NASA/TM--2002-211897 02PSC-61

DC Bus Regulation

Storage System

Barbara H. Kenny

Glenn Research Center, Cleveland, Ohio

Peter E. Kascak

University of Toledo, Toledo, Ohio

With a Flywheel Energy

October 2002
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NASA/TM--2002-211897 02PSC-61

DC Bus Regulation

Storage System

Barbara H. Kenny

Glenn Research Center, Cleveland, Ohio

Peter E. Kascak

University of Toledo, Toledo, Ohio

With a Flywheel Energy

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

October 2002
This report is a preprint of a paper intended for presentation at a conference. Because

of changes that may be made before formal publication, this preprint is made

available with the understanding that it will not be cited or reproduced without the

permission of the author.

NASA Center for Aerospace Information

7121 Standard Drive

Hanover, MD 21076

Available from

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22100

Available electronically at _sa. _ov
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

This paper describes the DC bus regulation control

algorithm for the NASA flywheel energy storage system

during charge, charge reduction and discharge modes of

operation. The algorithm was experimentally verified with

results given in a previous paper. This paper presents

the necessary models for simulation with detailed block

diagrams of the controller. It is shown that the flywheel

system and the controller can be modeled in three levels

of detail depending on the type of analysis required. The

three models are explained and then compared using

simulation results.

INTRODUCTION

The NASA Glenn Research Center is presently

developing technologies in several areas to enable the

use of flywheels as energy storage devices on future

space systems. One of the key elements of a flywheel

energy storage system is the electric machine which acts

as a motor to store energy and acts as a generator when

supplying energy to the loads. The machine must be

properly controlled during all operating modes for the

flywheel system to function correctly.

A new control algorithm which acts to regulate the

operation of the flywheel electric machine in both charge

(motoring) and discharge (generating) modes was

described in [1]. The new algorithm mimics the operation

of a battery system by charging the flywheel with

constant current during charge mode and regulating the

DC bus voltage during discharge mode. This paper

continues the previous work by focusing on simulation

and analysis of the proposed algorithm which was

demonstrated experimentally in [1]. Block diagrams are

used to describe the algorithm in more detail and to

show how the overall system can be modeled. Three

levels of detail are modeled and compared ranging from

the most simplistic, which assumes an ideal motor

controller, to the complex, which includes the inverter

switching harmonics.

SYSTEM DESCRIPTION

Figure 1 shows a high level block diagram of a portion of

a spacecraft power management and distribution

(PMAD) system. The solar arrays provide power to the

load and charging current to the flywheel during

insolation. The flywheel provides power to the load

during eclipse. The three required modes of control and

the corresponding current and voltage relationships are

documented in table 1.

The system is in charge mode as long as the solar array

is producing enough current to meet both the charging

current command, Icharge, and the required load current,

Iload. The system moves into charge reduction mode

when the load current demand plus the charging current

command exceeds the capability of the solar array. In

this mode, the flywheel is still charging (IflywheeI is still

positive), but with a current less than the commanded

charging current value. Finally, in discharge mode the

solar

I , , Is/a Iload ,

_rr_,[_4b.lsequential _ _ ^_.4

.... "1 -Ishuntunitl 1| I 'u'=u I

/1Iflywheel

_y_henel t J"

Figure 1: Basic block diagramof spacecraftPMAD.

Mode Current DC Bus Voltage

Full Sun Is/a= Iload + Icharge Regulated by

"Charge" iflywheeI = icharge solar array system

Regulated by

flywheel system

Partial Sun

"Charge

Reduction"

Eclipse

"Discharge"

Iload + Icharge > Is/a>

Iload

Icharge > IflywheeI > 0

Iload = - IflywheeI

IflywheeI < 0

Regulated by

flywheel system

Table 1: Flywheelsystem operating modecharacteristics.

NASA/TM--2002-211897 1
solar array is providing no current to the load and the

flywheel current is negative. Note that these relationships

are the same as in a system with battery storage.

SYSTEM (PLANT) MODEL

A simple model of the electrical system is shown in f

igure 2. The capacitor, Cfilter , filters the inverter current

and acts to stiffen the DC bus voltage. The flywheel

current, Iflywheel, will be positive for charging and

negative for discharging. The inverter current, iinv, can

also be positive or negative. It will consist of a DC

component approximately equal to IflywheeI and an

AC ripple component due to the high frequency switching

of the inverter that is approximately equal to ic.

r ........................................................

Is/a If ywhee iin v i

+ ic i

Is/a(_ Iload,.L_ Vdc _ I Inverter I_lywhee_l i

T_ Rl°ad - ,_fi,ter I

.............. F,. whee!..S ste . ............... !

