Modeling of Energy Power flow Dynamics for Control

Modeling of Energy/ Power flow Dynamics for Control in Multi-Physics Systems ©Marija Ilic ilic@mit. edu Exergy Analysis & Design for 21 st Century Aerospace Systems, Control, & Optimization AFRL-NASA-MIT Workshop Wright Bros. Innovation Institute April 17 -18, 2019 Based on joint work with Rupamathi Jaddivada, Ph. D student EECS MIT; summer internship at NETSS, Inc. ; protected by the provisional NETSS patent pending, 2018.

v. Motivation—Need v. Rate of mission matters- stable and efficient design/operation v. Overwhelming complexity v. Energy/power flow models for multi-physics systems v. Dynamics of exergy/anergy dynamics transparent v. Multi-layered modeling for complexity management/standards v. Formulation of near-optimal stable anergy management v. Examples of using it for model-based control design: • • • New DC motor control in energy/power flow space Hybrid electric aircraft model for making the case for fast storage control Proof of concept ---- stabilizing engine stall/surge by means of storage control

Need for modeling and control of aircraft dynamics v. Unconventional designs and challenging missions require modeling and control of dynamics for ensuring feasibility, stability and desired performance metrics v. There exist many non-unique control designs; closed-loop dynamics result in qualitatively different performance v. Aircraft electrification offers potential cooperative control within Te. DP (e. DP fast e. DP control/storage potentially effective for stable engine performance—no rotor stall/surge); diverse impact on aircraft design v. To explore these opportunities—view aircraft as a So. S comprising dynamic systems/subsystems

Aircraft performance using exergy/anergy concepts v. Game changer. . v. Unified modeling of interactions; common to all (types of) physical components [D. J. Moorhouse, Hayes] v. Mainly used to assess ``efficiency” ; to a lesser extent for assessing feasibility/stability and control design v. Unified modeling in Energy- Power flow (E-P) space § Captures both equilibria and dynamics of interactions § Helps establish stability conditions for component interactions § Can be used to formulate efficiency optimization in E-P space

MISSION RATE MATTERS: Example System: SGSM System v. Mission file [time (sec), Module. Name, New. Power (pu)]: § 30, MOT 1, -0. 02 § 150, MOT 1, -0. 1700 v. Large transient change of motor power from 20 k. W to 170 k. W [1] New Electricity Transmission Software Solutions (NETSS), Inc. , "Toward Autonomous Stable Energy Management of Hybrid Electric Aircraft Propulsion System, Phase I Final Report, " NASA Small Business Innovation Research (SBIR) report, Contract Number NNX 15 CC 89 P, December 16, 2015. [2] New Electricity Transmission Software Solutions (NETSS), Inc. , "Toward Autonomous Stable Energy Management of Hybrid Electric Aircraft Propulsion System, Phase II Final Report, " NASA Small Business Innovation Research (SBIR) report, Contract Number NNX 16 CC 06 C, to be completed in May 2018. [3] M. D Ilic, K. D. Bachovchin, S. Cvijic and J. H. Lang, “<Method for autonomous stable energy management of aircraft/ spacecraft Te. DP systems”, 5 Application Patent No. 62/578, 984, 10/30/2017

SAPSS Overview Mission requirements Framework to readily assemble, analyze, and simulate different topologies in a nearly “plug and play” manner for temporal progressions of set-points in response to the timevarying loading specifications while maintaining closed-loop stability around the moving set-points. [4] K. Bachovchin, R. Jaddivada and M. Ilic, "Centralized Automated Modeling of Power Systems (CAMPS) – a modular software for power system analysis, EESG Working Paper No. R-WP-7 -2017, " 2017. [5] M. Ilic and J. Lang, NETSSWorks software: An extended ac optimal power flow (AC XOPF) for managing available system resources, in AD 10 -12 Staff Technical Conference on Enhanced Power Flow Models Federal Energy Regulatory Commission, 2010.

