BQ25570 cold start min power

The cold start boost converter is only 5-10% efficient.  It also clamps VIN_DC to ~0.35V.  Does your solar panel still provide 0.15mA when its output is clamped to 0.35V?  If so, you can use a power balance (eff= Po/Pin=(VSTOR*ISTOR)/(0.35V*0.15mA) where ISTOR = super cap leakage + 1.8V/RSTOR(CS), where RSTOR(CS) is any additional resistance loading on VSTOR during cold start, to determine if you will have enough power.

No, the solar cell will not provide that 0.15mA power when clamped to 0.35V. The current is more likely 0.05mA.

And I connect the supercap to VOUT instead of VSTOR, My configuration is exactly the same in Figure 11 of BQ25570 Evaluation module.

So let's change the condition, can you confirm this: if I have a solar cell has 100uA@0.35V; The supercap (connected to VOUT) leakage is 10uA@1.8V; does that means that leakage alone may lead to problems during start up (10uA/5%=200uA required)? i.e. BQ25570 can't exit its cold start mode?

Another thing is the RSTOR(CS), let's say I just put a typical aluminum 100uF capacitor with DC resistance of 0.1 Ohm on the VSTOR pin of the BQ25570. What would be the value of RSTOR(CS)? The idea of 1.8V/RSTOR(CS) seems strange, because 1.8V/0.1Ohm=18A. So what is the suggested/reasonable value of RSTOR(CS)? I presume the energy transfer will mainly comes from Cin instead of the solar cell at the very beginning of the cold start, so is it true the ISTOR = super cap leakage + 1.8V/RSTOR(CS)??

If I increase the size of the input capacitor would that help the cold start? 

If the supercap is on VOUT, then it is isolated from VSTOR and so shouldn't load the cold start circuit.  In fact, the buck converter's current limit will provide a soft startup once the buck converter starts up.  In fact the article at the link below explains this:

http://www.edn.com/design/power-management/4422103/Fast-charging-a-supercapacitor-from-energy-harvesters

Regarding RCSTOR(CS), it was meant to be a simple way to model the loading on VSTOR during cold start and to emphasize that such loading could prevent the cold start circuit from ever starting up.  It is not the ESR of the capacitors at VSTOR or VBAT.   Like any boost converter, a power balance (eff=Po/Pi=Vo*Io/(Vin*IIn)) is required to know the maximum input required or output current available.  Since the cold start circuit runs until VSTOR reaches VSTOR_CHGEN with typical value of Vo=1.8V, we selected that value as the worst case. 

In your case, with Vin=0.35V and Iin=100uA, the solar panel is providing 35uW which is higher than minimum PIN(CS) typical value of 5uW and so you should startup. You could even compute the maximum loading on VSTOR during startup.  Even with the super cap on VOUT, we recommend at least a 100 uF capacitor on VBAT in order to filter the switching pulses from the boost converter. 

We sometimes recommend placing an external PFET between VSTOR and the system load that is turned on by an inverted VBAT_OK signal once VSTOR and VBAT are above VBAT_UV..  If your system has a UVLO that prevents it from pulling any load current until the voltage is above 1.8V or until it is turned on by VBAT_OK, then you would not need this external PFET and RSTOR(CS) would be very large.