Simulation of Power System Dynamics and Transient Stabilization Using Flywheel Energy 

Storage Systems

Kevin Bachovchinkbachovc@andrew.cmu.edu

10th CMU Electricity ConferencePre-conference Workshop

March 30, 2015

Joint work withProf. Marija Ilic

milic@ece.cmu.edu

Outline

Introduce and motivate flywheelsMethods for modeling power system dynamics and designing 

control using flywheels   Model nonlinear power system dynamics using the Lagrangian

formulation Variable speed drive controller for flywheels using time‐scale 

separation and nonlinear passivity‐based control logic Transient stabilization of interconnected power systems using 

flywheels

Smart Grid in a Room Simulator (SGRS) Implementation of simulating power system dynamics in a distributed 

manner Show demo of flywheel controller

2

Motivation for Flywheels

Transactive energy control does not guarantee dynamic stability Instabilities can happen on a fast time‐scale

Interest in implementing more wind power (and other renewable energy sources) into future power grids

Wind power is difficult to predict and control Large sudden deviations in wind power can cause  high deviations in frequency and voltage transient instabilities

One possible solution is to add fast energy storage, such as flywheel energy storage systems

3

Flywheel Energy Storage System

Stores mechanical energy by accelerating a rotor to a very high speed

Not appropriate for large scale applications Low energy capacity

Many advantages for small‐scale transient applications Very efficient Small time constants Not limited to a certain number of charge‐

discharge cycles

4

Objective

5

P

PP

P

Use flywheels for transient stabilization of power grids in response to large sudden wind disturbances 

Design nonlinear power electronic control so that the flywheel absorbs the disturbance and the rest of the system is minimally affected

Modeling of Power System Dynamics

To design and test control for flywheels, it is necessary to first derive the dynamic model for the interconnected power system

Large interconnected power systems contain many coupled electrical and mechanical components

Conventional modeling of dynamics: Electrical systems: Kirchhoff’s voltage and current law equations  Mechanical systems: Conservation of force Difficulty is determining the effect of subsystems on each other for 

mixed energy systems 

6Source: H. H. Woodson, J. R. Melcher, “Electromechanical Dynamics, Part I: Discrete Systems,” New York: Wiley, 1968.

Lagrangian Formulation

7Source: D. Jeltsema, J.M.A. Scherpen, "Multidomain modeling of nonlinear networks and systems," IEEE Control Systems, vol.29, no.4, pp.28-59, Aug. 2009

Therefore, for mixed energy systems, often advantageous to derive the dynamics using the Lagrangian formulation from classical mechanics Reformulation of Newtonian mechanics

Newtonian mechanics: model in terms of forcesLagrangian mechanics:  model in terms of kinetic energy and 

potential energy of the system Can be applied to other types of systems, such as electric systems, as 

well as to mixed energy systems

Motivation for the Lagrangian Formulation

Unified framework for the analyzing systems with multiple types of energy

Passivity‐based control Choose closed‐loop energy functions Need to derive error dynamics from those closed‐loop energy functions 

in order to derive the control law 8

Displacement Qgen

FlowFgen

LagrangianL

Rayleigh dissipationR

Forcing FunctionF

Mechanical(Rotational)

θ ω F

Electrical V

Electro-mechanical

θ, ω, F,V

2mech

12

BR

elec mech R R R

212elec RiR

elec mech L L L

Example Using Lagrangian Formulation

9

2 2 2 21 1 1 12 2 2 2

cos cos 2 / 3 cos 2 / 3

elec R R S Sa S Sb S Sc SS Sa Sb SS Sa Sc SS Sb Sc

Sa R Sb R Sc R

L i L i L i L i L i i L i i L i i

M i i M i i M i i

L 212mech JL

2 2 2 21 1 1 12 2 2 2elec R R S Sa S Sb S ScR i R i R i R i R

212mech BR

elec R Sa Sb Scv v v vF mmech F

( ) 0( ) ( ) ( )gen gen gen

d kdt k k k

F Q FRL L

F

Compute dynamic equations using the Lagrangian equations:

Electrical Subsystem: Mechanical Subsystem:

Source: R. Ortega, A. Loria, P. Nicklasson, H. Sira-Ramirez, Passivity-based Control of Euler-Lagrange Systems: Mechanical, Electrical and Electromechanical Applications, Springer Verlag, New York 1998.

Automated Modeling of Power System Dynamics

10

Implemented an automated procedure for symbolically deriving the dynamic equations using the Lagrangianformulation User specifies the power system topology Code symbolically solves for the energies of the system Code computes dynamic equations by evaluating the Lagrangian

equations and re‐expresses in standard state space form

( , )x ux f

Source: K. D. Bachovchin, M. D. Ilić, "Automated Modeling of Power System Dynamics Using the Lagrangian Formulation," International Transactions on Electrical Energy Systems [to appear, 2014]

0( 0 ) x xPower System

Topology ,L FR,

Variable Speed Drives for Flywheels

11

Use AC/DC/AC converter to regulate the speed of the flywheel (and hence the energy stored) to a different frequency than the grid frequency

Controllable inputs are the duty ratios of the switch positions in the power electronics

Source: K. D. Bachovchin, M. D. Ilic, "Transient Stabilization of Power Grids Using Passivity-Based Control with Flywheel Energy Storage Systems," IEEE Power & Energy Society General Meeting, Denver, USA, July 2015..

