Photovoltaic system

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"Solar park" or "PV farm"
PV array on an old house

Photovoltaic systems (PV system) use solar panels to convert sunlight into electricity. A system is made up of one or more solar panels, usually a controller or power converter, and the interconnections and mounting for the other components. A small PV system may provide energy to a single consumer, or to an isolated device like a lamp or a weather instrument. Large grid-connected PV systems can provide the energy needed by many customers.

Contents

[edit] Photovoltaic modules

Due to the low voltage of an individual solar cell (typically ca. 0.5V), several cells are wired in series in the manufacture of a "laminate". The laminate is assembled into a protective weatherproof enclosure, thus making a photovoltaic module or solar panel. Modules may then be strung together into a photovoltaic array. The electricity generated can be either stored, used directly (island/standalone plant)or fed into a large electricity grid powered by central generation plants (grid-connected/grid-tied plant) or combined with one or many domestic electricity generators to feed into a small grid (hybrid plant).[1] Depending on the type of application, the rest of the system ("balance of system" or "BOS") consists of different components. The BOS depends on the load profile and the system type. Systems are generally designed in order to ensure the highest energy yield for a given investment.[citation needed]

[edit] Photovoltaic arrays

A photovoltaic array is a linked assembly of PV modules.
The solar panels on this small yacht at sea can charge the 12 volt batteries at up to 9 amperes in full, direct sunlight.

A photovoltaic array (or solar array) is a linked collection of solar panels.[2]

The power that one module can produce is seldom enough to meet requirements of a home or a business, so the modules are linked together to form an array. Most PV arrays use an inverter to convert the DC power produced by the modules into alternating current that can power lights, motors, and other loads. The modules in a PV array are usually first connected in series to obtain the desired voltage; the individual strings are then connected in parallel to allow the system to produce more current. Solar arrays are typically measured under STC (standard test conditions) or PTC (PVUSA test conditions), in watts, kilowatts, or even megawatts.[citation needed]

Costs of production have been reduced in recent years for more widespread use through production and technological advances. As of 2011, the cost of PV has fallen well below that of nuclear power and is set to fall further. The average retail price of solar cells fell to $2.43/watt. For large-scale installations, prices below $1.00/watt are now common.[3] Crystal silicon solar cells have largely been replaced by less expensive multicrystalline silicon solar cells, and thin film silicon solar cells have also been developed recently at lower costs of production. Although they are reduced in energy conversion efficiency from single crystalline "siwafers", they are also much easier to produce at comparably lower costs.[citation needed]

[edit] Applications

[edit] Standalone systems

Solar powered parking meter.

A standalone system does not have a connection to the electricity "mains" (aka "grid"). Standalone systems vary widely in size and application from wristwatches or calculators to remote buildings or spacecraft. If the load is to be supplied independently of solar insolation, the generated power is stored and buffered with a battery. In non-portable applications where weight is not an issue, such as in buildings, lead acid batteries are most commonly used for their low cost. A charge controller may be incorporated in the system to:[citation needed] a) avoid battery damage by excessive charging or discharging and, b) optimizing the production of the cells or modules by maximum power point tracking (MPPT).[citation needed] However, in simple PV systems where the PV module voltage is matched to the battery voltage, the use of MPPT electronics is generally considered unnecessary, since the battery voltage is stable enough to provide near-maximum power collection from the PV module. In small devices (e.g. calculators, parking meters) only direct current (DC) is consumed. In larger systems (e.g. buildings, remote water pumps) AC is usually required. To convert the DC from the modules or batteries into AC, an inverter is used.[citation needed]

A schematic of a bare-bones off-grid system, consisting (from left to right) of photovoltaic module, a blocking-diode to prevent battery drain during low-insolation, a battery, an inverter, and an AC load such as a fluorescent lamp
off-grid PV system with battery charger

