1

REAL-TIME MULTI-PULSE RECTIFIER MODELS FOR POWER HARDWARE-IN-THE-

LOOP IMPLEMENTATION IN MEDIUM VOLTAGE DC MICROGRID APPLICATIONS

by

BRIAN J. MCREE

Presented to the Faculty of the Graduate School of

The University of Texas at Arlington in Partial Fulfillment

of the Requirements for the Degree of

DOCTOR OF PHILOSOPHY

THE UNIVERSITY OF TEXAS AT ARLINGTON

May 2019

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Copyright © by Brian J. McRee 2019

All Rights Reserved

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Acknowledgements

First and foremost, I want to thank my family for their continual support throughout my

undergraduate and graduate collegiate career. My parents and grandparents have been the bedrock

of support and encouragement that has allowed me to focus solely on the pursuit of higher

education. The sacrifices they have made to give me these opportunities are something I will never

forget.

I want to thank my advisor, Dr. David Wetz, for his mentorship and guidance in my graduate

career and the opportunities he has opened to me outside academia. Dr. Wetz has helped me grow

to new levels of engineering excellence and professionalism, which has been invaluable in making

important steps in my career. His friendship and understanding has made my time at his laboratory

one of the best and most fulfilling times in my life.

I want to thank all of my committee members, Dr. David Wetz, Dr. Greg Turner, Dr. Ali

Davoudi, Dr. Wei-Jen Lee, Dr. William Dillon, and Dr. Rasool Kenarangui for their valuable time

evaluating and guiding my work, as well as offering great suggestions and insights to my research.

For those who I was fortunate enough to take a class with, I thank you for your effort in imparting

knowledge and wisdom to me and my classmates.

I want to thank program sponsors Dr. John Heinzel, Don Hoffman, and Mike Giuliano for their

continual support of research efforts at UTA. None of the work presented here would be possible

without their involvement.

I would like to thank my more senior peers, now Dr. Isaac Cohen, Dr. Clint Gnegy-Davidson,

Dr. Derick Wong, Mr. Matthew Martin, and Mr. Chris Williams. Your peer mentorship was

invaluable to me finding my place in the lab and developing my own unique skillset to contribute

to the lab’s research efforts.

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Finally, I would like to thank my current colleagues, David, Chaz, and Jacob for their

incredible friendship and comradery. I believe the bonds we made working together throughout

the years will last a lifetime, and I wish you all the best of luck in the future.

-March 27, 2019

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Abstract

REAL-TIME MULTI-PULSE RECTIFIER MODELS FOR POWER HARDWARE-IN-THE-

LOOP IMPLEMENTATION IN MEDIUM VOLTAGE DC MICROGRID APPLICATIONS

Brian J. McRee, Ph.D.

The University of Texas at Arlington, 2019

Supervising Professor: David Wetz, Ph.D.

Microgrids have proliferated the landscape of the world’s power systems as distributed energy

generation, energy storage, and evolving electrical loads become more abundant. Microgrids offer

many advantages to the end user of electrical power over traditional power distribution networks

that rely on exceedingly large rotating machines producing power for a large group of electrical

loads over long physical distances. Microgrids provide a unique benefit to smaller electrical

networks that may be isolated, may have unique electrical loads, or may have a network of energy

storage devices that can be utilized to serve the microgrid in particular operational scenarios. With

the continual improvement and development of power electronic converters at the electrical grid

level, new distribution topologies, such as medium voltage DC distribution, have been proposed

for isolated microgrids that provide advantages to reliability, redundancy, and integrability. Since

rotating machines are essential as reliable sources of power generation for isolated microgrids, it

is necessary to convert the AC power they produce into DC power for distribution across the DC

microgrid. While rectifier circuits that convert AC power into DC power are well understood for

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individual converter and steady-state industrial applications, the DC microgrid provides a unique

set of circumstances that needs to be better understood before designing converters for DC

microgrid applications. While traditional modeling and simulation can provide a good check on

theoretical design, power hardware-in-the-loop emulation can extend these advantages by

interfacing the rectifier models with hardware loads. While power hardware-in-the-loop has been

verified as a legitimate tool, there is a lack of concrete data on the efficacy of power hardware-in-

the-loop at medium voltage and medium power levels.

Initially, rectifier models are developed for a real-time simulator for use in power hardware-

in-the-loop applications. It is shown that at standard rotating machine frequencies the limiting

factor in terms of developing valid models is modeling imbalances in the magnetic elements

inherent to multi-pulse rectifier circuits. A novel, data-based approach is used to approximate

unbalanced transformer saturation, circumventing an inherent limitation of the real-time simulator.

These more accurate models are validated against hardware over a wide range of rectifier

operation.

The validated rectifier models are used to emulate a real rectifier system by utilizing the real-

time simulator and a high slew-rate power supply, and then are then compared to data from the

low-voltage and low-power hardware testbed. It is then quantifiably shown that the power

hardware-in-the-loop system is a valid representation of the low voltage hardware testbed. Finally,

a medium voltage rectifier system is modeled and implemented in power hardware-in-the-loop

with a state-of-the-art medium voltage power supply. The results of the medium voltage rectifier

emulation are presented and quantifiably validated. This work concludes by commenting on

difficulties encountered in real-time simulation as well as the viability of particular power

hardware-in-the-loop applications once voltage and power are scaled up to unprecedented levels.

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Table of Contents

Acknowledgements ............................................................................................................. 3

Abstract ............................................................................................................................... 5

Table of Contents ................................................................................................................ 8

List of Figures ................................................................................................................... 10

Chapter 1: Introduction ..................................................................................................... 18

Chapter 2: Background ..................................................................................................... 23

Rotating Machines ........................................................................................................ 23

Multi-Pulse Rectifiers ................................................................................................... 24

Magnetics and Transformers ......................................................................................... 31

Power Hardware-in-the-Loop ....................................................................................... 34

Chapter 3: Real-time multi-pulse rectifier models for capacitor charging applications ... 40

Simulink Models ........................................................................................................... 41

Hardware Validation ..................................................................................................... 47

Results ........................................................................................................................... 51

Chapter 4: Model Validation of Real-Time Multi-Pulse Rectifiers with Nonlinear

Transformer Magnetics Using Iterative Methods ........................................................ 61

Limitations when developing HIL compatible models ................................................. 61

Modeling Approach ...................................................................................................... 63

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Model Validation .......................................................................................................... 71

Results: Input Power Quality ........................................................................................ 74

Chapter 5: Low Voltage PHIL Implementation of the Multi-Pulse Rectifier Model ....... 80

Low Voltage PHIL Experimental Setup ....................................................................... 80

Low Voltage PHIL Results ........................................................................................... 83

Chapter 6: Medium Voltage PHIL Implementation of the Multi-Pulse Rectifier Model . 88

Commissioning of a 1 kV to 6 kV DC/DC Power Supply for MVDC PHIL ............... 89

Implementation of PHIL for medium voltage levels .................................................... 95

Medium Voltage Results............................................................................................... 96

Conclusions ..................................................................................................................... 101

Sponsorship Acknowledgement...................................................................................... 103

References ....................................................................................................................... 104

Biography ........................................................................................................................ 109

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List of Figures

Fig. 1. Notional zonal topology for DC distributed microgrids [1]. ................................ 18

Fig. 2. One-line diagram of the MVDC microgrid testbed developed at UTA. .............. 21

Fig. 3. Picture of the AC/AC converter (foreground) [6] and motor-generator pair

(background) [12] in the MVDC testbed implemented at the University of Texas at

Arlington. .......................................................................................................................... 21

Fig. 4. The General Electric LM2500 is a common prime mover [13]. .......................... 24

Fig. 5. Half-wave single-phase rectifier (left), Full-wave single-phase rectifier (right), both

with resistive loads. ........................................................................................................... 25