Figure 2: Basic spacecraft electrical model.

The corresponding block diagram model is shown in

Figure 3. The solar array current, Is/a, is a variable input

to the model. It acts as a voltage dependent current

source during charge mode, a current source during

charge reduction mode and is equal to zero during

discharge mode (eclipse operation). The exact

characteristics of the Is/a block are determined by the

solar array controls of the particular spacecraft.

An additional input to the model that was not shown in

figure 1 is idisturbance. This is the current that would

result if a load is added to or removed from the system.

The additional load current, idisturbance, should have a

minimal effect on the DC bus voltage if the voltage

regulation is working properly.

lid,sturbancel

Figure 3: Block diagram of basic spacecraft electrical model.

Finally, the inverter current, iinv, is the control variable

that controls IflywheeI in charge mode and Vdc in

discharge and charge reduction modes. However, the

inverter current is not an independent variable; rather, it

is a result of the motor operation. The relationship

between the motor and the inverter current will be shown

next.

POWER RELATIONSHIPS

The power into the inverter, Pinv, is given by the product

of the inverter current, iinv, and the DC bus voltage as

shown in (1). The power out of the inverter is the

electrical power to the motor, Pelec. If the inverter losses

are neglected, the power into the inverter is equal to the

motor power, Pelec.

Pinv= iinvVdc = Pelec (1)

The mechanical shaft power of the motor is equal to the

product of the torque and the mechanical speed as

shown in (2).

Pmech = 1:eC0rmech (2)

The machine electrical power is equal to the mechanical

power plus or minus (motoring or generating,

respectively) any losses. In the flywheel application, the

flywheel shaft is suspended on magnetic bearings and

operated in a vacuum. Thus the typical machine losses,

friction and windage, are essentially eliminated so the

electrical power is approximately equal to the mechanical

shaft power as shown in (3). Additionally, eddy current

and hysteresis losses are minimal in the permanent

magnet machine used in this application.

Piny = iinvVdc = Pelec = Pmech = 1:eC0rmech (3)

The inverter current can then be expressed as a function

of the motor torque, the shaft speed and the DC bus

voltage as shown in (4).

l:eC0rmech

iinv - Vd c (4)

Also, the speed of the machine is related to the torque

and the inertia, J, as shown in equation (5). In this

application, the torque, %, is used only to accelerate or

decelerate the machine; there is no external load torque.

dcormech

1:e = J' dt (5)

These equations are expressed in block diagram format

and combined with Figure 3 to form a system model as

shown in Figure 4. This block diagram expresses the

basic relationship between the motor torque, the inverter

current, and the dc bus voltage.

Figure 4: System block diagram from motor torque to DC bus voltage.

NASA/TM--2002-211897 2
MOTOR TORQUECONTROL

From the previous discussion it can be seen that the

flywheel current (charge mode) or the DC bus voltage

(discharge and charge reduction modes) can be

controlled if the inverter current is controlled. It can also

be seen that the inverter current can be controlled if

the motor torque is controlled. There are two basic

approaches to achieving accurate, high bandwidth motor

torque control described in the literature: field orientation

control (vector control) and direct torque control. In the

NASA effort we have focused on the more established

field orientation approach although direct torque control

is a possibility for future research.

In the field orientation technique, the measured currents

are transformed to d-q variables in a synchronously

rotating rotor reference frame [2]. Torque control is

achieved by properly controlling the resulting currents, ices

and ices. The expression for torque is given in (6) [2].

3P

1:e = _"_" [ (Ldic_s+Xaf)ices-(Lqic_s)ic_s] (6)

current shown in (8), the flywheel control algorithms will

now be described. The basic procedure is as follows:

1, Calculate the commanded inverter current value,

iinv*, to achieve the desired IflywheeI in charge mode

and the desired Vdc in discharge and charge

reduction modes.

2. Convert the commanded inverter current, iinv*, to a

commanded motor current, ir* using equation (8).

qs,

3, Regulate the motor current, i r to the commanded qs,

value, ir* through a high bandwidth current regulator qs,

and the field orientation motor control algorithm.

The available feedback variables are the dc bus voltage,

Vdc, the flywheel system current, Iflywheel, the motor

speed, _, the motor position, Or, and the motor currents.

Note that in the steady state condition, when the DC bus

voltage is constant, iC = 0 and iinv = IflywheeI.

CHARGE CONTROL

The d-axis current, ices,is generally commanded to zero

which results in a linear relationship between the

machine torque and current as shown in equation (7).