[edit] Solar vehicles

Ground, water, air or space vehicles may obtain some or all of the energy required for their operation from the sun. Surface vehicles generally require higher power levels than can be sustained by a practically-sized solar array, so a battery is used to meet peak power demand, and the solar array recharges it. Space vehicles have successfully used solar photovoltaic systems for years of operation, eliminating the weight of fuel or primary batteries.[citation needed]

[edit] Small scale DIY solar systems

With a growing DIY-community and an increasing interest in environmentally friendly "green energy", some hobbyists have endeavored to build their own PV solar systems from kits [4] or partly diy.[5] Usually, the DIY-community uses inexpensive [6] or high efficiency systems[7] (such as those with solar tracking) to generate their own power. As a result, the DIY-systems often end up cheaper than their commercial counterparts.[8] Often, the system is also hooked up into the regular power grid to repay part of the investment via net metering. These systems usually generate power amount of ~2 kW or less. Through the internet, the community is now able to obtain plans to construct the system (at least partly DIY) and there is a growing trend toward building them for domestic requirements. The DIY-PV solar systems are now also being used both in developed countries and in developing countries, to power residences and small businesses.[citation needed]

[edit] Grid-connected system

Diagram of a residential grid-connected PV system

A grid connected system is connected to a large independent grid (typically the public electricity grid) and feeds power into the grid. Grid connected systems vary in size from residential (2-10kWp) to solar power stations (up to 10s of MWp). This is a form of decentralized electricity generation. In the case of residential or building mounted grid connected PV systems, the electricity demand of the building is met by the PV system. Only the excess is fed into the grid when there is an excess. The feeding of electricity into the grid requires the transformation of DC into AC by a special, grid-controlled solar inverter.[citation needed]

In kW sized installations the DC side system voltage is as high as permitted (typically 1000V except US residential 600V) to limit ohmic losses. Most modules (72 crystalline silicon cells) generate about 160W at 36 volts. It is sometimes necessary or desirable to connect the modules partially in parallel rather than all in series. One set of modules connected in series is known as a 'string'.[citation needed]

[edit] Building systems

In urban and suburban areas, photovoltaic arrays are commonly used on rooftops to supplement power use; often the building will have a connection to the power grid, in which case the energy produced by the PV array can be sold back to the utility in some sort of net metering agreement. Solar trees are arrays that, as the name implies, mimic the look of trees, provide shade, and at night can function as street lights. In agricultural settings, the array may be used to directly power DC pumps, without the need for an inverter. In remote settings such as mountainous areas, islands, or other places where a power grid is unavailable, solar arrays can be used as the sole source of electricity, usually by charging a storage battery.[citation needed]

There is financial support available for people wishing to install PV arrays. In the UK, households are paid a 'Feedback Fee' to buy excess electricity at a flat rate per kWh. This is up to 44.3p/kWh which can allow a home to earn double their usual annual domestic electricity bill.[9] The current UK feed-in tariff system is due for review on 31 March 2012, after which the current scheme may no longer be available.[10]

[edit] Power plants

A photovoltaic power station (solar park or solar farm) is a power station using photovoltaic modules and inverters for utility scale electricity generation, connected to an electricity transmission grid. Some large photovoltaic power stations like Waldpolenz Solar Park and Topaz Solar Farm cover tens or hundreds of hectares and have power outputs up to hundreds of megawatts.

[edit] System performance

[edit] Insolation and energy

At high noon on a cloudless day at the equator, the power of the sun is about 1 kW/m²,[11] on the Earth's surface, to a plane that is perpendicular to the sun's rays. As such, PV arrays can track the sun through each day to greatly enhance energy collection. However, tracking devices add cost, and require maintenance, so it is more common for PV arrays to have fixed mounts that tilt the array and face due South in the Northern Hemisphere (in the Southern Hemisphere, they should point due North). The tilt angle, from horizontal, can be varied for season, but if fixed, should be set to give optimal array output during the peak electrical demand portion of a typical year.[citation needed]