1) Incremental Transiently Stable scheduling: 20 k. W->100 k. W->170 k. W

2) Possible Transient instability: 20 k. W->170 k. W

Complexity involved in monolithic modeling of detailed energy conversion processes Non-trivial modular modeling 9

Unifying energy-based modeling of dynamics— manage complexity v. Component level (module, S within the So. S) v. Interactive model of interconnected systems v. Model-based system engineering (MBSE)— --multi-layered complexity --component (modules) – designed by experts for common specifications (energy; power; rate of change of power) --interactions subject to conservation of instantaneous power and reactive power dynamics; optimization at system level in terms of these variables --physically intuitive models

Basic ideas underlying the energy-based dynamical models Inertia used as a proxy to rates at which energy can be generated Gen 1 …… Gen n Fast varying generation Electric Grid Synthetic inertia used instead – nonphysical Inverter controlled solar PV …… Heterogeneous end-end energy conversion processes modeling is becoming critical - inertia (or synthetic inertia) – based approximated system analysis no longer are valid Basis for energy as a state variable Controlled WHs Power conservation laws always hold at the interfaces of components and/or sub-systems. Basis for real power as an interface variable Slow varying demand Not all power produced can be delivered fundamentally due to mismatch in rates at which energy conversion processes of connected components take place – non thermal losses ought to be captured. Basis for reactive power as an interface variable

Port variables in conventional and energy space Characterization of three types of ports with corresponding port variables in conventional space: • Control Input port • Disturbance injection port • Port characterizing interactions with neighbors

Revisiting fundamentals: Basic element characterization for deriving new energy-space-based models Let the element be characterized by ordered pairs such that Then the stored energy in the element is given by: Instantaneous real power entering a sub-system Stored energy in tangent space is defined as Instantaneous reactive power entering a sub-system [1] The time constant is defined as Note: This quantity is related but is different from traditionally used reactive power Wyatt, J. L. and Ilic, M. , 1990, May. Time-domain reactive power concepts for nonlinear, nonsinusoidal or nonperiodic networks. In Circuits and Systems, 1990. , IEEE International Symposium on (pp. 387 -390). IEEE.

Toward energy-space based modeling

Proposed stand-alone interactive model in energy space Why P and Q have been chosen as interface variables? v. P over a time quantifies useful work done v. Q at any time quantifies the associated inefficiencies in power transfer v. Both of them obey conservation laws at the interfaces

Simple example of interaction model Mech. Mass spring example Stored energy in moving mass Stored energy in spring Energy in Tang. Space in mass Energy in Tang. Space in Spring

Reactive power as a candidate supply function to assessment of stability Condition can be utilized for control design to ensure feasible and stable equilibrium. If uncontrollable, or has reached its physical or control limits, groups can be created and controlled – basis for cooperative control

Reactive power as a candidate supply function to assessment of stability Sub-System I Component 1 Component n Component 2

Application of the dissipativity conditions Dictated by the line time constant

Reactive power characterizing inefficiency The higher the instantaneous reactive power is, the lower is the efficiency of the component

Generalized reactive power— closely related to anergy rate

Multi-layered interactive model Notice that the instantaneous reactive power carries the information of rate at which the energy gets converted in the connected components

Generalized interpretation of exergy and anergy dynamics ----Marija’s conjectures Anergy dynamics Exergy dynamics v. Used for ensure stable transitions v. Near-optimize system level performance through minimal coordination

Example of a DC motor armature and field control Control objective is to drive the time-varying load torque while maintaining close to nominal shaft speed

Specifications on the load to be served Real power to be served Reactive power to be served

Load and frequency tracking From 0 -300 s

Armature and field currents

Armature and field voltage Armature voltage 2. 4 Field voltage 0. 9 0. 8 2. 2 Voltage[pu] 0. 7 2 From 0 -300 s 1. 8 0. 6 0. 5 0. 4 0. 3 1. 6 1. 4 0. 2 0. 1 0 200 400 600 time[s] 800 1000

Instantaneous reactive power—anergy rate Zoomed-out view from 0 -1000 s Zoomed-in view from 100 -112 s

Unifying energy-based modeling approach TWO EXAMPLE ARCHITECTURES MODELED BY THE SAME APPROACH v Architecture 1: Conventional single-spool turbo-engine aircraft

Architecture 2: Turbo-electric distributed propulsion (Te. DP)

Multi-layered interactive dynamical model of a complete turbo engine with intra and inter-layer interactions 32

Architecture 2: Turbo-electric distributed propulsion (Te. DP)

New energy-based dynamic model of e. DP system

Usage of higher layer interactive models for energy-based dynamic model of Te. DP system

