Power balancing in a DC microgrid elevator system through constrained - PowerPoint PPT Presentation

Power balancing in a DC microgrid elevator system through constrained optimization Thanh Hung PHAM, Ionela PRODAN and Laurent LEFEVRE Grenoble INP (Institut National Polytechnique de Grenoble), LCIS (Laboratoire de Conception et d’Int´ egration des Syst` emes), Valence, France, thanh-hung.pham@lcis.grenoble-inp.fr,phamthanhhung1204@gmail.com This work was supported by a mobility project of the Romanian National Authority for Scientific Research and Innovation, CNCS - UEFISCDI, project number PN-III-P1-1.1-MCT-2016-0037, within PNCDI III T.H. Pham, I. Prodan, L.Lef` evre (Grenoble INP (Institut National Polytechnique de Grenoble), LCIS (Laboratoire de Conception et d’Int´ Power balancing in a DC microgrid December 8th, 2016 1 / 27 egration

Introduction Outline Introduction 1 DC microgrid modeling 2 Port-Hamiltonian system on graphs DC microgrid elevator system modeling Battery scheduling by optimization-based control 3 Energy-preserving discrete-time model Scheduling formulation Simulation 4 Simulation software and numerical data Nominal scenario Perturbation-affected scenario Conclusions 5 Reference 6 T.H. Pham, I. Prodan, L.Lef` evre (Grenoble INP (Institut National Polytechnique de Grenoble), LCIS (Laboratoire de Conception et d’Int´ Power balancing in a DC microgrid December 8th, 2016 2 / 27 egration

Introduction DC microgrid elevator system DC/DC converter Battery Solar panel DC/DC converter Synschronous machine AC/DC converter Mechanical system AC/DC converter Three-phase electrical network DC microgrid elevator system, Pham et al. (2015) T.H. Pham, I. Prodan, L.Lef` evre (Grenoble INP (Institut National Polytechnique de Grenoble), LCIS (Laboratoire de Conception et d’Int´ Power balancing in a DC microgrid December 8th, 2016 3 / 27 egration

Introduction Introduction General goal: Constrained optimization control for for efficiently managing the DC microgrid operation. State of the art: bus voltage control (Alamir et al. (2014); Zonetti et al. (2015)) DC/DC ⇒ do not optimize electricity cost, converter Battery logic rules (Xu and Chen (2011)) Solar panel DC/DC converter ⇒ high storage capacity and not efficient, Synschronous offline optimization-based control approach machine (Lifshitz and Weiss (2014)) AC/DC converter ⇒ lack of the robustness, Mechanical system Economic MPC (Parisio et al. (2016); AC/DC converter Touretzky and Baldea (2016)) ⇒ looses relevant details in what regards Three-phase electrical the physical power-preserving connection, network DC microgrid elevator system, Pham et al. (2015) neglects the nonlinear storage dynamic and the system dissipation. Solution: Port-Hamiltonian (PH) formulation for the modeling (van der Schaft and Maschke (2013)), Energy-preserving time discretization model (Talasila et al. (2006)), Centralized economic Model Predictive Control (MPC) design (Rawlings and Mayne (2009)). T.H. Pham, I. Prodan, L.Lef` evre (Grenoble INP (Institut National Polytechnique de Grenoble), LCIS (Laboratoire de Conception et d’Int´ Power balancing in a DC microgrid December 8th, 2016 4 / 27 egration

DC microgrid modeling Outline Introduction 1 DC microgrid modeling 2 Port-Hamiltonian system on graphs DC microgrid elevator system modeling Battery scheduling by optimization-based control 3 Energy-preserving discrete-time model Scheduling formulation Simulation 4 Simulation software and numerical data Nominal scenario Perturbation-affected scenario Conclusions 5 Reference 6 T.H. Pham, I. Prodan, L.Lef` evre (Grenoble INP (Institut National Polytechnique de Grenoble), LCIS (Laboratoire de Conception et d’Int´ Power balancing in a DC microgrid December 8th, 2016 5 / 27 egration

DC microgrid modeling Port-Hamiltonian system on graphs Bond graph and Port-Hamiltonian system Bond Graph Dirac structure and PH system _ + + _ + + + + _ _ _ _ Dirac structure and port-Hamiltonian systems. Constrained input-output representation For all PH system, there exists λ ( t ) such that � e ( t ) = Jf ( t ) + G λ ( t ) , = G T f ( t ) , 0     ∇ H ( x ) − ˙ x ( t )  , f ( t ) =  , e ( t ) = e R ( t ) f R ( t )   e E ( t ) f E ( t ) Example: Bond Graph for simple series and parallel DC electrical circuit. = − J T J Advantage x ( t ) : state vector f ( t ) : flow vector (current, voltage, speed, force, ...) Explicit description of the exchange of power, of e ( t ) : effort vector (voltage, current, force, speed, ...) the dissipation and of the energy storage for H ( x ) : Hamiltonian (energy function) multi-physics system. ∇ H ( x ) : gradient of H ( x ) T.H. Pham, I. Prodan, L.Lef` evre (Grenoble INP (Institut National Polytechnique de Grenoble), LCIS (Laboratoire de Conception et d’Int´ Power balancing in a DC microgrid December 8th, 2016 6 / 27 egration