This relationship can also be added to the block diagram

representation as shown in Figure 5.

3P

1:e = 22 Xaf ices (7)

Figure 5: System block diagram (plant model) from motor current to

DC bus voltage.

The block diagram representation of the charge control

algorithm is shown in Figure 6. There are two

components to the controller: the proportional integral

(PI) and the feed-forward (FF). The respective outputs

are summed together to form the i inv command. The

inverter current command is then converted to a motor

current command through the relationship given in (8).

Icharge+ I

Iflywheel

Figure 6: Charge control block diagram.

Finally, the relationship between the motor current and

the inverter current can be derived by substituting

equation (7) into (4) where e_, the electrical frequency,

equals the product of the number of pole pairs, P/2, and

(£rmech, the mechanical frequency. The result is shown

in equation (8).

2Vdc

ices= iinv 3(@Laf (8)

CONTROLLER

Given the basic plant model shown in figure 5 and the

relationship between the inverter current and the motor

NASA/TM--2002-211897

The PI portion of the controller is a standard technique to

implement closed loop control. Proportional and integral

gains, Kpc and Kic, act on the DC current error

(Icharge - Iflywheel) which results in the i inv command.

One drawback to PI control acting alone is that the

system must wait for an error signal before a control

adjustment is made. The larger the gains of the PI, the

faster the response to the error becomes. However

there is a limit on the gains; too large of gains will either

lead to an unwanted system response to noise or an

unstable response. One technique that can be used to

minimize the dependence on the PI controller is

feedforward control. In feedforward control, the

necessary input signal, i inv, is calculated which will

produce the desired output signal, IflywheeI. The
calculationis basedonthe valueof thecommanded

signal,Icharge,andtheplantmodel.Fromfigure3,itcan

beseenthatin steadystateconditions,if the inverter

current,iinv,equalsthecommandedcurrent,Icharge, then

the flywheelcurrentwill also equalthe commanded

currentbecausethe capacitorcurrent,ic, is zeroin

steadystate.Thisisthebasisofthefeedforwardcontrol.

Usingthe PI controllerwithfeedforwardas shownin

Figure6 results in an accurateand fast system

response.ThePIportionensuresthesystemconverges

tothesetpointwhilethefeedforwardportiongivesafast

responsewithouthighPIgains.

DISCHARGEANDCHARGEREDUCTIONCONTROL

Theblockdiagramrepresentationofthedischargeand

chargereductioncontrolalgorithmisshowninfigure7.

Thereare two componentsto the controller:the

proportional integral(PI)andthedisturbancedecoupling

(DD).In thePIportion,proportionalndintegralgains,

KpdandKid,actontheDCvoltageerror (V_lywhee I - Vdc )

to create the iinv command. The negative gain is required

in the PI control because the inverter current is

considered positive when it is entering the inverter (fig.

2). This means that if the DC bus voltage is to increase,

for example if (V_lywhee I - Vdc ) is positive, then the

inverter current must actually be negative; it must come

from the inverter to the load and the capacitor.

irs_& 

vdc f heeO

Iflywheel

Figure 7: Discharge and charge reduction control block diagram.

When the system is operating in charge mode, the solar

array system regulates the DC bus voltage. This means

that if there is a change in the load (idisturbance) the solar

array current, Is/a, will increase or decrease so as to

cancel out the disturbance and keep the DC bus voltage

at a constant value (see fig. 3). However, when the

system is operating in discharge or charge reduction

mode, the solar array current will not be adjusted to

maintain the DC bus voltage . Instead, an increase or

decrease in load (idisturbance) will cause an increase or

decrease in the flywheel current, IflywheeI. The inverter

current must compensate for this change if the DC bus

voltage is to be maintained.

The PI controller will eventually respond to an additional

load because an increase or decrease in the flywheel

current, Iflywheel, will result in either a decrease or an

increase in the DC bus voltage respectively. However, in

this system the effect of the disturbance, Iflywheel, is

NASA/TM--2002-211897

actually measured and fed back to the controller. This

means that if a change in IflywheeI occurs, a

corresponding command to increase or decrease the

inverter current can easily be given immediately, without

waiting for an increase or decrease in the DC bus

voltage. This is known as disturbance decoupling control.

Using the PI controller with disturbance decoupling as

shown in figure 7 results in an accurate and fast system

response for the discharge and charge reduction

controller. The PI portion ensures the system converges

to the set point while the disturbance decoupling portion

results in quick changes in commanded current in

response to an increase or decrease in load.