For the weather and latitudes of the United States and Europe, typical insolation ranges from 4 kWh/m²/day in northern climes to 6.5 kWh/m²/day in the sunniest regions. Typical solar panels have an average efficiency of 12%, with the best commercially available panels at 20%. Thus, a photovoltaic installation in the southern latitudes of Europe or the United States may expect to produce 1 kWh/m²/day. A typical "150 watt" solar panel is about a square meter in size. Such a panel may be expected to produce 1 kWh every day, on average, after taking into account the weather and the latitude.[citation needed]

In the Sahara desert, with less cloud cover and a better solar angle, one could ideally obtain closer to 8.3 kWh/m²/day provided the nearly ever present wind would not blow sand on the units. The unpopulated area of the Sahara desert is over 9 million km², which if covered with solar panels would provide 630 terawatts total power.[citation needed] The Earth's current energy consumption rate is around 13.5 TW at any given moment (including oil, gas, coal, nuclear, and hydroelectric).[citation needed]

[edit] Tracking the sun

Trackers and sensors to optimise the performance are often seen as optional, but tracking systems can increase viable output by up to 100%.[2] PV arrays that approach or exceed one megawatt often use solar trackers. Accounting for clouds, and the fact that most of the world is not on the equator, and that the sun sets in the evening, the correct measure of solar power is insolation – the average number of kilowatt-hours per square meter per day. For the weather and latitudes of the United States and Europe, typical insolation ranges from 4kWh/m²/day in northern climes to 6.5 kWh/m²/day in the sunniest regions.[citation needed]

For large systems, the energy gained by using tracking systems outweighs the added complexity (trackers can increase efficiency by 30% or more).[citation needed]

[edit] Shading and dirt

Photovoltaic cell electrical output is extremely sensitive to shading. When even a small portion of a cell, module, or array is shaded, while the remainder is in sunlight, the output falls dramatically due to internal 'short-circuiting' (the electrons reversing course through the shaded portion of the p-n junction).

If the current drawn from the series string of cells is no greater than the current that can be produced by the shaded cell, the current (and so power) developed by the string is limited. If enough voltage is available from the rest of the cells in a string, current will be forced through the cell by breaking down the junction in the shaded portion. This breakdown voltage in common cells is between 10 and 30 volts. Instead of adding to the power produced by the panel, the shaded cell absorbs power, turning it into heat. Since the reverse voltage of a shaded cell is much greater than the forward voltage of an illuminated cell, one shaded cell can absorb the power of many other cells in the string, disproportionately affecting panel output. For example, a shaded cell may drop 8 volts, instead of adding 0.5 volts, at a particular current level, thereby absorbing the power produced by 16 other cells.[12] It is important that a PV installation is not shaded by trees or other obstructions.

Most modules have bypass diodes between each cell or string of cells that minimize the effects of shading and only lose the power of the shaded portion of the array. The main job of the bypass diode is to eliminate hot spots that form on cells that can cause further damage to the array, and cause fires.

Sunlight can be absorbed by dust, snow, or other impurities at the surface of the module. This can cut down the light that strikes the cells. Maintaining a clean module surface will increase output performance over the life of the module.

[edit] Temperature

Module output and life are also degraded by increased temperature. Allowing ambient air to flow over, and if possible behind, PV modules reduces this problem.

[edit] Module efficiency

In 2010, solar panels available for consumers can have a yield of up to 19%,[13] while commercially available panels can go as far as 27%.[14][dead link] Thus, a photovoltaic installation in the southern latitudes of Europe or the United States may expect to produce 1 kWh/m²/day[dated info]. In Australia, a typical 1 kW solar system may produce 3.5-5 kWh/day, though this is dependent on location, orientation, tilt and other factors [15]

