Why does the voltage from the transformer increase when a load is connected?

Question

Electronics

In general, I encountered such a problem, the power supply of the proportional hydraulic valve operates in the range of 18-30 VDC, I connected six hydraulic valves in parallel to a transformer with two windings 12V and 24V
- when a load is connected to the 24V winding, the voltage in the network rises up to 34V and the hydraulic valves heat up (an incomprehensible squeak is heard)
- when a load is connected to the 12V transformer winding, the voltage rises to 17V, which is not enough to operate the valve !!!
- where to look for a rake???
2nd - a question on the topic, I know that a smoothing capacitor should be parallel to the diode bridge
- how to choose the right value of the summing capacitor in microfarads "mF" parallel to the diode bridge ???
3rd question on the topic; - intuitively suspecting that the capacitor should be of a large capacity ..... nothing was at hand as I connected three 250mF capacitors in parallel ..... at the output after the diode bridge from 12V it turned out 16V, QUESTION; How does the capacitance of the capacitor affect the output voltage after the bridge? Is there a formula for calculating? at least approximately ;)))
Thank you!