NASA Technical Reports Server (NTRS) 20030016686: DC Bus Regulation with a Flywheel Energy Storage System

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by  NASA Technical Reports Server (NTRS)

NASA/TM—2002-211897/REV1 02PSC–61
DC Bus Regulation With a Flywheel Energy
Storage System
Barbara H. Kenny
Glenn Research Center, Cleveland, Ohio
Peter E. Kascak
University of Toledo, Toledo, Ohio
January 2003
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NASA/TM—2002-211897/REV1 02PSC–61
DC Bus Regulation With a Flywheel Energy
Storage System
Barbara H. Kenny
Glenn Research Center, Cleveland, Ohio
Peter E. Kascak
University of Toledo, Toledo, Ohio
Prepared for the
Power Systems Conference
sponsored by the Society of Automotive Engineers
Coral Springs, Florida, October 29–31, 2002
National Aeronautics and
Space Administration
Glenn Research Center
January 2003
Document Change History
This printing, numbered as NASA/TM—2002-211897/REV1, January 2003, replaces the previous version in its
entirety, NASA/TM—2002-211897, October 2002.
Page 9: Figures 23, 24, and 25 were modified
Page 10: Motor parameters were changed
Available from
NASA Center for Aerospace Information National Technical Information Service
7121 Standard Drive 5285 Port Royal Road
Hanover, MD 21076 Springfield, VA 22100
Available electronically at http://gltrs.grc.nasa.gov
DC Bus Regulation With a Flywheel Energy Storage System
Barbara H. Kenny
National Aeronautics and Space Administration
Glenn Research Center
Cleveland, Ohio 44135
Peter E. Kascak
University of Toledo
Toledo, Ohio 43606

ABSTRACT SYSTEM DESCRIPTION
This paper describes the DC bus regulation control Figure 1 shows a high level block diagram of a portion
algorithm for the NASA flywheel energy storage of a spacecraft power management and distribution
system during charge, charge reduction and discharge (PMAD) system. The solar arrays provide power to
modes of operation. The algorithm was experimentally the load and charging current to the flywheel during
verified in [1] and this paper presents the necessary insolation. The flywheel provides power to the load
models for simulation. Detailed block diagrams of the during eclipse. The three required modes of control
controller algorithm are given. It is shown that the and the corresponding current and voltage
flywheel system and the controller can be modeled in relationships are documented in Table 1.
three levels of detail depending on the type of analysis
required. The three models are explained and then The system is in charge mode as long as the solar
compared using simulation results. array is producing enough current to meet both the
charging current command, I*c h a r g e , and the required
INTRODUCTION load current, I . The system moves into charge
load
reduction mode when the load current demand plus
The NASA Glenn Research Center is presently the charging current command exceeds the capability
developing technologies in several areas to enable the of the solar array. In this mode, the flywheel is still
use of flywheels as energy storage devices on future charging (I is still positive), but with a current
flywheel
space systems. One of the key elements of a flywheel
less than the commanded charging current value.
energy storage system is the electric machine which

acts as a motor to store energy and acts as a I I
s/a load
generator when supplying energy to the loads. The sequential
solar array • load
machine must be properly controlled during all shunt unit
operating modes for the flywheel system to function
I
correctly. flywheel
flywheel
A new control algorithm which acts to regulate the system

