4 / System Analysis - Purdue Universitysudhoff/ee631/ibs_section4.pdf4 / System Analysis Thus far,...

4/4/2005 Copyright 2003 S.D. Sudhoff Page 40

4 / System Analysis Thus far, our consideration of immittance based stability analysis has been limited to simple one source, one load, problems. In this chapter, we consider immittance based stability analysis of systems of power converters, such as the laboratory power system shown in Figure 4-1 [1,2]. This system, referred to as the Naval Combat Survivability Testbed, was constructed at Purdue University and the Univeristy of Missouri-Rolla in the 2000-2005 time frame, and is representative of some notional ship power systems. Therein, PS-1 and PS-2 denote power supplies for the port and starboard bus, CM-P1, CM-P2, and CM-P3 are port bus converter modules, CM-S1, CM-S2, and CM-S3 are starboard bus converter modules. These converter modules reduce the voltage from the bus to each load and provide current limiting functions. Next, the converter marked IM is an inverter which supplies an AC bus and a load bank (LB), the MC is a motor controller, and CPL is a generic constant power load. In this chapter, the steps necessary to conduct the stability analysis of the entire system using the generalized immittance space based approach is set forth. Of particular interest in this process is the classification of power converters for stability analysis, and the derivation of mapping functions to facilitate network reductions.

Figure 4-1. Naval Combat Survivability Testbed.

4.1 CLASSIFICATION OF SINGLE PORT POWER CONVERTERS The first step in the stability analysis of the systems is to categorize the components which make up the system. These components generally fall into two classes – single port converters in which there is a single dc terminal, and two-port


converters in which there are two sets of terminals. Within each of the main groups, there are sub-classifications which will be important in the analysis of the system. In this section, we address single port converters which posses a single pair of dc terminals. In our work thus far, we have already addressed the two types of single port converters – a source, which we will abbreviate herein as an S converter, and a load, which we refer to as a L converter. Recall that the definition of a source, or S converter, and load, or L converter, do not necessarily correspond to a component that is supplying or consuming power. This is the reason that in this chapter the S and L converter notation is used. For the purpose of defining the input output relationships for single port converters, define xv as the small signal voltage across component x and xi as the small signal current into the positive terminal (passive sign convention) of component x , where x is a subscript that defines the component. Using these definitions, the two types of single port converters are reviewed below.

S Converters S Converters often, but not always, represent sources. In the sample system of Fig. 4-1, the two power supplies PS-1 and PS-2 will be categorized as S Converters. These components obey the small-signal relationship

xx

x Siv

= (4.1-1)

where xS is the impedance, and which may be expressed

xS

xSx D

NS

,

,= (4.1-2)

and where xSN , and xSD , represent the numerator and denominator of xSS , . The defining property of S converters is that they are stable when the current xi is fixed – the implication of this being that all the roots of xsD , are in the open left-half plane. Comparing this work to that of the previous chapters, we see that xS is the source impedance looking to the S converter, and so is nothing more or less than

sZ . However, the new notation will be useful in that it will help us to separate what physically represents a source from our stability definition.

L Converters L Converters often, but not always, represented loads. In our sample system of Fig. 4.1-1, the inverter module and load band (IM and LB), motor


controller MC, and constant power load CPL will all fall into the class of L Converters. These components obey the small-signal relationship

xx

x Lvi

= (4.1-3)

where xL is the admittance, which may be expressed

xL

xLx D

NL

,

,= (4.1-4)

and where xLN , and xLD , represent the numerator and denominator of xL . The defining property of L converters is that they are stable when the voltage xv is fixed – the implication of this being that all the roots of xLD , are in the open left-half plane. Again, casual inspection of xL will reveal that it is simply the load admittance formally denoted lY . However, this new notation will be useful in separating what physically constitutes a load from the mathematical definition we will use for stability analysis.

