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SIZING METHODOLOGY When describing PV systems, it is logical to follow the energy flow from the array side to the loads. However, when sizing a PV system, it is necessary to consider the energy demand before considering the supply. Therefore, PV-system sizing, particularly for stand alone systems, starts at the load side and proceeds backward to the array. See Ill. 1. The objective is to first determine the requirements of the system loads and then to determine the size of the inverter, battery bank, and array that are needed to meet the requirements. Since there are many possible PV-system configurations, each with different modes of operation and priorities, the approach and methodology used to size these systems may differ. There may also be a difference in the sizing tolerance; some systems may need to be sized more carefully than others. Sizing Interactive Systems Interactive systems require relatively simple calculations and allow the widest variance in component sizing. Since interactive systems operate in parallel with utility service, sizing is not critical because failure of the PV system to produce energy does not affect operation of electrical loads. Additional energy can be imported from the utility at any time. Sizing interactive systems begins with the specifications of a PV module chosen for the system. Module ratings at Standard Test Conditions (STC) are used to calculate the total expected array DC power output per peak sun hour. This is then de-rated for various losses and inefficiencies in the system, which includes the following: • Guaranteed module output that is less than 100% • Array operating temperature • Array wiring and mismatch losses • Inverter power conversion efficiency • Inverter MPPT efficiency Stand-Alone Systems: INVERTER; LOAD; -BATTERY BANK; Ill. 1. Sizing strategy for stand-alone systems starts at the load side and proceeds backward to the array. Ill. 2. Sizing interactive systems begins with calculating the peak array DC power output, which is then de-rated for various losses and in efficiencies in the system to arrive at a final AC power output. Interactive System Sizing INTERACTIVE SYSTEM SIZING PV-Module Rated DC Power Output 185 W Manufacturer Power Guarantee: 0.90 Number of Modules in Array; 16 Array Guaranteed Power Output; 2664 W Array Avg Operating Temperature 50 °C Temperature Coefficient for Power - PC Temperature-Corrected 2398 W Array Power Output Array Wiring and Mismatch Losses 0.03 I Net Array Power Output 2326 W Inverter Maximum DC Power Rating [ 2500 1W Inverter Power Conversion Efficiency 0.92 Inverter MPPT Efficiency; 1 .00 Inverter Maximum AC Power Output 2140 W Average Daily Insolation; 5.1 IP_sil/day Average Daily Energy Production; 10.9 kWh/day Ill. 3. Interactive-system sizing is very flexible because the utility can supply extra energy to the system loads and receive excess energy from the PV system. Sizing Systems: LARGE ARRAY; .ARRAY/ OUTPUT UTILITY/_SMALL ARRAY LOAD REQUIREMENTS LOAD SMALL ARRAY LARGE ARRAY UTILITY; EXCESS ENERGY ARRAY OUTPUT LOAD REQUIREMENTS The result is a final AC power output that is substantially lower but realistically accounts for expected real-world conditions. See Ill. 2. To determine the expected energy production per day, the final AC power output is multiplied by the insolation for the month or year. For example, if the calculated AC power output is 2140W per peak sun hour and the average annual insolation is 5.1 peak sun hours (kWh/m then the average energy production is expected to be 10.9 kWh/day. If the final system power output is not with in the desired range, such as above a minimum size requirement for an incentive program, different module and /or inverter choices can be made. Also, various system configurations can be compared with their associated system costs for a value-based analysis. The size of an interactive system is primarily limited by the space available for an array and the owner's budget. However, financial incentive requirements, net metering limits, and existing electrical infrastructure may also influence system size decisions. Even if short-term periods of high insolation or low demand result in excess electricity, it is not wasted because it can be sold back to the utility for credit against subsequent utility bills. See Ill. 3. The only exception is a system that is so large that it maintains a net energy export over several months or more. Because many utilities will not carry the credits for more than one year and /or will credit exported electricity at lower wholesale rates, it is not recommended to size an interactive system larger than needed for average annual on-site load requirements. However, since the avail able space usually can't accommodate an array this large, this is rarely an issue. Sizing Stand-Alone Systems Stand-alone PV systems are designed to power specific on-site loads, so the size of these systems is directly proportional to the load requirements. If the system is too small, there will be losses in load availability and system reliability. See Ill. 4. If the system is too large, excess energy will be unutilized and wasted. Therefore, sizing of stand-alone systems requires a fine balance between energy supply and demand. Because of this necessary balance, sizing stand-alone systems requires more analysis and calculations than are required for interactive systems. Most of these calculations build upon one another as the analyses proceed. Moreover, sizing stand-alone systems is an iterative process. That is, if the final calculations indicate that the components are improperly sized, the starting values must be changed and the calculation process repeated until the sys tem output matches the load requirements. Sizing Stand-Alone Systems SMALL ARRAY; ARRAY LOAD REQUIREMENTS UNDERSIZED ARRAY LARGE ARRAY; LOAD REQUIREMENTS LOAD OVERSIZED ARRAY WASTED ENERGY Stand-alone PV systems must be carefully designed to meet all the load requirements without excessive over-sizing. Sizing Bimodal Systems Bimodal systems normally operate as interactive systems, but can operate as stand-alone systems during utility outages. Therefore, the bimodal systems are typically sized according to the stand-alone methodology. However, a significant difference between bimodal systems and true stand-alone systems is that bimodal systems typically supply only a few select critical loads while in stand-alone mode. The load analysis used for sizing a bimodal system should include calculations for only these critical loads, which are needed during a utility outage. The rest of the subsequent calculations for inverter rating, battery-bank energy storage, and array output are identical to those for stand-alone systems. Similarly, the battery-bank sizing allows for the desired back-up period without grid power from a few hours to several days. The stand-alone sizing methodology deter mines the minimum size of a bimodal system. However, since excess energy produced during the normal interactive mode can be exported to the utility grid for credit; there is no penalty for oversizing a bimodal system, at least within the guidelines of sizing conventional utility-interactive systems. Sizing Hybrid Systems Hybrid systems are stand-alone, which can't rely on the utility as a source of electricity. These systems must be able to completely and reliably supply power to their on-site loads. However, there is more than one source of energy, such as a combination of a PV array and an engine generator or wind turbine. The presence of multiple power sources means that the array and battery bank can be smaller while maintaining