Battery-Powered Systems: Efficiency, Control, Economics ECEN 2060
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
Example
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
IDTDICTC
= voltage efficiency coulomb efficiency
+V(SOC) Ideal diodes
Rcharge(SOC)
Rdischarge(SOC)
+
Vbatt
Ibatt
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
PVarray
Chargecontroller
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
MPPT
Connect dc-dc converter betweenPV array and battery; control thisconverter with a maximum powerpoint tracker
8ECEN2060
Direct energy transfer
Vpv
Ipv
PVcharacteristic
Batterycharacteristic
PVarray
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
PVarray
Inverter ACloadsBuck
converter
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
DET
MPPT
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
$0.60/kWh
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