bq25504 + bq33100 + 2 supercaps

VSTOR is the output of the boost converter.  There is a PFET between VSTOR and VBAT that is controlled by the VBAT_UV threshold.  If the voltage at VBAT is lower than this threshold then the PFET opens and the only connection between the VSTOR and VBAT is the body diode of the PFET (i.e., VBAT = VSTOR - Vdiode).  It supposed to prevent over discharge. 

What is VOC and ISC of the solar panel?  How large are the super capacitors?  The bq25504 limits its input current to 100mA average so the charging current will be much less. 

Solar panel VOC = 5.1V, ISC = 120ma. Capacitors are 500F x 2.7V. I know about bq25504 current limitation but we have no much sun here so I choosed a bigger solar panel.

As I understand caps shouln't be discharged < 1.8V or bq25504 will go cold mode and this reduces charge current much. Is it right ?

The bq25504 must always boost.  Is VBAT_OV set higher than the MPPT%*5.1V?

Yes, when VSTOR drops below 1.8V, the IC enters cold start, which is a low efficiency (5%) boost converter.  I am concerned that the bq33100 Iq is too high for cold start.

If you do not need the VBAT_UV function to prevent the super caps from over-discharging you can short VSTOR and VBAT.

VBAT_OV > 5.1*75%. You told bq33100 Iq too high for cold start. Does this mean that this curcuit will not start with empty supercapacitors ? 

At what voltage does the bq33100 start consuming current?  If below 1.8V, then you will need to perform a power balance using the equation below to confirm that you have enough input power:

efficiency = Pout/Pin = VSTOR*ISTOR / (IIN *VIN)

where efficiency = 5% in cold start mode, VSTOR = 1.8V, ISTOR = Iq of bq33100, IIN and VIN are the minimum produced from lowest light on the solar panel.

From bq33100 datasheet: startup voltage = 5.2V, supply current = 0,45ma

It looks like it is better to get another charger with mppt :(