[edit] Monitoring

Photovoltaic systems need to be monitored to detect breakdown and optimize their operation. Several photovoltaic monitoring strategies depending on the output of the installation and its nature. Monitoring can be performed on site or remotely. It can measure production only, retrieve all the data from the inverter or retrieve all of the data from the communicating equipment (probes, meters, etc.). Monitoring tools can be dedicated to supervision only or offer additional functions. Individual inverters may include monitoring using manufacturer specific protocols and software. Energy metering of an inverter may be of limited accuracy and not suitable for revenue metering purposes. A third-party data acquisition system can monitor multiple inverters, using the inverter manufacturer's protocols, and also acquire weather-related information. Independent smart meters may measure the total energy production of a PV array system. Separate measures such as satellite image analaysis or a solar radiation meter (a pyranometer) can be used to estimate total insolation.[citation needed]

Data collected from a monitoring system can be displayed remotely over the World Wide Web. For example,The Open Solar Outdoors Test Field (OSOTF)[16] is a grid-connected photovoltaic test system, which continuously monitors the output of a number of photovoltaic modules and correlates their performance to a long list of highly accurate meteorological readings. The OSOTF is organized under open source principles -- All data and analysis is be made freely available to the entire photovoltaic community and the general public.[citation needed] Some companies offer analysis software to analyze system performance. Small residential systems may have minimal data analysis requirements other than perhaps total energy production; larger grid-connected power plants can benefit from more detailed investigations of performance.[citation needed]

[edit] Performance factors

Uncertainties in revenue over time relate mostly to the evaluation of the solar resource and to the performance of the system itself. In the best of cases, uncertainties are typically 4% for year-to-year climate variability, 5% for solar resource estimation (in a horizontal plane), 3% for estimation of irradiation in the plane of the array, 3% for power rating of modules, 2% for losses due to dirt and soiling, 1.5% for losses due to snow, and 5% for other sources of error. Identifying and reacting to manageable losses is critical for revenue and O&M efficiency. Monitoring of array performance may be part of contractual agreements between the array owner, the builder, and the utility purchasing the energy produced.[citation needed]

Access to the Internet has allowed a further improvement in energy monitoring and communication. Dedicated systems are available from a number of vendors. For solar PV system that use microInverters (panel-level DC to AC conversion), module power data is automatically provided. Some systems allow setting performance alerts that trigger phone/email/text warnings when limits are reached. These solutions provide data for the system owner and the installer. Installers are able to remotely monitor multiple installations, and see at-a-glance the status of their entire installed base.[citation needed]

[edit] Module life

Effective module lives are typically 25 years or more.[17] The payback period for an investment in a PV solar installation varies greatly. It is typically calculated to be between 10 and 20 years.[18]

[edit] Components

[edit] Trackers

A solar tracker tilts a solar panel throughout the day. Depending on the type of tracking system, the panel is either aimed directly at the sun or the brightest area of a partly clouded sky. Trackers greatly enhance early morning and late afternoon performance, increasing the total amount of power produced by a system by about 20–25% for a single axis tracker and about 30% or more for a dual axis tracker, depending on latitude.[19][20]

Trackers are effective in regions that receive a large portion of sunlight directly. In diffuse light (i.e. under cloud or fog), tracking has little or no value. Because most concentrated photovoltaics systems are very sensitive to the sunlight's angle, tracking systems allow them to produce useful power for more than a brief period each day.[citation needed]

Tracking systems improve performance for two main reasons. First, when a solar panel is perpendicular to the sunlight, it receives more light on its surface than if it were angled. Second, direct light is used more efficiently than angled light[citation needed]. Special Anti-reflective coatings can improve solar panel efficiency for direct and angled light, somewhat reducing the benefit of tracking.[21]


[edit] Inverters

Inverter for grid connected PV

On the AC side, these inverters must supply electricity in sinusoidal form, synchronized to the grid frequency, limit feed in voltage to no higher than the grid voltage including disconnecting from the grid if the grid voltage is turned off.[22]

Schematic drawing of current-voltage characteristics of a solar cell The area of the yellow rectangle gives the output power. Pmax denotes the maximum power point

