Overview:

Product Description:

Battery capacity (C) is described in terms of Amp-hours (Ah), which is the amount of current available over a given period of time. In order to calculate the required battery capacity for a stand-alone system, refer to the interactive appliance-specific sizing spreadsheet, and take note of the total Watt-hours (Wh) consumed. A true stand-alone system will at some point have to rely on this battery bank due to inclement weather. To provide enough storage to remain autonomous during these periods, multiply the day-long capacity requirement by the maximum number of consecutive cloudy days expected.

To find:             Cbank          

Equation:          Cbank = (Whtot / 0.9) / 24V x cloud factor

Where:             Cbank = battery bank capacity, (Ah)

                         Whtot = total Watt-hours of building, calculated on spreadsheet

                         0.9 = assumed inverter efficiency, 90%

                         24V = assumed system voltage

                         cloud factor = maximum number of consecutive cloudy days

 

The Coulomb efficiency of a battery is its ability to convert input energy into energy that is available for use. This correction factor is used to quantify the amount of Amp-hours that need to be delivered to the batteries from the PV array. Assume a 90% Coulomb efficiency.

To find:             Ah to batt.

Equation:          Ah to batt. = Cbank / Coulomb

Where:             Cbank = battery bank capacity, (Ah)

                         Coulomb = 0.9, Coulomb efficiency

 

Batteries are sold with a standard rating that allows comparison and specialization for certain applications. When sizing a battery bank, the capacity value that is needed to supply the demands within a building does not directly correlate to the rated capacity of the batteries. Also known as the nominal capacity (Cnominal), this value must be over-sized to account for additional losses.

Maximum Depth of Discharge, or MDOD, is a safety factor for the battery bank that prevents it from being completely discharged, which rapidly makes the battery unusable and unrecoverable. Unlike PV panels, the efficiency of batteries decreases as the ambient temperature decreases below 25°C. The following chart provides rough temperature-adjusted multipliers to be included in the nominal battery capacity equation;

Temperature (°C)	Multiplier
25	1.00
21	1.04
15	1.11
9	1.19
4	1.30
-1	1.40
-7	1.59

The equation below is intended to account for these corrections and determine the rated (nominal) capacity of the batteries. Assume an MDOD of 80%.

To find:            Cnominal

Equation:         Cnominal = (Cbank x Mtemp) / MDOD

Where:            Cnominal = rated battery bank capacity able to provide ample Cbank

                        Cbank = battery bank capacity (Ah)

                        Mtemp = Temperature multiplier, from above chart

                        MDOD = 0.8, Maximum Depth of Discharge

 

This nominal capacity value is the relevant Amp-hr value used to purchase and connect batteries. The following equations help determine the number of batteries that should be wired as a string in parallel, and the number strings that should be wired in series.  Parallel wiring allows the current of a system to be increased by adding each battery’s current together. This is done by wiring positive terminals to positive terminals and negative to negative for each battery. Voltage stays constant across a parallel arrangement. Series wiring adds voltages while the current stays the same, and is achieved by wiring a positive terminal from one string to a negative terminal on another string.

To find:             Bparallel

                         # of Strings

Equation:          Bparallel = Cnominal / Cbattery

                         # of Strings = Vsys / Vbatt

Where:             Bparallel = number of batteries wired in parallel

                        # of Strings = number of strings wired in series 

                        Cnominal = nominal battery bank capacity (Ah)

                        Cbattery = individual battery capacity (Ah)

                        Vsys = 24V, system voltage

                        Vbatt = 12V, individual battery voltage

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