dielectric junction from a plasma environment (wrapthrough interconnects); ii) to change a coverglass geometry (overhang); iii) to increase a coverglass thickness; iiii) to outgas areas of conductor-dielectric junctions. The operation of high-voltage array in LEO produces also the parasitic current power drain on the electrical system. Moreover, the current collected from space plasma by solar arrays determines the spacecraft floating potential that is very important for the design of spacecraft and its scientific apparatus. In order to verify the validity of suggested modifications and to measure current collection five different solar array samples have been tested in large vacuum chamber. Each sample (36 silicon based cells) consists of three strings containing 12 cells connected in series. Thus, arc rate and current collection can be measured on every string independently, or on a whole sample when strings are connected in parallel. The heater installed in the chamber provides the possibility to test samples under temperature as high as 80 C that simulates the LEO operational temperature. The experimental setup is described below.

Vayner, Boris↗
NASA NTRS1993

p-mode frequency variation in relation to global solar activity

We show that p-mode frequency variations correlate remarkably well with the variations of six solar activity indices over a 6 yr period from 1984 October to 1990 November, including both the large variation from solar minimum to solar maximum and smaller variations observed over approximately 1 month intervals during solar maximum. The quality of correlation as seen visually and as measured by two statistical tests differs significantly among the six activity indices, and we briefly speculate on possible reasons for this. Observations used in this study come from the HAO/NSO Fourier tachometer (FTACH) and include the spherical harmonic degree range l greater than 20 and equal to 60 or less and frequency range between 2600 and 3200 micro-Hz. The data are divided into 18 separate epochs with time string duration ranging from a minimum of 18 days to a maximum of 45 days. We have particularly good coverage during the early part of solar maximum of cycle 22.

Bachmann, Kurt T.↗
NASA NTRS2003

Experimental Study of Arcing on High-Voltage Solar Arrays

The main obstacle to the implementation of a high-voltage solar array in space is arcing on the conductor-dielectric junctions exposed to the surrounding plasma. One obvious solution to this problem would be the installation of fully encapsulated solar arrays which were not having exposed conductors at all. However, there are many technological difficulties that must be overcome before the employment of fully encapsulated arrays will turn into reality. An alternative solution to raise arc threshold by modifications of conventionally designed solar arrays looks more appealing, at least in the nearest future. A comprehensive study of arc inception mechanism suggests that such modifications can be done in the following directions: 1) To insulate conductor-dielectric junction from a plasma environment (wrapthrough interconnects); 2) To change a coverglass geometry (overhang); 3) To increase a coverglass thickness; 4) To outgas areas of conductor-dielectric junctions. The operation of high-voltage array in LEO produces also the parasitic current power drain on the electrical system. Moreover, the current collected from space plasma by solar arrays determines the spacecraft floating potential that is very important for the design of spacecraft and its scientific apparatus. In order to verify the validity of suggested modifications and to measure current collection five different solar array samples have been tested in a large vacuum chamber. Each sample (36 silicon based cells) consists of three strings containing 12 cells connected in series. Thus, arc rate and current collection can be measured on every string independently, or on a whole sample when strings are connected in parallel. The heater installed in the chamber provides the possibility to test samples under temperature as high as 80 C that stimulates the LEO operational temperature. The experimental setup is described below.

Vayner, Boris↗
NASA NTRS1986

Bimodality of the solar cycle

An alternative characterization of the solar cycle is offered that is consistent with the sunspot data for cycles 1-20 (1775-1976) but suggests a different physical interpretation. For sunspot cycles 1-20, all cycles occurred in strings (two to six cycles in length) during which the period remained longer or shorter than the sample mean period. These strings have coincided with long-term trends of growth or decay in the amplitude of the cycle. In six out of six cases, the period of the cycle has switched from long to short (or the reverse) in coincidence with the turning points in the long-term trend. This suggests that the solar dynamo has two modes with different mean periods. In the short-period mode, the amplitude of the cycle grows; in the long-period mode, the amplitude decays. The transition between modes has occurred at irregular intervals. A persistence of the long-period mode would eventually produce a grand minimum such as the Maunder minimum; a persistence of the short-period mode would produce a grand maximum. Unless the present interval between transitions turns out to be shorter than any previously observed interval, the present cycle (cycle 21) is part of a long-period, decaying trend and will be of longer-than-average duration (more than 133 months).