On the DC side, the power output of a module varies as a function of the voltage in a way that power generation can be optimized by varying the system voltage to find the 'maximum power point'. Most inverters therefore incorporate 'maximum power point tracking'.[citation needed]

A solar inverter may connect to a string of solar panels. In small installations a solar micro-inverter is connected at each solar panel.[citation needed]

For safety reasons a circuit breaker is provided both on the AC and DC side to enable maintenance. AC output may be connected through an electricity meter into the public grid.[citation needed]

The meter must be able to run in both directions.[citation needed]

In some countries, for installations over 30kWp a frequency and a voltage monitor with disconnection of all phases is required.[citation needed]

[edit] Mounting systems

Ground mounted system

Modules are assembled into arrays on some kind of mounting system. For solar parks a large rack is mounted on the ground, and the modules mounted on the rack.[citation needed]

For buildings, many different racks have been devised for pitched roofs. For flat roofs, racks, bins and building integrated solutions are used.[citation needed]

[edit] Connection to a DC grid

DC grids are only to be found in electric powered transport: railways trams and trolleybuses. A few pilot plants for such applications have been built, such as the tram depots in Hannover Leinhausen [23] and Geneva (Bachet de Pesay).[24] The 150 kWp Geneva site feeds 600V DC directly into the tram/trolleybus electricity network provided about 15% of the electricity at its opening in 1999.

[edit] Hybrid systems

Hybrid Power System.gif

A hybrid system combines PV with other forms of generation, usually a diesel generator. Biogas is also used. The other form of generation may be a type able to modulate power output as a function of demand. However more than one renewable form of energy may be used e.g. wind. The photovoltaic power generation serves to reduce the consumption of non renewable fuel. Hybrid systems are most often found on islands. Pellworm island in Germany and Kythnos island in Greece are notable examples (both are combined with wind).[25][26] The Kythnos plant has diocane diesel consumption by 11.2% [27]

There has also been recent work showing that the PV penetration limit can be increased by deploying a distributed network of PV+CHP hybrid systems in the U.S.[28] The temporal distribution of solar flux, electrical and heating requirements for representative U.S. single family residences were analyzed and the results clearly show that hybridizing CHP with PV can enable additional PV deployment above what is possible with a conventional centralized electric generation system. This theory was reconfirmed with numerical simulations using per second solar flux data to determine that the necessary battery backup to provide for such a hybrid system is possible with relatively small and inexpensive battery systems.[29] In addition, large PV+CHP systems are possible for institutional buildings, which again provide back up for intermittent PV and reduce CHP runtime.[30]

[edit] Standardization

Increasing use of photovoltaic systems and integration of photovoltaic power into existing structures and techniques of supply and distribution increases the value of general standards and definitions for photovoltaic components and systems. The standards are compiled at the International Electrotechnical Commission (IEC) and apply to efficiency, durability and safety of cells, modules, simulation programs, plug connectors and cables, mounting systems, overall efficiency of inverters etc.[citation needed]

[edit] Power costs

The table below[31] shows the total cost in US cents per kWh of electricity generated by a photovoltaic system. The row headings on the left show the total cost, per peak kilowatt (kWp), of a photovoltaic installation. The column headings across the top refer to the annual energy output in kWh expected from each installed kWp. This varies by geographic region because the average insolation depends on the average cloudiness and the thickness of atmosphere traversed by the sunlight. It also depends on the path of the sun relative to the panel and the horizon.