Fig. 6. Comparison of single-phase output voltage waveforms [22]: half-wave (left) and

full-wave (right). ............................................................................................................... 25

Fig. 7. Circuit schematic of a thyristor-based 6-pulse rectifier [20]. ............................... 26

Fig. 8. Time domain voltage waveforms of an ideal 6-pulse rectifier [20]. .................... 26

Fig. 9. Comparison of output voltage waveforms for multi-pulse rectifier topologies. .. 27

Fig. 10. Ideal 12-pulse rectifier schematic. ...................................................................... 28

Fig. 11. Zig-zag transformers allow for phase-shifts less than 30 degrees. ..................... 32

Fig. 12. Zig-zag transformer diagram for a 24-pulse rectifier [30]. ................................ 32

Fig. 13. Example of a hysteresis loop that is typical of transformer core material [31]. . 33

Fig. 14. Abstracted diagram of real-time simulation of the validated electrical system in

the OPAL-RT simulator. ................................................................................................... 36

Fig. 15. Introduction of a high slew-rate power supply and arbitrary load results in two

isolated systems: a real-time simulation (left), and a power hardware interface (right). .. 37

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Fig. 16. Terminal voltage of the modeled system is sent out of the simulator using the

analog output peripherals at a low voltage. This analog signal is then amplified by the

power amplifier to source the load.................................................................................... 37

Fig. 17. Feedforward and feedback measurements completes the PHIL concept. .......... 38

Fig. 18. Flowchart of PHIL implementation with real examples of hardware components.

........................................................................................................................................... 40

Fig. 19. All rectifier topologies consist of the above 5 subsystems. ................................ 42

Fig. 20. The source is modeled using a 3-phase source with equivalent series non-idealities.

........................................................................................................................................... 42

Fig. 21. The modeled load consists of two linear passive elements. A relay is used in the

‘engage’ subsystem to engage the load in a controlled manner........................................ 43

Fig. 22. The ‘Universal Bridge’ serves as an excellent all-in-one solution to generating the

rectifier topologies, especially on macro-scale simulations where the total simulation time

is much larger than switching times. ................................................................................. 44

Fig. 23. Paralleling recitifer bridges requires some form of reactor in between each bridge

and the positive output node. A detailed discussion on the theory of these reactors are given

in [35]. ............................................................................................................................... 44

Fig. 24. The thyristor firing control model utilizes a PLL to lock in the timing of the

measured phases................................................................................................................ 45

Fig. 25. Firing controllers for each bridge run in parallel to eachother. .......................... 45

Fig. 26. One of the 6-pulse topolgies utilizes a simple wye-delta transformer for isolation.

........................................................................................................................................... 46

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Fig. 27. 12-phase zig-zag transformer shifts the input phases by increments of 15 degrees.

........................................................................................................................................... 47

Fig. 28. 6-pulse rectifier assembly from Applied Power Systems Inc. [36]. ................... 48

Fig. 29. 24-pulse rectifier system from Applied Power Systems [36]. ............................ 48

Fig. 30. Amatek programmable power supply provides a source that is close to ideal. This

source allows for controlled modeling of the rectifiers [37]. ............................................ 49

Fig. 31. Phase-shifting transformer sets provide the necessary additional phases for each

corresponding pulse rectifier topology. ............................................................................ 49

Fig. 32. Aluminum electrolytic capacitor bank used as the load. .................................... 50

Fig. 33. Experimental Hardware Setup. ........................................................................... 51

Fig. 34. 6-pulse (no transformer) simulation and experimental capacitor voltage waveform.

........................................................................................................................................... 52

Fig. 35. 6-pulse simulation and experimental capacitor voltage waveform. ................... 52

Fig. 36. 12-pulse simulation and experimental capacitor voltage waveform. ................. 53

Fig. 37. 24-pulse simulation and experimental capacitor voltage waveform. ................. 53

Fig. 38. 6-pulse (no transformer) generator line currents at the beginning of the charge

cycle. ................................................................................................................................. 54

Fig. 39. Harmonic spectrum of the 6-pulse (no transformer) generator line currents for the

charge cycle. ..................................................................................................................... 54

Fig. 40. 6-pulse generator line currents at the beginning of the charge cycle. ................ 55

Fig. 41. Harmonic spectrum of the 6- pulse generator line currents for the charge cycle.

........................................................................................................................................... 56

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Fig. 42. Example of highly nonlinear and asymmetric magnetization currents observed in

the 6-phase transformer..................................................................................................... 57

Fig. 43. Average harmonic spectrum of the 6-pulse transformer’s magnetization currents.

........................................................................................................................................... 57

Fig. 44. Magnetization current harmonic spectrum magnitudes subtracted from the

harmonic spectrum magnitudes of the generator line currents during charging. .............. 57

Fig. 45. 12-pulse generator line currents at the beginning of the charge cycle. .............. 58

Fig. 46. Harmonic spectrum of the 12-pulse generator line currents for the charge cycle.

........................................................................................................................................... 59

Fig. 47. 24-pulse generator line currents at the beginning of the charge cycle. .............. 60

Fig. 48. Harmonic spectrum of the 24-pulse generator line currents for the charge cycle.

........................................................................................................................................... 60

Fig. 49. Developing switching multi-pulse rectifier models without any transformers

proves to be largely trivial, especially in a 60 Hz system. ................................................ 62

Fig. 50. Piece-wise linear switching models cannot account for nonlinearities in

transformer magnetics and power quality prediction is limited. ....................................... 62

Fig. 51. Observation of the magnetization currents in the transformer primary shows

unbalanced, non-characteristic distortion. ........................................................................ 63

Fig. 52. Delta primary of the transformer broken into its constituent coils. .................... 64

Fig. 53. During individual excitation, coil B shows much less saturation current magnitude

compared to coil A and coil C. ......................................................................................... 64

Fig. 54. Each transformer coil can be modeled independently as a saturable transformer,

and then be wired back into its original 3-phase transformer form. ................................. 65

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Fig. 55. Hysteresis curves are easily obtained but are unable to be implemented into the

OPAL-RT due to a restriction inherent to the simulator. .................................................. 66

Fig. 56. A very simple plant was used to generate saturated magnetization currents for

comparison against data. ................................................................................................... 68

Fig. 57. Minimization of error in the optimized magnetization current waveforms get close

to the waveshape but are unable to account for the residual magnetization and coercive

current in the true hysteresis characteristics. .................................................................... 69

Fig. 58. Using the optimized saturation characteristics, a 3-phase transformer with an open

secondary was constructed. ............................................................................................... 70

Fig. 59. A promising comparison of experimental data to simulation data shows the

individual coils approximate the waveshape of the transformer’s unbalanced magnetization

in each line current. ........................................................................................................... 71

Fig. 60. Efficacy of proposed model in predicting power quality in multi-pulse rectifier

systems will be determined by comparing experimental and simulation data of this system.