Rabin, D.↗
DOE OSTI2020

Solar/Photovoltaic DC Systems: Information for Electrical Workers and Firefighters

Solar photovoltaic (PV) systems are common and continue to gain popularity. This article helps electrical workers and firefighters understand basic operating principles and hazards of PV dc arrays. The effects of solar radiation and temperature on power output are discussed including; PV-module testing standards; methods for calculating the number of modules in a PV string; some National Electrical Code (NEC) guidelines that are aimed toward improving array safety; dc-array commissioning, periodic maintenance, and testing; arc-flash-hazard potential ways firefighters can work safely around PV arrays; potential risks posed by moonlight and other light sources; some unique dc-system hazards. We also present statistics on PV dc-array electrical incidents and injuries.

14 SOLAR ENERGY↗
DOE OSTI2023

Voltage mapping and local defects identification in solar cells using non-contact method

Electroluminescence, infrared imaging, and current–voltage curve techniques are used to detect and map underperforming cells in a photovoltaic module or the modules in a photovoltaic string. In this work, we present a non-contact electrostatic voltmeter technique to detect and map the underperforming spots in a cell and the cells in a module. This non-contact technique directly maps the charged surface voltage (671mV) of the superstrate glass, and it had an 11-mV difference with the voltmeter values (660mV). Another data set of voltage values obtained by electroluminescence images conversion into a voltage map showed a difference of 7mV with the non-contact voltmeter values. Further, the direct voltage values obtained at various good and poor-performing spots of the cells using this technique are 3.69V and 3.79V and are validated using the voltage values obtained in electroluminescence analysis and the difference in voltage obtained by the two techniques is determined to be less than 2%. In this work, we combine the strengths of two complementary techniques of the electrostatic voltmeter (strength: quantitative) and electroluminescence (strength: spatial mapping) to obtain a quantitative spatial mapping of defects. Furthermore, this work is extendable to detect the poor-performing modules in solar PV power plants.

14 SOLAR ENERGY↗
NASA NTRS2004

International Space Station Solar Array Wing On-Orbit Electrical Performance Degradation Measured

The port-side photovoltaic power module (P6) was activated on the International Space Station in December 2000. P6 provides electrical power to channels 2B and 4B to operate ISS power loads. A P6 is shown in the preceding photograph. This article highlights the work done at the NASA Glenn Research Center to calculate the on-orbit degradation of the P6 solar array wings (SAWs) using on-orbit data from December 2000 to February 2003. During early ISS operations, the 82 strings of photovoltaic cells that make up a SAW can provide much more power than is necessary to meet the demand. To deal with excess power, a sequential shunt unit successively shunts the current from the strings. This shunt current was the parameter chosen for the SAW performance degradation study for the following reasons: (1) it is based on a direct shunt current measurement in the sequential shunt unit, (2) the shunt current has a low temperature dependence that reduces the data correction error from using a computationally derived array temperature, and (3) the SSU shunt current is essentially the same as the SAW short-circuit current on a per-string basis.

Gustafson, Eric D.↗
DOE OSTI2026

Extending Component Lifetime And Improving Inverter Reliability (ECLAIIR)

