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 method for regulating and modifying the intra-day electrical load, the method comprising the steps of:
monitoring electrical load demand in an electrical power distribution system and controlling the distribution of electrical power from an electrical power generator to a plurality of customers through an electrical grid;
dividing a day into a plurality of time periods;
expressing an electrical load during each one of the plurality of time periods as a function of a customer utility valuation of electricity consumption during the plurality of time periods and a time-substitutability of customer demand among the plurality of time periods, the customer utility valuation comprising a function of at least one incentive signal capable of being adjusted to affect a modification in electricity consumption by customers during each one of the plurality of time periods; and
calculating a fraction of total daily electrical usage for each time period by dividing the electrical load for that time period by a sum of all electrical loads for all time periods and by shifting customer demand and electrical load among the plurality of time periods.
2. The method of claim 1 , wherein the customer utility valuation further comprises a function of at least one of a time of day, a day of a given week, a month of given year, and weather conditions.
3. The method of claim 1 , wherein the at least one incentive signal comprises a customer price for electricity.
4. The method of claim 1 , wherein the method further comprises
expressing total electrical load consumed for each time period using the at least one incentive signal; and
determining a value for the at least one incentive signal in each one of the plurality of time periods to achieve a pre-defined intra-day electrical load profile for total electrical load consumed across all time periods by shifting customer demand and electrical load among the plurality of time periods.
5. The method of claim 4 , further comprising using the fractions of total daily electrical load for all time periods to forecast future intra-day electricity loads for the plurality of time periods.
6. The method of claim 5 , wherein using the fractions of total daily usage to forecast future intra-day electricity loads comprises establishing a baseline electrical load for each time period.
7. The method of claim 6 , wherein establishing the baseline electrical load for each time period comprises using historical data on electrical demand to establish the baseline electrical load for each time period.
8. The method of claim 5 , wherein using the fractions of total daily usage to forecast future intra-day electricity loads further comprises modifying the at least one incentive signal during at least one time period to change the customer utility valuation, the total electrical load and the fraction of total daily electrical load associated with that time period and one or more additional time periods.
9. The method of claim 8 , wherein modifying the at least one incentive signal further comprises concurrently modifying the at least one incentive signal for all time periods.
10. The method of claim 8 , wherein modifying the at least one incentive signal further comprises modifying the at least one incentive signal to minimize a variance among the fractions of total daily electrical load across all time periods.
11. The method of claim 8 , wherein modifying the at least one incentive signal further comprises:
identifying an upper threshold and a lower threshold for any fraction of total daily electrical load in any time period; and
modifying the at least one incentive signal to maintain the fractions of total daily electrical load across all time periods within the upper and lower thresholds.
12. The method of claim 8 , wherein modifying the at least one incentive signal further comprises:
identifying an upper threshold for any fraction of total daily electrical load in any time period;
modifying the at least one incentive signal across all time periods to shift an existing peak time-of-day electrical load from a first time period to a second time period such that the shifted peak time-of-day load does not exceed the upper threshold.
13. The method of claim 8 , wherein:
the at least one incentive signal comprises a customer price for electricity; and
modifying the at least one incentive signal further comprises:
accounting for a cost of electricity to a supplier of the electrical load; and
modifying the customer price for electricity to maximize profitability to a supplier of the electrical load.
14. The method of claim 13 , wherein the method further comprises expressing the cost of electricity to the supplier an increasing function of total daily electrical load.
15. The method of claim 13 , wherein modifying the customer price to maximize profitability further comprises maximizing profitability subject to a pre-defined limit on a total cost of electricity to any single customer.
16. The method of claim 6 , wherein using the fractions of total daily usage to forecast future intra-day electricity loads further comprises:
using the established baseline electrical load for each time period and an associated customer price for electricity to determine a baseline total cost to the customer; and
modifying a customer price for electricity during at least one time period to change the customer utility, the electrical load and the fraction of total daily electrical usage associated with that time period while maintaining a modified total cost to the customer at a value less than or equal to the baseline total cost to the customer.
17. A non-transitory computer-readable storage medium containing a computer-readable code that when read by a computer causes the computer to perform a method for controlling intra-day electrical load, the method comprising:
monitoring electrical load demand in an electrical power distribution system and controlling the distribution of electrical power from an electrical power generator to a plurality of customers through an electrical grid;
dividing a day into a plurality of time periods;
expressing an electrical load during each one of the plurality of time periods as a function of a customer utility valuation of electricity consumption during the plurality of time periods and a time-substitutability of customer demand among the plurality of time periods, the customer utility valuation comprising a function of at least one incentive signal capable of being adjusted to affect a modification in electricity consumption by customers during each one of the plurality of time periods; and
calculating a fraction of total daily electrical usage for each time period by dividing the electrical load for that time period by a sum of all electrical loads for all time periods and by shifting customer demand and electrical load among the plurality of time periods.
18. The computer-readable storage medium of claim 17 , wherein the method further comprises:
expressing total electrical load consumed for each time period using the at least one incentive signal;
determining a value for the at least one incentive signal in each one of the plurality of time periods to achieve a pre-defined intra-day electrical load profile for total electrical load consumed across all time periods by shifting customer demand and electrical load among the plurality of time periods; and
using the fractions of total daily electrical usage for all time periods to forecast future intra-day electricity loads for the plurality of time periods by modifying the at least one incentive signal during all time periods to change the customer utility valuation, the electrical load and the fraction of total daily electrical usage associated with each time period.
19. The computer-readable storage medium of claim 18 , wherein modifying the at least one incentive signal further comprises:
identifying an upper threshold and a lower threshold for any fraction of total daily electrical usage in any time period; and
modifying the at least one incentive signal to maintain the fractions of total daily electrical usage across all time periods within the upper and lower thresholds.
20. The computer-readable storage medium of claim 18 , wherein:
the at least one incentive signal comprises a customer price for electricity; and
modifying the customer price further comprises:
accounting for a cost of electricity to a supplier of the electrical load; and
modifying the customer price to maximize profitability to the supplier of the electrical load subject to a pre-defined limit on a total cost of electricity to any single customer.