4.2 CLASSIFICATION OF MULTI-PORT POWER CONVERTERS Two port converters may be categorized by those converters that have a two pairs of dc terminals. For the purpose of defining the input output relationships for two port converters, define 1,xv and 2,xv as the small signal voltage across terminals 1 and 2 of component x and 1,xi and 2,xi as the current into the positive nodes of terminals 1 and 2 (passive sign convention) of component x , where x is a subscript that defines the component. Using these definitions, the various types of two port converters are defined below.

C Converter A C Converter, which usually represents a cable, is a passive element that obeys the relationship )( ,2,1,2,1 xxxxx vvCii −=−= (4.2-1) where

xC

xCx D

NC

,

,= (4.2-2)

4/4/2005 Copyright 2003 S.D. Sudhoff 3

All roots of xcD , must be in the open left-half plane for the component to be categorized as a C converter.

Z Converter Z Converters often represent two-port components which provide power from both sets of terminals. The input-output relationship definition is that

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡

x

x

xx

xx

x

xii

ZZZZ

vv

,2

,1

,22,21

,12,11

,2

,1 (4.2-3)

where

xZ

xZxZ

xZxZ

xx

xx

D

NNNN

ZZZZ

,

,22,21

,12,11

,22,21

,12,11⎥⎦

⎤⎢⎣

⎡

=⎥⎦

⎤⎢⎣

⎡ (4.2-4)

and where xZabN , and xZD , represent the ab ’th element of the numerator and denominator of the impedance matrix. For a converter to be a Z converter, it is necessary that all the roots of xZD , be in the open left-half plane. Physically, this means that to be classified as a Z converter, the two port converter must be stable when its two terminal currents are held constant.

Y Converter Y Converters often represent two-port components which are fed power from both sets of terminals. In the sample system of Fig. 4-1, CM-P2, CM-P1 and MC can together be viewed as a Z Converter. The input-output relationship definition is that

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡

x

x

xx

xx

x

xvv

YYYY

ii

,2

,1

,22,21

,12,11

,2

,1 (4.2-5)

where

xY

xYxY

xYxY

xx

xx

D

NNNN

YYYY

,

,22,21

,12,11

,22,21

,12,11⎥⎦

⎤⎢⎣

⎡

=⎥⎦

⎤⎢⎣

⎡ (4.2-6)

and where xYabN , and xYD , represent the ab ’th element of the numerator and denominator of the impedance matrix. For a converter to be a Y converter, it is


necessary that all the roots of xZY , be in the open left-half plane. Physically, this means the to be classified as a Y converter, the two-port converter must be stable if supplied from two ideal voltage sources.

H Converter A two-port converter which accepts power from one set of terminals and transfers it to the second set of terminals is often categorized as an H converter. An example of an H Converter will by the converter modules in Fig. 4-1. The input-output relationship for the H converter is:

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡

x

x

xx

xx

x

xiv

HHHH

vi

,2

,1

,22,21

,12,11

,2

,1 (4.2-7)

where

xH

xHxH

xHxH

xx

xx

D

NNNN

HHHH

,

,22,21

,12,11

,22,21

,12,11⎥⎦

⎤⎢⎣

⎡

=⎥⎦

⎤⎢⎣

⎡ (4.2-8)

and where xHabN , and xHD , represent the ab ’th element of the numerator and denominator of the H matrix. For a converter to be an H converter, it is necessary that all the roots of xHD , be in the open left-half plane. Physically, this means the to be classified as an H converter, the two-port converter must be stable if the port 1 voltage and port 2 current are constant.

H’ Converter The H’ converter is a special case of the H converter in which it is possible to parallel the port 2 terminals with another H converter. Mathematically, it is a H converter in which the roots of xHN ,12 are in the open left-half plane (in addition to

the roots of xHD , being in the open left-half plane).