load availability, especially if one source can provide power on demand, such as an engine-generator. The array and battery bank for a PV array and engine generator hybrid system are sized similarly to those for a stand-alone system, with three differences. First, the array is sized to supply only a portion of the total load requirement. For example, the hybrid system may be designed such that 80% of the load demand is supplied by the array and 20% is supplied by the generator on an average day. Second, the sizing calculations do not need to use the worst-case load-to-insolation months for sizing, since the engine generator can be called upon to provide additional power as needed. Average load and insolation values may be used. Finally, battery banks can be sized for a shorter autonomy period (typically only 1 or 2 days) than for PV-only stand-alone systems, also because the generator power is available on demand. PV array to engine generator output ratios range from 90%:10% to 40%:60%. The optimal ratio is determined by performing sizing calculations using several different ratios and choosing the system that best fits other requirements (such as available array space) and has the lowest expected life-cycle costs. Other factors, such as minimizing the average run time of noisy engines, may also influence sizing. Combination PV array and engine genera tor hybrid systems are relatively easy to size because the generator output is completely dependent on demand. Other energy-source combinations, however, such as a PV array and a wind turbine or a PV array and a micro- hydroelectric generator, are much more difficult to design and size adequately because their outputs are less predictable. With so many variables, sizing software is recommended to optimize these systems. Several applications are available free on-line, such as HOMER from NREL. SIZING CALCULATIONS Sizing PV systems for stand-alone operation involves four sets of calculations. First, a load analysis determines the electrical load requirements. Then, monthly load requirements are compared to the local insolation data to determine the critical design month. Next, the battery bank is sized to be able to independently supply the loads for a certain length of time, such as if cloudy weather reduces array output. Finally, the PV array is sized to fully charge the battery bank under the critical conditions. A hybrid PV and engine generator system utilizes array energy better (wastes less energy) than PV-only systems because more of the available energy is utilized In same cases, these systems may also cost less overall than PV-only or engine generator-only stand alone systems sized far the same toad requirements Load Analysis Analyzing the electrical loads is the first and most important step in PV-system sizing. The energy consumption dictates the amount of electricity that must be produced. All existing and potential future loads must be considered. Underestimating loads will result in a system that is too small and can't operate the loads with the desired reliability. However, overestimating the load will result in a system that is larger and more expensive than necessary. Comprehensive yet conservative load estimates will ensure that the system is adequately sized. A detailed load analysis completed during the site survey lists each load, its power demand, and daily energy consumption. See Ill. 5. If load profiles are not nearly identical throughout the year, a load analysis should be conducted for each month. Similar loads can be grouped into categories, such as lighting fixtures with the same power requirements. DC loads, if any, should be listed separately from AC loads. This is because energy for AC loads goes through the inverter, resulting in losses that must be accounted for separately. Power Demand. Peak-power information is usually found on appliance nameplates or in manufacturer's literature. When this information is not available, peak power demand can be estimated by multiplying the maximum current by the operating voltage, though this is less accurate for reactive loads. Measurements, meter readings, or electric bills may also be used to help establish existing load requirements. See Ill. 6. Load Analysis: Total AC Power Total DC Power Total Daily AC Energy Consumption Total Daily DC Energy Consumption Weighted Operating Time Inverter Efficiency Average Daily DC Energy Consumption: Wh/day, Wh/day, hr/day, Wh/day The peak power demands are then summed. The total power demand is considered when determining the required inverter AC-power output ratio. While it is not likely that every load would be ON at the same time, it is recommended to size the inverter with extra capacity. Energy Consumption. Electrical energy consumption is based on the power demand over time. Loads rarely operate continuously, so each load's operating time must be determined. See Ill. 7. This is the total number of hours per day that the load is operating. == Energy Efficiency: Because the size, and therefore the cost, of a stand-alone PV system is directly proportional to the load energy requirements, energy should be conserved as much as possible in stand-alone systems. This involves reducing wasted energy, reducing load usage, and increasing load efficiency. Even if these measures involve financial costs, it is usually far more practical and cost effective to implement energy conservation measures than to increase the size of the PV system. In 1980, the Federal Trade Commission began requiring manufacturers of certain home appliances to attach labels that provide an estimate of the product's energy consumption or efficiency. These EnergyGuide labels show the estimated annual operating cost (based on average energy prices) and how this compares with the operating costs for similar models. The EnergyGuide label is required on refrigerators, freezers, clothes washers, water heaters, dishwashers, air conditioners, heating equipment, and other household appliances. ENERGY STAR is a voluntary federal product labeling and certification program administered by the U.S. Environmental Protection Agency. It recognizes appliances and equipment that have exceeded energy efficiency standards. Products bearing the ENERGY STAR label include many common home appliances and office equipment. Both EnergyGuide and EN ERGY STAR labels can be used to identify and select the most efficient electrical loads for PV systems. == Ill. 5. A load analysis tabulates the various kinds of loads and their power and electrical-energy requirements. Ill. 6. Load power and energy requirements can be easily measured with inexpensive meters. Ill. 7. Load requirements include the power demand and electrical-energy consumption for all the expected loads in the system. TOASTER (1000 W)-\ COFFEEMAKER (600 W)-\ MICROWAVE (1200W) Lou Requirements 1200 1000 800 600 400 200 REFRIGERATOR! FREEZER (200 W) nfl ,'- LIGHTING / (100W TO/ 300W) The operating time for loads that cycle on and off automatically is typically determined from the duty cycle. Duty cycle is the percent age of time a load is operating. For example, a duty cycle of 40% means that a load is operating 40% of the time, or 9.6 hr/day (40% x 24 hr/day = 9.6 hr/day). Even loads that are plugged in all the time, such as refrigerators and air conditioners, have a variable power requirement based on duty cycle. User-operated loads are turned on and off manually. Determining the operating time for these loads is simple if they cycle only once per day. However, if loads are switched on and off several times per day, a metering device is probably the easiest method of determining the operating time. The daily energy