Controller Implementation

12

Time‐scale separation to simplify the control design

Regulate both the flywheel speed and the currents into the power electronics using passivity‐based control

Source: K. D. Bachovchin, M. D. Ilic, "Transient Stabilization of Power Grids Using Passivity-Based Control with Flywheel Energy Storage Systems," IEEE Power & Energy Society General Meeting, Denver, USA, July 2015..

Nonlinear Passivity‐Based Control

Nonlinear control method Exploits the intrinsic energy properties of the system dynamics Robust due to the avoidance of exact cancellation of 

nonlinearities Relies on Lyapunov stability argument For a dynamic system  , if there exists a Lyapunov function 

such that is positive definite

0 0 and  0∀ 0 is negative definite

0 0 and  0∀ 0then  0 is an asymptotically stable equilibrium

13Source: R. Ortega, A. Loria, P. Nicklasson, H. Sira-Ramirez, Passivity-based Control of Euler-Lagrange Systems: Mechanical, Electrical and Electromechanical Applications, Springer Verlag, New York 1998.

Automated Passivity‐Based Control Law Derivation

14

( , )x ux f

( , , )Dnx x r 1u g

( , , )Dn Dnx x r 2x g

State space model:

Closed-loop energy functions: ' ,m eW Wx x

Closed-loop dissipation function: x R

Set point equations: ( )Dr x f r

where D x x x

'm eV W W x x x

dV dV ddt d dt

x x x

x

Lyapunov function:

If

Passivity-BasedControl Law:

can derive control law in an automated manner

Source: K. D. Bachovchin, M. D. Ilić, "Automated Passivity-Based Control Law Derivation for Electrical Euler-Lagrange Systems and Demonstration on Three-Phase AC/DC/AC Converter," EESG Working Paper No. R-WP-5-2014, August 2014.

is negative definite

is positive definite

Then 0, D x x x

Non-directly controlled desired state variable dynamics must be stable for control to be physically realizable.

Power Electronics Passivity‐Based Control

15Source: K. D. Bachovchin, M. D. Ilić, "Automated Passivity-Based Control Law Derivation for Electrical Euler-Lagrange Systems and Demonstration on Three-Phase AC/DC/AC Converter," EESG Working Paper No. R-WP-5-2014, August 2014.

211

2C

eqWC

*1 1

Dd di i

*1 1

Dq qi i

Closed-loop energy functions:

Closed-loop dissipation function:

Set Point Equations:

Lyapunov function:Positive definite function

Negative definite function

1 1 1

1 1

,pe pe pe pe

Tpe d q C

T

pe d q

x u

i i q

u u

x f

x

u

2 2 21 1 1 1 1

1 12 2d q C RR i i R i R

2 21 1 1

1'2m d qW L i i

2

2 2 11 1 1

1

1 1'2 2

Cm e d q

qV W W L i iC

2

2 2 11 1 1 2

1 1

Cd q

C

qdV dV R i id dt C R

x

x

Dynamic Model: (Power electronic

time-scale)

Passivity‐Based Control for Power Electronics Controller

16Source: K. D. Bachovchin, M. D. Ilić, "Automated Passivity-Based Control Law Derivation for Electrical Euler-Lagrange Systems and Demonstration on Three-Phase AC/DC/AC Converter," EESG Working Paper No. R-WP-5-2014, August 2014.

Automated Control Law:

A stable equilibrium for  D only exists when

2 2

1 1 1 1 1 1 1 1 2 2 2 2

power output of power electronicspower input to power electronics

ref ref ref ref ref refd d q q d q S d d S q qV i V i R i R i v i v i

1 1 1 1 1 1 1 1 11

1

2 ref refd d q

d DC

C V C R i C L iu

q

1 1 1 1 1 1 1 1 1

11

2 ref refq q d

q DC

C V C R i C L iu

q

2 2

1 1 1 1 1 1 1 1 1 2 2 2 21

ref ref ref ref ref refD Dd d q q d q S d d S q q

C CD

C C

C V i V i R i R i v i v idq qdt q CR

Transient Stabilization Using Flywheels

17

P

P

Want to choose set points so that the wind disturbance power goes to the flywheel and rest of the system is minimally affected

P

P

Simulation Results: Flywheel

18

0 0.2 0.4 0.6 0.81230

1240

1250

1260

1270

1280

1290

time(sec)

angu

lar v

eloc

ity(ra

d/se

c)