operation of the flywheel electric machine in both
charge (motoring) and discharge (generating) modes Figure 1: Basic block diagram of spacecraft PMAD.
was described in [1]. The new algorithm mimics the
operation of a battery system by charging the flywheel Mode Current DC Bus Voltage
with constant current during charge mode and
Full Sun Is/a = Iload + I*c h a r g e Regulated by
regulating the DC bus voltage during discharge mode.
“Charge” solar array system
This paper continues the previous work by focusing on Iflywheel = Ic* h a r g e
simulation and analysis of the proposed algorithm Partial Sun Iload + I*c h a r g e > Is/a > Regulated by
which was demonstrated experimentally in [1]. Block “Charge flywheel system
Iload
diagrams are used to describe the algorithm in more Reduction”
I*c h a r g e > Iflywheel > 0
detail and to show how the overall system can be
modeled. Three levels of detail are modeled and Eclipse Iload = - Iflywheel Regulated by
compared ranging from the most simplistic, which “Discharge” Iflywheel < 0 flywheel system
assumes an ideal motor controller, to the complex,
which includes the inverter switching harmonics. Table 1: Flywheel system operating mode characteristics.
NASA/TM(cid:151)2002-211897/REV1 1
Finally, in discharge mode the solar array is providing Finally, the inverter current, i , is the control variable
inv
no current to the load and the flywheel current is that controls I in charge mode and V in
flywheel dc
negative. Note that these relationships are the same
discharge and charge reduction modes. However, the
as in a system with battery storage.
inverter current is not an independent variable; rather,
it is a result of the motor operation. The relationship
SYSTEM (PLANT) MODEL
between the motor and the inverter current will be
shown next.
A simple model of the electrical system is shown in
Figure 2. The capacitor, Cfilter, filters the inverter POWER RELATIONSHIPS
current and acts to stiffen the DC bus voltage. The
flywheel current, I , will be positive for charging The power into the inverter, P , is given by the
flywheel inv
and negative for discharging. The inverter current, i , product of the inverter current, i , and the DC bus
inv inv
can also be positive or negative. It will consist of a DC voltage as shown in (1). The power out of the inverter
component approximately equal to I and an AC is the electrical power to the motor, P . If the
flywheel elec
ripple component due to the high frequency switching inverter losses are neglected, the power into the
of the inverter that is approximately equal to i . inverter is equal to the motor power, P .
c elec
AAAAAAAAAAA
P = i V • P (1)
Is/a IflywheelAAiinAv AAAAAAAA inv inv dc elec
i
a
A+ AiAC AAAiAAAAA The mechanical shaft power of the motor is equal to
Is/a Iload Rload VAd-c ACfiAlter AInAvertAer iAbc AFlMyAwohtoeArel A the product of the torque and the mechanical speed as
AAAAAAAAAAA shown in (2).
Flywheel System
AAAAAAAAAAA
Pmech = τeωrmech (2)
Figure 2: Basic spacecraft electrical model.
The machine electrical power is equal to the
mechanical power plus or minus (motoring or
The corresponding block diagram model is shown in
generating, respectively) any losses. In the flywheel
Figure 3. The solar array current, I , is a variable
s/a application, the flywheel shaft is suspended on
input to the model. It acts as a voltage dependent
magnetic bearings and operated in a vacuum. Thus
current source during charge mode, a current source
the typical machine losses, friction and windage, are
during charge reduction mode and is equal to zero
essentially eliminated so the electrical power is
during discharge mode (eclipse operation). The exact
approximately equal to the mechanical shaft power as
characteristics of the I block are determined by the
s/a shown in (3). Additionally, eddy current and hysteresis
solar array controls of the particular spacecraft. losses are minimal in the permanent magnet machine
used in this application.
An additional input to the model that was not shown in
Figure 1 is idisturbance. This is the current that would Pinv = iinvVdc • Pelec • Pmech = τeωrmech (3)
result if a load is added to or removed from the
system. The additional load current, i , should The inverter current can then be expressed as a
disturbance
have a minimal effect on the DC bus voltage if the function of the motor torque, the shaft speed and the
voltage regulation is working properly. DC bus voltage as shown in (4).
iinv - _1_ _1_ Vdc i = τeωrmech (4)
• inv V
+ C s dc
i
flywheel Also, the speed of the machine is related to the torque
+ - _1_ and the inertia, J, as shown in equation (5). In this
i
s/a - RL application, the torque, τe, is used only to accelerate or
decelerate the machine; there is no external load
i torque.
disturbance
dω
Figure 3: Block diagram of basic spacecraft electrical model. rmech
τ = J (5)
e dt
NASA/TM(cid:151)2002-211897/REV1 2
Tfmohormedseaelt aeasqn udsa hctiooomwnsnb inaienrd e Fwiegitxuhpr reFe isg4su.er edT 3hi insto bbfolloorcmckk add siiaayggsrrteaammm iqrs _32__P2_λafτ•e _1J_ _1s_ωr•mechXPmech~1PinVv _•• iinv -+ _C1_ _1s_V•dc
expresses the basic relationship between the motor θ dc iflywheel
_1_ rmech
torque, the inverter current, and the dc bus voltage. s is/a + - _1_ •
- RL
τ
•e _1J_ _1s_ωr•mechXPmech~1Pelec~1Pinv _•• iinv -+ _C1_ _1s_V•dc idisturbance
V
_1_θrmech dc iflywheel FDiCgu breu s5 v: oSltyasgteem. block diagram (plant model) from motor current to
s is/a + - _1_ •
- RL Finally, the relationship between the motor current and
idisturbance the inverter current can be derived by substituting