consumption for each load is determined by the load's power demand multiplied by the daily operating time. For example, a 60 W light bulb that is on for 4 hr/day consumes 240 Wh of energy (60W x 4hr=240Wh). Some loads may not be used every day. In these cases, the average daily operating time is calculated by dividing the total operating time over a longer period by the number of days in the period. For example, a washing machine that operates for 2 hr/wk has an equivalent operating time of 0.29 hr/day (2 hr/wk - 7 days/wk = 0.29 hr/day). The AC energy consumption and DC energy consumption values are totaled separately. These values are used to determine the total amount of DC energy the system must produce. Operating Time. Load operating-time data is also used to size the battery bank. For consistent loads that operate for specific periods, calculating the daily operating time is very simple. For example, if the loads are night time lighting fixtures that operate for 6 hr each night, the daily operating time is 6 hr. Most often, however, there are multiple loads to consider that each operate for various lengths of time. The battery-bank discharge rate will then change as various loads turn ON and OFF during the day. In this case, a weighted average operating time is calculated where = weighted average operating time (in hr/day) E = DC energy required for load 1 (in Wh/day) t =operating time for load 1 (in hr/day) E = DC energy required for load 2 (in Wh/day) = operating time for load 2 (in hr/day) E = DC energy required for nth load (in Wh/day) ç = operating time for nth load (in hr/day) For example, one DC load uses 2400 Wh/day and operates for 4 hr and another DC load uses 1000 Wh/day and operates for 7 hr. What is the weighted average operating time? top = 4.9 hr/day The two loads have a combined effect of a single 694 W load operating for 4.9 hr/day R2400 Wh + 1000 Wh) ÷ 4.9 hr = 694 WI. If the system includes both AC and DC loads, the AC load energy requirement must be first be converted to equivalent DC energy. This is done by dividing each AC energy consumption amount by the inverter efficiency. Inverter Selection. If the system includes AC loads, an inverter must be selected. Several factors must be considered when selecting the inverter. First, the inverter must have a maxi mum continuous power output rating at least as great as the largest single AC load. A slightly oversized inverter is usually recommended to account for potential future load additions. The inverter must also be able to supply surge cur rents to motor loads, such as pumps or compressors, while powering other system loads. Inverter voltage output is another consideration. Most stand-alone inverters produce either 120 V single-phase output or 120/240 V split-phase output. Some higher-power inverters for commercial or industrial electrical systems output three-phase power. Alternatively, certain inverters can be stacked and operated in parallel for split-phase output. The inverter DC-input voltage must also correspond with either the array voltage (for interactive systems) or the battery-bank volt age (for stand-alone systems). Inverter Efficiency. Inverters are not 100% efficient. Some power is lost in the process of converting DC energy to AC energy. Therefore, more DC energy is required to produce a certain amount of AC energy. Both the AC and DC energy requirements from the load analysis are used to determine how much total DC energy will be required. See Ill. 8. The total amount of DC energy required by the loads is calculated using the following formula: where ESDC = required daily system DC electrical energy (in Wh/day) EAC = AC energy consumed by loads (in Wh/day) = inverter efficiency EDC = DC energy consumed by loads (in Wh/day). For example, if a load analysis determines that a system requires 800 Wb/day for the AC loads and 200 Wh/day for the DC loads and the inverter efficiency is 90%, what is the daily DC electrical energy required by the system? Ill. 9. A critical design analysis compares the load requirements and insolation for each month to determine the critical design month. = = = Load Analysis Example: Off-Grid Home in American Southwest A secluded home is being constructed in the mountains near Albuquerque, NM. Due to its remoteness, a stand alone PV system will power the building. Electrical load requirements will be minimized through the use of solar thermal systems, energy-conserving construction materials, and high-efficiency appliances. To size the PV sys tem, a load analysis is conducted for the expected loads. Most of the electrical load requirements are expected to be consistent each month. These include appliances, an entertainment center, a computer, miscellaneous plug loads, and a water pump. The appliances consist of a refrigerator/freezer, microwave oven, toaster, coffeemaker, and washing machine. The refrigerator consumes 730 kWh/yr, or an average of 2000 Wh/day (730 kWh/yr ÷ 365 days/yr = 2 kWh/day = 2000 Wh/day). The peak power consumption of the refrigerator is measured at 200 W when the compressor operates. The microwave oven uses 1200W and operates for about 30 mm (0.5 hr) each day. The toaster uses 1000W and operates for about 3 mm (0.05 hr) per day. The coffeemaker uses 600 W and operates for about 15 mm (0.25 hr) per day. The washing machine uses an average of 800 W for a complete 30 mm (0.5 hr) cycle. If four loads are washed per week, the equivalent is 0.29 hr/day (0.5 hr/cycle x 4 cycles/wk ÷ 7 days/wk = 0.29 hr/day). The entertainment center consists of a satellite receiver, TV, and DVD player. Together they consume an average of 200 W and are used about 3 hr per day. The computer system operates on 100 W and is used for about 2 hr per day. The miscellaneous plug loads are estimated at 200 W for an average of 1 hr per day. The submersible water pump consumes 800 W and operates about 20 mm (0.33 hr) per day. A few loads, however, will vary depending on the time of the year. Two 50W ceiling fans will be used primarily during the summer. The lighting loads will be used all year, but will have a longer daily operating time during the winter. Because the total load requirements will change during the year, a load analysis is conducted for each month. = = = Inverter efficiency is typically between 80% and 95%. Also, an inverter's efficiency varies with its power output, though usually not more than about 5% over most of its power range. Manufacturer's specifications will typically include efficiency ranges. For sizing calculations, the average efficiency for the expected operating power range should be used. Ill. 8. The total DC-energy requirement is determined from the requirements for the DC loads (if any) plus the requirements for the AC loads, taking inverter efficiency into account. Total DC Energy Requirement TOTAL DC ENERGY REQUIREMENT V -DC LOAD REQUIREMENT POWER LOSS FROM INVERTER INEFFICIENCY = = = LOAD ANALYSIS Month: August AC LOADS Load Description Qty power t in ° g ' Operating Time (hr/day) Energy Consumption (Wh/day) Refrigerator/Freezer 1 200 10 2000 Microwave 1 1200 0.5 600 Toaster 1 1000 0.05 50 Coffeemaker 1 600 0.25 150 Washing Machine 1 800 0.29 232 Entertainment Center 1 200 3 600 Computer System 1 100 2 200 Plug Loads 1 200 1 200 Water Pump 1 800 0.33 264 Ceiling Fans 2 50 24 2400 Fluorescent Lighting 4 15 6 360 Fluorescent Lighting 4 32 4 512 DC LOADS Total AC Power 5388 W Total DC Power; 0 W Total Daily AC Energy Consumption; 7568 Wh/day Total Daily DC Energy Consumption; 0 Wh/day Weighted Operating Time 11.2 hr/day Inverter Efficiency 0.90 I Average Daily DC Energy Consumption; 8409 Wh/day For the month of August, the load