I am going round in circles trying to understand how a battery (lithium) , PSU and inverter (traction) interact with each other by working out the voltages and currents.
Some notes:
 The PSU supplements the battery and will be used in 'power limit' mode.
 Any excess power from the PSU will be used to charge the battery AND power the inverter
 The PSU will have sense wires 'after' the series power diode (the power diode is to prevent current feeding back into the PSU).
I have created an interactive Excel spreadsheet, but I'm struggling with the equations to calculate the voltages and currents.
Screenshots are shown below for three different scenarios:

1. PSU charges battery (inverter not running)
In this scenario:
 the inverter is not drawing any power (0 W)
 the battery open circuit voltage is 600 V
 the battery internal resistance is 1 R
 the PSU power limit is set to 1,000W
 the PSU voltage is set to 800 V
Q. How do I calculate the DC link voltage ? My understanding is that the battery will 'clamp' the PSU voltage, so despite the PSU being set to 800 V the DC link will be clamped to just above 600 V.
Q. How do I calculate the PSU current (which will be the same as the battery current) ?

2. PSU charges the battery AND powers the inverter
In this scenario:
 the inverter is drawing 500 W
 the battery open circuit voltage is 600 V
 the battery internal resistance is 1 R
 the PSU power limit is set to 1,000W
 the PSU voltage is set to 800 V
 the PSU supplies 500 W to the inverter, leaving an excess of 500 W to charge the battery
Q. How do I calculate the DC link voltage ? My understanding is that the battery will 'clamp' the PSU voltage, so despite the PSU being set to 800 V the DC link will be clamped to just above 600 V.
Q. How do I calculate the PSU current ?
Q. How do I calculate the battery current ?
Q. How do I calculate the inverter current ?

3. PSU and battery power the inverter
In this scenario:
 the inverter is drawing 2,000 W
 the battery open circuit voltage is 600 V
 the battery internal resistance is 1 R
 the PSU power limit is set to 1,000 W
 the PSU voltage is set to 800 V
 the PSU supplies 1,000 W to the inverter and the battery supplies the remaining 1,000W to the inverter
Q. How do I calculate the DC link voltage ? My understanding is that the battery will 'clamp' the PSU voltage, so despite the PSU being set to 800 V the DC link will be clamped to just above 600 V.
Q. How do I calculate the PSU current ?
Q. How do I calculate the battery current ?
Q. How do I calculate the inverter current ?

The interactive spreadsheet is attached for reference 'PowerShareInteractive.zip' (I had to zip the spreadsheet as .xlsm files are prohibited) .
I would like to get this interactive spreadsheet working, but I don't fully understand how the circuit works and therefore the equations.
I had to use quadratic equations to try and solve the voltage and currents but I'm not sure this is correct, especially as the results are invalid in certain conditions.
Some notes:
 The PSU supplements the battery and will be used in 'power limit' mode.
 Any excess power from the PSU will be used to charge the battery AND power the inverter
 The PSU will have sense wires 'after' the series power diode (the power diode is to prevent current feeding back into the PSU).
I have created an interactive Excel spreadsheet, but I'm struggling with the equations to calculate the voltages and currents.
Screenshots are shown below for three different scenarios:

1. PSU charges battery (inverter not running)
In this scenario:
 the inverter is not drawing any power (0 W)
 the battery open circuit voltage is 600 V
 the battery internal resistance is 1 R
 the PSU power limit is set to 1,000W
 the PSU voltage is set to 800 V
Q. How do I calculate the DC link voltage ? My understanding is that the battery will 'clamp' the PSU voltage, so despite the PSU being set to 800 V the DC link will be clamped to just above 600 V.
Q. How do I calculate the PSU current (which will be the same as the battery current) ?

2. PSU charges the battery AND powers the inverter
In this scenario:
 the inverter is drawing 500 W
 the battery open circuit voltage is 600 V
 the battery internal resistance is 1 R
 the PSU power limit is set to 1,000W
 the PSU voltage is set to 800 V
 the PSU supplies 500 W to the inverter, leaving an excess of 500 W to charge the battery
Q. How do I calculate the DC link voltage ? My understanding is that the battery will 'clamp' the PSU voltage, so despite the PSU being set to 800 V the DC link will be clamped to just above 600 V.
Q. How do I calculate the PSU current ?
Q. How do I calculate the battery current ?
Q. How do I calculate the inverter current ?

3. PSU and battery power the inverter
In this scenario:
 the inverter is drawing 2,000 W
 the battery open circuit voltage is 600 V
 the battery internal resistance is 1 R
 the PSU power limit is set to 1,000 W
 the PSU voltage is set to 800 V
 the PSU supplies 1,000 W to the inverter and the battery supplies the remaining 1,000W to the inverter
Q. How do I calculate the DC link voltage ? My understanding is that the battery will 'clamp' the PSU voltage, so despite the PSU being set to 800 V the DC link will be clamped to just above 600 V.
Q. How do I calculate the PSU current ?
Q. How do I calculate the battery current ?
Q. How do I calculate the inverter current ?

The interactive spreadsheet is attached for reference 'PowerShareInteractive.zip' (I had to zip the spreadsheet as .xlsm files are prohibited) .
I would like to get this interactive spreadsheet working, but I don't fully understand how the circuit works and therefore the equations.
I had to use quadratic equations to try and solve the voltage and currents but I'm not sure this is correct, especially as the results are invalid in certain conditions.
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