4.3 NETWORK REDUCTIONS Thus far, all of our work has been based on the analysis of a simple source load system. Our objective in this chapter is, however, to analyze system such as the one in Fig. 4-1. The application of the generalized immittance based method to interconnected systems is basically one of reducing the system, by a series of mapping functions, to a single source / single load equivalent. At each application of a mapping function, two or more components are grouped together into a single component. Often, a stability test will be required to determine whether or not the subsystem being grouped is stable as part of the mapping process. If it is not, then system stability cannot be guaranteed. A description of the most commonly used mapping functions follows. The use of the mapping functions to transform a complicated interconnected system into a simple source load system will then by illustrated by example in the next section.

SC to S Mapping Figure 4.3-1 depicts a situation in which S converter x connected to C converter y may be represented as a equivalent S converter e .

Figure 4.3-1. SC to S Mapping.

Clearly, the impedance of the effective source may be readily calculated as yxe CSS += (4.3-1)


It should be kept in mind that the addition in (4.3-1) is generalized so that the generalized impedance of ES includes any impedance in xS plus any impedance in

yC . This operation is always valid and defined and thus no stability test is required.

LC to L Mapping Figure 4.3-2 depicts a situation in which L converter x connected to C converter y may be represented as an equivalent L converter e .

Figure 4.3-2. LC to S Mapping. The admittance of the effective L converter may be expressed

yx

xe CL

LL+

=1

(4.3-2)

where all mathematical operations are generalized. Note that for this reduction to be valid, then the system comprised of yC as a source (the other end of the C converter

is treated as an ideal source) and xL as a load must be stable. This guarantees that the aggregation of the two components will satisfy the conditions required to be categorized as an L converter. Thus a subsystem stability analysis must be performed prior to making this reduction. If the subsystem is stable the analysis may proceed (note it does not have to satisfy any particular stability criterion, it merely has to be stable by the smallest degree). If the subsystem is not stable, then the reduction cannot be accomplished and the system as a whole cannot be guaranteed to be stable.


HL to L Mapping Figure 4.3-3 illustrates the mapping of H converter x feeding L converter y into an effective load converter eL .

Figure 4.3-3. HL to L Mapping. The effective L converter admittance may be expressed

yx

yxxxe LH

LHHHL

,22

,21,12,11 1+−= (4.3-3)

In order for this operation to be valid, then a subsystem with xH ,22 as a source, and

yL as a load must be stable. If this is not the case, system stability cannot be guaranteed and further analysis along this path is not valid.

SH to S Mapping The mapping of S converter x connected to H converter y into an equivalent S converter eS is illustrated in Fig. 4.3-4. The effective source impedance may be expressed

yx

yyx

HSHHS

ye HS,11

,12,21

1,22 +−= (4.3-4)


Figure 4.3-4. SH to S Mapping.

The subsystem formed by xS as a source and yH ,11 as a load must be shown to be stable (thought not necessarily to satisfy a given stability criterion) for this operation to be valid.

Parallel L to L Mapping Paralleling an arbitrary number of L converters is depicted in Fig. 4.3-5. Therein L converter α , L-converter β through L converter ΩL are combined to form an effective L converter admittance eL given by Ω+++= LLLLe βα (4.3-5)


Figure 4.3-5. Parallel L to L Mapping. No stability test is required – this operation is always valid. As in the case with all mathematical operations in this discussion, it should be kept in mind that the basic algebraic operations of addition, subtraction, multiplication, and division are modified to operate on generalized sets.

Parallel Y to Y Mapping Figure 4.3-6 illustrates the mapping of Y converter α through Y converter Ω into an effective Y converter e whose Y parameters are given by Ω+++= YYYYe βα (4.3-6)


Figure 4.3-6 Parallel Y to Y Mapping.

As is the case of the Parallel L to L Mapping, this operation is always valid – no stability test is required.