analysis yields a total AC-power demand of about 5.4 kW and a daily energy consumption of 7568 Wh/day. If all loads operate at the same time, the inverter must have a continuous power output rating of at least 5.4 kW. Although it is unlikely that all loads will be operating simultaneously, a 5.5 kW inverter is selected to allow for future load additions. Since the efficiency of the inverter is 90%, the total average daily DC energy required is 8409 Wh/day. This number will be used in the critical design analysis, along with energy requirements for every other month, to determine the critical design month. The weighted operating time for the critical design month will be used in the battery-sizing calculations. = = = Ground mounts usually offer flexibility in orienting an array in the optimal direction and tilt for the critical design month. Critical Off-Grid Home: A critical design analysis determines the critical design month and insolation for sizing the PV array. If the insolation values for more than one possible orientation are compared, the critical design analysis indicates the best orientation choice of those analyzed. For the example system at the remote home, the array will be mounted in a ground rack mount. This allows the possible tilt angles of latitude, latitude- 150, and latitude +150. The insolation values for each month and at each of these orientations are found on the solar radiation data set for Albuquerque. The 8409 Wh/day load requirement for August is included, along with the load requirements for every other month as determined by separate load analyses. The critical design ratio is calculated for each month. For each orientation, the highest ratio of load requirement to insolation corresponds to the critical design month. For two of the orientations, the month is December. For the latitude+15° orientation, the month is July. Of the three possible critical design months, the month of December at the latitude orientation produces the lowest ratio. This indicates the optimal orientation. For this designated critical design month, the load requirement value is used for battery-bank sizing and the insolation value is used for array sizing. Critical Design Analysis A stand-alone system must produce enough electricity to meet load requirements during any month. Therefore, 'system' are sized for the worst-case scenario of high load and low insolation. A critical design analysis compares these two factors throughout a year, and the data for the worst case is used to size the array. See Ill. 9. The critical design ratio is the ratio of electrical energy demand to aver age insolation during a period. The load data comes from the load analysis, which is usually performed for each month. The insolation data is available from the solar radiation data sets. See Appendix. The ratio is calculated for each month. Critical Design Month The critical design month is the month with the highest critical design ratio. This is the worst-case scenario, and the associated load and insolation data are used to size the rest of the system. If the loads are constant over the entire year, the critical design month is the month with the lowest insolation on the array surface. For most locations in the Northern Hemisphere, this is a winter month, either December or January. However, when the load requirements vary from month to month, the critical design month must take into account both the loads and the available insolation. Because of these two factors, the critical design month may turn out to be any month of the year. Sizing for the critical design month typically results in excess energy at other times of the year, if this excess is significant, the system designer may want to consider adding diversion loads or changing to a different system configuration, such as a hybrid system, that better matches the available electrical energy to the loads. Array Orientation. Since array orientation has a significant effect on receivable solar radiation, array orientation must also be ac counted for in a critical design analysis. If the mounting surface restricts the array to only one possible orientation, then the analysis is conducted to determine the critical design factors for that orientation. However, if multiple orientations are possible, separate analyses are performed for each orientation. A critical design month can be identified for each of the array orientations, since the receivable solar radiation will be different for each. Of the resulting critical design months, the one with the smallest design ratio is the best choice. This orientation minimizes the required array size, while still accounting for the worst-case load-to- insolation situation. The orientations most commonly used in a critical design analysis are tilt angles equal to the latitude, latitude+ 15°, and latitude- 15°, each at an azimuth of due south. The greater array tilt angle maximizes the received solar energy in winter months, and the smaller array tilt angle maximizes the received solar energy in summer months. Insolation data for these orientations is available in the solar radiation data set for the nearest location. For azimuth angles other than due south, the insolation data must be adjusted to obtain the most accurate results. Computer models are available to predict average monthly insolation for alternate orientations. If tracking systems are to be used, receivable insolation data for the various tracking modes can be used instead of fixed array orientations. The critical design ratio is calculated for each month for each array orientation or tracking mode. The highest critical design ratio for each orientation corresponds to the critical design month for that orientation. When multiple orientations are considered, the lowest critical design ratio of the resulting critical design months corresponds to the optimal array orientation (of the orientations analyzed). The insolation and load requirements for this month and array orientation are used in sub sequent sizing calculations to design the array and battery system. DC-System Voltage The DC-system voltage is established by the battery-bank voltage in battery-based systems. This voltage dictates the operating voltage and ratings for all other connected components, including DC loads, charge controllers, inverters, and (for battery-based systems) the array. DC voltage in battery-based systems is critically important. The DC voltage for battery-based PV systems is usually an integer multiple of 12 V, usually 12 V, 24 V, or 48 V. DC loads, charge controllers, and inverters that operate at these voltages are commonly available. The selection of the battery-bank voltage affects system currents. See Ill. 10. For example, a 1200W system operating at 12 V draws 100A (1200W- l2V= 100A). The same l200Wsystem draws only 50A at 24V,or 25A at 48 V. Lower current reduces the required sizes of conductors, overcurrent protection devices, disconnects, charge controllers, and other equipment. Also, since voltage drop and power losses are smaller at lower currents, higher-voltage systems are generally more efficient. Higher-voltage systems also require fewer PV source circuits in the array design. As a rule of thumb, stand-alone systems up to 1 kW use a minimum 12 V battery-bank voltage, which limits DC currents to less than 84A. Similarly, battery voltages of at least 24 V are used for systems up to 2 kW, and at least 48 V for systems up to 5 kW. Very large stand alone systems may use battery voltages of 1 20V, though battery banks over 48 V involve additional code requirements and safety measures. SYSTEM PEAK POWER (kW): Ill. 10. DC-system voltage is chosen in