COMBINED CHARGE/DISCHARGE

CURRENTNOLTAGE REGULATOR (CDCVR)

The two controllers shown in figs. 6 and 7 are combined

to form the overall Charge/Discharge CurrentNoltage

Regulator (CDCVR) controller shown in figure 8. The

system is in charge mode (current regulation) when the

solar array provides enough current to meet both the

load demands and the charging current to the flywheel

system. Otherwise, the system is in charge reduction or

discharge mode which means the flywheel system is

regulating the DC voltage bus.

reset

+ + +

, (o r

I I I"_'[_"_'_'___!eue£S_2t i(n"_"

Ic_ current

[ FF +_

Figure 8: CDCVR control block diagram.

The transition from current regulation (fig. 6) to voltage

regulation (fig. 7) is accomplished in the following

manner. The solar array regulates the bus voltage to a

set point value higher than the flywheel regulation set

point as long as the solar array current is sufficient to

provide both the load and the charging current, Icharge.

Once the solar array current begins to drop off, the DC

bus voltage begins to fall and the flywheel current,

Iflywheel, also drops. This transition is detected in the

controller by comparing the difference between the

actual DC bus voltage and the flywheel set point voltage

to the "voltage transition constant", VTC, as seen in

figure 8. Once this difference is less than the VTC, the

integrator in the PI portion of the controller is reset. This

reduces the i inv command at point 2 to a value slightly
largerthanIflywhee I. Thisvalueisthencomparedto the

chargecurrentsetpoint,Icharge. Ifit islessthanIcharge,

whichit willbeifthesolararrayisnotproducingenough

current,thenthesystemtransitionsintochargereduction

modewherethe DCbusvoltageis regulatedby the

flywheel system•

Similarly,as the systemmovesfrom eclipse into

sunlight,the solararraywill producemoreandmore

current•Whenthesolararrayproducesenoughcurrent

tomeetheloaddemand,theiinvcommandatpoint2in

thecontrollerwillbecomepositive•Whenitexceedsthe

chargecurrentset point,Icharge, the integratorin the

currentregulatorportionofthecontrollerisresetandthe

systemtransitionsbackintochargemodewherethe

flywheelsystemregulatesthecurrentintotheflywheel

andthesolararraysystemregulatestheDCbusvoltage•

It is worthnotingthat thethreemodesof operation:

charge,chargereductionanddischarge,wereoriginally

definedbasedonabatteryenergystoragesystem•The

flywheelenergystoragesystemiscapableofregulating

theDCbusvoltageat alltimes,obviatingtheneedfor

currentandvoltageregulationmodesandthetransition

betweenthem.Thiswouldresultin an overallsimpler

controlstrategy,evenwhenconsideringthenecessary

provisionsto prevent over-speedor over-current

operation•Thistypeof controlwill be investigatedin

futureefforts•

OVERALL SYSTEM MODEL

The simplest end-to-end system model for the current

control (charge mode) and voltage control (charge

reduction and discharge modes) are shown in figures 9

and 10 respectively• These models essentially assume a

perfect motor controller and current regulator and no

losses in the motor or in the inverter• The models can be

made progressively more accurate (and more complex)

by adding more realistic transfer functions to the

blocks that are initially approximated as ideal• The most

.r

important of these is the Iqs transfer function which will

• r*

Iqs

be discussed next.

MOTOR CURRENT TRANSFER FUNCTION

A more accurate representation of the transfer function

• r*

between the commanded current, Iqs, and the actual

.r

current, Iqs, requires three additional components: the

current regulator, the inverter PWM, and the motor

model• This section addresses these three pieces•

Current Requlator

The charge and discharge/charge reduction algorithms

result in a motor q-axis current command as can be seen

from figs. 6, 7 and 8. To achieve this current, a current

regulator must be used. A synchronous frame current

regulator is a common choice in motor drive application

It

'%kg _"-L

Vdc

I Iflywheel

Vf,ywhe¢+(

Vdc_

 E Pmeoh Pin n i...... mm'

I-w- W-

' f COr F'_ C0_,.h I . rnerrnech vdcT iflywheeT

Figure 9: Simplified end-to-end system block diagram for current regulation (charge mode).

