Circuit design for adjusting the electrical load of a small wind turbine (MPPT)

Question

I am trying to make an MPPT controller for a small homemade wind turbine. The goal of the project is the MPPT itself and its performance. The application is direct water heating, and there are no batteries involved. The concept of MPPT is to ensure that the turbine operates with the optimal angular velocity / RPM for the present wind speed, and thus outputs the maximum amount of power for the given wind speed. For a given wind turbine, there is an optimal ratio between the tip speed of the rotors and the wind speed. The turbine speed can be controlled by adjusting the electrical load, and I am struggling to find a good way to achieve this. First some specs of my wind turbine and its generator, to give the problem some perspective:

The rotor radius is 0.4m, the wind speed operating range is 3-14 m/s, and the assumed optimal tip speed ratio and turbine efficiency is 6 and 0.25, respectively. The available wind power is thus 8 W at 3 m/s and 844 W at 14 m/s (using the "wind power formula"), while the corresponding electrical output power is 2 W and 211 W. When operating with the optimal speed ratio of 6, the RPM at 3 m/s and 14 m/s is 430 and 2005, respectively. I am using a stepper motor as a generator, and I have measured its voltage constant to 40 V/kRPM. This means that at 3 m/s and 430 RPM, the output voltage and current should be 17 V and 0.12 A (= 2 W), meaning a load resistance of 142 ohms. At 14 m/s and 2005 RPM, the output voltage and current should be 80 V and 2.6 A (= 211 W), meaning a load resistance of 30 ohms.

Now I need a way to adjust the load resistance so that I can operate the turbine at the maximum power point. The load resistance will be a water-heating element. Possible solutions that I have considered:

1. Simple PWM reglation Connecting a power MOSFET in series with the load, and controlling it with a PWM signal where the duty cycle effectively varies the load resistance. At 0% duty cycle, the load resistance is infinite (open-circuit), and at 100% the load resistance is equal to the resistance of the heating element (I would choose one with a resistance lower than 30 ohms). The problem here is that I don't see how I can measure the output voltage and current with the MCU, when they are switching on and off.

2. Using a buck converter I have seen that other MPPT controller projects use buck converters, but I don't see how they can do the job. I understand that a buck converter is just the above solution but with an LC low-pass filter on the output. This solves the measuring problem, as it smoothes the output. However, I get confused by this: Let's say the input voltage and current of the buck converter are 40 V and 1 A. An ideal buck converter has no power loss, so if the output voltage is 20 V, the output current must be 2 A. Step down to 10 V, and the current must be 4 A. But if the load resistance is the same, how can the current increase when the voltage decrease?

I have a feeling that the buck converter solution works, but I just don't understand the mechanics. If so, I would be grateful if someone could try to explain it. If solution 1 works I would prefer it over solution 2, as the design is cheaper and simpler. Or maybe I am missing another solution to the problem I am trying to achieve, i.e. adjusting the electrical load to operate the turine at the maximum power point. Any help here is appreciated!

Answer 1

An ideal buck converter has no power loss, so if the output voltage is 20 V, the output current must be 2 A. Step down to 10 V, and the current must be 4 A. But if the load resistance is the same, how can the current increase when the voltage decrease?

No, for an ideal buck converter in constant current mode, its output voltage is a function of the duty cycle, i.e.

$$V_{out}=D*V_{in}$$

If the load is the same and the duty cycle increases, the output voltage increases and the output current also increases (I=V/R), and vice versa.

A buck converter is indeed what you need if your intention is to step down, and it's simple enough. Its working principle is similar to chopping, that is, when the MOSFET is turned on, the energy of the power supply is output to the inductor and stored. Then when the MOSFET turns off, only the inductor energy is released to the load. From the perspective of load, the obtained energy is lower, so a low voltage is achieved.

Besides, buck-boost converters can also achieve step-down. But considering that your power is so high, you may need to use an isolated DC/DC converter, such as a flyback converter, etc. TI has a book called "Power Topology Handbook". You can find it on google easily.

Regarding the MPPT, there are many algorithms and implementation methods. It is recommended that you read relevant papers. At present, ICs for buck converters with MPPT function are very mature.