proportion with the array size and to keep the operating current below 100 A. Stand-alone systems may require large battery banks for the desired system availability. Ill. 11. System availability is approximated from the local insolation and the autonomy period. System Availability The size of a system in relation to the loads determines its system availability. System avail ability is the percentage of time over an average year that a stand-alone PV system meets the system load requirements. For example, 98% system availability means that a system is able to meet the energy demand about 98% of the time. This means that for 2% of the year, the system can't meet the load requirements. No energy-producing system can achieve 100% availability, because of unpredictable events that affect system output. Days or weeks of below-average insolation, such as unusually cloudy weather, will reduce short-term system availability. System availability can also vary between years due to long-term weather pat terns. Component failures and lack of maintenance also contribute to system downtime and reduce system availability. System availability is determined by insolation and autonomy. Accurate estimates of system availability require software to evaluate energy flow in the system on an hour-by-hour basis, but rough estimates are adequate for most PV applications. For a desired system availability, the designer chooses the appropriate length of autonomy. See Ill. 11. Autonomy is the amount of time a fully charged battery system can supply power to system loads without further charging. Autonomy is expressed in days. Most stand-alone systems are sized for a system availability of about 95% (about 3 to 5 days of autonomy) for noncritical applications or 99% or greater (about 6 to 10 days or more) for critical applications. However, each percentage-point increase in system availability is increasingly more expensive for larger battery banks and arrays, which is impractical from an economic stand point for all but the most critical applications. Sizing of stand-alone systems must achieve an acceptable balance between system availability and cost goals for a given application. See Ill. 12. The solar resource for a location also affects the increasing costs of availability. Costs for increasing availability rise more steeply for locations with large seasonal differences in insolation than do costs for locations with more constant insolation. Ill. 12. Increasing system availability significantly increases the cost of the system. = = = Ba# Sizing BATTERY-BANK SIZING Average Daily DC Energy Consumption for Critical Design Month ________ Wh/day DC System Voltage; j VDC Autonomy ________ days Required Battery-Bank Output; Ah Allowable Depth-of-Discharge ________ Weighted Operating Time hrs Discharge Rate hrs Minimum Expected Operating Temperature ________ Temperature/Discharge Rate De-rating Factor Battery-Bank Rated Capacity Ah Selected Battery Rated Capacity ________ Selected Battery Nominal Voltage JVDC Number of Batteries in Series Number of Battery Strings in Parallel Total Number of Batteries Actual Battery-Bank Rated Capacity Ah ___ Load Fraction Average Daily Depth-of-Discharge Ill. 13. The battery-bank sizing worksheet uses in formation from the load analysis to determine the required size of the bank. = = = Battery Sizing Batteries store excess energy the array produces during periods of high insolation, and supply power to the system loads at nighttime and during periods of low insolation. In stand alone systems, they also establish the system DC operating voltage and supply surge cur rents to electrical loads and inverters. Battery-Bank Required Output. Batteries for stand-alone PV systems are sized to store enough energy to meet system loads for the desired length of autonomy without any further charge or energy contributions from the PV array. See Ill. 13. The amount of battery capacity required for a given application depends on the load requirements and desired autonomy. Greater autonomy requires larger and costlier battery banks, but reduces the average daily depth of discharge, which prolongs battery life. The required battery-bank capacity is deter mined from the electrical-energy requirements to operate the loads during the critical design month for the length of the autonomy period and at the desired battery-system voltage. The required battery-bank capacity is calculated using the following formula: where B = required battery-bank output (in Ah) E = daily electrical-energy consumption during critical design month (in Wh/day) autonomy (in days) VSDC = nominal DC-system voltage (in V) For example, consider a system that re quires 450 Wh of energy daily during the critical design month and the nominal DC-system voltage is 24 V. If the system specifies 4 days of autonomy, what is the required capacity to operate those loads from the battery bank? Therefore, the battery bank will need to supply 75 Ah to the system loads. However, the total of the nameplate ratings of the battery bank must be higher than this, because the usable capacity of a battery is always less than its rated capacity. = = When high availability is required for critical toads, a PV-only system may be prohibitively expensive due to very large array and battery bank requirements In these cases a hybrid system may be the best choice = = Battery-Bank Rated Capacity. Three factors affect the amount of usable capacity in a battery. These factors are used to estimate the larger battery-bank rated capacity necessary to supply the required output. See Ill. 14. First, most batteries can't be discharged to a depth of discharge of 100% without permanent damage. Depending on the battery type, common allowable depths of discharge range from 20% to 80%. Most PV systems use deep-cycle lead-acid batteries, which can be discharged to about 80%. This is the maximum fraction of the total rated capacity that is permitted to be withdrawn from the battery at any time. Also, low operating temperatures and high discharge rates further reduce battery capacity. Most battery ratings are specified for operation at 25°C (77°F) at a certain discharge rate. At other conditions for these two factors, the usable battery capacity may be lower. For example, a battery operating at -10°C (14°F) and at a discharge rate of C/120 has about only 90% of the capacity it has at 25°C (77°F). These two factors are used together to deter mine a second capacity-derating factor. Battery-Bank Capacity: ALLOWABLE DEPTH-OF-DISCHARGE; LOST DUE TO LOW TEMPERATURES and HIGH DISCHARGE RATES; Ill. 14. Due to the allowable depth-of discharge, low temperatures, and high discharge rates, the amount of useful output in a battery bank is less than the rated capacity The operating temperature is the minimum expected operating temperature for the battery bank. This depends on where the batteries will be stored. If they will be stored indoors, the temperature will be relatively steady and equal to the normal indoor temperature. If they will be outside, measures should be taken to minimize large daily and seasonal temperature swings, but the lowest expected temperature in these conditions is used in the analysis. The average discharge rate is determined from the total operating time over the period of autonomy, taking the allowable depth of discharge into account. Using the daily operating time calculated in the load analysis, the average discharge rate is calculated using the following formula: where r = average discharge rate (in hr) top = weighted average operating time (in hr/day) = autonomy (in days) DOD = allowable depth of discharge. For example, if the daily operating