Paper Introduction

1. PaperIntroduction Optimal Residential Load Control With Price Prediction in Real- Time Electricity Pricing Environments ------ IEEE Trans. on Smart Grid, Sep 2010 Authors: Amir-Hamed Mohsenian-Rad, Member, IEEE Alberto Leon-Garcia, Fellow, IEEE For Group Meeting on Oct 27, 2011

2. Outline • Background • What’s the contribution? • System Model • Price Prediction • Optimal Residential Load Control • Simulation Results

3. Background • Since electricity is nonstorable economically, wholesale prices (set by competing generators to regional electricity retailers) vary from day to day, and also fluctuate between low-demand time (i.e., night) and high-demand time (i.e., afternoon) • However, almost all retail consumers are charged average price not reflecting the actual wholesale price. • As solution, various time-differentiated pricing models: • Real-time pricing (RTP) • Day-ahead pricing (DAP) • Time-of-use-pricing (TOUP) • Critical-peak pricing (CPP) • Main idea: allowing retail price to reflect the wholesale price, encouraging users to shift load.

4. Background • Inclining block rates (IBR) • another alternative to the common flat rates in retail electricity • In IBR pricing, the marginal price increases by the total quantity consumed. i.e., beyond a certain threshold in the residential load, the electricity price will increase to a higher value. • IBR helps in load balancing and reducing peak-to-average ratio (PAR) • Two major barriers of RTP and IBR • The lack of knowledge among the users about how to respond to time-varying prices • The lack of effective home automation systems

5. What’s the contribution • Propose a computationally feasible and automated residential load control scheme in a retail electricity market with RTP combined with IBR • Aiming at minimizing the household’s electricity payment by optimally scheduling the operation and energy consumption for each appliance, subject to the special needs indicated by the users. • Implementation: • Each residential consumer equipped with a smart meter • Can periodically receive the updated price information from the utility • Each smart meter includes an energy scheduling unit • The energy scheduling unit is complemented by a price predictor unit, estimating the upcoming prices.

6. System Model • An illustration of the wholesale electricity market formed by multiple generators and several regional retail companies.

7. System Model • Consider a residential unit participating in a real-time pricing program. It may include a set of appliances such as washer/dryer, refrigerator, PHEV… • For each appliance a, define an energy consumption scheduling vector: • H: scheduling horizon, indicating the number of hours ahead which are taken into account for decision making in energy consumption scheduling. • : the corresponding 1-h energy consumption that is scheduled for appliance a.

8. System Model • : the total energy needed for the operation of appliance a. E.g., for a PHEV, in total is required to charge the battery for a 40-mi driving range. • Setting constraints on the beginning and end of a time interval in which the energy consumption for appliance a is valid to be scheduled, it is required that • Note that the time length needs to be not less than the time duration required to finish the normal operation of appliance a, e,g, for a PHEV, the duration is required to be at least 3h.

9. System Model • All home appliances have certain maximum power levels. E.g., for a PHEV, it may be charge only up to per hour. Some appliances may also have minimum stand-by power levels. Therefore, it is required that • There is usually a limit on the total energy consumption at each residential unit at each hour. It can be set by the utility to impose the following set of constraints on energy scheduling:

10. System Model • Feasible scheduling set for all possible energy consumption scheduling vectors: • x demotes the vector of energy consumption scheduling variables for all appliances.

11. System Model Smart meter operation Wireless HAN

12. System Model • RTP with IBR • Temporarily assume that the future pricing parameters are known to the users ahead of time. • A general hourly pricing function: • : the total hourly household energy consumption at each upcoming hour h.

13. System Model Nonflat pricing model 1 Nonflat pricing model 2

14. System Model • The user’s total electricity payment corresponding to all appliances within the upcoming scheduling horizon is: • The cost of waiting can be modeled as: • Note that the cost of waiting increases as more energy consumption is scheduled at later hours. • : an adjustable control parameter, the higher value, the higher cost

15. System Model • The energy consumption scheduling problem: • Note that the problem is not tractable in its current form due to the non-differentiability of price function.

16. Price Prediction • Removing the assumption that each end user is fully aware of the upcoming price values set by the utility company within the scheduling horizon H. • Consider more dynamic pricing scenarios where the upcoming prices are announced only for hours ahead of time, where P is the price announcement horizon. • Price prediction based on prior knowledge • Wholesale market price? • Higher during the afternoon? • Higher on hot days in the summer, cold days in the winter? • Depending on working days or weekends? • How to develop a price predictor that have low computational complexity and can be implemented easily in residential smart meter?

17. Price Prediction • According to studying the history of price variation with time of day, month, day in week…an observation from the following figure suggests that an efficient prediction is likely by looking at the prices on yesterday, the day before yesterday and the same day last week.

18. Price Prediction • The proposed price parameter prediction model: • Similar models can be applied to predict and , however, in practice, is usually fixed and does not change on a daily basis. Then the predicted price is derived as: • How to determine the coefficients? • All-days-same coefficients: 17% prediction error on average • Each-day-different coefficients: 13% prediction error on average

19. Price Prediction • Comparison results between the actual price and the prediction:

20. Optimal Residential Load Control • Note that if the utility company does not release the price for all upcoming hours within the scheduling horizon, i.e., if the price announcement horizon P is strictly less than the scheduling horizon H, then part of the original energy scheduling problem needs to be constructed based on the price prediction. • Then the problem becomes:

21. Optimal Residential Load Control • An illustration of the hourly payment with IBR.

22. Optimal Residential Load Control • According to the figure, it can be found that the hourly payment is formed based on two intersecting lines: • Therefore, the payment can be written as:

23. Optimal Residential Load Control • The original energy scheduling problem can be reformulated as:

24. Optimal Residential Load Control • By introducing auxiliary variables : • It can be proved that these two problems are equivalent and have exactly the same optimal solutions. Also, it can be solved by applying linear programming techniques.

25. Simulation Results • Performance gains from users prospectives:

26. Simulation Results • Performance gains from utility prospectives:

27. Simulation Results • The impact of price announcement horizon and price prediction:

28. Simulation Results • The impact of scheduling control parameter:

29. Simulation Results • The impact of scheduling control parameter (cont):

30. Simulation Results • The impact of adopting inclining block rates:

31. Thank you for attention!