I am working to implement an Extended Kalman Filter to estimate the dynamic state of a synchronous generator connected to a Power System. I am using Power World Software to generate simulation data to use it as input to the estimator, and I am adding gaussian white noise to the data as "measurement noise".
Can someone tell me how can I add "process noise" to this simulation data?
I can only speak of ordinary linear (not extended) Kalman filters. If the simulation software generates data according to some transition equation x(n) = Phi(n) x(n-1), where x is the state vector of the system, and you add noise to this data, x(n) = Phi(n) x(n-1) + w(n), then w(n) is process noise, not measurement noise. Perhaps you can execute the Kalman filter with noiseless measurements y(n) = H(n)x(n).
I happened to add noise to dynamic simulation when I was validating an electromechanical oscillation monitoring algorithm based on PMU (simulations were to emulate PMU recordings).
If you just add noise to simulated results, *after* the simulation has run you'll only see the measurement noise. On the other hand, directly adding noise to the state vector could be difficult - you might have to change the models inside the simulator - and, in my opinion, would be a "spurious" solution, because you would inject noise where, physically speaking, there's no "real" stochastic behavior.
On the contrary, load consumption is "truly" stochastic. So, in my experience the best way to add noise to simulation results is to emulate the stochastic behavior of the load by adding noise to the power consumption of each injection. This would bring the noisy values through the entire dynamic of the power systems (the state space) and make also noisy output measurement (currents, voltages, etc.).
In this way, with no change to the dynamic models, you'll simulate a truly noisy dynamic behavior. I tested what I'm saying by applying FFT to simulated currents of lines and finding exactly the oscillation that I expected from eigenvalues calculations.
Hope this could help.
Hello. You don't usually add process noise to the simulated data. The assumption is that the dynamical process obeys some physical laws that can be described by a system of ordinary differential equations. The process noise is introduced in the filter to obtain a least-squares type problem for which the Kalman filter is the optimal estimator (under certain conditions). The process noise covariance Q is usually adjusted as a tuning parameter to trade of the state estimation performance. The rule of thumb is: higher Q, better tracking of the data (and the noise); lower Q - better rejection of the noise (and ignoring the data) - hence smoother estimates.
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