........................................................................................................................................... 72

Fig. 61. A previously procured LabVolt 6-pulse thyristor module was used as the hardware

6-pulse rectifier [38]. ........................................................................................................ 72

Fig. 62. Simulink block diagram implemented in OPAL-RT was utilized as a controller to

fire both simulated and hardware rectifiers in the same way. ........................................... 73

Fig. 63. A Chroma 63804 AC/DC programmable load was used in a constant resistance

mode to load the hardware testbed [39]. ........................................................................... 73

Fig. 64. Experimental data shows that the %THD in a 6-pulse rectifier system varies

smoothly for a given firing angle and rated resistive load. ............................................... 75

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Fig. 65. Simulation data shows a distinctly similar characteristic in %THD profile

compared to experimental data. ........................................................................................ 76

Fig. 66. Error in the predicted %THD is minimal across variations in both firing angle and

load, with the exception of a small region in low firing angle and load. .......................... 76

Fig. 67. At one of the lowest error operation points, it is observed that individual line

current harmonics are modeled to high degree. ................................................................ 77

Fig. 68. The time domain waveforms at this operation point show superb matching

between experimental and simulation data. ...................................................................... 77

Fig. 69. Increasing the firing angle at high load shows good matching in harmonic content,

though slight deviations in individual harmonics are apparent. ....................................... 78

Fig. 70. Time domain waveforms of the simulation at a higher firing angle operation point

still show the characteristic waveshape of the experimental data. .................................... 78

Fig. 71. In the worst performing region in terms of error in %THD, harmonics are still

predicted to a fair degree. .................................................................................................. 79

Fig. 72. Time domain waveforms at this operation point fit the rough shape of experimental

data but lacks the ability to predict the highly nonlinear and transient nature of line currents

at such a low load and high firing angle. .......................................................................... 80

Fig. 73. Abstract diagram of PHIL implementation of a modeled power system. .......... 81

Fig. 74. 6-Pulse rectifier model implemented in OPAL-RT for output voltage validation.

........................................................................................................................................... 82

Fig. 75. Experimental setup for validating the emulated PHIL rectifier output against the

hardware rectifier output. .................................................................................................. 82

Fig. 76. %THD calculated from the hardware rectifier’s output voltage. ....................... 83

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Fig. 77. %THD calculated from the PHIL emulated rectifier show a very similar contour

to experimental data. ......................................................................................................... 84

Fig. 78. Comparison of the harmonic spectrums between the experimental and PHIL data

at various operation points. ............................................................................................... 85

Fig. 79. Percent error overall between experimental %THD and the PHIL %THD. ...... 86

Fig. 80. Comparisons of simulation, hardware, and PHIL emulated 6-pulse rectifier output

voltage waveforms at various power draws and firing angles. ......................................... 87

Fig. 81. Mean absolute error calculation between the hardware rectifier and PHIL

rectifier’s output voltage waveforms across the investigated range of operation. ............ 87

Fig. 82. Commercially available medium voltage power supply [7]. .............................. 88

Fig. 83. Dual DB-25 connections are utilized in the commercially available MVPS. .... 90

Fig. 84. Portion of the custom PLC realized through National Instruments hardware [41].

........................................................................................................................................... 90

Fig. 85. Block diagram of the solution to interfacing a NI-based custom PLC with the

MVPS. ............................................................................................................................... 91

Fig. 86. Block diagram showing the signal breakdown of the DB-25 cables that bridge the

PLC and the MVPS ........................................................................................................... 92

Fig. 87. Final assembly of the interface PCB, providing signal rerouting, digital and analog

signal conditioning, diagnostic and monitoring, and conversion to optical fiber. ............ 92

Fig. 88. A relatively simple LabVIEW program (front panel pictured here) was developed

to operate the MVPS. ........................................................................................................ 94

Fig. 89. Graphical code of the LabVIEW program. ........................................................ 94

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Fig. 90. Analog control of the MVPS in test mode shows that voltage, current, and power

follow the contours and rapid transients of the control signal, lending this supply to

potential in medium voltage PHIL. ................................................................................... 95

Fig. 91. OPAL-RT block diagram used to control the MVPS for MV PHIL emulation. 96

Fig. 92. MVPS fails to follow the wide ripple of the simulation voltage. ....................... 97

Fig. 93. Characteristic harmonics are present in the MVPS waveform but are significantly

reduced in magnitude compared to the theoretical values. ............................................... 97

Fig. 94. The MVPS cannot properly emulate the significant voltage ripple of the 6-pulse

rectifier but is able to accurately model the average magnitude of the rectifiers output

voltage given a change in firing angle control. ................................................................. 99

Fig. 95. MVPS is able to emulate variations in average DC output when step loaded. 100

Fig. 96. Closer inspection of the MV output waveforms shows the transient capability of

the MVPS for PHIL emulation. ...................................................................................... 100

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Chapter 1: Introduction

A prominent notional power system topology has been proposed as a solution to integrate

traditional rotating machines along with distributed energy storage to serve electrical loads in

commercial isolated DC microgrids [1]. This topology is a transition from traditional AC

distribution in existing commercial isolated DC microgrids with limited organization, to a new

paradigm of zonal DC distribution and conversion with power electronic converters [2],

summarized visually in Fig. 1. The topology in question divides the microgrid into zones that

divide up the overall electric generation assets and load groups as evenly as possible. Spanning the

zones are two DC busses that allow for power distribution. These busses are located geographically

apart from each other and attempt to not deviate far physically from any load group. Both busses

operate and are independently regulated at a nominal medium voltage in the proposed topology.

Various DC voltage magnitudes have been proposed for these DC microgrids, such as 1 kVDC, 6

kVDC, 12 kVDC, and up, though this voltage is far from certain.

Fig. 1. Notional zonal topology for DC distributed microgrids [1].

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In this microgrid topology, dual-wound generators provide isolated power independently to

each bus. The AC generation is always converted to DC and fed to the MVDC busses; there is no

AC distribution to the rest of the microgrid directly from the generators. All electric loads draw

power from the DC busses, but individual loads are serviced from a load center that may have its

own energy storage. Despite localized energy storage, this proposed topology does not allow for

reverse power flow from load center energy storage to the busses. In other words, the 12 kVDC

busses are regulated solely by generation conditions and power electronic converters [1].

To convert the AC power to DC power, it is necessary to utilize a power electronic rectifier of

some kind [3]. The most traditional method of rectifying AC power is through a full-wave bridge

rectifier. In a 3-phase system, this type of converter is referred to as a 6-pulse rectifier. It is

understood that while these rectifiers can convert AC power to DC power, they also introduce high

magnitudes of harmonic distortion, leading to a low power factor in the generators [4, 5]. The more

the power factor diverges from unity, the more the power generation must be oversized to meet

the demand of the load. It is important for future microgrids to be able to anticipate what the power

quality will be for the generators given the choice in rectifier design.

In order to evaluate the proposed topology, a testbed was built at the University of Texas at

Arlington (UTA) that could test many different configurations and medium voltage ratings,

ranging from 480 to 4160 VAC and 1 to 12 kVDC, at power ratings in the hundreds of kilowatts.

This test bed contains a multitude of commercial-off-the-shelf (COTS) type equipment for use in

evaluating the different topologies and operational scenarios of isolated DC microgrids. Starting

at the left of Fig. 2, since MVDC microgrids may be integrated with traditional grid power (at least

in some scenarios) a 3-phase, 480 VAC grid connection is present. In cases of microgrid isolation,

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a VFD driven motor-generator set, seen in Fig. 3, that accepts 480 VAC grid power and produces

separate 3-phase 480 VAC power as the microgrid’s prime power source. Either the grid or the

motor-generator can be used as the supply for the main 3-phase 480 VAC bus in the center of the

diagram in Fig. 2. Moving further to the right of the 480 VAC bus, there is an AC/AC converter

implemented with a General Electric MV6 [6], pictured in Fig. 3. In addition, there are a couple

AC/DC converters that convert what would be the isolated microgrid’s prime power source to

various medium voltage levels. Immediately available off the bus are 480 VAC to 1 kVDC and

480 VAC to 12 kVDC AC/DC converters [7]. These converters serve as the basis for the medium

voltage distribution concept being implemented in hardware. Further, the 1 kV bus has two

possible energy storage options as a 1 kV lead-acid battery assembly and a 1 kV lithium-ion battery

assembly [8] to represent one possible implementation of a distributed energy storage element in

the overall zonal concept. Also, on the 1 kV bus is a 1 kV to 6 kV DC/DC converter that serves as

the realization of a 6 kV MVDC bus. In almost all cases, these power converters are attached to

discretely variable resistive loads. Aside from drawing variable load by introducing more or less

resistance, the outputs of all converters (AC and DC) are all controllable with analog following,

allowing for the converters to implement arbitrary load profiles and even exhibit behaviors and

characteristics of modeled converters, machines, and power systems. The later ability is

accomplished through the use of Power Hardware-In-The-Loop methods [9, 10, 11] implemented

with the testbed power converters and a real-time simulator.