HLH’ to Y Mapping In zonal power systems, there is often a need to collapse an entire zone or part of a zone into a single equivalent Y converter. The HLH’ to Y mapping depicted in Fig. 4.3-7 illustrates the procedure by which H converter α , H’-converter β , and L converter x are combined to form an effective Y converter eY . In terms of the effective converter,

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡

ββ

α

,1

a,1

e,22e,21

e,12e,11

,1

,1

vv

YYYY

ii

(4.3-7)


where

( )

βααβ

βααα

,22,22,22,12

,22,21,12,11,11

1HHLHH

HLHHHY

x

xe ++

+−= (4.3-8)

βααβ

βα

,22,22,22,12

,21,12,12 HHLHH

HHY

xe ++= (4.3-9)

βααβ

βα

,22,22,22,12

,12,21,21 HHLHH

HHY

xe ++= (4.3-10)

( )

βααβ

αβββ

,22,22,22,12

,22,21,12,11,22

1HHLHH

HLHHHY

x

xe ++

+−= (4.3-11)

Figure 4.3-7 HLH’ to Y Mapping.


For this operation to be valid two stability tests must be met. First, the subsystem comprised of α,22H as a source and 1

,22−

βH as a load must be stable. Second, the

subsystem comprised of the parallel combination of α,22H and β,22H as a source

and xL as a load must be stable.

YS to L Mapping Figure 4.3-8 depicts the mapping of Y converter x connected to S converter y into an effective L converter e . The load admittance of the effective L converter is given by

yx

yxyxe SY

YYSYL

,22

,21,12,11 1+−= (4.3-12)

Figure 4.3-8. YS to L Mapping. The validity of this mapping is contingent upon the subsystem consisting of yS as a

source and xY ,22 as a load being stable.

Y to L Mapping The final mapping function depicted herein is that depicted in Fig. 4.3-9. In this case, the two ports of the Y converter x are tied together. The load admittance of the effective L converter eL is given by xxxxe YYYYL ,22,21,12,11 +++= (4.3-13) This operation is always valid.


Figure 4.3-9 Y to L Mapping.

4.4 CASE STUDY PART 1: SYSTEM DESCRIPTION In order to illustrate the use of these concepts and their incorporation into a system analysis, let us perform a stability analysis on the system shown in Figure 4-1. Before we can do this, however, we need to set forth a more detailed description of the system and the mathematical models used to represent it. The NCS Testbed depicted in Figure 4-1 will be the example system for this work. In this system, there are two power supplies (PS-1 and PS-2), that can each be fed from an independent power source. One power supply feeds the port bus, and the other feeds the starboard bus. There are three zones of dc distribution. Each zone is fed by a converter module (CM) on the port bus (CM-P1,CM-P2, or CM-P3) and a converter module on the starboard bus (CM-S1, CM-S2, or CM-S3). Diodes prevent a fault from one bus from being fed by the opposite bus. The converter modules feature a droop characteristic so that they can share power. The three loads consist of an inverter module (IM) which in turn feeds an ac load bank (LB), a motor controller (MC), and a generic constant power load (CPL). Robustness in this system is achieved as follows. First, in the event that either a power supply fails, or a distribution bus is lost, then the other bus can pick up full system load without interruption in service. Faults between the converter module and diode are mitigated by imposing current limits on the converter modules; and again the bus opposite the fault can supply the component. Finally,


faults within the components are mitigated through the converter module controls. The result is a highly robust system. The discussion of the system components will begin with the power supply. The power supplies PS-1 and PS-2 are identical, but have three operating modes. For the studies to be considered herein, the uncontrolled rectifier mode will be considered. A schematic of the power supply is depicted in Figure 4.4-1.

Figure 4.4-1. Power Supply Schematic.

The nonlinear average value model (NLAM) [4,5] equivalent circuit of the power supply appears in Figure 4.4-2.

Figure 4.4-2. Power Supply Equivalent Circuit.

Variables of interest which are not directly defined by the figures include the rms primary line-to-line voltage, pllv , the radian source frequency eω , the transformer

primary to secondary turns ratio, psn , and the transformer commutating inductance

cL (the sum of the primary and secondary leakage inductances referred to the secondary winding). Parameter values for pllv , eω , psn , and cL are 456-504 V, 358-396 rad/s, 1.30, and 1.24 mH, respectively. Note that since generalized parameters are used, all combinations of input voltage and frequency are considered in the analysis. The circuit diagram for the converter modules along with circuit element values is depicted in Fig. 4.4-3.


