Callback Functions

7.2 Callback Functions

The second method, based on deﬁning a set of callback functions, oﬀers several distinct advantages, especially for more complex scenarios or for adding a feature for others to use, such as the zonal reserve requirement or the interface ﬂow limits mentioned previously. This approach makes it possible to:

deﬁne and access variable/constraint/cost sets as individual named blocks
deﬁne constraints, costs only in terms of variables directly involved
pre-process input data and/or post-process result data
print and save new result data
simultaneously use multiple, independently developed extensions (e.g. zonal reserve requirements and interface ﬂow limits)

With this approach the OPF formulation is modiﬁed in the formulation callback, which is described and illustrated below in Section 7.3.2. The modiﬁcations to the formulation are handled by adding variables, costs and/or constraints to the OPF Model object (om) using one of the add_* methods. Please see the documentation for each of these methods for more details.

7.2.1 User-deﬁned Variables

Additional variables are added using the add_var method.

om.add_var('myV', N, myV0, myV_min, myV_max);

Here myV is the name of the variable set, N the number of variables being added (i.e. this is an $N × 1$ vector being appended to the current optimization variable $ˆx$ ), and myV0, myV_min, myV_max are vectors of initial values, lower bounds and upper bounds, respectively.

7.2.2 User-deﬁned Costs

Quadratic Costs are added using the add_quad_cost method.
om.add_quad_cost('myQcost', Q, c, k, varsets);

Here myQcost is the name of the cost set, Q, c and k are the $Qj$ , $cj$ and $kj$ parameters from (6.47), respectively, and var_sets is an optional cell array of variable set names. If var_sets is provided, the dimensions of Q and c will correspond, not to the full optimization vector $ˆx$ , but to the subvector formed by stacking only the variable sets speciﬁed in var_sets.
General Nonlinear Costs are added using the add_nln_cost method.
om.add_nln_cost('myNonlinCost', 1, fcn, varsets);

Here myNonlinCost is the name of the cost set, fcn is a function handle and var_sets is an optional cell array of variable set names. The function handle fcn must point to a function that implements the $j fnln(xˆ)$ function from (6.46), returning the value of the function, along with its gradient and Hessian. This function has a format similar to that required by MIPS for its cost function.
If var_sets is provided, instead of the full optimization vector $ˆx$ , the x passed to the function fcn will be a cell array of sub-vectors of $ˆx$ corresponding to the speciﬁed variable sets.
Legacy Costs are added using the add_legacy_cost method.
om.add_legacy_cost('myLegacyCost', cp, varsets);

Here myLegacyCost is the name of the cost set, cp is a struct containing the cost parameters $H$ , $C$ , $N$ , $ˆr$ , $k$ , $d$ and $m$ from (6.48)–(6.51) in ﬁelds H, Cw, N, rh, kk, dd and mm, respectively, and var_sets is an optional cell array of variable set names. If var_sets is provided, the number of columns in N will correspond, not to the full optimization vector $ˆx$ , but to the subvector formed by stacking only the variable sets speciﬁed in var_sets.

7.2.3 User-deﬁned Constraints

Linear Constraints are added using the add_lin_constraint method.
om.add_lin_constraint('myLinCons', A, l, u, varsets);

Here myLinCons is the name of the constraint set, A, l and u correspond to additional rows to add to the $A$ , $l$ and $u$ parameters in (6.38), respectively, and var_sets is an optional cell array of variable set names. If var_sets is provided, the number of columns in A will correspond, not to the full optimization vector $ˆx$ , but to the subvector formed by stacking only the variable sets speciﬁed in var_sets.
Nonlinear Constraints are added using the add_nln_constraint method.
om.add_nln_constraint('myNonlinCons', N, iseq, fcn, hess, varsets);

Here myNonlinCons is the name of the constraint set, N is the number of constraints being added, iseq is a true or false value indicating whether this is a set of equality (or else inequality) constraints, fcn and hess are function handles and var_sets is an optional cell array of variable set names. The function handle fcn must point to a function that implements the corresponding constraint function $j gu(x)$ or $hju(x)$ and its gradients, and hess to one that evaluates the corresponding term in the Hessian of the Lagrangian function. This function has a format similar to that required by MIPS for its cost function. See more details in Section 7.1.2.
If var_sets is provided, instead of the full optimization vector $ˆx$ , the x passed to the function fcn will be a cell array of sub-vectors of $ˆx$ corresponding to the speciﬁed variable sets.

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