Managing time-substitutable electricity usage using dynamic controls
A predictive-control approach allows an electricity provider to monitor and proactively manage peak and off-peak residential intra-day electricity usage in an emerging smart energy grid using time-dependent dynamic pricing incentives. The daily load is modeled as time-shifted, but cost-differentiated and substitutable, copies of the continuously-consumed electricity resource, and a consumer-choice prediction model is constructed to forecast the corresponding intra-day shares of total daily load according to this model. This is embedded within an optimization framework for managing the daily electricity usage. A series of transformations are employed, including the reformulation-linearization technique (RLT) to obtain a Mixed-Integer Programming (MIP) model representation of the resulting nonlinear optimization problem. In addition, various regulatory and pricing constraints are incorporated in conjunction with the specified profit and capacity utilization objectives.
1. A system for controlling intra-day electrical load, the system comprising:
an electrical power distribution system comprising:
at least one electrical power generator;
an electrical grid in communication with the electrical power generator; and
an electrical power grid controller to monitor electrical load demand in the electrical power distribution system and to control distribution of electrical power from the electrical power generator through the electrical grid; and
an intra-day electrical load controller in communication with the electrical power grid controller, the intra-day electrical load controller comprising:
a timer module configured to monitor a current time and to divide a day into a plurality of time periods;
a database comprising electrical load data, price per unit of electricity for a given time-of-day data, a baseline price and a desired load profile across the plurality of time periods;
an electrical load prediction module in communication with the database and configured to:
calculate a predicted fraction of total daily usage in each one of the plurality of time periods as a ratio of a value of a variable comprising an exponential function of a measure of customer utility for electricity in a given time period to a sum of values of the variable for all time periods, each measure of the customer utility comprising a function of the natural log of a recommended price per unit of electricity usage at a given time-of-day multiplied by an estimated price effect coefficient;
predict a day-ahead load profile comprising the predicted fraction of total daily usage in each one of the plurality of time periods;
adjust the price per unit of electricity for one or more given time-of-days within a predefined range from the baseline price per unit of electricity to minimize a deviation of the predicted day-ahead load profile from the desired load profile across the plurality of time periods; and
display each adjusted price per unit electricity for the given time-of-day to a plurality of customers in the electrical power distribution system as consumer price incentive values.
2. The system of claim 1 , wherein the measure of customer utility further comprises a function of temperature and a weekend indicator variable.
3. The system of claim 1 , wherein the electric load prediction module is configured to adjust the price per unit of electricity for one or more given time-of-days to minimize a variance among the predicted fractions of total daily usage in each one of the plurality of time periods.
4. The system of claim 1 , wherein the electric load prediction module is further configured to:
estimate a total daily electricity usage; and
multiply the estimated total daily electricity usage by the predicted day-ahead load profile to predict a day-ahead electricity usage profile.
5. The system of claim 1 , wherein the electric load prediction module is further configured to:
account for a cost of electricity to a supplier of the electrical load; and
adjust the price per unit of electricity for one or more given time-of-days to maximize profitability to a supplier of the electrical load subject to a pre-defined limit on a total cost of electricity to any single customer.