# Analysis of a Bi-directional DC-DC converter

I'm building a bi-directional DC-DC converter that will be used to charge and discharge a supercapacitor stack. The design we came up with uses a 4-quadrant chopper, to allow buck-boost both ways. I've made a design in PSIM which can be seen here:

I'm having a bit of trouble with correctly predicting the simulations behaviour. For instance, if Q1 is open, Q2 and Q3 are closed and Q4 is Active (A). Then the circuit becomes a boost converter from the left to the right side (Fuel Cell->BoostCaps), with a purely capacitive load. I want to boost the FC voltage, which is set to 24V, to the voltage of the BC, lets say 30V. Since the output voltage always equals the BC voltage, regardless of duty cycle, i want to be able to control the amout of current going towards the BC.

I've tried rewriting the state equations for a boost converter, but still don't seem to be getting a good result. For reference, if the FC voltage is 24V and the BC's is 30V, then a duty cycle of 0.03 on Q4 corresponds to a load current of around 1A. While my calculations say this should be at least 0.11.

I would really like some help with finding a way to make a mathematical model so a controller can be implemented. A link to a paper or book would be welcome too!

Some clarification:

• In the schematic, the "BoostCaps" are the supercapacitor stack.
• The voltage source and resistor on the left side simulate the Fuel Cell. You are correct that it does only generate power. The diode is to prevent back current into the fuel cell.
• For simplicity in this simulation i used the voltage controlled current source on the right (the diamond thing) as a constant load. (in reality it will be a 3-phase brushless motor + controller.)
• Don't mind the triangular thing, it's not taken into account here.
• The converter is full-bridge because we aren't certain yet on the supercapacitor stack voltage. Can be either higher or lower than the FC voltage of 24V, hence the full-bridge.
• Bi-directional because the supercaps act as an energy buffer. If the load current is low, the supercaps can be charged. If the load current is high, the supercaps provide some extra current to support the fuel cell.

 and this is the topology:

• Unless you want to use the MOSFET body diodes, you're going to need two FETs active at any one time. If power comes in from the left and the left-hand FETs are active, you have a buck. If power comes in from the left and the right-hand FETs are active, you have a boost. You need to better highlight what your problem is, as the only problem you mentioned was that you were getting a 1A load current instead of 0.11A. Your circuit just looks like a buck and a boost in series sharing a common inductor, if only one is active at any one time, why can't you use traditional transfer functions? – Sam Dec 28 '16 at 20:48
• By the way, there are SMPS modules and controllers from Linear Tech that do 2 quadrant and pass through/convert the power in both directions between input and output. If interested, take a look at LTM8052 for a 36V/5A micromodule (built in inductor). I'm using the bare controller version of that module with my own FETs to emulate a rechargeable battery (can be charged or discharged), similar to your application. – Vince Patron Dec 29 '16 at 2:05
• Why does the second FET need to be active? I believe if i have 1 active and 1 just constantly open as in the table on the picture it should work fine right? The question really is, which equations do i need to use? Vout/Vin = 1/(1-D) doesnt work for some reason. And this also doesnt let me regulate current. I looked at some simulation and found that i am probably working in DCM so maybe thats the problem? – Thomas Gerrits Dec 29 '16 at 10:40