equation (7) into (4) where ω, the electrical frequency,
r
equals the product of the number of pole pairs, P/2,
Figure 4: System block diagram from motor torque to DC bus
voltage. and ωrmech, the mechanical frequency. The result is
shown in equation (8).
MOTOR TORQUE CONTROL
2V
dc
ir = i (8)
From the previous discussion it can be seen that the qs inv3ωλ
r af
flywheel current (charge mode) or the DC bus voltage
(discharge and charge reduction modes) can be
CONTROLLER
controlled if the inverter current is controlled. It can
also be seen that the inverter current can be controlled
Given the basic plant model shown in Fig. 5 and the
if the motor torque is controlled. There are two basic
relationship between the inverter current and the motor
approaches to achieving accurate, high bandwidth
current shown in (8), the flywheel control algorithms
motor torque control described in the literature: field
will now be described. The basic procedure is as
orientation control (vector control) and direct torque
follows:
control. In the NASA effort we have focused on the
more established field orientation approach although
1. Calculate the commanded inverter current value,
direct torque control is a possibility for future research.
i *, to achieve the desired I in charge mode
inv flywheel
and the desired V in discharge and charge
In the field orientation technique, the measured dc
currents are transformed to d-q variables in a reduction modes.
synchronously rotating rotor reference frame [2].
Torque control is achieved by properly controlling the 2. Convert the commanded inverter current, iinv*, to a
resulting currents, iqr s and idr s. The expression for commanded motor current, iqr*s, using equation (8).
torque is given in (6) [2].
3. Regulate the motor current, ir , to the commanded
qs
τ = 3 P [ (L ir + λ ) ir - (L ir )ir ] (6) value, iqr*s, through a high bandwidth current
e 2 2 dds af qs qqs ds
regulator and the field orientation motor control
algorithm.
The d-axis current, ir , is generally commanded to
ds
zero which results in a linear relationship between the The available feedback variables are the dc bus
machine torque and current as shown in equation (7). voltage, V , the flywheel system current, I , the
dc flywheel
This relationship can also be added to the block motor speed, ω, the motor position, θ, and the motor
r r
diagram representation as shown in Figure 5.
currents. Note that in the steady state condition, when
the DC bus voltage is constant, i = 0 and i =
C inv
3P
τe = 2 2 λaf iqr s (7) Iflywheel.
NASA/TM(cid:151)2002-211897/REV1 3
CHARGE CONTROL DISCHARGE AND CHARGE REDUCTION CONTROL
The block diagram representation of the charge control The block diagram representation of the discharge
algorithm is shown in Figure 6. There are two and charge reduction control algorithm is shown in
components to the controller: the proportional integral Figure 7. There are two components to the controller:
(PI) and the feed-forward (FF). The respective outputs the proportional integral (PI) and the disturbance
are summed together to form the i* command. The decoupling (DD). In the PI portion, proportional and
inv
inverter current command is then converted to a motor integral gains, Kpd and Kid, act on the DC voltage error
current command through the relationship given in (8). (V* - V ) to create the i command. The
flywheel dc inv
negative gain is required in the PI control because the
_1s_ Kic inverter current is considered positive when it is
* entering the inverter (Fig. 2). This means that if the
Ich•arge+ • Kpc + + PI DC bus voltage is to increase, for example if (V*fl y w h e e l
-
FF + iinv* _2_V__d_c_ iqrs* - Vdc) is positive, then the inverter current must
^ actually be negative; it must come from the inverter to
+ 3ωrλaf
the load and the capacitor.
Vωdcr _1s_ Kid
Iflywheel Vf*lywheel + +PI+ iinv* _2_V__d_c_ iqrs*
Figure 6: Charge control block diagram. + - -1 • Kpd + 3ωrλ^af
Vdc IflywheelDD
The PI portion of the controller is a standard technique • Vωdc
r
to implement closed loop control. Proportional and
Iflywheel
integral gains, K and K , act on the DC current error
pc ic
(I*c h a r g e - Iflywheel) which results in the i *in v command. Figure 7: Discharge and charge reduction control block diagram.
One drawback to PI control acting alone is that the
system must wait for an error signal before a control When the system is operating in charge mode, the
adjustment is made. The larger the gains of the PI, the solar array system regulates the DC bus voltage. This
faster the response to the error becomes. However means that if there is a change in the load (idisturbance)
there is a limit on the gains; too large of gains will the solar array current, I , will increase or decrease
s/a
either lead to an unwanted system response to noise so as to cancel out the disturbance and keep the DC
or an unstable response. One technique that can be bus voltage at a constant value (see Fig. 3). However,
used to minimize the dependence on the PI controller when the system is operating in discharge or charge
is feedforward control. In feedforward control, the reduction mode, the solar array current will not be
necessary input signal, i *in v, is calculated which will adjusted to maintain the DC bus voltage. Instead, an
produce the desired output signal, I . The increase or decrease in load (i ) will cause an
flywheel disturbance
calculation is based on the value of the commanded increase or decrease in the flywheel current, I .
