1. 1 Optimal operation of energy storage in buildings: The use of hot water system Emma Johansson Supervisors: Sigurd Skogestad and Vinicius de Oliveira

2. 2 Agenda Project description Work done Model validation Further work

3. 3 Project description Optimal operation of energy storage in buildings with focus on the optimization of an electrical water heating system. Objective is to minimize the energy cost of heating the water Main complications: Electricity price and future demand Goal: To propose, implement and compare different simple policies that result in near-optimal operation of the system.

4. 4 Should be robust in some to-be-defines sense (e.g. must be feasible for at least 95% of the cases) Should result in significant savings compared to trivial solution Should be simple to implement in practice. Proposed policies

5. 5 Process flow scheme Dynamic model:

6. 6 Model assumptions qhw and Thws controlled directly by the consumer Perfect control when feasible Perfect control: else

7. 7 Model equation Definition of the state, input and disturbance vectors.

8. 8 Model validation

9. 9 PID controller

10. 10 Demand profile Randomly generated demand profiles from MATLAB script, qhw.

11. 11 Electricity Price On-off peak price Time varying price

12. 12 Implementing a switch

13. 13 Price threshold, p B Defining set-points for the temperature at the switch

14. 14 Results Switching between set-points as the price is higher or lower than the price threshold P B.

15. 15 Weekly average P B average from previous week

16. 16 Average from previous day

17. 17 Average current day Comparing the total cost with different boundaries, also assuming the electricity price for the current day is known, and the average of this day can be used.

18. 18 No boundary? The lowest price threshold resulted in the lowest cos, what are the result with no boundary?

19. 19 No boundary? T start = 90 °C, low total cost. T start = 65 °C, higher total cost.

20. 20 Cost function Original cost function: Implementing a penalty into the cost function:

21. 21 Further work Optimization problem: min J(P B, T buffer ) Decision variables: P B and T buffer Finding the optimal P B and T buffer which provides the lowest total cost. Simulate for longer periodes and generalizing the simulation Find near optimal policies