Simulation variables: pumping systems
The following variables are calculated during the simulation process of the pumping system, and are available as results.
The Irradiance and PV-Array variable topic describes all the preceding simulation variables, which lead to the last quantity really independent of the system running conditions, the Array virtual energy at MPP.
The set of variables involved in the pumping system simulation, as well as their significance and order, is dependent on the System Configuration. The energies (in blue) at different levels of the system are visualized on the Loss diagram.
Direct coupling configuration
With Direct coupling configurations, including improved solutions with booster, pump cascading or Array reconfiguration, the set of main variables is defined as:
EArrMpp | Virtual available energy at the maximum power point. |
| MPPLoss | Loss with respect to the MPP running (EArrMpp - EArray) |
| EArray | Effective energy at the output of the array, according to the real Voltage operating point. This contribution is also accounted for when the pump is stopped due to full tank conditions, assuming normal voltage of the pump, as if it were running. |
| IArray | Corresponding current, instantaneous [A] or cumulated [Ah]. |
| UArray | Corresponding voltage, instantaneous or averaged [V]. Cascading or array reconfiguration configurations: |
| 1_PmpON | Operation duration with one pump / low voltage array |
| 2_PmpON | Operation duration with two pumps / high voltage |
| A_PmpON | Operation duration with all pumps |
| EPStart | Energy loss under the starting current threshold (EArray when pump not started) (only for positive displacement pumps, without booster). |
| EPmpThr | Energy loss under pump producing threshold (EArray when FlowR = 0) (for centrifugal pumps, which should attain a given speed before reaching the useful head). |
| EPmpOvr | Pump overload energy (EArray in excess of the pump's maximum power) |
| EPmpAv | Available useful energy at pump when running (EArray - EPStart - EPmpThr - EPmpOvr) (before taking the Pump stopping due to hydraulic constraints into account). |
MPPT converter configuration
EArray | Effective energy at the output of the array (normally = EArrMpp) (may be slightly different with step-down converter voltage limitations. |
| IArray | Corresponding current at MPP, instantaneous [A] or cumulated [Ah]. |
| UArray | Corresponding voltage at MPP, instantaneous or averaged [V]. |
| CL_Oper | Converter efficiency loss during operation. |
| CL_PMax | Converter overload loss (acc. to the specified strategy, limitation or cut). |
| EOutConv | Energy at the output of the converter |
| EPmpThr | Energy loss under pump producing threshold (EOutConv when FlowR = 0). |
| EPmpAv | Available useful energy at pump when running (EOutConv - EPmpThr). |
NB: The converter Voltage or Power threshold losses are included in EPmpThr.
These losses are accounted even when the Pump is stopped for Hydraulic reasons.
Fixed Voltage DC converter configuration
| EArrMpp | Virtual available energy at the maximum power point. |
| MPPLoss | Loss with respect to the MPP running (EArrMpp - EArray) |
| EArray | Effective energy at the output of the array, at the fixed converter voltage. |
| IArray | Corresponding current |
| CL_Oper | Converter efficiency loss during operation. |
| CL_PMax | Converter overload loss (acc. to the specified strategy, limitation or cut). |
| EOutConv | Energy at the output of the converter |
| EPmpThr | Energy loss under pump producing threshold (EOutConv when FlowR = 0). |
| EPmpAv | Available useful energy at pump when running (EOutConv - EPmpThr). |
For all of the above configurations: hydraulic constraints
These manage the Hydraulic commands of the pump. When the pump is OFF the losses listed above remain, and the lost energy is part of the EPmpAvail.
| ELowLev | Pump stopped due to low level aspiration (deep well, drawdown safety) |
| ETkFull | Pump stopped when tank is full |
| EPmpOp | Pump real operating energy (EPmpAvail - ELowLev - ETkFull). |
Battery Buffer Configuration
The Battery-buffered configuration has a quite different operating mode, as the pump is connected to the battery voltage, which is quasi-constant and independent of the PV-array production. The PV-battery-load simulation process is similar to the Stand-alone strategy, with the pump as load.
With this configuration we have chosen to account for the "hydraulic" losses due to "Low level" (drawdown limit) and "Tank Full" upstream the battery operating losses, as we consider them as electrical losses, between the "Available PV energy" (at fixed nominal voltage) and the "Unused energy" when the battery is full.
Indeed, there is no loss when the pump is stopped but the battery is not full: the available PV energy is simply stored into the battery.
The necessary variables involved in the simulation are the following:
EArrMpp | Virtual available energy at the maximum power point. |
| MPPLoss | Loss with respect to the MPP running (EArrMpp - EArray at Vnom) |
| ELowLev | Energy lost when Pump stopped due to low level aspiration (deep well, drawdown safety) |
| ETkFull | Energy lost when Pump stopped due to tank is full These two above losses are accounted only when the battery charging is OFF due to full battery. |
| EArray | Effective energy at the output of the array (at operating voltage) Accounted only when the charging condition is ON |
| IArray | Corresponding charging current, instantaneous [A] or cumulated [Ah]. |
| UArray | Corresponding charging voltage, instantaneous or averaged [V]. |
| SOC_Beg | State of Charge, beginning of interval |
| SOC_End | State of Charge, end of interval |
| UBatt | Average battery voltage |
| IBatCh | Battery charging current [A or Ah] |
| IBatDis | Battery discharging current [A or Ah] |
| IBEffL | Battery Charge/Discharge current efficiency loss |
| IBGass | Gassing current (electrolyte dissociation when full) |
| IBSelf | Battery self-discharge current |
| EBatCh | Battery charging energy |
| EBatDis | Battery discharging energy |
| ESOCBal | Stored energy, Balance between SOCEnd and SOCBeg |
| EBatLss | Battery Overall energy loss (EBatCh - EBatDis - ESOCBal) |
| EEffLss | Battery efficiency loss (EBatLss - (IBGass+IBSelf) * UBatt)**** |
| EPmpOp | Pump operating energy |
NB: The balances of the battery energies can never be rigorous due to the very complex behaviour of the battery. For example its effective capacity, which strongly varies with the discharge current, the temperature, etc. If the current balances are well determined in the simulation process, the corresponding energies involve the operating voltage, which is also model-dependent and varies with state of charge, charge and discharge currents, etc. |
Hydraulic part, for all configurations
Remember that the Hydraulic Energy is the product of the Head and Volume pumped.
The last part of the Energy Loss diagram refers to Hydraulic energy. Implicitly, when it shows pumped water volumes, this is under a given Head. Inversely, the arrows for Dynamic Head Losses express a Head loss at constant volume.
| E_Hydro | Pump hydraulic energy (energy to the fluid) |
| P_Effic | Global pump efficiency (E_Hydro / E_PmpOp) |
| H_Pump | Average total Head at pump (During Pump_ON) |
| H_Stat | Static head requirement |
| H_Loss | Friction head loss |
| H_DrawD | Well: drawdown head loss (Only deep well systems) |
| FlRate | Average flowRate when running |
| WPumped | Water pumped volume [m3] |
| WStored | Stored water in the tank |
| W_Used | Water drawn by the user |
| W_Miss | Missing water, with respect to the user's needs. |
A lot of further (secondary) variables are available for results, which are not described here.