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Solar Storage System Design

Solar energy systems that are not connected to an electrical grid system usually require back-up or storage equipment to provide energy during unusually cloudy days. Unusually cloudy conditions occurring over a number of consecutive days continually draw reserve power from batteries or other storage devices for solar systems not connected to an electrical grid. Storage devices must be designed to withstand continuous below-average conditions in various regions of the globe.

Different industry organizations use different methods to size either battery or other types of backup systems. One example of this is an international aid organization requires that all stand-alone medical equipment must be able to operate for 6 Black or No-Sun days in parts of the tropics. Other requirements or methods of storage need different solar insolation parameters. Four types of parameters are provided in the POWER data set. They are listed below in the info box then described in the subsequent text and also in Whitlock et al (2005).

Parameters for Solar Storage System Design

  • Minimum Insolation Over a Consecutive Day Period
  • Solar Irradiance Deficit Over a Consecutive Day Period
  • Equivalent No-Sun Days Over a Consecutive Day Period
  • Surplus Insolation Over a Consecutive Day Period

For the following equations a parameter enclosed by "< >" indicates the average value for the parameter.

Minimum Insolation Over a Consecutive Day Period

Minimum percentage insolation over a consecutive day period (1, 3, 7, 14, or 21 days) is the difference between the user defined multi-year (Jan 1984-Present) monthly averaged insolation and the multi-year monthly averaged minimum insolation over the requested period within each month. The running average is computed over the indicated days within each month.

Equation
\begin{align}\ <\text{SRAD}>^p_{jk} = [∑^pi=i(<\text{SRAD}>_{ijk})]/p \end{align}
\begin{align} \normalsize{Where:} \\ \normalsize{<\text{SRAD}>_{ijk}: } & \normalsize{\text{ Daily averaged surface insolation for day } i \text{, in month } j \text{, and year } k \text{.} } \\ \normalsize{i: } & \normalsize{\text{ Day in month for } j \text{.}} \\ \normalsize{j: } & \normalsize{\text{ Month of year. }} \\ \normalsize{k: } & \normalsize{\text{ Year in n-year time multi-year span. }} \\ \normalsize{p: } & \normalsize{\text{ Averaging period equals 1, 3, 7, 14, or 21 days. }} \\ \end{align}

The multi-year monthly average of the running sum of insolation over the consecutive p day average in month j is given by

\begin{align}\ <\text{SRAD}>^p_j = [∑^nk=1(<\text{SRAD}>^p_{jk})]/n \end{align}
\begin{align} \normalsize{Where:} \\ \normalsize{n: } & \normalsize{\text{ The number years in time span. }} \\ \end{align}

The parameter \text{Min}/p\text{-day} for month j is the % difference between multi-year monthly average value, <\text{SRAD}>^p_{j}, and the minimum value of <\text{SRAD}>^p_{j} over the time period and is given by

\begin{align}\ & [\text{Min}/p\text{-day}]^p_j = 100 – (100*[<\text{SRAD}>^p_{j} - <\text{SRADmin}>^p_{j}]/ <\text{SRAD}>^p_{j}) \\ \\ & <\text{SRADmin}>^p_{j} = MIN(<\text{SRAD}>^p_{j}) \end{align}

Solar Irradiance Deficit Over a Consecutive Day Period

Solar radiation deficits below expected values incident on a horizontal surface over a consecutive day period is the multi-year monthly averaged deficit calculated as follows:

Equation
\begin{align}\ <\text{SRADdef}>^p_{j} = <\text{SRADsum}>^p_{j} - <\text{SRADsumMin}>^p_{j} \end{align}
\begin{align} \normalsize{Where:} \\ &\normalsize{ <\text{SRADsum}>^p_{j} = ∑^nk=1(<\text{SRADsum}>^p_{jk})/n } \\ &\normalsize{ <\text{SRADsum}>^p_{j} = ∑^nk=1(<\text{SRADsum}>^p_{jk})/n } \\ &\normalsize{ <\text{SRADsum}>^p_{jk} = ∑^pi=1(<\text{SRAD}>^p_{ijk})/n } \\ \normalsize{<\text{SRAD}>_{ijk}: } & \normalsize{\text{ Daily averaged surface insolation for day i, in month j, and year k. }} \\ \normalsize{i: } & \normalsize{\text{ Day in month for } j \text{.}} \\ \normalsize{j: } & \normalsize{\text{ Month of year. }} \\ \normalsize{k: } & \normalsize{\text{ Year in n-year time multi-year span. }} \\ \normalsize{p: } & \normalsize{\text{ Averaging period equals 1, 3, 7, 14, or 21 days. }} \\ \normalsize{And:} \\ &\normalsize{ <\text{SRADsumMin}>^p_{j} = MIN(<\text{SRADsum}>^p_{j}) } \\ \end{align}

