soft4pes.control.mpc.solvers#

Solvers for model predictive control (MPC) algorithms.

Submodules#

Classes#

IndirectMpcQP

Problem formulation and QP solver for indirect MPC.

MpcBnB

Branch-and-bound (BnB) solver for model predictive control (MPC).

MpcEnum

Enumeration-based solver for model predictive control (MPC).

Functions#

switching_constraint_violated(nl, u_abc, u_km1_abc)

Check if a candidate three-phase switch position violates a switching constraint.

squared_weighted_second_norm(vector, Q)

Compute the squared weighted second norm of a vector. The elements of the norm are weighted by

make_QP_matrices(sys, ctr)

Create the QP matrices.

make_Gamma(Np, C, A)

Make Gamma matrix for the QP.

make_Upsilon(Np, C, A, B)

Make Upsilon matrix for the QP.

Package Contents#

class soft4pes.control.mpc.solvers.IndirectMpcQP[source]#

Problem formulation and QP solver for indirect MPC.

QP_matrices#

Namespace containing the matrices used in the QP problem.

Type:

SimpleNamespace

__call__(sys, ctr, y_ref)[source]#

Formulate and solve the MPC QP.

Parameters:

  • sys (system object) – System model.

  • ctr (controller object) – Controller object.

  • y_ref (ndarray of floats) – Reference vector [p.u.].

Returns:

u_abc – The three-phase modulating signal.

Return type:

1 x 3 ndarray of floats

class soft4pes.control.mpc.solvers.MpcBnB(conv)[source]#

Branch-and-bound (BnB) solver for model predictive control (MPC).

Parameters:

conv (converter object) – Converter model.

J_min#

Minimum cost.

Type:

float

U_seq#

Sequence of three-phase switch positions (switching sequence) with the lowest cost.

Type:

1 x 3*Np ndarray of ints

U_temp#

Temporary array for incumbent swithing sequence.

Type:

1 x 3*Np ndarray of ints

SW_COMB#

All possible three-phase switch positions.

Type:

1 x conv.nl^3 ndarray of ints

__call__(sys, ctr, y_ref)[source]#

Solve MPC problem by using a simple BnB method.

Parameters:

  • sys (system object) – System model.

  • ctr (controller object) – Controller object.

  • y_ref (ndarray of floats) – Reference vector [p.u.].

Returns:

u_abc – The three-phase switch position.

Return type:

1 x 3 ndarray of ints

solve(sys, ctr, x_ell, y_ref, u_ell_abc_prev, ell=0, J_prev=0)[source]#

Recursively compute the cost for different switching sequences.

Parameters:

  • sys (object) – System model.

  • ctr (object) – Controller object.

  • x_ell (ndarray of floats) – State vector [p.u.].

  • y_ref (ndarray of floats) – Reference vector [p.u.].

  • u_ell_abc_prev (1 x 3 ndarray of ints) – Previous three-phase switch position.

  • ell (int) – Prediction step. The default is 0.

  • J_prev (float) – Previous cost. The default is 0.

class soft4pes.control.mpc.solvers.MpcEnum(conv)[source]#

Enumeration-based solver for model predictive control (MPC).

Parameters:

conv (converter object) – Converter model.

U_seq#

Array for sequences of three-phase switch positions (switching sequences).

Type:

3*Np x conv.nl^(3*Np) ndarray of ints

sw_pos_3ph#

Possible one-phase switch positions.

Type:

1 x conv.nl ndarray of ints

__call__(sys, ctr, y_ref)[source]#

Solve MPC problem with exhaustive enumeration.

Parameters:

  • sys (system object) – System model.

  • ctr (controller object) – Controller object.

  • y_ref (ndarray of floats) – Reference vector [p.u.].

Returns:

u_abc – The three-phase switch position with the lowest cost.

Return type:

1 x 3 ndarray of ints

solve(sys, ctr, xk, y_ref, u_km1_abc)[source]#

Recursively compute the cost for different switching sequences

Parameters:

  • sys (system object) – System model.

  • ctr (controller object.) – Controller object.

  • xk (ndarray of floats) – Current state vector [p.u.].

  • y_ref (ndarray of floats) – Reference vector [p.u.].

  • u_km1_abc (1 x 3 ndarray of ints) – Three-phase switch position applied at step k-1.

Returns:

J – Cost array.

Return type:

1 x nl^(3*Np) ndarray of floats

soft4pes.control.mpc.solvers.switching_constraint_violated(nl, u_abc, u_km1_abc)[source]#

Check if a candidate three-phase switch position violates a switching constraint. A three-level converter is not allowed to directly switch from -1 and 1 (and vice versa) on one phase.

Parameters:

  • nl (int) – Number of converter voltage levels.

  • u_abc (1 x 3 ndarray of ints) – three-phase switch position.

  • u_km1_abc (1 x 3 ndarray of ints) – Previously applied three-phase switch position.

Returns:

Constraint violated.

Return type:

bool

soft4pes.control.mpc.solvers.squared_weighted_second_norm(vector, Q)[source]#

Compute the squared weighted second norm of a vector. The elements of the norm are weighted by the weighting matrix Q, i.e. sqrt(x.T * Q * x)^2 = x.T * Q * x.

Parameters:

  • vector (ndarray) – Vector.

  • Q (ndarray) – Weighting matrix.

Returns:

Squared weighted second norm.

Return type:

float

soft4pes.control.mpc.solvers.make_QP_matrices(sys, ctr)[source]#

Create the QP matrices.

Parameters:

  • sys (system object) – System model.

  • ctr (controller object) – Controller object.

Returns:

Namespace containing the QP matrices.

Return type:

SimpleNamespace

soft4pes.control.mpc.solvers.make_Gamma(Np, C, A)[source]#

Make Gamma matrix for the QP.

Parameters:

  • Np (int) – Prediction horizon.

  • C (ndarray) – Output matrix of the system.

  • A (ndarray) – State matrix of the system.

Returns:

Gamma matrix.

Return type:

ndarray

soft4pes.control.mpc.solvers.make_Upsilon(Np, C, A, B)[source]#

Make Upsilon matrix for the QP.

Parameters:

  • Np (int) – Prediction horizon.

  • C (ndarray) – Output matrix of the system.

  • A (ndarray) – State matrix of the system.

  • B (ndarray) – Input matrix of the system.

Returns:

Upsilon matrix.

Return type:

ndarray