T.W.Scholten, C. de Persis, P. Tesi Modeling and Control of Heat Networks with Storage: the Single-Producer Multiple-Consumer Case T.W.Scholten, C. de Persis, P. Tesi

Outline District heating Problem description Setup Control goal Flows Introduction District heating Problem description Model Setup Control goal Control Flows Heat injection Case study Conclusion Conclusions Future work

Introduction Model Control conclusion District heating Introduction Model Control conclusion

Introduction Model Control conclusion Examples Waste incinerators Geothermal energy Industrial users Storage tank Domestic users Greenhouses Introduction Model Control conclusion

Introduction Model Control conclusion Problem description Balance demand and supply Options: Control production Include storage Control demand Dynamic pricing Do optimization over time horizon: Design a controller such that the stored energy converges to the desired setpoints Introduction Model Control conclusion

Introduction Model Control conclusion Setup Heat exchangers Stratified storage Introduction Model Control conclusion

Introduction Model Control conclusion Volume dynamics Hot storage: Cold storage: Constraints both layers: where Introduction Model Control conclusion

Introduction Model Control conclusion Temperature dynamics Introduction Model Control conclusion

Introduction Model Control conclusion Input and disturbance Let: where Introduction Model Control conclusion

Introduction Model Control conclusion Control goal Find controllers and such that: under disturbance Introduction Model Control conclusion

Introduction Model Control conclusion Overall Model Introduction Model Control conclusion

Introduction Model Control conclusion Overall Model Linear if and are constant and exists. Introduction Model Control conclusion

Introduction Model Control conclusion Controller design 1. Design flow controller such that: 2. Design controller for the heat injection assuming 3. Proof boundedness and stability without assuming Introduction Model Control conclusion

Introduction Model Control conclusion 1. Flow controller Flow controller: Volume dynamics: exists Recall where Introduction Model Control conclusion

Introduction Model Control conclusion 2. Heat injection Let Controller design (Internal model) Always exist! Introduction Model Control conclusion

Introduction Model Control conclusion 3. Main result The solutions of system in closed loop with controllers and are bounded and Introduction Model Control conclusion

Introduction Model Control conclusion Remark Where No! Need to know and a priori? IM is robust against parameter uncertainties Introduction Model Control conclusion

Case study: time varying demand Store to 900m³ Drain to 100m³ Saturation applied Setpoint 85°C Extra injection Low injection rate Not in the analysis Introduction Model Control conclusion

Case study: time varying demand Introduction Model Control conclusion

Case study: time varying demand; heat exchanger Introduction Model Control conclusion

Introduction Model Control conclusion Conclusions Model derived and control problem defined Able to reject time varying disturbances Global asymptotic stability proven Some remarks: Flow of the consumer is set constant Simple model: easy to use, but wat about accuracy? What about the time delays? Introduction Model Control conclusion

Introduction Model Control conclusion Future work Extend to multiple consumers and multiple storages Consider optimal production Investigate possibilities of cascading Delays Dissipation Include dynamic pricing Introduction Model Control conclusion

Introduction Model Control conclusion Thank you for your attention! Questions? Introduction Model Control conclusion