flywheel
signal, I*c h a r g e , and the plant model. From Figure 3, it The inverter current must compensate for this change
can be seen that in steady state conditions, if the if the DC bus voltage is to be maintained.
inverter current, i , equals the commanded current,
inv
I* , then the flywheel current will also equal the The PI controller will eventually respond to an
charge
additional load because an increase or decrease in the
commanded current because the capacitor current, i ,
C
flywheel current, I , will result in either a
is zero in steady state. This is the basis of the flywheel
decrease or an increase in the DC bus voltage
feedforward control.
respectively. However, in this system the effect of the
disturbance, I , is actually measured and fed
Using the PI controller with feedforward as shown in flywheel
Figure 6 results in an accurate and fast system back to the controller. This means that if a change in
response. The PI portion ensures the system Iflywheel occurs, a corresponding command to increase
converges to the set point while the feedforward or decrease the inverter current can easily be given
portion gives a fast response without high PI gains. immediately, without waiting for an increase or
decrease in the DC bus voltage. This is known as
disturbance decoupling control.
NASA/TM(cid:151)2002-211897/REV1 4
Using the PI controller with disturbance decoupling as VTC, as seen in Figure 8. Once this difference is less
shown in Figure 7 results in an accurate and fast than the VTC, the integrator in the PI portion of the
system response for the discharge and charge controller is reset. This reduces the i* command at
inv
reduction controller. The PI portion ensures the system point 2 to a value slightly larger than I . This
flywheel
converges to the set point while the disturbance
value is then compared to the charge current set point,
decoupling portion results in quick changes in
I* . If it is less than I* , which it will be if the
charge charge
commanded current in response to an increase or
solar array is not producing enough current, then the
decrease in load.
system transitions into charge reduction mode where
the DC bus voltage is regulated by the flywheel
COMBINED CHARGE/DISCHARGE CURRENT/
system.
VOLTAGE REGULATOR (CDCVR)
Similarly, as the system moves from eclipse into
The two controllers shown in Figs. 6 and 7 are
sunlight, the solar array will produce more and more
combined to form the overall Charge/Discharge
current. When the solar array produces enough
Current/Voltage Regulator (CDCVR) controller shown
current to meet the load demand, the i* command at
in Figure 8. The system is in charge mode (current inv
point 2 in the controller will become positive. When it
regulation) when the solar array provides enough
exceeds the charge current set point, I* , the
current to meet both the load demands and the charge
charging current to the flywheel system. Otherwise, integrator in the current regulator portion of the
the system is in charge reduction or discharge mode controller is reset and the system transitions back into
which means the flywheel system is regulating the DC charge mode where the flywheel system regulates the
voltage bus. current into the flywheel and the solar array system
regulates the DC bus voltage.
< VTC? yes It is worth noting that the three modes of operation:
rinetseegtr ator charge, charge reduction and discharge, were
• _1s_ Kid originally defined based on a battery energy storage
Vf*lywhee+l -1 • Kpd ++ PI+ iin•v* 2 scyasptaebmle. o f Trehgeu lafltyinwgh etheel DenCe rbguys vsotoltraaggee ats yasllt etimm esis,
- + DD
Vdc Iflywheel Iflywheel obviating the need for current and voltage regulation
•
nvool,t age • Vωdrc modes and the transition between them. This would
regulation2 result in an overall simpler control strategy, even when
- + > 0? iinv* _2_V__d_c_ iqrs* considering the necessary provisions to prevent over-
Ic*h•arge+ -• KicKpc _1s+_ + PIrinetseegtr ator ycreeugsrru,e lantti on1 3ωrλ^af swpilel ebde ionrv eosvteigr-actuerdr einn tf uotupreer aetfiofonr.t s .T his type of control
FF + + iinv* 1 OVERALL SYSTEM MODEL
The simplest end-to-end system model for the current
Figure 8: CDCVR control block diagram.
control (charge mode) and voltage control (charge
The transition from current regulation (Fig. 6) to reduction and discharge modes) are shown in
voltage regulation (Fig. 7) is accomplished in the Figures 9 and 10 respectively. These models
following manner. The solar array regulates the bus essentially assume a perfect motor controller and
voltage to a set point value higher than the flywheel current regulator and no losses in the motor or in the
regulation set point as long as the solar array current is inverter. The models can be made progressively more
sufficient to provide both the load and the charging accurate (and more complex) by adding more realistic
current, I* . Once the solar array current begins to transfer functions to the blocks that are initially
charge
approximated as ideal. The most important of these is
drop off, the DC bus voltage begins to fall and the
r
flywheel current, Iflywheel, also drops. This transition is iqs
the transfer function which will be discussed next.
detected in the controller by comparing the difference ir*
qs
between the actual DC bus voltage and the flywheel
set point voltage to the "voltage transition constant,"

