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Battery-Powered Systems: Efficiency, Control, Economics ECEN 2060

Battery-Powered Systems: Efficiency, Control, · If we discharge the battery more slowly, say at a current

Feb 08, 2018



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  • Battery-Powered Systems:Efficiency, Control, Economics

    ECEN 2060

  • 2ECEN2060

    Battery capacity

    The quantity C is defined as the current that discharges the battery in 1 hour,so that the battery capacity can be said to be C Ampere-hours (units confusion)

    If we discharge the battery more slowly, say at a current of C/10, then we mightexpect that the battery would run longer (10 hours) before becomingdischarged. In practice, the relationship between battery capacity anddischarge current is not linear, and less energy is recovered at faster dischargerates.

    Peukerts Law relates battery capacity to discharge rate:

    Cp = Ik t

    where Cp is the amp-hour capacity at a 1 A discharge rate

    I is the discharge current in Amperes

    t is the discharge time, in hours

    k is the Peukert coefficient, typically 1.1 to 1.3

  • 3ECEN2060


    Our lab batteries

    k = 1.15

    C = 36 A

    Cp = 63 A-hr

    Prediction of Peukertequation is plotted atleft

    Nominal capacity: A-hrs @ 25C to 1.75 V/cell

    36 A-hr

    1 hr

    56 A-hr49 A-hr46 A-hr45 A-hr

    24 hr8 hr4 hr2 hr

    What the manufacturersdata sheet specified:

  • 4ECEN2060

    Energy efficiency

    Efficiency = ED/EC

    EC = Total energy during charging = vbatt (-ibatt) dt VCICTC

    ED = Total energy during discharging = vbatt ibatt dt VDIDTD

    Energy efficiency =VDVC


    = voltage efficiency coulomb efficiency

    +V(SOC) Ideal diodes






    Coulomb efficiency = (discharge A-hrs)/(charge A-hrs)

    Voltage efficiency = (discharge voltage)/(charge voltage)

  • 5ECEN2060

    Energy efficiency

    Energy is lost during charging when reactions other than reversal of sulfation occur

    At beginning of charge cycle, coulomb efficiency is near 100%

    Near end of charge cycle, electrolysis of water reduces coulomb efficiency. Canimprove this efficiency by reducing charge rate (taper charging)

    Typical net coulomb efficiency: 90%

    Approximate voltage efficiency: (2V)/(2.3V) = 87%

    Energy efficiency = (87%)(90%) = 78%

    Commonly quoted estimate: 75%

  • 6ECEN2060

    Charge profile

    A typical good charge profile:

    1. Bulk charging at maximum power

    Terminate when battery is 80%charged (when a voltage set pointis reached)

    2. Charging at constant voltage

    The current will decrease

    This reduces gassing and improvescharge efficiency

    3. Trickle charging / float mode

    Equalizes the charge on series-connected cells without significantgassing

    Prevents discharging of battery byleakage currents

    Occasional pulsing helps reversesulfation of electrodes

    The three-step charge profile usedby the chargers in our power lab

  • 7ECEN2060

    Battery charge controller



    Inverter ACloads

    Prevent sulfation of battery

    Low SOC disconnect

    Float or trickle charge mode

    Control charge profile

    Multi-mode charging, set points

    Nightime disconnect of PV panel

    Direct energy transfer

    Charge battery by direct connectionto PV array


    Connect dc-dc converter betweenPV array and battery; control thisconverter with a maximum powerpoint tracker

  • 8ECEN2060

    Direct energy transfer






    Inverter ACloads

    Charge controller may simply beseries switches

    Bulk charge: connect battery directlyto PV array

    Other charge modes: pulse current onand off to reduce average current

    Nighttime disconnect of PV frombattery

    Disconnect inverter when state ofcharge is low

  • 9ECEN2060

    Maximum power point tracking


    Inverter ACloadsBuck


    Insert buck converter into charge controller, and perform maximumpower point tracking in bulk charging mode

    Battery reaches full charge earlier in the day

    Batterystate ofcharge100%

    0%time of daySunrise Sunset



    In a closed system, the input energy must always equal the loadconsumption. Excess generated energy must be dumped.

    Can you adjust the load consumption?

  • 10ECEN2060

    Economics of battery storage

    Example: the deep dischargebatteries in our lab

    Retail cost: $150

    Assumptions:50% depth of discharge

    20 hour uniform discharge

    Average voltage 12.4 V

    1000 cycles

    Energy of each dischargecycle:

    I = (Cp/t)1/k = (63/20)1/1.15 = 2.7A

    ED = (2.7A)(12.4V)(20hrs) = 0.67 kWh

    Battery capital cost per kWh:

    ($150)/[(0.67 kWh)(1000 cycles)] = $0.22/kWhTypically $0.10/kWh for large optimized installations

    Battery costs more than the energy it stores!

  • 11ECEN2060

    Backup gas generation

    Cost of gasoline

    Estimated 5 kWh/gallon, $3/gal


    Capital cost

    $0.50 to $1.00 per Watt

    Adds another $0.05 to $0.10 per Watt if amortized over 19 years

  • 12ECEN2060

    The value of grid energy

    Power supplied by the utility is available

    Estimated cost $0.10/kWh in Colorado

    Available on demand, very high reliability

    To reproduce this in a standalone PV system:

    1. Must generate the power with PV; est. cost $0.21/kWh

    2. Must store in batteries, est $0.10 to $0.4 / kWh

    3. May additionally need other backup power sources, with additionalcosts but substantially improves reliability

    Utility bill has a charge for kWh consumed only

    Reliability is worth at least as much per kWh as theenergy itself, but is not included in current pricingschemes approved by PUC