I had a 120 meter borehole.
I was able to pump water from it with a DC pump. This type of pump runs on solar panels directly, without a need for controller, battery, or inverter.
I bought a Chinese brand submersible 850W pump. The pump required six 250W solar panels to handle the start up power requirement of the DC pump.

The problem with DC pumps is that they are expensive. The installation wires can also be expensive if you have a long wire run. This is due to voltage loss. The other problem for me was that the pump only lasted for about one year. For a pump that costs over US$1,000 (N350k), $1,000 is insanely expensive. A comparable AC pump costs only about N72k. That means DC pump costs 5x more than AC pump.

This large price difference between AC and DC pumps is what got me thinking about a way to run AC pump using solar, and without batteries.

To use AC pump, we must convert the DC from the solar panels to AC. This requires an inverter.

Also, due to fluctuating sun intensity all through the day, we must stabilize the output voltage from the panels. To do that, we need a DC-to-DC converter. I bought a 1.5hp AC submersible pump for the 120m borehole, which requires 1.1kW when running normally.

A 2.5KVA inverter I had could not power the pump. So I started researching more. It turned out that the start up surge for the 1.5hp pump is about 4kW.

More research revealed that I needed a Controller for the pump. It is called "soft start control box". This controller allows a much smaller inverter to be used since the start up surge is reduced by increasing the amps to the pump gradually during initial start up. I found a 1.5hp Interdab pump controller for N10k.

The controller specs showed 45uF (micro Farad). This means it is a capacitor. It means we could increase the efficiency of the system by using a bigger capacitor. A 16V 500F capacitor on aliexpress was US$160 + $100 shipping to Nigeria. It may be better to replace the N10k controller with a real supercapacitor. This video shows how to use a supercapacitor: https://www.youtube.com/watch?v=T3zr4G55WSM.

There is also: Motor Start Capacitors, and Motor Run Capacitors.

Motor Start Capacitors
The primary purpose of a motor start capacitor is to briefly increase the motor starting torque as well as to allow a motor to be cycled on and off very quickly.

Motor Run Capacitors
Motor run capacitors will then operate after the circuit is started. Using a motor run capacitor will run the motor with greater efficiency. Motor run capacitors are designed for continuous duty. They are energized while the motor is in operation.

Some capacitors are also Dual Motor Start and Run Capacitor.

For the DC-to-DC converter, I used a 1800W 40A converter. So the final setup looked like this

6x 250W solar panels --> DC-to-DC inverter --> 2.5KVA inverter --> 1.5hp Interdab controller --> 1.5hp AC pump

Cost analysis:

DC-to-DC inverter = US$31 = 11k
2.5KVA inverter = 120k
1.5hp Interdab AC pump = 72k
1.5hp Interdab controller = 10k
Total: 213k

With this setup, if the AC pump dies, it would only cost 72k to replace it. Compare that to a DC pump that costs 350k.

The downside to AC is that many components are required to run an AC pump on solar. Any of them could go out at any time. However, the only expensive component is the inverter. However, one should be able to get many years of use out of a good inverter.

Looking at this cost analysis, which is preferable - DC or AC pump?