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PhD Thesis - Energy Systems Research Unit - University of Strathclyde

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equired (kW) = maxkWh x bulk% (5.16)<br />

time x time%<br />

Where maxkWh = maximum storage capacity (kWh)<br />

bulk% = maximum percentage from bulk phase<br />

time = recharge time<br />

time% = percentage <strong>of</strong> recharge time for bulk phase<br />

If the percentage charge <strong>of</strong> the battery is above the bulk percentage level, the<br />

percentage charge being added to the battery decreases exponentially with time,<br />

as defined by Equation 5.17.<br />

Percentage Charge Added = (1 - e -t/τ ) (5.17)<br />

In order for this to happen, the power drawn by the recharge unit (the recharge<br />

rate (kW required)) will decrease exponentially with time, as defined by<br />

Equation 5.18.<br />

Power Drawn by Recharge <strong>Unit</strong> = ( e -t/τ ) (5.18)<br />

As the vehicle may come to be recharged with varying percentage charges, and<br />

there may not always be enough excess electricity to fully supply the recharging<br />

demand, the time in these equations will not be known to ascertain the power<br />

required. Therefore, the shape <strong>of</strong> the recharge rate pr<strong>of</strong>ile (kW required) with<br />

percentage charge must be found. From Equations 5.17 and 5.18, it can be seen<br />

that this pr<strong>of</strong>ile can be defined by,<br />

This is shown graphically in Figure 5.4.<br />

x = 1-y (5.19)<br />

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