Panels are usually mounted at an angle based on latitude, and often they are adjusted seasonally to meet the changing solar declination. Solar tracking can also be utilized to access even more perpendicular sunlight, thereby raising the total energy output. The calculated values in the table reflect the total cost in cents per kWh produced. They assume a 10% total capital cost (for instance 4% interest rate, 1% operating and maintenance cost,[32] and depreciation of the capital outlay over 20 years). Normally, photovoltaic modules have a 25 year warranty.[citation needed]

20 years 2400
kWh/kWp y
2200
kWh/kWp y
2000
kWh/kWp y
1800
kWh/kWp y
1600
kWh/kWp y
1400
kWh/kWp y
1200
kWh/kWp y
1000
kWh/kWp y
800
kWh/kWp y
200 $/kWp 0.8 0.9 1.0 1.1 1.3 1.4 1.7 2.0 2.5
600 $/kWp 2.5 2.7 3.0 3.3 3.8 4.3 5.0 6.0 7.5
1000 $/kWp 4.2 4.5 5.0 5.6 6.3 7.1 8.3 10.0 12.5
1400 $/kWp 5.8 6.4 7.0 7.8 8.8 10.0 11.7 14.0 17.5
1800 $/kWp 7.5 8.2 9.0 10.0 11.3 12.9 15.0 18.0 22.5
2200 $/kWp 9.2 10.0 11.0 12.2 13.8 15.7 18.3 22.0 27.5
2600 $/kWp 10.8 11.8 13.0 14.4 16.3 18.6 21.7 26.0 32.5
3000 $/kWp 12.5 13.6 15.0 16.7 18.8 21.4 25.0 30.0 37.5

[edit] Regulation

The State of California prohibits Homeowners' associations from restricting solar devices.[33]

Many localities require a license to install a photovoltaic system. A grid-tied system normally requires a licensed electrician to make the connection between the system and the grid-connected wiring of the building.[34]

In the UK, installations are not allowed in some areas and on some buildings, and on others, planning permission may be required.[35]

