Advanced Passivity-Based Control for a Fuel

Cell/Super-Capacitor Hybrid Power System with

Aging Tolerant Control

Suyao KONG PhD student

Université Bourgogne Franche - Comté, France

FEMTO-ST Institute / FCLAB

Supervisors: Mickaël HILAIRET, Robin ROCHE

Email: suyao.kong@utbm.fr

17/05/2018

Context

1. ANR Project Datazero

2. Introduction to IDA-PBC

3. Advanced passivity-based control

4. Aging tolerant control

5. Simulation and Hardware In the Loop results

6. Conclusion and future works

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1. ANR Project Datazero

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ANR Project DATAZERO Objective Designing a zero-emissions, 100% renewable energy supply for a datacenter

Challenges Ensuring the quality of service for IT (Information Technologies)

Avoiding over-redundancy and over-provision in power lines and IT

Intermittence of renewable generation

How to coordinate the different energy sources

Target market Small and middle size datacenters for Cloud / Virtualization (1000 𝑚2, 1 MW)

Partners LAPLACE, IRIT, EATON, FEMTO-ST (Besançon and Belfort)

Renewable energy + Long term storage + Flexibility of IT

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Framework of DATAZERO

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Components of the microgrid

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Connection with the project

Objective of this research:Proposing an advanced passivity-based control and an aging-tolerant control for a

fuel cell/super-capacitor hybrid power system.

This work discusses: Energy management control for hybrid systems

IDA-PBC: Interconnection and Damping Assignment - Passivity Based Control

Aging tolerant control of fuel cell

Fuel cell / Super capacitors

Validation using Hardware In the Loop (HIL)

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2. Introduction to IDA-PBC

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IDA-PBC

• Rewrite the closed-loop state space equations to a PCH form (Port-controlled Hamitonian):

• Consider a nonlinear system:

𝐻𝑑( 𝑥) is the natural energy function of the system; 𝐽 𝑥 is a skew-symmetric matrix representing the interconnections between states; 𝑅 𝑥 is a positive semi-definite symmetric matrix representing the natural damping of the system.

Passivity-based control (PBC)

• A controller design methodology that achieves stabilization by rendering the system passive with a

desired storage function and damping injection. The conception method is called IDA-PBC:

Interconnection and damping assignment passivity-based control

𝑥 = 𝑓 𝑥 + 𝑔 𝑥 𝑢; 𝑥 ∈ 𝑅𝑛; 𝑢 ∈ 𝑅𝑚

𝑦 = ℎ 𝑥 ; 𝑦 ∈ 𝑅𝑚

𝑥 = 𝐽 𝑥 − 𝑅 𝑥 𝛻𝐻𝑑 𝑥 + 𝑔 𝑥 𝑢𝑦 = 𝑔𝑇( 𝑥)𝛻𝐻𝑑( 𝑥)

𝐽 𝑥 = −𝐽 𝑥𝑅 𝑥 = 𝑅( 𝑥)𝑇

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IDA-PBC

• « Matching equation »

So that

• The objective of IDA-PBC is to find a static state-feedback control u 𝑥 = 𝛽 𝑥 such that the closed-loop

dynamics is a Port controlled Hamitonian system with the interconnection and the dissipation of the form:

𝐻𝑑(𝑥) is qualified as a Lyapunov function and the system is asymptotically stable.

Find 𝛽 𝑥

𝑥 = 𝐽𝑑 𝑥 − 𝑅𝑑 𝑥 𝛻𝐻𝑑

𝐻𝑑 = − 𝛻𝐻𝑑𝑇𝑅𝑑 𝑥 𝛻𝐻𝑑 ≤ 0 𝐻𝑑 𝑥 = 𝑥∗ = 0

𝐽 𝑥 − 𝑅( 𝑥)𝜕𝐻

𝜕𝑥 𝑥 + 𝑔( 𝑥)𝛽( 𝑥) = 𝐽𝑑 𝑥 − 𝑅𝑑 𝑥

𝜕𝐻𝑑

𝜕𝑥 𝑥

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3. Advanced Passivity-Based Control

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Control structure with IDA-PBC [1]

Main

source

Transient

source

Energy

management

[1] M. Hilairet, M. Ghanes , O. Bethoux , V. Tanasa , J-P. Barbot , D. Normand-Cyrot.

(2013). A passivity-based controller for coordination of converters in a fuel cell system.

Control Engineering Practice 21 1097–110912/30

In practice, two saturation functions are applied:

Saturation

Saturations

A dynamic saturation of SCs current.

A static saturation of FC current.

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Advanced Passivity-Based Control

Main idea of the new strategy:

Take into account the saturation directly into the controller in order to preserve the stability

property of the passivity controller, as follows:

• If the voltage of the SCs is low (𝑣𝑠𝑐𝐿 < 𝑣𝑠𝑐 < 𝑣𝑠𝑐𝑙), limit the discharge of the SCs during

a discharge operation, or accelerate the charge during a generating mode of the load.

• If the voltage of the SCs is high (𝑣𝑠𝑐ℎ < 𝑣𝑠𝑐 < 𝑣𝑠𝑐𝐻), limit the charge during a generating

mode of the load, or accelerate the discharge during a discharge operation.

