Simulink Design Optimization
This example shows how to use parameter bounds to improve estimation performance. This is illustrated by estimating the power rating, P, of a synchronous machine.
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The Simulink® model for the system is shown below.
A three-phase, four-wire alternator rated 2000 kVA, 1600 kW, 0.8 power factor, 600 V, 1800 rpm is connected to a 1600 kW, 400 kvar inductive load. The stator neutral point is grounded. The internal impedance of the generator (Zg = 0.0036 + j*0.16 pu) represents the armature winding resistance Ra and direct axis transient reactance X'd. The total inertia constant of the generator and prime mover is H = 0.6 s, corresponding to J = 67.5 kg.m^2.
A three-phase breaker is used to switch out a 800 kW resistive load. The breaker is initially closed and it is opened at t = 0.2 s, resulting in a 50% load shedding.
The machine is excited with a constant voltage. The mechanical torque is modeled as a two-step signal. The first step has a magnitude of 1.0 and a duration of 1.8s. The second step is has a magnitude of -0.5 for a duration of 0.2s. The input and output data are shown below
There is a project already associated with this model. You can access it by double-clicking the orange block in the lower left corner of the model. You can view the data set added by clicking on the "Transient Data" node and selecting "New Data". There is only one data set used for this example.
The Estimation variables are selected by clicking on the "Variables" node and pressing the "Add" button. We have already loaded the parameters for this model. There is only one parameter in this model that we are interested in estimating, the nominal power (P) of the Simplified Synchronous Machine.
We know from the specs that this value should be around 2000kW but here we assume that we only have an initial guess of 3000kW. We also set a maximum value of the nominal power to be 4000kW.
In order to run an estimation, we first need to create an "Estimation" node. This is done by clicking on the "Estimation" node and pressing the "New" button in the right-hand-side panel.
In our project, we have already created an estimation node called "New Estimation". We can click on this node to set up its various options.
The first panel is where we select the data sets to be used in this estimation. It is possible to use one or more data sets at once in a given estimation. For this model, we will use the data set called "New Data".
The next panel called "Parameters" is where we select which parameters to adjust in this estimation. Even though we have already added our nominal power parameter, P, we still need to make sure that the variable is used in this estimation.
Before we proceed with our estimation we would like to monitor the results of the estimation process. We will create a number of dynamics plots, called "Views".
To add a plot to view we select the "Views" node and select "New". This will create a "New Views" node. If we select this node then we can choose which plots we would like see. For this example we will just view the Measured vs. Simulated responses.
To run the estimation press the "Start" button in the Estimation tab of the "New Estimation" node. The estimation will begin and keep iterating the parameters values until optimal values of the parameters are found.
The plot below shows the experimental data overlaid with the simulated data. The simulated data comes from the model with the estimated parameters. As expected the estimation terminated quickly and the results were not so good because of our initial guess and bounds of the parameter (P).
Since we are not satisfied with our results, we will choose a different initial guess. This is quite simple to do with the Simulink® Design Optimization™ parameter estimation GUI. We can go back to the "New Estimation" node and select the parameters tab. Here we will change the initial guess to 1000 kV and the lower and upper bounds to 0 kV and 3000 kV respectively.
To run another estimation simply go to the Estimation Tab and press Start. Once the estimation is complete we can verify that our results are more accurate by looking once again at the Measured vs. Simulated response.
Placing inappropriate bounds on your parameters can lead to inaccurate results and most often the estimation will not converge successfully. However, with the parameter estimation GUI, it is simple to change these bounds to run another estimation without creating a new estimation project.