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Simulation of Power System Dynamics and Transient Stabilization Using Flywheel Energy
Storage Systems
Kevin [email protected]
10th CMU Electricity ConferencePre-conference Workshop
March 30, 2015
Joint work withProf. Marija Ilic
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
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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
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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
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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
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( , )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
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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
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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
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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
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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
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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
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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
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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