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Chapter 9 System Sizing Sizing Methodologies • Sizing Utility-Interactive Systems • Sizing Stand-Alone Systems • Sizing Multimode Systems • Sizing Hybrid Systems • Sizing Calculations • Load Analysis • Critical Design Analysis • DC-System Voltage • System Availability • Battery-Bank Sizing • Array Sizing

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**Sizing strategy for stand-alone systems starts at the load side and proceeds backward to the array.**

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 Figure 9-1. 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.

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Sizing interactive systems begins with calculating the peak array DC power output, which is then derated for various losses and inefficiencies in the system to arrive at a final AC power output. Sizing interactive systems begins with the specifications of a PV module chosen for the system. Module ratings at STC are used to calculate the total expected array DC power output. This is then derated for various losses and inefficiencies in the system. The result is a final AC power output that is substantially lower but realistically accounts for expected real-world conditions. See Figure 9-2. To determine the expected energy production per day, the final AC power output is multiplied by the average daily insolation (peak sun hours) for the month or year on the array plane. For example, if the AC power output is estimated to be 2140 W and the average annual insolation is 5.1 peak sun hours (kWh/m²/day), then the average energy production is expected to be 10.9 kWh/day. The energy output can be additionally derated for shading, soiling, or downtime.

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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. 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 Figure 9-3.

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Stand-alone systems must be carefully matched to load requirements to avoid reducing load availability or producing more energy than is needed. 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 Figure 9-4. 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.

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A load analysis tabulates the various kinds of loads and their power and electrical-energy requirements. A detailed load analysis completed during the site survey lists each load, its power demand, and daily energy consumption. See Figure 9-5. 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.

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**Load power and energy requirements can be easily measured with inexpensive meters.**

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 Figure 9-6.

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Load requirements include the power demand and electrical-energy consumption for all the expected loads in the system. 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 Figure 9-7. This is the total number of hours per day on average that the load is operating.

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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. 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 Figure 9-8.

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A critical design analysis compares the load requirements and insolation for each month to determine the critical design month. A stand-alone system must produce enough electricity to meet load requirements during any month. Therefore, systems 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 Figure 9-9. The critical design ratio is the ratio of electrical energy demand to average 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.

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DC-system voltage is chosen in proportion with the array size and to keep the operating current below 100 A. The selection of the battery-bank voltage affects system currents. See Figure For example, a 1200 W system operating at 12 V draws 100 A (1200 W ÷ 12 V = 100 A). The same 1200 W system draws only 50 A at 24 V, or 25 A 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.

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**System autonomy is approximated from the local peak sun hours and desired 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 based on peak sun hours. See Figure 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 or sometimes in hours. 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.

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**Increasing system availability significantly increases the size and cost of the system.**

However, each percentage-point increase in system availability is increasingly more expensive for larger battery banks and arrays, which is impractical from an economic standpoint 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 Figure 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.

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The battery-bank sizing worksheet uses information from the load analysis to determine the required size of the battery bank. 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 Figure 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.

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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. 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 Figure First, most batteries cannot 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.

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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. 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 Figure Most battery manufacturers report capacity at various discharge rates and temperatures in their specifications.

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**Battery labels list the rated capacity of the battery and important safety information.**

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 Figure 9-16.

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Batteries are configured in series and parallel to match the battery-bank rated capacity needed to produce the required output. 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 Figure The required battery-bank rated capacity divided by the individual-battery rated capacity determines 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 as close to the size required to minimize the amount of rounding.

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**The array sizing worksheet uses insolation data and load requirements to size the array.**

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 Figure 9-18.

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Actual array output is often less than rated output due to soiling, shading, and higher operating temperatures. 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 Figure 9-19.

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Modules are configured in series and parallel to match the array rated capacity needed to produce the required output. The number of parallel strings of modules required is determined by dividing the rated array current output by the selected module maximum-power current output and rounding up to the next whole number. See Figure 9-20.

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