Flywheel Speed

ref

Since the power output of the wind generator decreases during the disturbance, the flywheel set point decreases

0 0.2 0.4 0.6 0.80.23

0.235

0.24

0.245

0.25

0.255

0.26Wind Generator Mechanical Torque

time(sec)

torq

ue(N

*m)

Simulation Results: Power Electronics

19

The set points for the power electronic currents are chosen so that the total current out of Bus 2 remains constant during the disturbance

0 0.2 0.4 0.6 0.81.6

1.8

2

2.2

2.4

curre

nt(A

)

Power Electronic and Wind Currents

i1d+iSdW

0 0.2 0.4 0.6 0.819.98

19.99

20

20.01

20.02

t(sec)

curre

nt(A

)

i1q+iSqW

0 0.2 0.4 0.6 0.8-254

-253

-252

-251

curre

nt(A

)

Power Electronic Currents

0 0.2 0.4 0.6 0.833

34

35

36

37

t(sec)

curre

nt(A

)

i1d

i1dref

i1q

i1qref

Simulation Results: Rest of System

20

With the control, the effect on the rest of the system is very minimal and lasts only a short time

0 0.2 0.4 0.6 0.80.064

0.065

0.066Bus 1 Voltage: Direct Component

volta

ge(V

)

Vd (Control)

Vd (No Control)

0 0.2 0.4 0.6 0.81.99

1.995

2Bus 1 Voltage: Quadrature Component

t(sec)

volta

ge(V

)

Vq (Control)

Vq (No Control)

0 0.2 0.4 0.6 0.80.0725

0.073

0.0735

0.074

0.0745Bus 2 Voltage: Direct Component

volta

ge(V

)

Vd (Control)

Vd (No Control)

0 0.2 0.4 0.6 0.81.99

1.995

2

2.005Bus 2 Voltage: Quadrature Component

t(sec)

volta

ge(V

)

Vq (Control)

Vq (No Control)

SGRS: Modular Modeling of Open‐Loop Dynamics

Open‐loop dynamics of each object depend on State variables  Controllable inputs  Exogenous inputs  Port inputs 

, , ,k k k k k kx p u mx f

Source: K. D. Bachovchin, M. D. Ilić, "Automated and Distributed Modular Modeling of Large-Scale Power System Dynamics," EESG Working Paper No. R-WP-8-2014, October 2014

For the Smart Grid in a Room Simulator, a modular object‐oriented approach is used for modeling power system dynamics lends itself to distributed computing scalable for large systems

21

SGRS: Modular Modeling of Closed‐Loop Dynamics

Controllable inputs depend on State variables  Outputs of connecting modules  1

Internal set points  ref

1, , refk k k ck kx y yu g

22

1 1 2 2

1 1 1 2 2 2

1

2 1 1

T

k d q d qT

k d q C S d S q RT

ck d qTref ref ref ref

k d q

u u u u

i i q i i i

v v

i i

u

x

y

y Internal set points depend on

Outputs of connecting modules  2

Set points from market  ref

2 ,ref refk k cky ry h

Variable Speed Drive Controller:

2

T

ck Wd WqTref ref ref

Totd Totq

i i

i i

y

r

, , refk k k ckx y ru G

1 2T

ck ck cky y y

1

1

ref refd Totd Wd

ref refq Totq Wq

i i i

i i i

ExplicitEquations

Dynamics of the interconnected power system can be symbolically solved for in a distributed manner 

SGRS: Modeling of Interconnected Power System

( , , , )k k k k k kx p u mx f( , , , )i i i i i ix p u mx f 1 2( , , , , )j j j j j j jx p p u mx f

1 1 2( ), ( )i j j ip g y p g y

Bus 1 solves for Bus 2 solves for

Dynamics of each module depend only on its own state variables and the outputs of connecting modules

( , , , )k k k ck k kx y u mx F

1 2 2( ), ( )k j j kp h y p h y

23Source: K. D. Bachovchin, M. D. Ilić, "Automated and Distributed Modular Modeling of Large-Scale Power System Dynamics," EESG Working Paper No. R-WP-8-2014, October 2014

SGRS: Communication Structure for Distributed Simulation of Dynamics and Control

0ix

Initial Conditions

Compute for time step t

1n n

Take next iteration step

Processor A

0jx

Initial Conditions

Compute for time step t

1n n

Take next iteration step

Processor B

0kx

Initial Conditions

Compute for time step t

1n n

Take next iteration step

Processor C0iy

0jy

niy

njy

0ky

0jy

nky

njy

24

Conclusions Designed a novel variable speed drive for flywheels using three 

time‐scale separations and passivity‐based control logic Demonstrated the effectiveness of this controller in the SGRS for 

transiently stabilizing an interconnected power system against a wind generator disturbance

25

Future Work Larger power systems with multiple wind generator disturbances 

and multiple flywheelsMore general flywheel control logic for systems where the source 

of the disturbance is not known