PMSG Modeling

The model developed above using the MATLAB Simulink software is important for many reasons to the design and implementation of our NPD hydroelectric conversion. This specific layout 2 generator design was chosen. Although more design options were given by Voith following our meetings with larger output power and more generators we chose to stick with this model as it best met the standards for our site’s NPD conversion. With the site we selected we planned to implement our generators within the existing concrete flume structure as this would reduce the complexity, and cost of instillation, and decrease many risk factors with dam building that more generators would cause, like the redirection of the entire river and possible washing away of larger coffer dams from Kentucky’s many seasonal heavy flooding events. The purpose of developing this model is to allow the team to have a better understanding of the planned system as well as validate and verify the power generation expectation Voith supplied us for production estimations. In the process of building this model, one of the main issues that held back creating more accurate modeling of the Voith Stream diver PMSG is that companies like Voith for obvious reasons do not often open source their performance ratings. Therefore, it was decided that the generic PMSG block should be used to give a moderately effective model, therefore no parameters within the block were changed. Aside from the PMSG block, we were able to estimate other aspects of the turbine and inputs to the system. A subsystem block was created to calculate the turbine output power estimation and the torque input required to simulate the PMSG operation. The torque is multiplied by ‘-1’ to symbolize that the PMSM is running in generator mode as a PMSG. Scopes were included to display these generation effects and the system’s transient response under load. 

ηρgQH              τ ω P​ 

The figure above displays the built Simulink estimation equations subsystem, used to produce the power and torque outputs we would get from the changing inputs. To calculate these equations, we needed two known constants, two inputs we were able to recognize following our intensive modeling of flow and pressure at our turbine intake, and one estimation based on common industry standards. By adjusting these parameters, we were able to simulate a power output that was very similar to the estimates supplied by Voith for their stream diver turbines and our calculated flow inputs. 


Flow rate – The input water flow to the turbine which will change depending on the valve intake and size of stream diver used for generation.  

Head – A constant input to both of our turbines and does not change with the stream diver specs as this is dependent on the river and floods, for this model the average head over a year experienced at the site was used for simplicity’s sake.

RPM – Used to produce the torque output of our system for the PSMG input, the stream diver models are used in the range of 400-800 RPM in industry. However, we chose the lower end of this allowance to properly simulate what would be used in our site’s low head and low flow averages.  

Turbine efficiency – This value was chosen based on common industry values for turbine efficiency and could be adjusted to allow the output power/torque to match that of the voith-supplied estimations.  

Water density – This is a known average constant for the equations that can slightly change depending on environmental conditions like temperature.

Acceleration due to gravity – A well-known value of gravity’s effect on the surface of the earth to a falling object.

For the simulation of the Simulink design, the model had to be tuned down significantly as running such simulations with MW and kW values resulted in each simulation taking hours for even a second of output. Instead, it is easy enough to understand the operation of such mechanisms using just a single PMSG and tuning down the input values by nearly 10,000 units. After the corrections were made for simulation, it is easy to see the smooth transient response of a PMSG reacting to a load placed upon it. The speed ramps up for a second to reach its steady-state value. Torque can be seen doing nearly the same, being proportional to the rpm or speed of the machine. The stator currents were similar for a, b, and c besides light phase differences, so only stator current a is displayed. Showcasing the alternating current induced from the rotor and spinning magnets upon the stator coil, causing current to flow from the generator.