Systems and methods for optimally delivering electrical energy in a network

A method for optimally delivering electrical energy comprising:

• receiving a first objective function and a second objective function for optimizing delivery of an energy resource over a power grid;
• receiving a set of constraints representing electrical load capacities of a plurality of elements of the power grid;
• executing a first optimization process, using the set of constraints and the first objective function, to identify (i) a load matrix embodying a set of optimal electrical loads for each of the plurality of elements of the power grid and (ii) a first feature matrix representing values corresponding to the optimal electrical loads, wherein the load matrix and first feature matrix optimize the first objective function and satisfy the set of constraints;
• determining that one or more of the elements of the plurality of elements is fully loaded if the optimal load of the respective one or more elements is equal to the electrical load capacity of the respective one or more elements;
• determining that one or more of the elements of the plurality of elements is non-binding if the value corresponding to the respective one or more elements is zero;
• if the load matrix does not include an element that is both non-binding and fully loaded:
• transmitting the first load matrix and the first feature matrix to at least one power generator to instruct the at least one power generator to generate electrical power;
• and
• if the load matrix includes an element that is both non-binding and fully loaded:
• performing a second optimization process, using the first feature matrix and the second objective function as inputs, to identify a second feature matrix which optimizes the second objective function, wherein the second feature matrix preserves the optimality of the first objective function and satisfies the set of constraints, and wherein the second feature matrix assigns a non-zero value to the element that was determined to be non-binding and fully-loaded;
• and
• transmuting the first load matrix and the second feature matrix to the least one power generator to instruct the at least one power generator to generate electrical power.