[edit] See also

[edit] References

  1. ^ Types of PV systems. University of Florida.
  2. ^ a b "Small Photovoltaic Arrays". Research Institute for Sustainable Energy (RISE), Murdoch University. http://www.rise.org.au/info/Applic/Array/index.html. Retrieved 5 February 2010. 
  3. ^ John Quiggin (January 3, 2012). "The End of the Nuclear Renaissance |". National Interest. http://nationalinterest.org/commentary/the-end-the-nuclear-renaissance-6325?page=1. 
  4. ^ People building their own solar systems from kits. Greenplanet4energy.com. Retrieved on 2012-04-23.
  5. ^ Example of diy PV system with pictures. Instructables.com (2007-11-05). Retrieved on 2012-04-23.
  6. ^ Graham, Michael. (2005-10-15) Low-cost PV solar kit preferred by diy-communities. Treehugger.com. Retrieved on 2012-04-23.
  7. ^ Ken Darrow and Mike Saxenian Appropriate Technology Sourcebook. villageearth.org
  8. ^ "Alternative Energy Development: Michigan will be Nation’s Leader in Alternative Energy Technology, Jobs". State of Michigan, Office Of The Governor. http://www.michigan.gov/documents/gov/Alternative_Energy_223194_7.pdf. Retrieved February 22, 2012. 
  9. ^ Feed in Tariffs. Microgeneration.com. Retrieved on 2012-04-23.
  10. ^ FAQs on Solar Photovoltaic Panels at Swithenbanks, Solar Panels, Solar Hot Water, Water Turbines, Wind Turbines. Swithenbanks.co.uk. Retrieved on 2012-04-23.
  11. ^ El-Sharkawi, Mohamed A. (2005). Electric energy. CRC Press. pp. 87–88. ISBN 978-0-8493-3078-0. 
  12. ^ Ursula Eicker, Solar Technologies for Buildings, Wiley 2003, ISBN 0-471-48637-X, page 226
  13. ^ "Sunpower offers solar modules boasting 19% efficiency". http://www.brighterenergy.org/9715/news/solar/sunpower-offers-solar-modules-boasting-19-efficiency/. Retrieved 2010-05-03. 
  14. ^ "Concentrix Solar: Concentrator Modules". http://www.concentrix-solar.de/technology/concentrator-modules/?L=1. Retrieved 2008-12-03. 
  15. ^ "How much energy will my solar cells produce?". http://www.solarchoice.net.au/blog/how-much-energy-will-my-solar-cells-produce/. Retrieved 2012-05-30. 
  16. ^ Pearce, Joshua. M; Adegboyega Babasola, Rob Andrews (2012). "Open Solar Photovoltaic Systems Optimization". Proceedings of the 16th Annual National Collegiate Inventors and Innovators Alliance Conference (NCIIA): 1-7. http://nciia.org/sites/default/files/features/conference/2012/papers/Pearce-Babasola-Andrews-queensu.pdf. 
  17. ^ "Solar Power (Photovoltaic, PV)". Agriculture and Agri-Food Canada. http://www4.agr.gc.ca/AAFC-AAC/display-afficher.do?id=1187620075153&lang=eng. Retrieved 5 February 2010. 
  18. ^ It's payback time for home generation. BBC News (2010-06-22). Retrieved on 2012-04-23.
  19. ^ A Performance Calculator. Rredc.nrel.gov. Retrieved on 2012-04-23.
  20. ^ Technological advantages. Mecasolar.com. Retrieved on 2012-04-23.
  21. ^ Reflective Coating Silicon Solar Cells Boosts Absorption Over 96 Percent. Scientificblogging.com (2008-11-03). Retrieved on 2012-04-23.
  22. ^ Grid-Tied Inverter Safety. Homepower.com. Retrieved on 2012-04-23.
  23. ^ Innovative Electrical Concepts. International Energy Agency (2001)
  24. ^ site7. Ecotourisme.ch. Retrieved on 2012-04-23.
  25. ^ PV resources website, Hybrid power station accessed 10 Feb 08
  26. ^ Daten und Fakten. Pellworm island website (in German)
  27. ^ Darul’a, Ivan; Stefan Marko (2007). "Large scale integration of renewable electricity production into the grids" (PDF). Journal of Eelectrical Engineering 58 (1): 58–60. ISSN 1335-3632. http://iris.elf.stuba.sk/JEEEC/data/pdf/1_107-10.pdf. Retrieved 2008-02-10. 
  28. ^ J. M. Pearce (2009). "Expanding Photovoltaic Penetration with Residential Distributed Generation from Hybrid Solar Photovoltaic + Combined Heat and Power Systems". Energy 34: 1947–1954. DOI:10.1016/j.energy.2009.08.012. http://hdl.handle.net/1974/5307. 
  29. ^ P. Derewonko and J.M. Pearce, “Optimizing Design of Household Scale Hybrid Solar Photovoltaic + Combined Heat and Power Systems for Ontario”, Photovoltaic Specialists Conference (PVSC), 2009 34th IEEE, pp.1274–1279, 7–12 June 2009.
  30. ^ M. Mostofi, A. H. Nosrat, and J. M. Pearce, “Institutional-Scale Operational Symbiosis of Photovoltaic and Cogeneration Energy Systems” International Journal of Environmental Science and Technology 8(1), pp. 31–44, 2011. Available open access: [1]
  31. ^ p = \frac{I\cdot (1+i)+\sum_{t=0}^T \frac{I \cdot b}{(1+i)^t}}{\sum_{t=0}^T\frac{E\cdot (1-v)^t}{(1+i)^t}}
  32. ^ PV operation and maintenance costs. (PDF) . Retrieved on 2012-04-23.
  33. ^ "California Solar Rights Act". http://www.dsireusa.org/solar/incentives/incentive.cfm?Incentive_Code=CA45R&re=1&ee=1. Retrieved February 25 2012. 
  34. ^ "Requirements for Solar Installations". bootsontheroof.com. 2011 [last update]. http://www.bootsontheroof.com/index.php?option=com_content&view=article&id=32:requirements-for-solar-installation-a-incentives-by-state&catid=14&Itemid=65. Retrieved March 31, 2011. 
  35. ^ http://www.planningportal.gov.uk/permission/commonprojects/solarpanels/

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