DC microgrid modeling Port-Hamiltonian system on graphs PH system on graphs for RC circuit RC circuit graph RC electrical circuit: example Consider a circuit including: _ 2 2 + N e edges: N S capacitors, N R resistors, N E 3 + + external elements, + + + _ _ _ _ _ N v vertices: nodes between the edges. The incidence matrix B ∈ R N v × N e : 1 1  1 , if node i is a head vertex of edge j,  B ij = − 1 , if node i is a end vertex of edge j, 0 , else.  PH system on graphs formulation = − B T v p ( t ) , � e ( t ) Edge order: C-R-E = Bf ( t ) , 0     ∇ H ( x ) − ˙ x ( t )  , f ( t ) =  , e ( t ) = v R ( t ) i R ( t )   v E ( t ) i E ( t ) Energy stored in the capacitor: x ( t ) : capacitor charge (state vector) x ( t ) 2 H ( x ) = 1 i R ( t ) , i E ( t ) : current . 2 v R ( t ) , v E ( t ) : voltage C v p ( t ) : potential of the vertices T.H. Pham, I. Prodan, L.Lef` evre (Grenoble INP (Institut National Polytechnique de Grenoble), LCIS (Laboratoire de Conception et d’Int´ Power balancing in a DC microgrid December 8th, 2016 7 / 27 egration

DC microgrid modeling DC microgrid elevator system modeling DC microgrid elevator system model DC/DC converter Battery Solar panel DC/DC v ( t ) : voltage converter i ( t ) : current P ( t ) : power Synschronous d ( t ) : converter duty cycle machine : ith state variable (charge) xi ( t ) AC/DC ∂ xi H : partial derivative of H with respect to xi (voltage) converter xi ( t ) ˙ : time derivative of xi (current) Mechanical R : resistor system AC/DC converter Three-phase electrical network _ + _ _ _ 2 + + + 4 Load power 3 + + source 7 + + _ _ _ 1 _ _ + 1 Renewable power source External _ + 6 grid 5 _ _ + + 1 1 T.H. Pham, I. Prodan, L.Lef` evre (Grenoble INP (Institut National Polytechnique de Grenoble), LCIS (Laboratoire de Conception et d’Int´ Power balancing in a DC microgrid December 8th, 2016 8 / 27 egration

DC microgrid modeling DC microgrid elevator system modeling Model of the components _ + _ _ _ 2 + + 4 + Load power 3 + + source 7 + _ _ + 1 _ _ _ + 1 Renewable power source External _ + 5 6 grid _ _ + + 1 1 Battery admits the stored energy: External grid is a current source i e ( t ): H ( x ) � x ( t ) T Q 1 + 1 2 x ( t ) T Q 2 x ( t ) , i e , min ≤ i e ( t ) ≤ i e , max . Load is a power profile P l ( t ): Battery charge limitation: i l ( t ) v l ( t ) = P l ( t ) . 0 . 5 x max ≤ x ( t ) ≤ x max , Renewable source is a power profile P r ( t ): Battery current limitation: i r ( t ) v r ( t ) = P r ( t ) . i min ≤ i b , R 2 ( t ) ≤ i max . T.H. Pham, I. Prodan, L.Lef` evre (Grenoble INP (Institut National Polytechnique de Grenoble), LCIS (Laboratoire de Conception et d’Int´ Power balancing in a DC microgrid December 8th, 2016 9 / 27 egration

DC microgrid modeling DC microgrid elevator system modeling Model of the components _ + _ _ _ 2 + + 4 + Load power 3 + + source 7 + _ _ + 1 _ _ _ + 1 Renewable power source External _ + 5 6 grid _ _ + + 1 1 DC/DC converter respects the power-preserving Resistor network includes relation: the resistors of battery, � the resistors of transmission lines. d ( t ) i c 1 ( t ) = − i c 2 ( t ) , v c 1 ( t ) = d ( t ) v c 2 ( t ) , The Ohm’ law is: v R ( t ) = − Ri R ( t ) , with the positive duty cycle: where R is positive diagonal matrix. d ( t ) > 0 . T.H. Pham, I. Prodan, L.Lef` evre (Grenoble INP (Institut National Polytechnique de Grenoble), LCIS (Laboratoire de Conception et d’Int´ Power balancing in a DC microgrid December 8th, 2016 10 / 27 egration