Inverter reliability remains one of the most persistent challenges limiting the performance, availability, and economic viability of utility‑scale photovoltaic (PV) plants. Industry data consistently show that inverters account for the highest share of corrective maintenance events and unplanned outages across PV fleets. These failures result in energy losses, increased O&M costs, and reduced confidence in long‑term solar asset performance. Motivated by these challenges, this project—Extending Component Lifetime and Improving Inverter Reliability (ECLAIIR)—was undertaken to systematically investigate inverter degradation and failure mechanisms, develop predictive maintenance capabilities, and establish data‑driven pathways to improve service life and reduce the Levelized Cost of Energy (LCOE) for large‑scale PV systems. The primary goal of the project was to identify pre‑failure signatures in string inverters using both lab‑based accelerated lifetime testing and field‑based data and to develop predictive maintenance algorithms that can anticipate inverter faults before they occur. Through collaboration with inverter testing laboratory, solar PV plant owner, and failure‑analysis experts, the project advanced the technical understanding of inverter reliability. By instrumenting inverters with thermistors, humidity sensors, power‑quality meters, and acoustic sensors, the research established how multiple sensing modalities can reliably detect deviations from normal behavior hours to days before failure. These findings substantially enhance scientific understanding of inverter failure kinetics and provide the PV industry with the most comprehensive cross‑OEM characterization of early‑stage failure indicators reported to date. Technically, the project demonstrated the effectiveness of predictive maintenance by developing and validating the PreDICT (Predictive Diagnostics of PV Inverters Using Condition Monitoring and Trend Analysis) framework—a multi‑layer diagnostic architecture combining peer‑to‑peer analytics, historical trend modeling, and advanced machine‑learning techniques such as the Sequential Conditional Variational Autoencoder (SCVAE). This predictive model achieved more than 90% accuracy in detecting pre‑failure conditions and provided up to four days of lead time before inverter failure in field scenarios. Economically, the project’s LCOE analysis showed that predictive maintenance can reduce lifetime energy losses and minimize corrective maintenance interventions. Modeling indicated that, depending on inverter failure rates and replacement timelines, predictive maintenance can significantly reduce LCOE impacts associated with inverter downtime: from as high as 19.4% under conventional maintenance strategies to 0.1%–10.17% when predictive analytics are adopted. These results confirm that predictive maintenance is both technically feasible and economically advantageous for utilities and plant operators. The project’s findings also have broad public benefit. By improving inverter reliability and reducing downtime, predictive maintenance directly increases electricity generation from existing PV assets. Enhanced reliability lowers operational costs for utilities, which can translate over time into lower energy costs for consumers. Furthermore, the project’s technical publications, conference presentations, and industry workshops ensure that knowledge gained is shared broadly across the solar industry, supporting workforce development and enabling utilities of all sizes to adopt modern asset‑health monitoring practices. The retrofitting case study and service‑life prediction framework further support informed decision‑making for aging PV fleets, helping operators extend system life and reduce electronic waste. In summary, the ECLAIIR project significantly advanced the state of knowledge on inverter degradation, demonstrated the technical and economic value of predictive maintenance, and delivered actionable tools and insights that support more reliable, cost‑effective, and sustainable PV plant operation. The outcomes of this project will continue to inform utility practices, guide inverter design improvements, and strengthen the long‑term performance of solar assets nationwide.

14 SOLAR ENERGY↗
NASA NTRS1983

Hiding Solar-Array Bus Bars

End terminals mounted under cells, maximizing usable illuminated area. Reconfigured solar panel bus bars placed under cells, reducing portion of module area not occupied by active silicon. Underside of last cell in string of cells serves as contact for positive bus. Negative tab of last cell in string is wrapped around from top of cell. Tabs are connected to output boards mounted under cells.

Hufnagel, W. F.↗
DOE OSTI2023

Using Current Data to Detect Hardware Faults at Solar Plants

Monitoring amperage data is an effective means of detecting faults in PV plant data. Utilizing amperage data collected at the combiner box gives plant operators an up-to-date list of faulted equipment, allowing them to coordinate maintenance needs at much shorter intervals than previously. Shorter maintenance intervals will increase PV plant production levels, narrowing the gap between expected and actual PV plant performance. The amperage monitoring method performs at a high level, with a string-outage related fault detection True Positive Rate of 46% and False Positive Rate of 8%.

14 SOLAR ENERGY↗
NASA NTRS2006

In-Vacuum Photogrammetry of a Ten-Meter Square Solar Sail

Solar sailing is a promising, future in-space propulsion method that uses the small force of reflecting sunlight to accelerate a large, reflective membrane without expendable propellants. One of two solar sail configurations under development by NASA is a striped net approach by L'Garde, Inc. This design uses four inflatably deployed, lightweight booms supporting a network of thin strings onto which four quadrants of ultrathin aluminized membranes are attached. The NASA Langley Research Center (LaRC) provided both experimental and analytical support to L'Garde for validating the structural characteristics of this unique, ultralightweight spacecraft concept. One of LaRC's responsibilities was to develop and apply photogrammetric methods to measure sail shape. The deployed shape provides important information for validating the accuracy of finite-element modeling techniques. Photogrammetry is the science and art of calculating 3D coordinates of targets or other distinguishing features on structures using images. A minimum of two camera views of each target is required for 3D determination, but having four or more camera views is preferable for improved reliability and accuracy. Using retroreflective circular targets typically provides the highest measurement accuracy and automation. References 3 and 4 provide details of photogrammetry technology, and reference 5 discusses previous experiences with photogrammetry for measuring gossamer spacecraft structures such as solar sails. This paper discusses the experimental techniques used to measure a L Garde 10-m solar sail test in vacuum with photogrammetry. The test was conducted at the NASA-Glenn Space Power Facility (SPF) located at Plum Brook Station in Sandusky, Ohio. The SPF is the largest vacuum chamber in the United States, measuring 30 m in diameter by 37 m in height. High vacuum levels (10(exp -6) torr) can be maintained inside the chamber, and cold environments (-195 C) are possible using variable-geometry cryogenic cold walls. This test used a vacuum level of approximately 1 torr (sufficient for structural static/dynamic characterization) and instead of using the cryogenic cold walls, used local LN2 cold plates underneath each of the four cold-rigidizable solar sail booms instead.