Figure 4.4-3 Converter Module Schematic.

The control algorithm is illustrated in Figure 4.4-4.

Figure 4.4-4. Converter Module Control.

The principal variables not defined by Figure 4.4-4 and Figure 4.4-5 are the commanded output voltage *

outv and the commanded inductor current *li . This

current command, in conjunction with the measured current li is used by a hysteresis modulator so that the actual current closely tracks the measured current. The transfer function of the stabilizing feedback )(sHsf [6,7] is given by

)1)(1(

)(21

1

++=

sss

KsHsfsf

sfsfsf ττ

τ (4.4-1)

Parameter values are listed in Table 4.4-1. The final two values listed therein,

mninv , and mxinv , , represent the minimum and maximum expected input voltage – this is used for determining the generalized immittance description of the converter. The numbers are based on the range of power supply parameters and input and load conditions.


Table 4.4-1. Converter Module Control Parameters msinvc 17.0=τ msinvout 17.0=τ msiniout 17.0=τ

1=d A/V 628.0=pvK AV 197=ivK AS/V

1.0=sfK 201 =sfτ ms 42 =sfτ ms

7.15=iiK kA/s 20* =∆ outmaxv V 20=limiti A

2=intlimi A 548, =mninv V 450, =mxinv V

For the purposes of this stability analysis the inverter module (including its load bank), motor controller, and constant power load are treated as a capacitor with capacitance xC and effective series resistance xr in parallel with a ideal constant power load of xp as depicted in Fig. 4.4-5. Parameters for the three loads are set forth in Table 4.4-2. The nominal input voltage xv ,0 and power xp are included in this table as a range; every possible value within this range in every combination will be considered.

Figure 4.4-5. Load Model.

Table 4.4-2. Load Converter Parameters Component µF,xC

mΩ,xr

V,0 xv kW,xp

IM 590 127 400-420 0-5 MC 580 253 400-420 0-5 CPL 479 189 400-420 0-5


4.5 CASE STUDY PART 2: SYSTEM ANALYSIS With the basic tools, network reduction mapping functions, and system description in place, the stability analysis of the system shown in Figure 4-1 can now be conducted. In order to facilitate this process, first consider Figure 4.5-1, which again depicts the system architecture, but focuses on the classification of the components of the system. Therein, psS represents the generalized impedance of

the power supplies, cmH (which will be shorthand for the generalized H-parameters of the converter modules – that is cmH ,11 , cmH ,12 , cmH ,21 , and cmH ,22 ), and imL ,

mcL , and cplL the generalized admittance of the inverter module, the motor controller, and constant power load respectively.

Figure 4.5-1. NCS Testbed (Showing Converter Classification)

As stated previously, the basic approach to system wide stability analysis is to methodically reduce the system to a single-source single-load system, checking to make sure that each reduction is valid. The mathematical manipulation of the generalized immittances is readily accomplished using a Matlab™ toolbox [8]. The first set of reductions to be made in this case is to reduce each zone to an equivalent Y-Converter. To this end, consider Zone 1. Our first step will be to combine the converter module P1, converter module S1, and the inverter module IM into an equivalent Y converter characterized by the generalized Y-parameters 1,11 zY ,

1,12 zY , 1,21 zY , and 1,22 zY . To do this, we must first examine the stability of a source with generalized impedance 1

,22−

cmH and a load with generalized load admittance cmH ,22 . This is illustrated in Fig. 4.5-2, wherein generalized admittance cmH ,22 is plotted in along


with a constraint based upon 1,22

−cmH in conjunction with the ESAC stability

criterion with a 30 dB gain margin and a 30 degree phase margin. In this figure, hybrid coordinates are used. These coordinates constitute a mixed linear / logarithmic representation. Mathematically, if x and y denote the real and imaginary part of an immittance at a frequency, then the representation of this point in hybrid coordinates is given by