Equivalent No-Sun Days Over a Consecutive Day Period

Equivalent number of Black or No-Sun or days is based upon the deficit solar radiation below expected multi-year monthly averaged value and calculated as follows:

Equation
\begin{align}\ <\text{NoSunDa}>^p_{j} = <\text{SRADdef}>^p_{j} / <\text{SRAD}>^p_{j} \end{align}
\begin{align} \normalsize{Where:} \\ &\normalsize{ <\text{SRADdef}>^p_{j} = <\text{SRADsum}>^p_{j} - <\text{SRADsumMin}>^p_{j} } \\ &\normalsize{ <\text{SRADsum}>^p_{j} = ∑^nk=1(<\text{SRADsum}>^p_{jk})/n } \\ &\normalsize{ <\text{SRADsum}>^p_{j} = ∑^nk=1(<\text{SRADsum}>^p_{jk})/n } \\ &\normalsize{ <\text{SRADsum}>^p_{jk} = ∑^pi=1(<\text{SRAD}>_{ijk}) } \\ &\normalsize{ <\text{SRADsumMin}>^p_{j} = MIN(<\text{SRADsum}>^p_{jk}) } \\ \normalsize{And:} \\ &\normalsize{ <\text{SRADsum}>_{j} = ∑^nk=1(<\text{SRAD}>_{jk})/n = \text{ Multi-year monthly average for month } j \text{.} } \\ &\normalsize{ <\text{SRADsum}>_{jk} = ∑^mi=1(<\text{SRAD}>_{ijk})/m = \text{ Monthly average SRAD for month } j \text{ in year } k \text{.} } \\ &\normalsize{<\text{SRAD}>_{ijk}: } = \normalsize{\text{ Daily averaged surface insolation for day } i \text{, in month } j \text{, and year } k \text{.} } \\ \normalsize{i: } & \normalsize{\text{ Day in month for } j \text{.}} \\ \normalsize{j: } & \normalsize{\text{ Month of year. }} \\ \normalsize{k: } & \normalsize{\text{ Year in n-year time multi-year span. }} \\ \normalsize{m: } & \normalsize{\text{ days in month } j \text{.}} \\ \end{align}

Surplus Insolation Over a Consecutive Day Period

Available surplus insolation over consecutive day period (1, 3, 7, 14, or 21 days) is calculated for each month as the climatological average (i.e. multi-year monthly average) over the user defined period (1984-Present) as a percentage of the expected average insolation over the same consecutive day period. The parameter Max/p-day for month j is the percent (%) difference between multi-year monthly average value, <\text{SRAD}>_{pj}, and the maximum value of <\text{SRAD}>_{pj} over the time period. The following summarizes the procedure for calculating the multi-year monthly average value of \text{Max}/\text{p-day}:

Equation
\begin{align}\ [\text{Max}/\text{p-day}]^p_j = 100 – (100*[<\text{SRAD}>^p_{j} - <SRADmax>^p_j] / <\text{SRAD}>^p_{j}) \end{align}
\begin{align} \normalsize{Where:} \\ &\normalsize{ <\text{SRAD}>^p_{j} = ∑^nk=1(<\text{SRAD}>^p_{jk})/n = \text{ Multi-year monthly average for month } j \text{.} } \\ &\normalsize{ <\text{SRAD}>^p_{jk} = [∑^pi=i(<\text{SRAD}>_{ijk})]/p = \text{ Running average of the daily insolation over } p \text{ days for month } j \text{ & year } k \text{.} } \\ &\normalsize{ <\text{SRAD}>^{ijk} = \text{ Daily averaged surface insolation for day } i \text{ in month } j \text{ & year } k \text{.} } \\ \normalsize{i: } & \normalsize{\text{ Day in month for } j \text{.}} \\ \normalsize{j: } & \normalsize{\text{ Month of year. }} \\ \normalsize{k: } & \normalsize{\text{ Year in n-year time multi-year span. }} \\ \normalsize{p: } & \normalsize{\text{ Averaging period equals 1, 3, 7, 14, or 21 days. }} \\ \normalsize{n: } & \normalsize{\text{ Year in n-year time multi-year span. }} \\ \end{align}

\normalsize{ <\text{SRADmax}>^p_{j} = MAX(<\text{SRAD}>^p_{j})}