time for system loads is 16 hr/day over an autonomy of 3 days, and the allowable depth of discharge is 80%, what is the average discharge rate? The battery bank will discharge at a rate that would completely discharge the batteries in 60 hr. Therefore, the battery-bank average discharge rate is C/60. With the minimum expected operating temperature and the average discharge rate, the percentage of usable capacity is determined from a graph of discharge rates and operating temperatures. See Ill. 15. Most battery manufacturers report capacity at various discharge rates and temperatures in their specifications. Battery Capacity Loss vs. Temperature and Discharge Rate: Ill. 15. The amount of available capacity from a battery bank depends partly on the operating temperature and discharge rate. These factors may have different effects for different batteries. To calculate the total rated capacity of the battery bank, the required battery-bank output is increased proportionally to both the allowable depth of discharge and the temperature and discharge-rate de-rating factor. The required capacity is calculated using the following formula: BCd = battery-bank rated capacity (in Ah) B = battery-bank required output (in Ah) DODa = allowable depth of discharge CTr = temperature and discharge-rate; derating factor For example, consider a system that requires a total battery bank output of 500 Ah. The allowable depth of discharge is 75%, the minimum operating temperature is -10°C (-4°F), and the average discharge rate is C/SO. From the manufacturer's documentation on battery capacity, this yields a temperature and discharge-rate derating factor of approximately 80%. What is the required battery-bank rated capacity? Bd = 833 Ah Battery Selection. Individual batteries or cells are selected with enough capacity to avoid or minimize parallel battery connections. Due to wiring resistance and small differences among individual cells, paralleled strings of batteries may not charge and discharge uniformly. A single series-connected string of batteries is preferable but capacity requirements and the ' size of batteries available may require more than one string. Generally, the number of parallel battery connections should be limited to no more than 3 to 4 strings. Also, the size and weight of the batteries must be considered with regard to transportation and installation. The nominal voltage and rated capacity of the selected battery is used to determine the configuration of the battery bank. This information is found on battery nameplates or in manufacturer's literature. See Ill. 16. Ill. 16. Battery labels list the rated capacity of the battery and important safety in formation. The nominal DC-system voltage divided by the nominal battery voltage determines the number of batteries in a string. This number should calculate evenly. See Ill. 17. The required battery-bank rated capacity divided by the individual-battery rated capacity deter mines the number of strings to be connected in parallel. This number will likely not be a whole number, but should be rounded up to the nearest whole number. To prevent unnecessarily oversizing the capacity, the battery capacity should be chosen to minimize the amount of rounding. When the battery is chosen and the battery- bank design is configured, the final rated capacity of the battery bank is equal to the rated capacity of an individual battery multiplied by the number of parallel strings. For example, a battery bank must supply 600 Ah and will operate at 24 V nominal. A nominal 12 V battery is chosen with a rated capacity of 250 Ah. To produce a nominal voltage of 24 V. two 12 V batteries will be connected in series for each string. The number of strings in parallel is calculated to be 2.4 (600 Ah ÷ 250 Ah = 2.4). Rounded up to a whole number of 3 strings, the rated capacity of the battery bank will then be 750 Ah (250 Ah/string x 3 strings = 750 Ah). This is acceptable, but very conservative, and would result in an unnecessary increase in cost. Choosing a different battery with a rated capacity closer to 200 Ah would be better if the bank were to have 3 strings. A battery with a rated capacity of 300 Ah or slightly higher would be even better, as it would allow a battery bank with only 2 strings. Battery choices may require changes and recalculations to optimize the design of the battery bank. Battery-Bank Operation. With the final battery-bank configuration and battery choice determined, the predicted average daily depth of discharge is calculated. This will be less than the allowable depth of discharge because the final rated capacity of the battery bank is usually higher than the required rated capacity. First, the daily load fraction supplied by the battery bank is estimated. At any moment, the power to operate loads in a stand-alone system may be supplied by the array, the battery, or a combination of both. The load fraction is the portion of load operating power that comes from the battery bank over the course of a day. For example, a system with only nighttime loads, such as lighting, has a load fraction of 1.0 because all the electrical energy required by the loads is supplied by the battery bank. For daytime-only loads, the average load fraction is zero because the array will normally supply all the required electrical energy to the loads. Ill. 17. Battery-Bank Configurations --Batteries are configured in series and parallel to match the battery-bank rated capacity needed to produce the required output. BATTERY STRINGS IN PARALLEL (BUILDS CAPACITY) For most systems, however, the load fraction is somewhere in between. During periods of high irradiance, the array supplies all of the energy needed by on-site loads (in addition to charging the batteries), but most of the time, energy is supplied in a mix from both the array and the battery bank. With variable loads operating intermittently and for different lengths of time, an accurate calculation of load fraction is complicated. Instead, a load fraction estimate of 0.75 is a common rule of thumb used for most PV systems. The load fraction estimate does not affect any of the sizing calculations, so the rough estimate provided by the rules of thumb are adequate for the subsequent daily depth-of- discharge estimate calculations. With the load fraction estimate, the average battery-bank daily depth of discharge is then estimated with the following formula: where DOD_avg = average battery-bank daily depth of discharge LF = estimated load fraction EdaV = average daily electrical-energy consumption (in Wh) B = actual total rated battery-bank capacity (in Ah) VSDC = DC-system voltage (in V). For example, a 24 V battery bank has a rated capacity of 800 Ah. The estimated load fraction is 0.75, and the average daily electrical-energy consumption is 3900 Wh. What is the predicted average battery-bank daily depth of discharge? The array for a stand-alone system must be sized to meet the load requirements during the critical design month. Array Sizing For stand-alone systems, the array must be sized to produce enough electrical energy to meet the load requirements during the critical design month while accounting for normal system losses. This ensures that the battery will always be properly charged and that system availability is high throughout the year. See Ill. 18. Required Array Output. First, the required array current is calculated from the load requirement and insolation of the critical design month, and the nominal DC system voltage. However, because battery efficiency is less than 100%, more current must be supplied to charge a battery than is withdrawn on discharge. A battery-system charging efficiency