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Fig. 2. One-line diagram of the MVDC microgrid testbed developed at UTA.

Fig. 3. Picture of the AC/AC converter (foreground) [6] and motor-generator pair (background)

[12] in the MVDC testbed implemented at the University of Texas at Arlington.

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Power Hardware-In-The-Loop (PHIL) offers a unique tool for anticipating how design choices

will affect the overall power system. PHIL utilizes a real-time simulator and power amplifiers to

emulate a physical component or power system that is not in possession. Theoretically, system

level integration of the emulated component or power system with other real hardware can be

achieved. This is most useful when there is existing hardware that the PHIL emulated power

system can interface with. This way, without having to procure entire motor-generators,

transformers, and rectifier systems, power quality and system performance of the full microgrid

can be studied. In addition, many different types of generation sources, transformers, and rectifier

topologies can be investigated with only investing in one real-time simulator and one robust power

amplifier. The MVDC testbed at UTA can be utilized by the real-time simulator to implement

PHIL at medium voltage levels to study isolated DC microgrid topologies for commercial

applications. It is theoretically possible for a multitude of power system topologies converting

rotating machine AC power to DC power to be studied; however, it has not been shown

quantifiably that PHIL can properly emulate rectifiers at the medium voltage level. This work

strives to present data on PHIL’s ability to emulate rectifiers with validated models at a medium

voltage level, and present precisely to what fidelity they can be implemented with state-of-the-art

technology.

First, a background on relevant topics is given in chapter 2. In chapter 3, early work on

developing linear, real-time simulator compatible multi-pulse rectifier models for charging

capacitors is presented. These models are validated against a low-voltage rectifier test bed.

Limitations imposed by the simulator and the effect they had on the model results is discussed. In

chapter 4, significant improvements to the model is made by a novel method of modeling

transformer characteristics. The model is validated on its input power quality characteristics, and

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a quantifiable comparison is made to the low-voltage experimental testbed. In chapter 5, the

validated model is implemented in PHIL at a low voltage. The hardware rectifier output and the

PHIL emulated output are compared and quantifiably analyzed. In chapter 6, the validated model

is scaled up to the medium voltage level of the MVDC hardware testbed. This scaled model is

implemented with a state-of-the-art power amplifier, and the ability to perform PHIL for medium

voltage hardware is quantifiably presented and discussed. Finally, conclusions and discussion on

PHIL emulation overall is presented.

Chapter 2: Background

Rotating Machines

Large rotating machines providing AC power to microgrids are typically driven by a diesel or

gas-turbine prime mover, such as the GE LM2500 [13] in Fig. 4. The generator typically produces

3-phase power at 60 Hz. Line-to-line voltage of the generators can range from 450 VAC to 4160

VAC to up to 13.8 kVAC, at hundreds of kilowatts to tens of megawatts. In general, these large

machines have poor transient capabilities; meaning that they cannot effectively handle significant

changes in their load [4, 5, 14]. Future electric loads may be transient, or at least stochastic in

nature [15, 16, 17, 18], so the new DC microgrid approach presented here is an attempt to alleviate

stress on a single motor-generator by utilizing distributed generation in the form of other rotating

machines and energy storage.

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Fig. 4. The General Electric LM2500 is a common prime mover [13].

Multi-Pulse Rectifiers

The conversion from AC power to DC power for newly proposed DC microgrid systems is

accomplished by power electronics topologies called rectifiers [3, 19, 20, 21]. Rectifiers typically

utilize diodes as a unidirectional switch in these topologies, though other semiconductor or value

switches can be used. Diodes are often used because they lack any control inputs compared to

other switches such as, thyristors or FETs. For rectifying single phase AC, two general topologies

are used [22]. First, the half-wave rectifier in Fig. 5 (left) requires only one diode switch to perform

rectification. On the positive half-cycle of the AC source, the diode will conduct, and power will

be delivered to the load. On the negative half-cycle of the source, the diode will turn off and power

flow is stopped. This way, the load only experiences a positive voltage when the diode is

conducting, shown in Fig. 6, and effectively no voltage when the diode is not conducting.

Significant harmonics exist in the input current waveform as well as the output voltage

waveform due to the negative-half cycle of the current waveform being cut off. The second

topology, the full-wave rectifier, also in Fig. 5 (right), utilizes four diodes to rectify both the

positive and negative half-cycles of the AC source. Both topologies have an output voltage ripple

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magnitude equal to the amplitude of the AC source voltage. However, for a full-bridge rectifier,

the input current harmonics are almost nonexistent for a linear resistive load. Since both half-

cycles of the AC voltage is rectified, both positive and negative half-cycles of current waveforms

are conducted, producing a sinusoidal current waveform with minor harmonic content due to diode

switching commutation, line inductance, etc.

Fig. 5. Half-wave single-phase rectifier (left), Full-wave single-phase rectifier (right), both with

resistive loads.

Fig. 6. Comparison of single-phase output voltage waveforms [22]: half-wave (left) and full-

wave (right).

26

Three-phase rectifiers offer some interesting tradeoffs compared to single-phase rectification

[3, 19]. 3-phase, full-wave rectifiers produce six voltage pulses at their output, and are commonly

called 6-pulse rectifier, shown in Fig. 7. In addition to this nomenclature, any rectifier with a pulse

number greater than or equal to six is considered a multi-pulse rectifier. Notably, 6-pulse rectifiers

are the first topology so far that offers a voltage output waveform that does not return to zero volts,

observed in Fig. 8, meaning that the output voltage ripple is inherently much smaller in magnitude

compared to single-phase rectifiers. As the pulse number is increased, the ripple magnitude is

decreased and the ripple frequency increases [19, 23], as seen in Fig. 9.

Fig. 7. Circuit schematic of a thyristor-based 6-pulse rectifier [20].

Fig. 8. Time domain voltage waveforms of an ideal 6-pulse rectifier [20].

27

Fig. 9. Comparison of output voltage waveforms for multi-pulse rectifier topologies.

The 6-pulse output voltage ripple also has considerable improvements in harmonic content

[19], where the first theoretical harmonic appearing after the average DC voltage is the 6th

harmonic. The higher order the harmonics in the system is, the easier it is to filter the waveform

as smaller value (thus smaller physical size and weight) passive filter components can be used.

The rectifier pulse number can be increased by multiples of 6 by using additional three-phase full-

wave bridges and phase-shifting transformers [3, 19]. The phase-shifting transformers create

separate, galvanically isolated, three-phase voltage waveforms at the input of each respective

rectifier bridge. Since the newly generated three-phase waveforms are galvanically isolated from

each other due to the transformers, the three-phase rectifier bridges can be placed in series or

parallel to increase the effective pulse number of the overall system. If phase-shifting is done

properly, harmonic cancellation can be observed in the input line currents and the output voltage

[3, 19, 21].

Each additional group of 3-phase power must be properly spaced in phase for harmonic

cancelation. There are existing rigorous derivations that can be referenced for a more detailed

28

explanation of the harmonic cancelation phenomenon [3, 19]. The phase-shift necessary for any

multi-pulse rectifier with a pulse number greater than six can be calculated with equation (1).

𝜑 =360°

𝑛 (1)

𝑛 = 12, 18, 24,…

The 30-degree shift needed for 12-pulse rectifiers can be achieved with a delta-wye

combination as shown in Fig. 10. It is inconsequential whether the phase shift is leading or lagging

by 30 degrees. For multi-pulse rectifiers with a pulse number 18 or greater zig-zag transformers

are necessary to achieve phase shifts less than 30 degrees [3, 19, 23].