Pappa, Richard S.↗
NASA NTRS1981

Design description of the Schuchuli Village photovoltaic power system

A stand alone photovoltaic (PV) power system for the village of Schuchuli (Gunsight), Arizona, on the Papago Indian Reservation is a limited energy, all 120 V (d.c.) system to which loads cannot be arbitrarily added and consists of a 3.5 kW (peak) PV array, 2380 ampere-hours of battery storage, an electrical equipment building, a 120 V (d.c.) electrical distribution network, and equipment and automatic controls to provide control power for pumping water into an existing water system; operating 15 refrigerators, a clothes washing machine, a sewing machine, and lights for each of the homes and communal buildings. A solar hot water heater supplies hot water for the washing machine and communal laundry. Automatic control systems provide voltage control by limiting the number of PV strings supplying power during system operation and battery charging, and load management for operating high priority at the expense of low priority loads as the main battery becomes depleted.

Ratajczak, A. F.↗
NASA NTRS2003

Advanced Rainbow Solar Photovoltaic Arrays

Photovoltaic arrays of the rainbow type, equipped with light-concentrator and spectral-beam-splitter optics, have been investigated in a continuing effort to develop lightweight, high-efficiency solar electric power sources. This investigation has contributed to a revival of the concept of the rainbow photovoltaic array, which originated in the 1950s but proved unrealistic at that time because the selection of solar photovoltaic cells was too limited. Advances in the art of photovoltaic cells since that time have rendered the concept more realistic, thereby prompting the present development effort. A rainbow photovoltaic array comprises side-by-side strings of series-connected photovoltaic cells. The cells in each string have the same bandgap, which differs from the bandgaps of the other strings. Hence, each string operates most efficiently in a unique wavelength band determined by its bandgap. To obtain maximum energy-conversion efficiency and to minimize the size and weight of the array for a given sunlight input aperture, the sunlight incident on the aperture is concentrated, then spectrally dispersed onto the photovoltaic array plane, whereon each string of cells is positioned to intercept the light in its wavelength band of most efficient operation. The number of cells in each string is chosen so that the output potentials of all the strings are the same; this makes it possible to connect the strings together in parallel to maximize the output current of the array. According to the original rainbow photovoltaic concept, the concentrated sunlight was to be split into multiple beams by use of an array of dichroic filters designed so that each beam would contain light in one of the desired wavelength bands. The concept has since been modified to provide for dispersion of the spectrum by use of adjacent prisms. A proposal for an advanced version calls for a unitary concentrator/ spectral-beam-splitter optic in the form of a parabolic curved Fresnel-like prism array with panels of photovoltaic cells on two sides (see figure). The surface supporting the solar cells can be adjusted in length or angle to accommodate the incident spectral pattern. An unoptimized prototype assembly containing ten adjacent prisms and three photovoltaic cells with different bandgaps (InGaP2, GaAs, and InGaAs) was constructed to demonstrate feasibility. The actual array will consist of a lightweight thin-film silicon layer of prisms curved into a parabolic shape. In an initial test under illumination of 1 sun at zero airmass, the energy-conversion efficiency of the assembly was found to be 20 percent. Further analysis of the data from this test led to a projected energy conversion efficiency as high as 41 percent for an array of 6 cells or strings (GaP, AlGaAs, InGaP2, GaAs, and two different InGaAs cells or strings).

Mardesich, Nick↗
NASA NTRS1995

On the universality of microlensing in quadruple gravitational lenses

It is well known that multiply imaged quasars are likely to be affected by microlensing. Quadruply imaged systems are especially useful laboratories for studying microlensing because their macrolens models are relatively well constrained. We begin with analytical results for a simple family of galaxy models. These results can be used to estimate the magnifications and time delays for the quadruple systems. We compute expected brightness fluctuations due to microlensing in several such systems for a range of source sizes. Among these we treat for the first time the limiting case of a completely unresolved source. For the case of MG 0414+0534 we interpret the discrepant optical-to-radio flux ratios for the different components as the result of microlensing. On the assumption that the lensing galaxy is roughly isothermal this gives a 95% confidence upper limit on the optical source size of 10(exp 16) cm x (mean value of M)/0.1 solar mass(exp 1/2) where (M) is the average stellar mass of the lensing galaxy. For more centrally concentrated macromodels the upper limit is greater. Sufficiently long strings of photometric observations can in principle constrain the degree of concentration.

Witt, Hans J.↗