÷ + PI iinv* F _ i;( r_i)_si-_% e I-TL ITIcorm_ch_p n

_'_" .A t_I_l-ll'-p'l_-_'-/_-d_'l ....... i mechi._lrinw i'_l_ i; .... -__ I 1 I i'q-I',

Iflywheel DD Vdc" T C°r IP--'I--_ EOrm_r.h _hl_ 1[--lermech_lff _

Figure 10: Simplifiedend-to-endsystem block diagramfor voltage regulation(chargereductionand discharge modes)•

NASA/TM--2002-211897 5
[3]. The basic form is a PI control on each of the two

currents, icesand ices,as shown in figure 11. Each current

regulator operates on DC quantities because the control

variables are in the rotor reference frame. This means

that the PI gains are independent of the fundamental

frequency of the actual motor current and can be set for

the desired torque response.

iqs* ¢O__+ rvq..__

i_s. ¢ r_

i&t -

Figure 11: Synchronousframe current regulatorfor motor currents.

Inverter PWM

The output of the current regulator is rotor reference

r* *

frame voltage commands, Vqs and Vc_s. These are

S*

converted to stationary reference frame commands, Vqs

and vc%, through the transformation given in (9) where Or

is the rotor angle [4]. The stationary reference frame

commands are AC voltages that are synthesized from

the DC bus voltage through a pulse width modulation

(PWM) algorithm known as space vector modulation

(SVM). The SVM algorithm calculates the necessary duty

cycles for each switch to synthesize the required AC

voltage from the available DC bus. Equations (10), (11)

and (12) give the method used to calculate the duty

cycles for the "high" side switches of the inverter [5]. The

"low" side switch duty cycles are the inverse of the high

side ones.

, r •

EVI*] -cosO r sin Or ]rVq]

LvsU = _-sin Or cos odLv U (9)

[1- 1 = Fv;]

vc { ]Rv s, (10)

For simulation purposes, there are several ways to

model this block. The simplest technique is to neglect

the PWM harmonics altogether which means that the

voltage applied to the machine is exactly equal to the

voltage commanded by the current regulator. This is a

good model for an initial evaluation of the control

methodology because it executes quickly and the results

give a good indication of the expected performance.

S* *

Another technique is to calculate Vqs and vc% using the

duty cycles given in (11), the DC bus voltage and the

PWM switching frequency. The resulting voltages are a

series of pulses from the DC bus that are applied to the

machine. This simulation is quite a bit slower because

each PWM pulse is calculated but the effect of the

switching harmonics on the system current and voltage

can be studied.

Finally, the switches and diodes that form the inverter

could be explicitly simulated with their respective

characteristics (for example, turn-on time, on-state

resistance, reverse recovery, etc.) and characteristics

such as switching and conduction losses could be

studied. However, this would have the longest execution

time of the three types of models. In this paper, only the

first two methods to model the inverter are considered.

Motor Model

The motor model is based on the differential equations

governing the performance of the PM machine as given

in [2]. A block diagram of the electrical portion of the

motor model is shown in Figure 12.

meon

Figure 12:Block diagramof PM motor.

Ida]Va] - V O

dFo = ,,I-_- [vFo- V 0

dc Vdc LvC -vo

4- il (11)

max(va, vl_, vc) + min(va, v_, vc)

Vo - 2 (12)

COMPLETE SYSTEM MODEL

The entire system model, with the current regulator,

inverter and motor, is shown in figure 13. Three models

can be derived from figure 13 depending on which blocks

are used. The simplest version, referred to in the

simulation results section as the "simple model", does

not include the middle three blocks and was given in

figure 9 for charge and fig. 10 for discharge. This model

NASA/TM--2002-211897 6
Vdc

I£ha._

Ifly_

Vd(

leel

• r*

3 _1_1 Current v_il£.l Inv

/I Regulator: _w'-I M(

.__11 FiN11and I,,s*l "In\

_' ds

, .r* transform _._1 P_'

i =0 eqn.(9) I- _Parapara

_f9 _4r_l' iqs '

,,rte'_--Ir @ " Flywh

dr_r erter ['_s _'_ e I _

,, v bus mc /M s

i_eph _1__1 b U_ig_

- T Ir T

Figure 13: Overall system model.

_heel

neglects the electrical dynamics of the motor control and

assumes perfect current regulation. The "simple model"

is suitable for initial large system simulations of the

flywheel with the rest of the spacecraft PMAD.

The next level of fidelity includes all of the blocks of

figure 13 except for the center inverter one. This model

neglects the inverter losses and PWM switching

harmonics. This is suitable to study the overall

effectiveness of the PM motor control and different

current regulators on the system performance. This

model is referred to as the "motor model" in the

simulation section.

Finally, all five blocks can be included in the simulation

so the effects of the switching harmonics can be seen.

This simulation takes four to five times longer to execute

than the previous ones so is best used when issues

specifically related to switching harmonics are studied. It

is referred to as the "PWM model" in the simulation

section.

