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quantity-name="magnetic_flux"/> <unit unit-name="tesla" quantity-name="magnetic_flux_density"/> <unit unit-name="watt" quantity-name="power"/> <unit unit-name="pascal" quantity-name="pressure"/> <unit unit-name="ohm" quantity-name="resistance"/> <unit unit-name="liter" quantity-name="volume"/> </derivedUnits> </customUnitSystem> </units> </calculation> <editor view-annotations="false" view-regions="false"> <ruler is-visible="true" ruler-unit="in"/> <plotTemplate> <xy item-idref="1"/> </plotTemplate> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="true" save-text-images="false" screen-dpi="120"/> <miscellaneous> <handbook handbook-region-tag-ub="1338" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="804" left="36" top="7.8" width="416.4" height="13.8" align-x="53.4" align-y="18" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Battery Sizing.xmcd<sp count="3"/>Charles Kim 2013</p> </text> </region> <region region-id="1234" left="24" top="31.8" width="684" height="96.6" align-x="27.6" align-y="42" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">A Cabin near Salt Lake City, Utah, has an AC energy demand of 3 kWh per day in the winter months.<sp count="2"/>With a battery system, a 95% availability will be provided, while a back-up generator will be kept to cover the other 5%.<sp count="2"/>The battery system will be kept in a ventilated shed where the temperatue may go as low as - 10 C degrees.<sp count="2"/>The system voltage is 24 V, and an inverter efficiency is 85%.<sp count="3"/>Assume 80% deep discharge (MDOD) and 97 % discharge rate (T,DR)</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">(Q) Calculate the size of the battery system.</p> </text> </region> <region region-id="1299" left="390" top="162" width="309.6" height="61.2" align-x="390" align-y="162" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="2" display-width="308.4" display-height="60"/> </picture> <rendering item-idref="3"/> </region> <region region-id="1303" left="120" top="163.2" width="71.4" height="15" align-x="166.2" align-y="174" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">MDOD</ml:id> <ml:real>0.8</ml:real> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="1304" left="132" top="181.2" width="65.4" height="15" align-x="166.2" align-y="192" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">TDR</ml:id> <ml:real>0.97</ml:real> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="1246" left="132" top="211.2" width="44.4" height="15" align-x="160.2" align-y="222" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Eac</ml:id> <ml:real>3</ml:real> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="1248" left="192" top="211.8" width="64.8" height="13.8" align-x="200.4" align-y="222" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">kWh / day</p> </text> </region> <region region-id="1252" left="414" top="234" width="241.2" height="264" align-x="414" align-y="234" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="7" display-width="240" display-height="262.8"/> </picture> <rendering item-idref="8"/> </region> <region region-id="1253" left="138" top="235.2" width="63" height="15" align-x="169.8" align-y="246" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">D2A</ml:id> <ml:real>0.85</ml:real> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="1255" left="228" top="235.8" width="136.8" height="13.8" align-x="248.4" align-y="246" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Inverter Efficiency</p> </text> </region> <region region-id="1263" left="144" top="259.2" width="58.2" height="15" align-x="180" align-y="270" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Bvolt</ml:id> <ml:real>24</ml:real> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="1265" left="234" top="259.8" width="158.4" height="13.8" align-x="252.6" align-y="270" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Battery System Voltage</p> </text> </region> <region region-id="1260" left="18" top="295.8" width="75" height="27.6" align-x="48" align-y="306" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">SOLUTION</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">========= </p> </text> </region> <region region-id="1236" left="18" top="337.8" width="195" height="13.8" align-x="21.6" align-y="348" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">1. DC energy demand (Edc):</p> </text> </region> <region region-id="1256" left="48" top="352.8" width="121.2" height="32.4" align-x="76.2" align-y="372" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Edc</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:id xml:space="preserve">Eac</ml:id> <ml:id xml:space="preserve">D2A</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>3.5294117647058822</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="1259" left="186" top="361.8" width="57.6" height="13.8" align-x="194.4" align-y="372" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">kWh /day</p> </text> </region> <region region-id="1262" left="18" top="403.8" width="21.6" height="13.8" align-x="21.6" align-y="414" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">2. </p> </text> </region> <region region-id="1267" left="42" top="403.8" width="288" height="55.2" align-x="69" align-y="414" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Expression of the energy demand in terms</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">of Amp-Hour per day.