factor increases the required array output to a slightly higher value. A value between 0.85 and 0.95 is appropriate for most batteries. The required array current is calculated using the following formula: where 'array = required array maximum-power current (in A) E_crit = daily electrical-energy consumption during critical design month (in Wh/day) 1 = battery-system charging efficiency VSDC = nominal DC system voltage (in V) t_PSH = peak sun hours for critical design month (in hr/day) For example, consider a nominal 24 V system in a location with 4.9 peak sun hours that must supply 1580 Wh per day. The battery-system charging efficiency is estimated at 0.90. What is the required array current? Ill. 18. The array sizing worksheet uses insolation data and load requirements to size the array. Very large PV systems typically divide the array output among many inverters. Array Sizing ARRAY SIZING Average Daily DC Energy Consumption for Critical Design Month DC System Voltage Critical Design Month Insolation Battery Charging Efficiency Required Array Maximum-Power Current __ Soiling Factor Rated Array Maximum-Power Current; A Temperature Coefficient for Voltage Maximum Expected Module Temperature Rating Reference Temperature Rated Array Maximum-Power Voltage Module Rated Maximum-Power Current ___IA Module Rated Maximum-Power Voltage; VDC Module Rated Maximum Power; 1W Number of Modules in Series Number of Module Strings in Parallel Total Number of Modules Actual Array Rated Power, W [The overall size of the system indicates that the battery bank should be a 48 V system in order to keep DC currents within an acceptable range. Since the loads are not critical and a small engine generator is available for emergencies, the autonomy period is set at 3 days. Using the average daily energy consumption for the critical design month, the required battery-bank output is calculated at 411 Ah. Based on the allowable depth of discharge, operating temperature, and discharge rate, the rated battery-bank capacity must be higher than 411 Ah. Since deep-cycle batteries will be used, the allowable depth of discharge is about 80% (0.80). A derating factor for temperature and discharge rate is determined from the battery specifications based on the minimum expected operating temperature and the discharge rate. The battery bank will be located in an unconditioned space in the basement, but the operating temperature will never fall below 0°C. The discharge rate is calculated from the daily weighted operating time from the critical design month, the number of days of autonomy, and the allowable depth of discharge. After applying the allowable depth of discharge and the derating factor, the required battery-bank rated capacity is 571 Ah. ] A flooded lead-acid 12 V nominal battery is selected with a manufacturer-specified rated capacity of 295 Ah. Four batteries in series are required to provide a system voltage of 48 V. Two series strings of batteries are required to provide the required rated capacity. A total of 8 batteries are needed for the battery bank. The actual rated capacity will be 590 Ah, just slightly above the required rated capacity. In this application, the load fraction is estimated at 0.75. The average daily depth of discharge is 17%. From the manufacturer's data, this battery has an expected life of 4000 cycles at 20% aver age daily depth of discharge. Correspondingly, at least 10 years of service should be expected in this application. BATTERY-BANK SIZING Average Daily DC Energy Consumption for Critical Design Month 1 65781 Wh/day DC System Voltage 48 Autonomy 3 days Required Battery-Bank Output 411 Ah Allowable Depth-of-Discharge 0.80 Weighted Operating Time 11 .2 hrs Discharge Rate 42 hrs Minimum Expected Operating Temperature I; 0 Temperature/Discharge Rate; Derating Factor 0.901 Battery-Bank Rated Capacity 571 Ah Selected Battery Nominal Voltage VDC Selected Battery Rated Capacity 295 Ah Number of Batteries in Series 4 Number of Battery Strings in Parallel 2 Total Number of Batteries 8 Actual Battery-Bank Rated Capacity; 590 Ah ___ Load Fraction 0.75j Average Daily Depth-of-Discharge: 0.17 A standard module with 36 series-connected PV cells is particularly suited for battery-based systems Its maximum power voltage IS about 15 V to 1 6V which is ideal for charging a 12 V battery system Correspondingly, multiple modules in series strings, or 72 cell modules are used for charging higher-order battery banks Array Rated Output. Just as with battery banks, certain factors reduce the array output from the factory ratings to actual output values. Therefore, these factors are applied to the required array output to determine the necessary increase in array ratings for sizing and module selection. See Ill. 19. Soiling is the accumulation of dust and dirt on an array surface that shades the array and reduces electrical output. The magnitude of this effect is difficult to accurately determine, but estimates will account for most of this effect. A derating factor of 0.95 is used for light soiling conditions with frequent rainfall and /or a higher tilt angle, and a derating factor of 0.90 or less is used for heavy soiling conditions with long periods between rainfalls or cleanings. The rated array maximum-power current is calculated using the following formula: Where 'raird = rated array maximum-power current (in A) I = required array maximum-power array current (in A) Cs = soiling derating factor Ill. 19. Actual array output is often less than rated output due to soiling and high temperatures. High temperature reduces voltage output. A temperature coefficient of -0.004/°C is applied to voltage, indicating that voltage falls by about 0.4% for every degree above the reference or rating temperature, which is usually 25°C (77°F). The maximum module temperature is estimated from the maximum ambient temperature for the location. In addition, the array voltage must be higher than the nominal battery-bank voltage in order to charge the batteries. An array with a 12 V maximum-power voltage will not charge a nominal 12 V battery because the actual voltage of a nearly charged battery is about 14.5 V. The array voltage must beat least 14.5 V to charge a to ensure that the array voltage is sufficient to nominal 12 V battery. Therefore, the rated array maximum-power voltage is multiplied by 1.2 charge the battery bank. The rated array maximum-power voltage is calculated using the following formula: where V_rated = rated array maximum-power voltage (in V) VSDC = nominal DC-system voltage (in V) C% V = temperature coefficient for voltage (in 1°C) T = maximum expected module temperature (in °C) T = reference (or rating) temperature ref (in °C) For example, consider an array for a nominal 24 V DC system that must output 18 A. The soiling conditions are expected to be light and the maximum module temperature is estimated at 50°C. What are the minimum rated maximum- power current and voltage parameters? Vd = 1.2 x [ + (24 x -0.004 x 25)] V rated = 1.2 x (24 - 2.4) Vd = 25.9 V Arrays in hot climates produce less than their rated power because of high temperatures. Module Selection. The final step of the sizing process involves selecting a PV module and determining the array configuration based Oil the current and voltage parameters. For each module, three parameters are needed for sizing: the maximum power, the maximum-power (operating) current, and the maximum-power (operating) voltage. As with batteries, modules should be chosen to result in an array that is as close as possible to the desired array ratings, but slightly higher. The number of parallel strings of modules required is determined by dividing