SIMULATION RESULTS

There are three groups of gain parameters to set in the

controller algorithm: the charge mode PI, the discharge

mode PI (voltage regulation) and the motor current

regulator PI. In addition, one estimated motor

parameter, ;L_f, is necessary. In the following

simulations, the PI gains were initially determined and

then not varied from simulation to simulation. Simulation

results are shown from the three models with three

motor parameter estimates: ;L'_f= ;Laf, and ;L'_f=.8 ;Laf and

X"_f=l.2Xaf. In addition, the poor performance of the

controller without feedforward or disturbance decoupling

is also shown.

The PI gains for the current regulator were set at Kp=1.2

and Ki=3000. These gains give a torque response

bandwidth of about 1kHz for this machine.

The PI gains for both the discharge and charge

controllers were set at Kp=l.2 and Ki=12. Although the

tuning is essentially an heuristic process, an initial

determination of appropriate gains for the discharge

controller can be made in the following manner. If the

disturbance decoupling is neglected, ;L'_f =;Laf , and the

simple model of figure 10 is used, all that remains is a PI

controller and a parallel resistor-capacitor (RC) circuit.

Essentially, the PI controller is producing a current

command which will force the voltage on the capacitor to

the desired value. The "first guess" gains on the PI

controller can be set by using pole-zero cancellation

where Kp 1

Ki = RL_ and Kp=2_RLCfbw. A high bandwidth,

fbw, is not necessary because of the disturbance

decoupling in the total controller. The motor parameters,

PWM frequency and DC bus voltage are given in the

appendix.

Figures 14 through 25 show the simulation results of the

three models with three different values of the estimated

A

motor parameter _af' In each simulation the same

charging and discharging profile is used: the system

starts off in charge mode with a flywheel speed of 60,000

rpm, then the solar array current ramps down to zero,

then there is a step change increase in the load at 5

seconds, then the solar array current ramps back up

again. The results show the transitions between modes

and the accurate DC bus regulation during the discharge

and charge reduction modes.

Electrically, it can be seen that the three models give

essentially the same results (figures 14 to 22). The

"PWM model" has more ripple on the DC bus voltage

due to the switching action as would be expected. There

is no fluctuation in the DC bus voltage in response to the

A

additional load at t = 5 seconds when Xaf is perfectly

estimated. Even with a 20% error in the estimate, the

regulation is still excellent.

The motor speeds are shown in figures 23 to 25. It can

be seen that the simple model motor speed estimate is

not as accurate as the other two models. This is due to

the fact that any losses in the motor (for example, stator

resistance) are not modeled. The PWM model and the

motor model results are virtually identical.

Figures 26 and 27 compare the motor voltage for the

PWM model and the motor model. Figures 28 and 29

compare the motor current for the PWM model and the

motor model. The motor current is seen to be larger in

the PWM model than the motor model. This is due to

the low inductance of the machine which causes a large

switching current ripple on top of the fundamental. In the

actual experimental set up, there is a filter between the

inverter and the motor which is not yet included in the

simulation models. The filter reduces this current ripple.

Finally, figure 30 shows the response with PI only in the

controller: no feedforward and no decoupling inputs, and

with the back emf constant estimated improperly where

A

Xaf =1.2 ;Laf. It can be seen that the transitions between

modes are much worse and there is a greater response

to the load disturbance.

NASA/TM--2002-211897 7
351 _15

349

347

g

345

O 343

341

339

........ i......................................................... ,:.................. ilo

• i • ESla : i / s ................. 4,q

: /

: ........ i!Ib,s,,__Lj

Vdc

i i i i ,-.!5

2.5 5 7.5 10 12.5

time, seconds

A

Figure 14: )_af = Xaf, simple model.

350

348

o

_346

o

344

g

342

340

", i ',js,',_ i il /

......... _ Vdci i i ..................

I0

#

--10

2.5 5 7.5 10

time, seconds

Figure 17: Xaf = Xaf, motor model.

--15

351i i

12.5

15

34_i ......... i.................................................. /. ................. ,it0

347 ...._'_i: .................. i .................. i....?,( ......................... @ _-

o 345.......... _,<.:..__ 'L':L_#..........{....../ .................. _0

i 1 "( _: i / _>

o i i "_----_{=,,.,+... I i i .................. i-_

i _ i'2U2 !.'2".....iz !

341 _-................. I- i................... _.................. _. : Vdc _ ................................... _'_

i I,i i i

339_ 2.5 5 7.5 10 12.5 L5

time, seconds

Figure 20: Xaf = Xaf, PWM model.