System-level convex problem with linear constraints

Component level control example: compressor • The control design will be such that the set points for instantaneous reactive power are exactly tracked. • During rotational stall, the system level control would dispatch e. DP reactive power set point higher than that of the engine reactive power setpoints, resulting in much lower value of shaft reactive power setpoint which can easily be tracked by hydraulic valves without the requirement of high gain controllers. • Notice also that the control is being designed to track reactive power which is a function of acceleration. Same statement can be put forward in battery control of e. DP as well

Near-optimal stable multi-layered interactive control Step 3: Given the mission requirements and predictions of exogenuous inputs, compute the real reactive power flows at each of the component interaces Step 2: Given the limits on control interfaces, compute the limits a t the aggregate engine/EDP interfaces Step 1: Knowing the present operating conditions and safe operating limits, compute the limits real and reactive power injections page 38

Near-optimal stable multi-layered interactive control Step 4: Given the schedules, compute the component specific optimal interactions page 39

Near-optimal stable multi-layered interactive control Step 4: Given the schedules, compute the component specific optimal interactions Step 5: Given the component specicfications, compute the internal control signal of the modules page 40

Near-optimal stable multi-layered interactive control page 41

Potential application to rotor stall control and surge v. Four scenarios --Scenario #1 –reproduce rotor stall and surge instabilities in open loop --Scenario #2 –demonstrate instabilities with conventional closedloop throttle control ---Scenario #3 –demonstrate potential of proposed control of engine throttle --Scenario #4 –demonstrate potential of proposed control of combined engine throttle and generator torque

Port variable characterization for the hybrid electric aircraft in conventional space Fuel injection Cold Air injection BURNER (b) Hot air COMPRESSOR (c) TURBINE (t) Compressed Air Engine (e) Generator (g) ~ Battery (b) Field excitation Pulse width modulation signals

Port variable characterization for the hybrid electric aircraft in energy space Fuel injection Cold Air injection BURNER (b) Hot air COMPRESSOR (c) TURBINE (t) Compressed Air Engine (e) Generator (g) ~ Battery (b) Field excitation Pulse width modulation signals

Rotor stall instability and its control -B=. 5, Moore-Greitzer model Scenario #1 (Open-loop) Annulus averaged flow settles but local flow is always fluctuating indicating rotating stall Scenario #2 (Bifurcation theory based throttle control) – Liaw, Abed Amplitude of rotating stall oscillations reduced. Linearized analysis and then gain tuning can be used to completely make the oscillations zero

Rotor stall instability and its control -B=. 5, More-Greitzer model Scenario #3 (Proposed throttle control) Notice the faster and quicker stabilization Scenario #4 (Proposed throttle and electric drive control) Notice the smoother response obtained by harnessing flexibility of electrical sub-system

Surge instability and its control -B=1. 0, Moore-Greitzer model Scenario #2 (Bifurcation theory based throttle control) – Liaw, Abed Notice the chattering phenomenon Scenario #4 (Proposed throttle and electric drive control) Notice the smoother response

Conclusions and open questions v. Possible to have unifying modeling framework for control design v. Interpretation in terms of exergy and energy (including thermal processes) v. Allows development for specifications in terms of common inputs and outputs across multi-physics components v. Optimization enables stable and efficient system-level performance; provable (convex optimization problem) v. Opportunities for nonlinear control of different technologies (differential flatness; sliding mode control; FBLC) v. Exciting questions: Data enabled control iterative co-design

References [1] Ilić, M. D. and Jaddivada, R. , 2018. Multi-layered interactive energy space modeling for nearoptimal electrification of terrestrial, shipboard and aircraft systems. Annual Reviews in Control. [2] Ilic, M. and Jaddivada, R. , 2018, September. Exergy/energy dynamics-based integrative modeling and control for difficult hybrid aircraft missions. In AIAA/IEEE Electric Aircraft Technologies Symposium (EATS), Aug 22 -24, 2019. (Abstract submitted) [3] Ilic, M. D. and Jaddivada, R. , 2018, December. Fundamental Modeling and Conditions for Realizable and Efficient Energy Systems. In 2018 IEEE Conference on Decision and Control (CDC) (pp. 5694 -5701). IEEE. [4] Ilic, M. D. and Jaddivada, R. , 2019. New Energy Space Modeling for Optimization and Control in Electric Energy Systems. In Modeling and Optimization: Theory and Applications Springer, Cham (To Appear). [5] Ilic, M. and Jaddivada, R. , Exergy/energy dynamics-based integrative modeling and control for difficult hybrid aircraft missions, Utility patent Application No. 62/730, 203, Filed on 9/12/2018