⎪⎪⎪

⎩

⎪⎪⎪

⎨

⎧

≥+

⎟⎠⎞

⎜⎝⎛ −+⎟

⎠⎞

⎜⎝⎛ +

+

+

≤++

=+

20

if20log20

20if10

''

22

2222

2220/

yx

Byxyx

jyx

yxjyx

jyx

B

(4.5-1)

where B is a breakpoint in dB. In this system if a complex number has a magnitude less than B dB, it is in the linear region. A number with a magnitude of B dB will always have a magnitude of 20 in this coordinate system. Finally, for numbers with a magnitude greater than B dB will have a magnitude equal to its dB value plus 20 – B (the offset is for continuity).

Figure 4.5-2. Admittance Space Plot of CM to CM Interface (Testing 1,22

−cmH of CM-P1 as load admittance with admittance

constraint based on cmH ,22 of CM-S1 as a source).


Upon examination of Fig. 4.5-2, it is seen that cmH ,22 does not intersect the forbidden region – thus stability of this load source system is guaranteed. Recall that to make a H’LH to Y conversion, a second stability test is required. In particular, given the subsystem consisting of cmH ,22 of the CM-P1 in parallel with cmH ,22 (from the CM-S1, which is identical to that of the CM-P1) as a source and imL as a load must be stable. This admittance constraint based on this effective load and the chosen stability criterion (the ESAC criterion, with a 3 dB gain margin and 30 degree phase margin) is illustrated in Fig. 4.5-3.

Figure 4.5-3. Admittance Space Plot of Dual CM to IM Interface (Testing imL as load admitance with admittance constraint based

on cmH ,22 of CM-P1 in parallel with cmH ,22 of CM-S1 as a source).

The reduction of the other two zones to Y converters is identical and is not shown for brevity. After this first round of system reduction, the resulting reduced system has the topology shown in Figure 4.5-4. As indicated therein, the next step is to conduct a parallel Y to Y mapping. This step does not require a subsystem analysis. The result is the further reduced system shown in Figure 4.4-5.


Figure 4.5-4. System After HLH’ to Y Mapping.

Figure 4.5-5. System After Parallel Y to Y Mapping.

The next step in the reduction is to reduce the effective Y converter representing the three zones (with admittance z3Y and the starboard power supply PS-2 with impedance psS to an effective load converter with admittance zpsL3 . This is accomplished with a YS to L mapping, an operation that requires that a subsystem with a source with impedance psS and a load with admittance zY 3,22 to be stable. Figure 4.5-6 depicts this stability test; therein a load admittance constraint based on source impedance psS and the ESAC stability criterion is plotted along with the load admittance. As can be seen – there is no intersection and hence the


system is stable. Thus the YS to L Mapping can be used to reduce the system shown in Fig. 4.5-5 to that shown in Figure 4.5-7.

Figure 4.5-6. Admittance Space Plot of Three Zones / PS-2 Interface (Testing zY 3,22 as a load admittance with admittance constraint based on

psS as a source).

Figure 4.5-7. System After YS to L Mapping.

In Fig. 4.5-7 , the entire system has been reduced to two components. The source is PS-1 has a generalized source impedance psS . The load represents the aggregation of the remainder of the system – the three zones plus the starboard power supply and has an admittance zpsL3 . In Fig 4.5-8, the generalized admittance

zpsL3 is shown along with the admittance constraint calculated from the source

impedance psS in conjunction with the selected stability criterion. As can be seen, there is no intersection and hence the system is stable in a small-signal sense for all operating points.


Figure 4.5-8. Admittance Space Plot of PS-1 / Rest of System Interface. (Testing zpsL3 as a load admittance with admittance constraint

based on psS as a source).