60.5

_5_15._i _i._.i_!"<;.::: ',....... 25

time, seconds

Figure 23: Xaf = Xaf, motor speed.

351

349

347

345

O 343

341

33g

] i 5

................. 5

......... _:_,,i,,.,_Ji ................. i__

..................... ,.,.:..../ i

.................. 7'_.............. _................... i../:......................... 4-5

f "- ...... Vdc _.,< , <" . i "

2.5 5 7.5 10 12.5 ""

time, seconds

A

Figure 15: )_af = .8 Xaf, simple model.

351

34g

g 347

345

O 343

341

33g

] ] ] I .E

.................. 7................... : .................. i ................ /'i ................ 410

.............. ii!!:',}................... i.iii ii_iiiii_ .................. ii i ' /.iili, ......... I {._!_iji_5..__

time, seconds

A

Figure 18: )_af = .8 Xaf, motor model.

34g............................. : .................................. /_ ................ i

!Oi i i / i i

_ 345 -. • •• t..x,_>.i\i............ , is/_ "_i............ _'i".......... /l/i ........ ]i..u _

=: -t ''_'<.............. '.................. "/.......... ':t......... i--'-_

341 ................... i................... Vdc ii.................. i:i................... ii1"" .................. -- • •• "-]i-i0

330 2.5 5 7.5 10 12:515

time, seconds

A

Figure 21: gaf = .8 Xaf, PWM model.

0 2.5 7.5 10 12.5

time, seconds

A

Figure 24: )_af = .8 Xaf, motor speed.

g

g

351

349

347

345

343

341

33%

Z, , i/27:

n

2.5 5 7.5 10 12.5

time, seconds

Figure 16: Xaf = 1.2 Xaf, simple model.

351

349

347

345

343

341

339

 !!!iii,i i::iiiiiiiiiiiiliil iili

2.5 5 7.5 10 12.5

time, seconds

Figure 19: Xaf = 1.2 Xaf, motor model.

351

349

o 347

o 345

O 343

341

339

................. ;7................... _............... "7' .............................

.......... ?_..i.X._"'_'__.- ............ 5::........... _'.

x,i i i / ...................

.................. 7.<.............. 7.................. :"! .............................

" ? fly',,_heei i<'

Vdc i

0 2.5 5 7.5 10 12.5

time, seconds

Figure 22: Xaf = 1.2 Xaf, PWM model.

60.5j i

"<::ii................ _.................. i

"_ .sim£_i_ modal

5_.5 ................. ::.............. r!i<_<'j_.,!.,! ! !_:_._!..i.,_

59

60

2.5 5 7.5 10 12.5

time, seconds

Figure 25: Xaf = 1.2 Xaf, motor speed.

-10

e>

-5

-10

5 _

-10

NASA/TM--2002-211897 8
25O

150

100

i, 50o

5o

loo

15o

2oo

25o 3 9958 3 9963 3 9_68 3 9973 3 9978

250[ A f_'

200 .._ .................... :...................... , .................... _..................... [

A #t •

........ t _l..._ ............. .............. _._-_ ............. t._ ..............

100_ "'@'"'{ ............ ............. _'"'" _*'"'"'""" "_"" _.............

5o[#U i_ #t _ i

& ol-.f-......i........._ _ u.......t......@.._ [

5ol _tFil / ,qt_t ! _

,o4 i$........._...4.i _ ]b.......t....i$.. _ _ [

150_ ....................................... , ............... "}"_................. 'tl ......

_/i _CJi 'gi vi vi

2ool- ..s .................... ...................... .................... s ..................... }

25o, i i i i i

s 995s s 996s s 996s s 997s s 997s

_me_ seconds

A

Figure 26: Xaf = Xaf, motor

voltage, PWM model.

Figure 27: Xaf = Xaf, motor

voltage, motor model.

20

_o

*_ 5 • .

5

lo' ............

15

20 3 9958 3 9963 8

S

h! £] A /1\! A

', L!, LL/ iiiii ii!iil/',,/ i!! 'i

.............................................................................................

3 9958 3 9963 3 9968 3 9973 3 9978

time seconds time seconds

A

Figure 28: Xaf = Xaf, motor

current, PWM model.

Figure 29: Xaf = Xaf, motor

current, motor model.

352 i 4

35C i._ i i. • .,< _i

• i i i /

348 ......... 6

%] i :. / i

_ 34_344...................I'_'_'_' "4'i _................ iI_l ................... --[,/:"e ............./ "t"................. 2 1 _'_t

O 342 ....... ............... ................... ........... ...................