• Otherwise (𝑣𝑠𝑐𝑙 ≤ 𝑣𝑠𝑐 ≤ 𝑣𝑠𝑐ℎ), the controller operates normally as the previous release

of the controller.

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Advanced Passivity-Based Control

=0

New strategy based on the control law obtained by M. Hilairet et al. [1]:

𝑟2 = −𝐶𝐽12 𝑣𝑏

𝐶𝑠𝑐 𝑣𝑠𝑐to impose 𝑖𝑠𝑐

∗ =0 at 𝑣𝑠𝑐 = 𝑣𝑠𝑐𝐿 or 𝑣𝑠𝑐 = 𝑣𝑠𝑐𝐻 15/30

Simulation and comparison

Simulation results - Comparison of the new and previous controller [1]

16/30[1] M. Hilairet, M. Ghanes , O. Bethoux , V. Tanasa , J-P. Barbot , D. Normand-Cyrot.

(2013). A passivity-based controller for coordination of converters in a fuel cell system.

Control Engineering Practice 21 1097–1109

4. Aging tolerant control

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New control structure with IDA-PBC

Main

source

Transient

source

Dissipation

of energy

Estimation of

the fuel cell

SoH

Energy

management

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FC aging

P-I curvesPolarisation curves

Objective: Finding the current of maximum power for different SoH in order to avoid overloading of the fuel cell.

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Aging model (works of Mathieu BRESSEL [2])

[2] M. Bressel, M. Hilairet, D. Hissel, B. Ould-Bouamama, Remaining Useful Life Prediction and

Uncertainty Quantification of Proton Exchange Membrane Fuel Cell Under Variable Load, IEEE

Transactions on Industrial Electronics, Vol. 63-4, 19 janvier 2016, pp. 2569-2577 20/30

Calculation of FC’s limit current

Maximum power current under different temperature

Estimation of State of Health Extended Kalman Filter [2]

Estimation of 𝐼𝑚𝑎𝑥𝑓𝑐

From the curves, the maximum power current is

almost independent from the temperature.

𝐼𝑚𝑎𝑥𝑓𝑐 can be expressed by a function of 𝑆𝑜𝐻:

𝐼𝑚𝑎𝑥𝑓𝑐 = 𝑓(𝑆𝑜𝐻)

Curve fitting for 80℃ ( the average)

𝐼𝑚𝑎𝑥𝑓𝑐 = −186 × 𝑆𝑜𝐻 + 189.5

Saturation of 𝐼𝑓𝑐

𝐼𝑚𝑎𝑥𝑓𝑐𝑠𝑎𝑡 = 𝐼𝑚𝑎𝑥𝑓𝑐 × 80%

[2] M. Bressel, M. Hilairet, D. Hissel, B. Ould-Bouamama, Remaining Useful Life Prediction and

Uncertainty Quantification of Proton Exchange Membrane Fuel Cell Under Variable Load, IEEE

Transactions on Industrial Electronics, Vol. 63-4, 19 janvier 2016, pp. 2569-2577 21/30

5. Simulation and Hardware In the Loop results

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Operation modes

Modes of SCs: mode = 0: no limitation of SCs in charging or discharging mode = 1: limitation of SCs discharging when the SCs voltage is low mode = 4: limitation of SCs charging when the SCs voltage is high + energy dissipation mode = 5: saturation at −𝑖𝑠𝑐𝑚𝑎𝑥

+ energy dissipation

mode = 6: saturation at 𝑖𝑠𝑐𝑚𝑎𝑥

Bonus: mode = 2: acceleration of SCs charging when the SCs voltage is low to increase the convergence

of 𝑣𝑏 to 𝑣𝑏∗

mode = 3: acceleration of SCs discharging when the SCs voltage is high to increase theconvergence of 𝑣𝑏 to 𝑣𝑏

∗

Modes of FC: mode = 0: no saturation mode = 7: saturation at 𝑖𝑓𝑐𝑚𝑎𝑥

mode = 8: saturation at 𝑖𝑓𝑐𝑚𝑖𝑛0 + energy dissipation

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Simulation

Simulation with accelerated FC aging

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Hardware In the Loop

Hardware In the Loop scheme

dSPACE boardSimulation of hybrid system (ds1006 board) and communication with the controller (ds5203 board)

DE1_SoC ALTERA boardImplementation of the controller and EKF algorithms3 PWMs, 6 data decoder, 1 NIOS II microcontroller

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Hardware In the Loop

Hardware In the Loop results

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6. Conclusion and future works

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Conclusion

Energy management control using IDA-PBC (Interconnection and Damping

Assignment Passivity Based Control)

An aging aware control [2] of the fuel cell realized by an Extended Kalman Filter

(EKF);

A dissipative load in order to avoid over-voltage of the DC bus;

A dynamic saturation of SCs current that considers the SoC;

A dynamic saturation of the FC current to protect the system from instability;

Integration of some component constraints in the controller equations;

The stability in saturated mode;

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Energy management for complete system (Once the battery is integrated, a large

proportion of theoretical work will be done.)

Element Done Doing To do

Fuel cell ✓

Super-capatitors ✓

Battery ✓

PV ✓

Electrolyser ✓

Wind turbine ✓

Optimization algorithms for IT and electrical planes

Control of micro grid

Power Hardware in the Loop (PHIL)

Future works

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Thank you for your attention

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