In order to see a situation in which an instability can arise, let us consider the same system with the following modifications: (1) the output capacitance of the two power supplies is removed, (2) the input capacitance of all of the converter modules ( inC in Figure 4.4-3) is reduced to µF100 , and (3) the stabilizing gain

sfK (see Table 4.4-1) is reduced to zero. The analysis proceeds much as before; however when the analysis reaches the point where the interface of the 3 zone equivalent to the starboard power supply ( zY 3,22 as a load, psS as a source), it is found that stability of this subsystem (three zones and the starboard power supply) cannot be guaranteed. This is illustrated in Fig. 4.4-9 wherein the admittance zY 3,22 enters the forbidden region calculated from

psS . Thus stability of this subsystem cannot be guaranteed. Note that further analysis cannot be conducted because the 3-zone equivalent / starboard power supply do not constitute a valid L converter.


Figure 4.4-9. Admittance Space Plot of Three Zones / PS-2 Interface for Modified System (Testing zpsL3 as a load admittance with

admittance constraint based on psS as a source).

4.6 CLOSING REMARKS In this chapter, the methodology to apply immittance based stability analysis was set forth. This began with a classification scheme for power converters in terms of their stability properties. Next, a variety of network reductions were introduced which allow a complex system to be reduced to a simple one. The chapter concluded with an example. It should be noted that the example analysis presented here is considered and viewed in terms of measured system behavior. It was found that the techniques shown here were consistent with experimentally observed behavior.

4.7 ACKNOWLEDGEMENTS A monograph supported by grant N00014-02-1-0623, “National Naval Responsibility for Naval Engineers: Education and Research for the Electric Naval Engineer”


4.8 REFERENCES [1] S.D. Sudhoff, S.D. Pekarek, B.T. Kuhn, S.F. Glover, J. Sauer, D.E. Delisle,

“Naval Combat Survivability Testbeds for Investigation of Issues in Shipboard Power Electronics Based Power and Propulsion Systems,” proceedings of the IEEE Power Engineering Society Summer Meeting, July 21-25, 2002,Chicago, Illinois, USA

[2] S. Pekarek, S.D. Sudhoff, D.E. Delisle, J. Sauer, E.J. Zivi, “Overview of a Naval Combat Survivability Program, Paper 233, 7-9 April 2003, Orlando, Florida, USA

[3] S.D. Sudhoff, S.D. Pekarek, S.F. Glover, S.H. Zak, E. Zivi, J.D. Sauer, D.E Delisle, “Stability Analysis of a DC Power Electronics Based Distribution System,” SAE2002 Power Systems Conference (Paper Offer #: 02PSC-17) , October 29-31, 2002, Coral Springs, Florida, USA.

[4] S.D. Sudhoff, S.F. Glover, “Modeling Techniques, Stability Analysis, and Design Criteria for DC Power Systems with Experimental Validation,” Proceedings of the 1998 SAE Aerospace Power Systems Conference, pp. 55-69.

[5] S.D. Sudhoff and K.A. Corzine, H.J. Hegner, D.E. Delisle, “Transient and Dynamic Average-Value Modeling of Synchronous Machine Fed Load-Commutated Converters,” IEEE Transactions on Energy Conversion, Vol. 11, No. 3, September 1996, pp. 508-514.

[6] S.D. Sudhoff et. al., “Control of Zonal DC Distribution Systems: A Stability Perspective,” Sixth IASTED International Multi-Conference On Power and Energy Systems, May 12-15, 2002, Marina del Rey, California, USA

[7] S.D. Sudhoff, K.A. Corzine, S.F. Glover, H.J. Hegner, and H.N. Robey, “DC Link Stabilized Field Oriented Control of Electric Propulsion Systems,” IEEE Transactions on Energy Conversion, Vol. 13, No. 1, March 1998.

[8] S.D. Sudhoff, “DC Stability Toolbox Version 2.1”, January 4, 2002, Purdue University.

[9] S.P. Pekarek et. al., “Development of a Testbed for Design and Evaluation of Power Electronic Based Generation and Distribution System,” SAE2002 Power Systems Conference (Paper Offer #: 02PSC-28), October 29-31, 2002, Coral Springs, Florida, USA

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