34C ........... i0

338 -14

2.5 5 7.5 10 12.5

time, seconds

A

Figure 30: Xaf = 1.2Xaf, system response without feedforward and

disturbance decoupling in the controller.

CONCLUSIONS

This paper has presented detailed block diagrams of the

DC bus regulation control algorithm for the NASA

flywheel energy storage system which was previously

experimentally verified [1]. The block diagrams are

necessary for system simulations to predict

performance. It was shown that the flywheel system and

the controller can be modeled in three levels of detail

depending on the type of analysis required. The three

models give similar electrical results however for the

most accurate representation of the motor speed the

simple model is not appropriate.

The simulation results showed the control algorithm to be

effective even in the presence of parameter errors. The

controller successfully transitions between current

regulation in charge mode and DC bus voltage regulation

in discharge mode.

Future work will include evaluating a modified flywheel

control such that the flywheel system maintains the DC

bus regulation continuously, during both charge and

discharge operation.

REFERENCES

1. Kascak, P, B. Kenny, T. Dever, W. Santiago, R.

Jansen, "International Space Station Bus Regulation

with NASA Glenn Research Center Flywheel Energy

Storage System Development Unit", July 2001

IECEC Conference Proceedings, Savannah,

Georgia, 2001.

2. Krishnan, Ramu, Permanent Magnet Synchronous

and Brushless DC Motor Drives: Theory, Operation,

Performance, Modeling, Simulation, Analysis and

Design, Virginia Tech., Blacksburg, Virginia, 1999.

3. Rowan, T. and R. Kerkman, "A New Synchronous

Current Regulator and an Analysis of CurrentRegulated PWM Inverters", IEEE Transactions on

Industry Applications, Vol IA-22, No. 4, July/August

1986, pp. 678-690.

4. Kenny, B.H., P. Kascak, et. al, "Advanced Motor

Control Test Facility for NASA GRC Flywheel Energy

Storage System Technology Development Unit", July

2001 IECEC Conference Proceedings, Savannah,

Georgia, 2001.

5. Mohan, Ned, Workshop Proceedings, NSF-Faculty

Workshop on Teaching of Courses in Power

Electronics and Electric Drives, Tempe, Arizona,

January 3-5, 2002.

DEFINITIONS, ACRONYMS, ABBREVIATIONS

I,V Current, voltage where capital letters denote a

DC quantity.

i,v Current, voltage where small letters denote an

AC quantity.

I*,V* Commanded current, commanded voltage; the

asterisk denotes a commanded value.

Electrical rotor speed, radians per second

O)rmech Mechanical rotor speed, radians per second

P Number of poles in motor

A

Xaf Back EMF constant, volt-seconds; the carrot

denotes an estimated quantity.

APPENDIX

Motor parameters: Rs=.06_, L_=139mH, Ld=116mH,

Xaf=.0141 volt-sec., J=.0153 kg-m :?,4 pole

DC bus voltage set points: charge mode: 350 volts,

discharge mode: 340 volts.

PWM frequency: 40 kHz.

NASA/TM--2002-211897 9
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October 2002 Technical Memorandum

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

DC Bus Regulation With a Flywheel Energy Storage System

6. AUTHOR(S)

Barbara H. Kenny and Peter E. Kascak

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

John H. Glenn Research Center at Lewis Field

Cleveland, Ohio 44135-3191

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

WU-755-1A-09-00

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E-13579

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AGENCY REPORT NUMBER

NASA TM--2002-211897

02PSC-61

11. SUPPLEMENTARY NOTES

Prepared for the Power Systems Conference sponsored by the Society of Automotive Engineers, Coral Springs, Florida,

October 29-31, 2002. Barbara H. Kenny, NASA Glenn Research Center, and Peter E. Kascak, University of Toledo,

Toledo, Oho 43606. Responsible person, Barbara H. Kenny, organization code 5450, 216-433-6289.

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Available electronically at http://gltrs.grc.nasa.gov

This publication is available from the NASA Center for AeroSpace Information, 301-621-0390.

12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

This paper describes the DC bus regulation control algorithm for the NASA flywheel energy storage system during

charge, charge reduction and discharge modes of operation. The algorithm was experimentally verified with results

given in a previous paper. This paper presents the necessary models for simulation with detailed block diagrams of

the controller algorithm. It is shown that the flywheel system and the controller can be modeled in three levels of detail

depending on the type of analysis required. The three models are explained and then compared using simulation results.

14. SUBJECT TERMS

Flywheel energy storage; Simulation; DC bus regulation; Permanent magnet motor control

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