Fig. 10. Ideal 12-pulse rectifier schematic.

Multi-pulse rectifiers can be enhanced by replacing diode switches with thyristors for

controllability. Thyristors (sometimes referred to as Silicon Controlled Rectifiers or SCRs) are 4-

layer semiconductor devices that behave much like diodes [24, 25]. The major difference to note

29

between the two devices for this work is that a thyristor has an addition terminal called the gate

along with the cathode and anode terminals like a diode. A thyristor must be triggered with a

positive voltage from the gate to the cathode while the anode-cathode is under forward bias for the

device to begin to conduct. For rectifiers, delaying the triggering signals to each thyristor relative

to the input phase voltages effectively lowers the average DC voltage output of the rectifier [19,

24, 25]. The introduction of this delay, otherwise known as firing angle, allows for full control of

the output voltage. The theoretical average DC output voltage of a multi-pulse rectifier with a set

firing angle α can be derived by finding the average value over one pulse of the system. First, the

pulse number of a rectifier can be defined by:

𝑛 = 6𝑘 (2)

𝑘 ∈ ℕ

where 𝑘 is the number of 6-pulse full-wave bridges. Next, we define the line-to-line voltage being

rectified as a sinusoid with no phase relative to the origin

𝑉𝑥𝑦 = 𝑉𝑚cos(𝜔𝑡) (3)

where 𝑉𝑚 is the peak magnitude of the phase-phase voltage, and 𝜔 is the AC frequency in radians

per second. Now, the average output voltage of a n-pulse rectifier can be determined by evaluating

the following integral and evaluation limits:

𝑉𝑜 =1

𝜑𝑓−𝜑𝑖∫ 𝑓(𝜑𝑓𝜑𝑖

𝜔𝑡)𝑑𝜔𝑡 (4)

30

𝜑𝑓 − 𝜑𝑖 =2𝜋

𝑛 (5)

𝜑𝑓 =𝜋

𝑛 (6)

𝜑𝑖 = −𝜑𝑓 (7)

Substituting relevant parameters into (4) leads to:

𝑉𝑜 =𝑉𝑚𝑛

2𝜋∫ cos(𝜔𝑡)𝑑𝜔𝑡𝜋

𝑛+𝛼

−𝜋

𝑛+𝛼

(8)

Evaluation of this integral results in:

𝑉𝑜 =𝑛𝑉𝑚

2𝜋sin(𝜔𝑡)|

−𝜋

𝑛+𝛼

𝜋

𝑛+𝛼

(9)

𝑉𝑜 =𝑛𝑉𝑚

2𝜋[sin (

𝜋

𝑛+ 𝛼) − sin(−

𝜋

𝑛+ 𝛼)] (10)

𝑉𝑜 =𝑛𝑉𝑚

2𝜋[sin

𝜋

𝑛cos 𝛼 + cos

𝜋

𝑛sin 𝛼 − sin

−𝜋

𝑛cos 𝛼 − cos

−𝜋

𝑛sin 𝛼] (11)

𝑉𝑜 =𝑛𝑉𝑚

2𝜋[sin

𝜋

𝑛cos 𝛼 + cos

𝜋

𝑛sin 𝛼 + sin

𝜋

𝑛cos 𝛼 − cos

𝜋

𝑛sin 𝛼] (12)

𝑉𝑜 =𝑛𝑉𝑚

𝜋sin (

𝜋

𝑛) cos 𝛼 (13)

Using Equation (13), the maximum average output voltage of each multi-pulse rectifier can be

estimated. In all defined multi-pulse rectifiers, the average output voltage can be attenuated by a

factor of cos 𝛼 by adjusting the firing angle α accordingly [3].

31

Magnetics and Transformers

Zig-zag transformers, such as in Fig. 11, utilize secondary coils that are magnetically coupled

to more than one phase of the primary. Changing the turn ratio of these secondary coils relative to

the primary results in a secondary voltage waveform defined by equations (14) and (15).

𝑀𝑋 = 𝛼∠𝛽° (14)

{

𝑀 = √

𝛼2

(√3−tan𝛽

4tan2 𝛽)(tan𝛽+√3)+1

𝑁 =𝑀(tan𝛽−√3)

2 tan𝛽

(15)

For example, an 18-pulse rectifier would require a 20° shift between each of the three, three-

phase groups. To achieve one of the 20° shifts, a wye-star configuration, as shown in Fig. 11, can

be used. Using a normalized turn ratio of -0.742 (inverse polarity) on the first coil and a normalized

turn ratio of 0.395 of the second coil, a secondary voltage with a normalized magnitude of 1 and a

phase shift of 20° is produced. Further calculations can be made to determine any other phase shift

needed for any other multi-pulse topology, such as 15° shift needed in the 24-pulse rectifier in Fig.

12. More rigorous descriptions of designing zig-zag and other transformers is outside the scope of

this work and is available in [26, 27, 28, 29].

32

Fig. 11. Zig-zag transformers allow for phase-shifts less than 30 degrees.

Fig. 12. Zig-zag transformer diagram for a 24-pulse rectifier [30].

33

As will become apparent in the following chapters, understanding transformer nonlinearities

is crucial. The relationship between magnetic flux density B and magnetic field strength H is

determined by the core material characteristics of the transformer. For free space or air, the B-H

characteristic remains approximately linear across excitation. For other materials, such as iron or

steel, the B-H curve starts to exhibit nonlinear characteristics. The nonlinear characteristic is

saturation, where further increases in magnetic field strength results in diminishing returns to the

flux density. In terms of electrical circuit parameters, applying too much excitation voltage over

time will result in ever increasing current levels until an upper limit is reached by the coil’s

resistivity. The second nonlinear characteristic observed is hysteresis. In essence, the transformer’s

core has a “memory effect” where the core will tend to stay magnetized to one polarity and resist

reversal to the opposite polarity. This resistance results in a hysteresis loop like in Fig. 13 where

each application of positive or negative flux deviates from a single saturation path [31]. This

hysteresis loop can introduce harmonic distortion in 3-phase line currents beyond what is typical

to rectifier systems.

Fig. 13. Example of a hysteresis loop that is typical of transformer core material [31].

34

Power Hardware-in-the-Loop

This section provides the overall concept of PHIL as a method for power system emulation in

real-time. PHIL allows for the real-time simulation of a physical component that is not in

possession. PHIL is an extension of normal Hardware-In-The-Loop (HIL) by introducing high

power components as the system being emulated by HIL simulator. The process begins by

developing a model of the power hardware that is to be emulated. The more accurate the model is,

the more effective PHIL will be in assisting the design process. This means that model validation,

or comparing model data to real-world data, is a crucial first step in PHIL. A model can be

developed and validated against a low power and low voltage hardware testbed. Once the low

power model has been validated, the model can be scaled up to the power and voltage levels of the

original hardware in question at medium voltage and power levels for isolated DC microgrids.

Since the low-power model has been validated, it is likely that the scaled-up model will produce

valid results as well. Further validation against similar medium voltage hardware can as well be

performed to improve the PHIL emulations validity.

In order to accomplish real-time simulation, the newly validated model must be deployed onto

a real-time computing system. In this case, all models developed were created in the MATLAB

Simulink environment, and deployed on an OPAL-RT real-time simulator. OPAL-RT is common

commercially available real-time simulator and is the de facto standard of real-time simulators for

engineering groups developing isolated DC microgrids [32], therefore it is the system that will be

used in the following studies.