NASA/TM(cid:151)2002-211897/REV1 5
_1_
s Kic
Ic*harge+ + + PI
• • Kpc
-
FF ++ iinv* _32_ωV_r_dλ^c_af_ iqrs* ~1iqrs _32__P2_λafτ•e _1J_ _1s_ωr•mechXPmech~1Pinv _•• iinv -+ _C1_ _1s_V•dc
Vdc ωr _P_ ωrmech • _1_θrmech Vdc iflywheel•
Iflywheel 2 s is/a + - _1_ •
- RL
idisturbance
Figure 9: Simplified end-to-end system block diagram for current regulation (charge mode).
_1s_ Kid
Vfl*ywheel+ - -1 • Kpd + +PI++ iinv* _32_ωV_r_dλ^c_af_ iqrs* ~1iqrs _32__P2_λafτ•e _1J_ _1s_ωr•mechXPmech~1Pinv _•• iinv -+ _C1_ _1s_V•dc
Vdc Iflywheel DD Vdc ωr _P_ ωrmech • _1_θrmech Vdc iflywheel•
2 s is/a + - _1_ •
- RL
idisturbance
• •
Figure 10: Simplified end-to-end system block diagram for voltage regulation (charge reduction and discharge modes).

MOTOR CURRENT TRANSFER FUNCTION _1s_ Ki
A more accurate representation of the transfer function iqrs* + Kp + +Vrq*s
-
between the commanded current, iqr*s , and the actual iqrs
current, iqrs , requires three additional components: the _1s_ Ki
current regulator, the inverter PWM, and the motor idrs* + + +Vdr*s
model. This section addresses these three pieces. Kp
r -
ids

Current Regulator
Figure 11: Synchronous frame current regulator for motor currents.
The charge and discharge/charge reduction algorithms
result in a motor q-axis current command as can be Inverter PWM
seen from Figs. 6, 7 and 8. To achieve this current, a
current regulator must be used. A synchronous frame The output of the current regulator is rotor reference
current regulator is a common choice in motor drive r* r*
frame voltage commands, v and v . These are
application [3]. The basic form is a PI control on each qs ds
converted to stationary reference frame commands,
of the two currents, ir and ir , as shown in Figure 11.
qs ds s* s*
v and v , through the transformation given in (9)
Each current regulator operates on DC quantities qs ds
because the control variables are in the rotor reference where θr is the rotor angle [4]. The stationary
frame. This means that the PI gains are independent reference frame commands are AC voltages that are
of the fundamental frequency of the actual motor synthesized from the DC bus voltage through a pulse
current and can be set for the desired torque response. width modulation (PWM) algorithm known as space

NASA/TM(cid:151)2002-211897/REV1 6