the rated array current output by the selected module maxi mum-power current output and rounding up to the next whole number. See Ill. 20. The number of series-connected modules in each string is determined by dividing the rated array voltage by the selected module maximum-power voltage and rounding up to: The rated array maximum power is calculated by multiplying the rated module maximum power by the total number of modules. Ill. 20. Modules are configured in series and parallel to match the array rated capacity needed to produce the required output. ==== Thin Film Module Initial Ratings Some thin-film PV modules' power and current output are slightly higher for the first few weeks or months of use and then stabilize for the rest of its lifetime. (This does not apply to crystalline silicon modules.) The nameplate or rated parameters for power, current, and voltage may give either the long term values or the initial values. The nameplate should also specify which is the case. Long-term values can be used without adjustment in sizing I. However, if the module ratings specify only the initial power, current, and voltage parameters, these values may then be derated. Derating results in ratings that are more realistic for sizing calculations. The module label or specifications will [ … ] guaranteed long-term parameters, which are generally about 90% to 95% f the initial values If this information is not readily available, derating factors of 0.90 for power and 0.95 for current are generally appropriate. == The required array current at maximum power is determined from the daily load requirement and insolation for the critical design month, along with the DC system voltage and an estimated battery-charging efficiency. Battery-charging efficiency is usually approximated at 85% (0.85). The result is 32.2 A. This means the PV array must be sized to produce at least 32.2 A under peak sun conditions. The required current rating is adjusted upward to 33.9 A to account for reduced current due to a soiling factor of 0.95. The required voltage rating is adjusted upward to 64.1 V to account for reduced voltage due to high temperatures and for adequate battery charging. The selected PV module has a rated maximum power of 185 W at STC. Rated maximum-power current is 5.11 A, and rated maximum-power voltage is 36.2 V. Two modules in series will provide the necessary array voltage, and 7 parallel strings will provide the necessary current. The array will consist of 14 modules, for a total rated power output of 2590 W, or 2.59 kW. ARRAY SIZING __ Average Daily DC Energy Consumption; 6578 I Wh/day for Critical Design Month I DC System Voltage I 481VDC Critical Design Month Insolation; 5.OIPSH/day Battery Charging Efficiency 0.851 Required Array Maximum-Power Current 32.2 A Soiling Factor I 0.95 Rated Array Maximum-Power Current 339 A Temperature Coefficient for Voltage - Maximum Expected Module Temperature I 50 Rating Reference Temperature I 251°C Rated Array Maximum-Power Voltage 51.8 VDC Module Rated Maximum-Power Current: I 5.11 Module Rated Maximum-Power Voltage I 36.2 IVDC Module Rated Maximum Power I 185]W Number of Modules in Series 2 Number of Module Strings in Parallel 7 Total Number of Modules 14 Actual Array Rated Power 2590 W === Summary: • Sizing analysis for stand-alone systems starts at the load side and proceeds backward to the array. • Interactive systems are generally sized to be as large as possible within the limits of available space and budget since, in most locations, occasional excess energy can be sold back to the utility. • Sizing of stand-alone systems involves a fine balance between energy supply and demand. If the system is too small, there will be losses in load availability and system reliability. If the system is too large, excess energy will be unutilized and wasted. • Bimodal systems are typically sized in the same way as stand-alone systems. • The PV array and battery bank in a hybrid system can be significantly smaller than in a stand-alone system if the secondary power source is available on demand. • A detailed load analysis completed during the site survey lists each load, its power demand, and daily energy consumption. • A weighted average operating time accounts for multiple loads operating for varying lengths of time per day. • Inverters lose some power in the process of converting DC energy to AC energy, so more DC energy is required to produce a certain amount of AC energy. • A stand-alone system must produce enough electricity to meet load requirements during any month, so systems are sized for the worst-case scenario of high load and low insolation. • If the load requirements vary from month to month, the critical design month may turn out to be any month of the year. • The highest critical design ratio in each orientation corresponds to the critical design month for that orientation. When multiple orientations are considered, the lowest ratio of the resulting critical design months corresponds to the optimal array orientation (of the orientations analyzed). • The DC voltage for battery-based PV systems is usually an integer multiple of 12 V, usually 12 V, 24 V, or 48V. • Noncritical systems are typically designed for 3 to 5 days of autonomy, while critical applications may have 6 to 10 days of autonomy or more. • Because several factors reduce the useful capacity of a battery, the ratings of battery banks must be higher than the required battery-bank output. • The nominal voltage and rated capacity of the selected battery are used to determine the configuration of the battery bank. • Like batteries, several factors reduce the output of a PY module, so the array ratings must be higher than the required array output. • Each percentage-point increase in system availability costs increasingly more money for larger battery banks and arrays, which is impractical from an economic standpoint for all but the most critical applications. Terms: • Duty cycle is the percentage of time a load is operating. • The critical design ratio is the ratio of electrical energy demand to average insolation during a period. • The critical design month is the month with the highest critical design ratio. • System availability is the percentage of time over an average year that a stand-alone PV system meets the system load requirements. • Autonomy is the amount of time a fully charged battery system can supply power to system loads without further charging. • The load fraction is the portion of load operating power that comes from the battery bank over the course of a day. • Soiling is the accumulation of dust and dirt on an array surface that shades the array and reduces electrical output. Quiz: 1. What is involved in sizing interactive systems? 2. Why does the sizing of a stand-alone system require critical calculations and tight tolerances? 3. What methodology is used to size bimodal systems? 4. Explain the three differences between sizing a stand-alone system and sizing the PV portion of a PV array and engine generator hybrid system. 5. Describe the basic analysis procedure for sizing a stand-alone system. 6. Why must AC loads and DC loads be listed separately in a load analysis? 7. What factors are involved in inverter selection? 8. How does sizing for the critical design month improve system availability? 9. How does system availability affect system cost? 10. What three factors affect the required rating of the battery bank in relation to the required battery-bank output? 11. What three factors are used to determine the required voltage and current ratings of the array from the required array voltage and current outputs? Next: Mechanical Integration Prev: Inverters |