Initially, the hardware that is desired to be emulated needs to be identified. This hardware can

be a single component, it can be a certain circuit, such as multi-pulse rectifier, or it can be a full

35

power system, such as a DC microgrid itself. As an example for explaining PHIL, a simple circuit

of an ideal voltage source with a series resistance is used. First a model of the system must be

developed and then validated. This circuit is overly simple and trivial to model for the sake of this

example, but for more complex and unideal systems, care must be taken to develop a model that

is an accurate representation of the physical hardware. In any case, the modeled power system has

at least one electrical input or output port that can be characterized by a voltage or current. For

example, a rectifier system’s main purpose is to output a voltage at its output terminals from which

electrical current can flow. Despite the nature of switches, magnetics, or input AC power, the

rectifier system can be represented as a black box with a single, two-terminal voltage output. In

order to assure that the black box is representative or rectifier dynamics, careful measurements of

the hardware must be taken across a relevant area of operation to ensure the dynamics of the model

are representative to the highest degree possible. There are many ways to address the validity of

modeled systems, and emphasis may be placed on certain aspects of the system behavior that

qualifies the model as “valid”.

Once the model is validated, it can be imported into a real-time simulator like the OPAL-RT

for real-time simulation. Each simulator will have its own advantages and drawbacks depending

on the type of hardware it utilizes. For example, a simulator with a multi-core processor will be

able to simulate larger models, such as a distributed power system, if the model can be divided up

among the processors cores. However, this type of simulator may lack the ability to solve the

simulation in ever decreasing time-steps. An FPGA-based simulator, on the other hand, may be

limited to small models, but can solve fast enough to emulate the switching of power electronics

converters at very small timesteps. Beyond these constraints are limitations of the simulation

platform that the simulator operates on. Some simulators utilize MATLAB Simulink as the

36

simulation platform, which has its own benefits and drawbacks, while other simulators have

developed their own simulation platform for specific specialized applications. In Fig. 14, the

validated model has been loaded onto the OPAL-RT platform, and may interact with system

peripherals that allow for digital and analog signals to be sent in or out to communicate with the

physical world.

Fig. 14. Abstracted diagram of real-time simulation of the validated electrical system in the

OPAL-RT simulator.

The power hardware used to emulate the power system in question has no inherent knowledge

of the dynamics of the modeled power system, as seen in Fig. 15. The power system’s output may

have any combination of DC, AC, transient, or stochastic characteristics, and the power supply

that is emulating the power system must be selected such that it has the bandwidth and slew rate

to meet the dynamic needs of the modeled system. The selected power supply can then be loaded

by any arbitrary physical load. The load could be a passive load, such as a resistor or capacitor, a

nonlinear load, or an entire additional power system itself, such as a hardware testbed for isolated

DC microgrids. Obviously, the power supply selected should be rated such that it can fully supply

power to the load without any significant loading effects or variations in response.

37

Fig. 15. Introduction of a high slew-rate power supply and arbitrary load results in two isolated

systems: a real-time simulation (left), and a power hardware interface (right).

The real-time simulation and power hardware can be interfaced together to complete PHIL. At

first, the example model is only an open circuit system with a voltage at its output terminals in Fig.

16. The voltage of the power system’s output is known in the simulation and then sent out to the

controllable power supply as a feedforward analog control signal.

Fig. 16. Terminal voltage of the modeled system is sent out of the simulator using the analog

output peripherals at a low voltage. This analog signal is then amplified by the power amplifier

to source the load.

Next, by adding a controllable load in the simulation, such as the current sink in Fig. 17, the

model can be loaded. As soon as the model’s terminal voltage is sent to and actualized by the

38

controllable power supply, the attached load draws current. The load current is fed back into the

simulator as an analog feedback signal, and then scaled back to the level seen in the power

hardware. This is then used by the current sink to load the running model in real-time. Now both

the output voltage 𝑉0 and output current 𝐼0 in Fig. 17 are represented in both the simulation and

the hardware. With PHIL fully implemented now, the power supply is now emulating the model

without the real power system being present.

Fig. 17. Feedforward and feedback measurements completes the PHIL concept.

Table 1 summarizes the iteration the simulator must take to perform PHIL. As an example, the

simulated DC source is selected to be 10 volts, the simulated series resistance is selected to be 1

ohm, and the physical power resistor is selected to be 9 ohms. So, ideally, the output voltage should

be 9 volts and the output current should be 1 amp. Also, it is assumed for sake of the example the

controllable power supply is ideal, though in reality there will be some error in the true output

voltage of the power supply due to noise, error in analog control and simulator gains, bandwidth

of all relevant subsystems, etc. Note that these values are updating on the order of ten

microseconds, which is around the magnitude of solving speed for most simulators, though faster

solving speeds are absolutely possible. In the initial time step, the output voltage of both the

39

simulation and the power supply is 10 volts. At this point, current is flowing in the physical load,

but the simulation must wait until the next time step to sample the load current and implement it

in the model, so the output remains at zero. In the second time step at 10 microseconds, the current

of the load is 1.111 amps because the power supply is still being commanded to produce 10 volts

with a 9 ohm load. This current feedback commands the current sink to draw 1.111 amps in the

model. The output voltage of the model then becomes loaded and is solved to be about 8.889 volts.

This change in simulation voltage is then fed out to the power supply, commanding it to change

the physical output voltage to 8.889 volts, thus completing the PHIL iteration cycle. This process

of measurement, solving, and updating repeats in real-time until a steady state is reached. The

simulator continues to operate, so even if the load changes abruptly for an arbitrary reason, the

simulation is constantly being solved to react to the change in output current due to a change in

hardware load.

Table 1. Solving iterations of an example PHIL system

𝑇𝑠 (μs) 𝑉0(𝑉) 𝐼0(𝐴)

0 10.000 0.000

10 8.889 1.111

20 8.988 1.001

30 8.999 1.000

40 9.000 1.000

More complex power systems than the given example can be implemented for emulation. This

way, whole microgrids can be represented by a real-time PHIL simulation, but still be able to

40

interact with physical loads, or other microgrids. A major objective of PHIL is the ability to not

only emulate the overall macro behavior of a power system, but to also emulate the power quality

and harmonic content of various components so they can be predicted and analyzed in PHIL

simulation before designs are finalized. In addition, depending on the goals of the simulation, it is

just as important for the input characteristics of a system to be modeled as well as the output

characteristics. A final diagram of PHIL emulation with example equipment is presented in Fig.

18.

Fig. 18. Flowchart of PHIL implementation with real examples of hardware components.

Chapter 3: Real-time multi-pulse rectifier models for capacitor charging applications

Initial work with multi-pulse rectifiers sought to evaluate the power quality of the input 3-

phase waveforms for charging capacitor banks. The following material in this chapter has been

previously documented in [33]. Rectifier topologies have been well established in literature [3, 19,

21, 22, 23, 25, 30, 34]; however, there is little to no documented work on utilizing rectifier circuits

41

to charge capacitive loads. This lack of published knowledge was the initial thrust of the

development of rectifier models for isolated DC microgrids in the context of real-time simulation.

Primarily, the magnitude of harmonic distortion in the input current waveforms was investigated

in order to make the multi-pulse rectifier circuits conform to standards of operation of isolated DC

microgrids, similar to existing standards for other microgrid applications. The focus of this work

was to develop models of multi-pulse rectifiers that allowed the designer to predict the impact the

chosen rectifier topology would have on the power quality of the line currents of the rotating

machines producing prime power in the isolated DC microgrids. As a major requirement, these

models need to be compatible with the OPAL-RT real-time simulator utilizing standard Simulink

blocks in the Simscape Power Systems block set, as compared to more mathematics-based models

in [34]. This was done to allow the techniques presented in this work to be implemented in practice

by engineering groups involved in the development of isolated DC microgrids.

Simulink Models

The rectifier models developed here were completed using the Simscape Power Systems

toolbox in MATLAB Simulink that is the main ‘language’ of the OPAL-RT system. This toolbox

contains many pre-built passive circuit and active switching elements that are deployable to an

OPAL-RT HIL platform. In general, the model of each rectifier topology consists of five

subsystems as seen in Fig. 19, namely the source, phase-shifting transformers (if necessary),

rectifier bridges, thyristor firing controller, and the capacitive load.

