Stochastic economic optimization of electrical systems, and related systems, apparatuses, and methods

A method of operating an electrical system, the method comprising:

• generating probability distribution functions corresponding to probability density of a given random variable value occurring at different points in time of a future period of time, the probability distribution functions each taking into consideration uncertainty of one or more random variables associated with the economic cost of operating the electrical system;
• constructing a cost function based on the one or more random variables;
• determining a set of control values for a set of control variables that correspond to a minimum expected value of the economic cost of operating the electrical system over the future period of time based on the cost function;
• and
• controlling the electrical system based on the determined set of control values.

One or more non-transitory computer-readable storage media including computer-readable instructions stored thereon, the computer-readable instructions configured to instruct one or more processors to:

• construct a cost function comprising an expected value of an economic cost of operating an electrical system over a future period of time, the cost function further including one or more decision variables, the one or more decision variables related to controllable features of the electrical system, the cost function including cost elements corresponding to net electricity payments to an electrical grid plus net equipment operating costs;
• determine optimal values for the decision variables corresponding to a minimum value of the expected value of the economic cost of operating the electrical system over the future period of time;
• and
• issue one or more commands to the electrical system to operate according to the determined optimal values for the decision variables.