Simulation variables: Stand alone system

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Simulation variables: Stand alone system

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The following variables are calculated during the simulation process, and available as results:

Meteo and irradiation variables: see previous page.

PV array behaviour

EArrMPPArray virtual energy at MPP   (after wiring, module quality and mismatch losses),

Virtual calculation independent of the system running and voltage operation

EArUfixArray virtual energy at fixed voltage

Voltage as calculated by the balance loop (real battery voltage),

or   Battery reference voltage when PV-array disconnected.

EUnusedUnused energy (full battery) loss        (EArUFix when Charging OFF)
MPPLossLoss with respect to the MPP operation        (when charging ON)
EarrayEffective energy at the output of the array        (when charging ON)
IArrayArray Current        (accumulated in Ah)
UArrayArray Voltage        (average when Charging ON)
ArrayONState / Duration of the PV production of the array

If converter present: converter losses

CL OperConverter loss during operation (efficiency curve)
CL PminConverter Loss due to power threshold'
CL PmaxConverter Loss due to power overcharging
CL VminConverter Loss due to low voltage MPP window
CL VmaxConverter Loss due to upper voltage MPP window
CnvLossGlobal converter losses
OutConvEnergy at converter output

Battery operation: storage, losses and ageing

EBatChBattery Charging Energy
U BattAverage battery voltage,  any conditions,
UBatChBattery Voltage during charging operation
IBatChBattery Charging Current        (all currents accumulated  [Ah])
ChargONCharging duration
EBatDisBattery Discharging Energy
UbatDisBattery Voltage during discharge operation
IBatDisBattery Discharging Current        (all currents accumulated  [Ah])
DischONDischarging duration
ESOCBalStored energy balance        (according to  SOCEnd - SOCBeg)
SOCmeanAverage State of Charge during the period
SOC BegState of Charge at beginning of time interval'
SOC EndState of Charge at end of time interval'
NB: The SOC current calculations are referred to the actual capacity of the battery, which is defined at nominal current, but varies with the discharge current level and temperature. Therefore it is not quite well determined, and not reversible (i.e. it can be different when charging and discharging).
EBatLssBattery global energy loss        (EBatCh - EBatDis - ESOCBal)
IBEffLBattery charge/discharge current loss        (coulombic efficiency  [Ah])
IBGassGassing Current loss        (electrolyte dissociation  [Ah])
IBSelfBattery Self-discharge Current        (depends on temperature  [Ah])
EBattEffBattery energy efficiency        (IBEffL   *  U Batt)
EBGassGassing Current energy loss        (IBGass *  U Batt)
EBSelfBattery Self-discharge Energy        (IBSelf   *  U Batt)
NB:The sum of the detailed battery losses contributions appearing on the loss diagram should in principle match this Battery Global Energy Loss calculated above, i.e:
EBattLss  =  EBattEff + EBSelf + EBGass
But during the simulation, all these contributions are determined from the Currents balance of the system  (PV array - Battery - Load), multiplied by the Battery Voltage, which is varying with currents, charge/discharge state, state of charge, temperature, etc.  The resulting energies are therefore defined with some uncertainties.
On the other hand, as explained above, the ESOCBal is also not well determined.
Therefore the overall energy balance on the battery cannot be quite rigorous.
WeCycleWearing due to cycling
WeStateWearing state (cycling and age)
MGassDissociated Electrolyte Mass per cell

System operating conditions

E BkUpBack-up Generator Energy        (UBatt * I BkUp)
I BkUpBack-up Generator Current'        (accumulated in Ah)
BkUp ONBack-up Generator running duration
FuelBUFuel consumption of Back-up Generator

Energy  use

E AvailAvailable Solar Energy                Energy at the output of the array when producing - converter loss + Unused energy
                                       E Avail = E Array - CnvLoss + E Unused  
E LoadEnergy need of the user (Load)        Defined as Input data
E UserEnergy supplied to the user                Including back-up energy
SolFracSolar fraction                                (EUser  - EBkUp) /  ELoad

When no back-up generator defined

E MissMissing energy        Eload - Euser
SolFracSolar fraction                            EUser / ELoad
T LOLDuration of "Loss of Load"            Duration user not supplied
Pr LOLProbability of  "Loss of Load"          Idem as percentage of time


EffArrRArray Efficiency:        EArray / rough area
EffArrCArray Efficiency:        EArray / cells area        (=0 when cells area not defined)
EffSysRSystem efficiency        E User / rough area
EffSysCSystem efficiency        E User / cells area        (=0 when cells area not defined)
EffBatIBattery current charge/discharge efficiency
EffBatEBattery energy charge/discharge efficiency

Normalised performance index

YrReference Incident Energy in collector plane        = GlobInc  [kWh/m²/day]
YuNormalized Potential PV Production  (battery never full)        [kWh/kWp/day]
YaNormalized Array Production        = EArray        [kWh/kWp/day]
YfNormalized System Production        = EAvail        [kWh/kWp/day]
PrPerformance ratio                = Yf  / Yr.
LuNormalized Unused energy        = Yr - Yu
LcNormalized Array Losses        = Yu - Ya
LsNormalized System Losses        = Ya - Yf
LurUnused (full battery) Loss / Inc. Energy Ratio        = Lu / Yr
LcrArray Loss / Incident Energy Ratio                = Lc / Yr
LsrSystem Loss / Incident Energy Ratio                = Ls / Yr