42

Fig. 19. All rectifier topologies consist of the above 5 subsystems.

Across each of the topologies studied, there are several subsystems that remain identical. For

simplicity initially, the source in all cases is an ideal 3-phase voltage source with series resistance-

inductance added in each line, seen in Fig. 20. A 3-phase measurement block is used to extract the

waveform data from the simulation.

Fig. 20. The source is modeled using a 3-phase source with equivalent series non-idealities.

Another identical subsystem across all topologies is the load as seen in Fig. 21, which consists

of a current limiting resistor and the load capacitor in series. Series resistance is necessary to avoid

a large inrush current to the capacitor during at the application of each voltage pulse. In practical

applications, this resistor can be reduced or replace with a choke inductor; however, for modeling

purposes it serves as a simple way to ensure safety and stability, while also removing the need for

a controller that may vary across experiments and introduce error. Aside from standard

43

measurement blocks, the only additional element in the load is an ideal switch that allows the load

to be connected to the circuit in a controlled manner.

Fig. 21. The modeled load consists of two linear passive elements. A relay is used in the

‘engage’ subsystem to engage the load in a controlled manner.

The differences among the various topologies studied largely consists of the addition of similar

block sets in parallel as the pulse number is increased. In the following comparisons subsystems

from the 6-pulse and 24-pulse topologies are used. Fig. 22 presents a universal 6-pulse rectifier

block that includes a 3-phase bridge constructed using thyristor switches, along with the interphase

inductor used to balance the different voltages of each rectifier bridge’s output when multiple

bridges are connected in parallel. Fig. 23 demonstrates how ‘universal bridges’ blocks can be

placed in parallel with each other to form higher-order pulse rectifiers. The negative output of each

respective universal rectifier bridge is electrically connected creating a single negative output

node. The rectifier’s interphase inductors are tied together to form a single positive output node.

44

Fig. 22. The ‘Universal Bridge’ serves as an excellent all-in-one solution to generating the

rectifier topologies, especially on macro-scale simulations where the total simulation time is

much larger than switching times.

Fig. 23. Paralleling recitifer bridges requires some form of reactor in between each bridge and

the positive output node. A detailed discussion on the theory of these reactors are given in [35].

Fig. 24 presents the firing control subsystem that consists of a 3-phase PLL block that is used

to effectively lock on to the frequency and phase of the 3-phase source and a pre-made pulse

generator block that is used to apply the trigger pulse to each respective thyristor gate. The firing

angle, input in degrees, can be manually entered as a constant or varied using a user designed

controller.

45

Fig. 24. The thyristor firing control model utilizes a PLL to lock in the timing of the measured

phases.

Fig. 25 presents the firing control schematic used in the implementation of a 24-pulse rectifier.

Notice that the control blocks implemented in Fig. 25 are the same as those presented in Fig. 24

but utilized four times. One set of blocks for each of the four respective active rectifier bridges is

needed to achieve 24-pulse rectification. The phase-shifted voltages on the secondary windings of

the phase-shifting transformer are used to time the firing of each respective phase.

Fig. 25. Firing controllers for each bridge run in parallel to each other.

46

The phase-shifting transformer utilized in each topology varies considerably. In a 6-pulse

rectifier, the transformer does not shift any phases, but instead only galvanically isolates the 3-

phase source from the rectifier. This is because each phase of a 3-phase source directly feeds its

own dedicated rectifier bridge. Fig. 26 presents the wye-primary to delta-secondary isolation

transformer block utilized in the 6-pulse rectifier simulation. The turns ratios of each transformers

can be adjusted by the user, and in this case is set to a 1:1 ratio. In a 12-pulse rectifier, which is

not shown here, a transformer that has a single delta primary winding for each of the three input

phases and both a wye and delta secondary. This results in six output phases that are rectified by

two rectifier bridges.

As the pulse number increases, the secondary windings become more complicated. In the cases

of the 24-pulse system, the transformer output phases increase to twelve with a phase shift of 15

degrees. Fig. 27 presents schematic of the 24-pulse transformer model studied here. The first zig-

zag block is set to phase shift 15 degrees, the second block is set to phase shift 30 degrees, the

third to 45 degrees, and the fourth to 60 degrees.

Fig. 26. One of the 6-pulse topolgies utilizes a simple wye-delta transformer for isolation.

47

Fig. 27. 12-phase zig-zag transformer shifts the input phases by increments of 15 degrees.

Hardware Validation

In order to validate the computer-aided models, equivalent 6-pulse, 12-pulse, 24-pulse

hardware rectifiers custom designed by Applied Power Systems [36] were procured for study with

operational parameters of 120 VAC line-to-line, 60 Hz frequency, and power output as high as a

few kilowatts. Each respective rectifier was constructed using thyristors so that the output voltage

can be adjusted as needed. Once validated, it is intended that the rectifier models can be deployed

in an experimental hardware setup in which an OPAL-RT HIL platform can be used to implement

the rectifiers at scaled levels applicable to the commercial isolated DC microgrid applications

being studied.

Thyristor rectifier systems were procured from Applied Power Systems Inc. [36]. The 6 and

24-pulse systems are shown in Fig. 28 and Fig. 29, respectively. The thyristor modules consist of

48

two thyristors as a half bridge. Three thyristor modules are used to make one 3-phase full-wave

rectifier bridge.

Each rectifier is assembled with its own unique onboard controller that is used to send trigger

signals to the gates of the thyristors. The rectifier output voltage, set through adjustment of the

thyristors firing angles, and current limits are each able to be adjusted using its own respective

user-varied potentiometer. Optionally, connection to each respective potentiometer connector can

be removed, and a 0-5 V analog signal can be applied by an external controller so that the firing

angle can be adjusted remotely.

Fig. 28. 6-pulse rectifier assembly from Applied Power Systems Inc. [36].

Fig. 29. 24-pulse rectifier system from Applied Power Systems [36].

49

Ametek® CSW5550 programmable 3-phase power supplies, seen in Fig. 30, are being used as

the electrical input source to the rectifiers being studied. A unique phase-shifting transformer was

procured for use with each multi-pulse rectifier, seen in Fig. 31, that has the correct number of

phase-shifted secondary windings. In each experiment performed here, the rectifiers are loaded

with a module of ten 400 V aluminum electrolytic capacitors in parallel with an equivalent

capacitance of 4.8 mF. The capacitor module is shown photographically in Fig. 32.

Fig. 30. Amatek programmable power supply provides a source that is close to ideal. This

source allows for controlled modeling of the rectifiers [37].

Fig. 31. Phase-shifting transformer sets provide the necessary additional phases for each

corresponding pulse-rectifier topology.

50

Fig. 32. Aluminum electrolytic capacitor bank used as the load.

To validate the models, the hardware was assembled and instrumented, shown in Fig. 33. To

perform the capacitor charge, the experimental setup is first brought to steady-state operation at a

constant firing angle. Data acquisition begins and a load relay is used to engage the capacitive

load. The system charges the capacitor with a constant voltage for five seconds as an example of

a typical capacitor charging profile in an isolated DC microgrid. After the charge period has

completed, the capacitor is disengaged from the rectifier system by opening the load relay. The

energy stored in the capacitor is dumped though discharge resistors with a discharge relay.

In addition to power quality, the main objective of these rectifier topologies is to charge

capacitor banks, so modeling of the capacitors voltage during a charge cycle is important for

validation. Data has been taken from the test setup described above to determine the model’s ability

to predict both the capacitor voltage and power quality during a charge cycle on experimental

hardware. A high level of matching in the time and/or frequency domain waveforms will show

model validation.

51

After the experiments were performed, the experimental data was imported into MATLAB-

Simulink for post processing. Experimental data and simulation data were synchronized in phase

with each other for each corresponding topology, and relevant plots were generated. In addition,

the harmonic spectrums of relevant waveforms were generated and plotted using MATLAB’s

discrete Fourier transform function.

