Design and Development of Model Predictive Primary Control of Micro Grids by Puvvula Vidyasagar & K. Shanti Swarup

Author:Puvvula Vidyasagar & K. Shanti Swarup
Language: eng
Format: epub
ISBN: 9789811958526
Publisher: Springer Nature Singapore

(4.10)

X is the state vector with n states, Y is the output vector with nop outputs, and V is the input vector with nip inputs. At this stage, it is necessary to understand that, unlike L-MPC, most of the N-MPC formulations are formulated in the continuous-time analog mode. With the above continuous-time nonlinear model (4.10), the optimal control problem of the N-MPC is non-convex as given below:

(4.11)

W is the output reference set-point vector. R is the input penalty matrix. ts is the present continuous-time moment at which the analysis is being carried out on the system. Tp and Tc are the prediction and control horizon lengths in the continuous-time domain. H1and H2 are the vectors containing inequality and equality constraints which can be either linear or nonlinear. L1 and L2 are the vectors with the bounds for these constraints. Vmin and Vmax are the minimum and maximum limits on the inputs. Xmin and Xmax are the minimum and maximum limits on the states. Solving the above optimal control problem (4.11) online is extremely difficult as, most of the time, it will be an NP-hard problem due to its non-convexity.

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