<sp count="2"/>Remember that </p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Energy=Power*Time = V*A*time,</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">==> A*hour = Wh/V</p> </text> </region> <region region-id="1268" left="42" top="472.8" width="163.8" height="32.4" align-x="68.4" align-y="492" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">AH</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">Edc</ml:id> <ml:real>1000</ml:real> </ml:apply> <ml:id xml:space="preserve">Bvolt</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>147.05882352941177</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="1270" left="210" top="481.8" width="43.2" height="13.8" align-x="216.6" align-y="492" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Ah/day</p> </text> </region> <region region-id="1318" left="18" top="516" width="507" height="90" align-x="18" align-y="516" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="13" display-width="505.8" display-height="88.8"/> </picture> <rendering item-idref="14"/> </region> <region region-id="1320" left="54" top="607.8" width="492" height="22.2" align-x="63" align-y="624" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="20">http://rredc.nrel.gov/solar/pubs/redbook/</f> </p> </text> </region> <region region-id="1321" left="30" top="648" width="717" height="394.2" align-x="30" align-y="648" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="15" display-width="715.8" display-height="393"/> </picture> <rendering item-idref="16"/> </region> <region region-id="1322" left="12" top="1092" width="658.8" height="391.2" align-x="12" align-y="1092" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="17" display-width="657.6" display-height="390"/> </picture> <rendering item-idref="18"/> </region> <region region-id="1272" left="18" top="1609.8" width="446.4" height="13.8" align-x="21.6" align-y="1620" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">3. Find the usable storage Ah at -10 C degree<sp count="2"/>(use the graph)</p> </text> </region> <region region-id="1278" left="36" top="1633.8" width="201.6" height="13.8" align-x="38.4" align-y="1644" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">a. Peak-Sun-Hour information</p> </text> </region> <region region-id="1285" left="36" top="1657.8" width="540" height="13.8" align-x="39.6" align-y="1668" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">b. Find the # of days of usuable storage(Dus) on the 95% availability curve</p> </text> </region> <region region-id="1279" left="36" top="1680" width="327" height="375" align-x="36" align-y="1680" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="19" display-width="325.8" display-height="373.8"/> </picture> <rendering item-idref="20"/> </region> <region region-id="1288" left="414" top="1825.8" width="230.4" height="13.8" align-x="426.6" align-y="1836" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">From the curve, we find for Dus:</p> </text> </region> <region region-id="1289" left="432" top="1867.2" width="53.4" height="15" align-x="460.2" align-y="1878" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Dus</ml:id> <ml:real>4.6</ml:real> </ml:define> </math> <rendering item-idref="21"/> </region> <region region-id="1293" left="504" top="1867.8" width="36" height="13.8" align-x="515.4" align-y="1878" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">days </p> </text> </region> <region region-id="1291" left="36" top="2125.8" width="396" height="13.8" align-x="39.6" align-y="2136" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">c. Now we calculate the Usuable Storage Amp-Hour (AHus)</p> </text> </region> <region region-id="1294" left="72" top="2155.2" width="164.4" height="15" align-x="109.2" align-y="2166" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">AHus</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">AH</ml:id> <ml:id xml:space="preserve">Dus</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>676.470588235294</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="22"/> </region> <region region-id="1297" left="252" top="2155.8" width="22.8" height="13.8" align-x="258.6" align-y="2166" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Ah </p> </text> </region> <region region-id="1314" left="42" top="2203.8" width="345" height="13.8" align-x="45.6" align-y="2214" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">d. Finally, the nominal (C/20, 25 C) capacity:</p> </text> </region> <region region-id="1300" left="54" top="2238" width="534.6" height="73.2" align-x="54" align-y="2238" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="23" display-width="533.4" display-height="72"/> </picture> <rendering item-idref="24"/> </region> <region region-id="1327" left="456" top="2311.2" width="94.2" height="15" align-x="500.4" align-y="2322" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">MDOD</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.8</ml:real> </result> </ml:eval> </math> <rendering item-idref="25"/> </region> <region region-id="1298" left="54" top="2334" width="348.6" height="250.8" align-x="54" align-y="2334" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="26" display-width="347.4" display-height="249.6"/> </picture> <rendering item-idref="27"/> </region> <region region-id="1328" left="456" top="2329.2" width="82.2" height="15" align-x="488.4" align-y="2340" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">TDR</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.97</ml:real> </result> </ml:eval> </math> <rendering item-idref="28"/> </region> <region region-id="1336" left="474" top="2377.2" width="131.4" height="15" align-x="555.6" align-y="2388" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">MDOD</ml:id> <ml:id xml:space="preserve">TDR</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.776</ml:real> </result> </ml:eval> </math> <rendering item-idref="29"/> </region> <region region-id="1305" left="456" top="2434.8" width="208.8" height="32.4" align-x="508.2" align-y="2454" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">AHnorm</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:id xml:space="preserve">AHus</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">MDOD</ml:id> <ml:id xml:space="preserve">TDR</ml:id> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>871.74044875682216</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="30"/> </region> <region region-id="1307" left="672" top="2443.8" width="21.6" height="13.8" align-x="678.6" align-y="2454" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Ah </p> </text> </region> <region region-id="1330" left="462" top="2491.8" width="43.2" height="22.2" align-x="468.6" align-y="2508" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="20">Cf.</f> <sp/> </p> </text> </region> <region region-id="1334" left="462" top="2521.8" width="216" height="55.2" align-x="474" align-y="2532" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">With Dus=4.6 (~ 5 ) days = 72 hours,C/72 Rate, at -10 C, the value is 0.97.</p> </text> </region> </regions> <binaryContent> <item item-id="1" content-encoding="gzip">H4sIAAAAAAAA/4yQwW7CMAyG7aZbS9etu3AhSOUZeIIdENph2iT2ACiUAkVUTF2ROPLm3W8n u+w0R3b+Ot/vRsmJiJGfyEy1QS228/W+c1+H9e7cta5PSGKMHGl74XqnLZog07b62Bzrqvet 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