Fig. 33. Experimental Hardware Setup.

Results

A) Load capacitor charge voltage

It is initially observed from the models that the capacitors charge in the simulation at the same

rate as the experiment. Despite some discrepancy in the matching between the simulation and

experimental harmonics of the generator currents discussed later, all models of the 6, 12, and 24-

pulse topologies appear to be valid in charging the capacitors to a desired voltage as seen in Fig.

34 through Fig. 37. This consistency shows the model’s validation due to their ability to properly

model the rectifier’s output.

52

Fig. 34. 6-pulse (no transformer) simulation and experimental capacitor voltage waveform.

Fig. 35. 6-pulse simulation and experimental capacitor voltage waveform.

53

Fig. 36. 12-pulse simulation and experimental capacitor voltage waveform.

Fig. 37. 24-pulse simulation and experimental capacitor voltage waveform.

B) 6-pulse rectifier validation without the use of an isolation transformer

Time domain source current waveforms collected during evaluation of the 6-pulse rectifier are

shown in Fig. 38 for the case when it was operated without the use of an isolation transformer

between the source and the rectifier. Simulated current waveforms are also presented for

54

comparison with the experimentally collected data. A plot of the harmonic content within the

current waveforms shown in Fig. 39. Within the plot, both experimentally measured and simulated

harmonic content, respectively, are presented. As shown, there is excellent agreement between the

simulated and experimental data collected in this experiment.

Fig. 38. 6-pulse (no transformer) generator line currents at the beginning of the charge cycle.

Fig. 39. Harmonic spectrum of the 6-pulse (no transformer) generator line currents for the

charge cycle.

55

C) 6-pulse rectifier validation (with inclusion of an isolation transformer)

The next series of experiments performed are with the same 6-pulse converter just shown;

however, the isolation transformer has been added between the source and the rectifier. A

comparison of the experimental and simulated source current data, respectively, is presented in

Fig. 40. As shown, there are significant differences between the experimental and simulated data.

In addition, in the harmonic spectrum plot seen in Fig. 41, there is uncharacteristic distortion in

the lower order harmonics when compared with the simulation results. This discrepancy is directly

the result of the nonlinear saturation and hysteresis characteristics of the transformer core.

Fig. 40. 6-pulse generator line currents at the beginning of the charge cycle.

56

Fig. 41. Harmonic spectrum of the 6-pulse generator line currents for the charge cycle.

Fig. 42 shows the highly nonlinear and asymmetric nature of the transformer magnetization

currents and Fig. 43 shows the average harmonic spectrum of those currents. When the

magnetization current harmonics are subtracted from the generator harmonics under load in Fig.

44, the resulting harmonic spectrum matches quite well for most harmonics except for the 5th

harmonic. This shows that not only do the transformers add harmonic distortion in general, but the

transformers also perform some nonlinear transformation on the harmonics introduced by the

power electronics. This realization is important when trying to predict power quality, as the extra

distortion introduced by the transformer cannot just be subtracted out in post. It is clear that the

transformer’s core characteristics must be modeled if the power quality is to be modeled properly.

57

Fig. 42. Example of highly nonlinear and asymmetric magnetization currents observed in the 6-

pulse transformer.

Fig. 43. Average harmonic spectrum of the 6-pulse transformer’s magnetization currents.

Fig. 44. Magnetization current harmonic spectrum magnitudes subtracted from the harmonic

spectrum magnitudes of the generator line currents during charging.

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D) 12-pulse rectifier validation

When the 12-pulse rectifier is evaluated, similar results are observed. The experimental and

simulated waveforms, presented in Fig. 45, closely match each other, though distortion is

introduced by the model due to the phase shifting transformer. Comparison of the experimental

and simulated harmonic content measured during evaluation of the 12-pulse rectifier is quite good,

remaining within roughly 1% with respect to the fundamental as shown in Fig. 46. A result of the

distortion introduced by the transformer is less predictive power as compared to the 6-pulse

topology. When compared with the harmonic content of the 6-pulse rectifier, there is considerable

reduction in the magnitude of the higher order harmonics measured from the 12-pulse rectifier due

to the expected harmonic cancelling.

Fig. 45. 12-pulse generator line currents at the beginning of the charge cycle.

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Fig. 46. Harmonic spectrum of the 12-pulse generator line currents for the charge cycle.

E) 24-pulse rectifier validation

Similar trends as those observed during the evaluation of the 12-pulse rectifier topology are

observed during the validation of the 24-pulse rectifier topology, shown in Fig. 47. As expected,

the source currents become more sinusoidal as the number of phases and rectifier bridges increase.

There is still a slight mismatch in harmonic distortion; however, there is better agreement between

the simulated and experimental data. As shown in Fig. 48, the characteristic harmonics, notably

the 23rd, 25th, 47th, 49th, etc.) are modeled within a few fractions of a percent of the fundamental.

Unfortunately, the distortion introduced by the transformer still affects the low order harmonics.

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Fig. 47. 24-pulse generator line currents at the beginning of the charge cycle.

Fig. 48. Harmonic spectrum of the 24-pulse generator line currents for the charge cycle.

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Chapter 4: Model Validation of Real-Time Multi-Pulse Rectifiers with Nonlinear

Transformer Magnetics Using Iterative Methods

Limitations when developing HIL compatible models

As seen in the previous chapter, transformer-less rectifiers are fairly trivial to model. Harmonic

content of the 3-phase source line currents is almost entirely predicted, repeated in Fig. 49. This is

especially true in 60 Hz systems where switching speeds and their transients happen on a much

smaller time scale, and their effects are negligible. In this work, piece-wise linear switching models

were used to best model the system and still satisfy the requirements imposed by OPAL-RT. All

components in the hardware testbed were approximately linear, and the nonlinear elements of

switch transitions were unmodeled. Despite the linear modeling, there was no significant deviation

in the harmonic content, which results in a predictable power quality.

The introduction of transformers (phase-shifting, step-up, or otherwise) eliminates this

modeling paradigm, as the harmonic magnitudes are no longer predicted well, repeated in Fig. 50.

Observation of just the magnetization currents in Fig. 51 (line currents with primary excitation and

an open secondary) indicate an unbalanced system due to the lack of uniformity in the waveshape

between lines. These uncharacteristic waveforms were predicted to be the result of the interaction

of the individual primary coils of the transformer wired into a delta.

The nonlinear transformer magnetization currents require a different approach for real-time

modeling. The Simscape power systems toolbox offers both saturation and hysteresis

characteristics as a solution for modeling transformer dynamics. Unfortunately, OPAL-RT is

unable to implement a hysteresis characteristic in real-time due to the need to load said

characteristic from a file. This is an inherent problem in the design of Simscape power systems

and a limitation of OPAL-RT. It is proposed that in order to get the best results despite these

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limitations a saturation characteristic must be selected to provide the best results possible. It can

then be determined if a saturation characteristic will be sufficient, or there is too significant a

limitation in UTA’s current real-time simulation paradigm that needs a different solution.

Fig. 49. Developing switching multi-pulse rectifier models without any transformers proves to

be largely trivial, especially in a 60 Hz system.

Fig. 50. Piece-wise linear switching models cannot account for nonlinearities in transformer

magnetics and power quality prediction is limited.

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Fig. 51. Observation of the magnetization currents in the transformer primary shows

unbalanced, non-characteristic distortion.

Modeling Approach

In order to investigate the unbalanced magnetization, it was necessary to break the overall 3-

phase transformer into its constituent coils. As shown in Fig. 52, the delta primary of the

transformer was disassembled such that each primary coil was galvanically isolated from each

other. Each coil was energized with the rated AC voltage with a sinusoidal programmable power

supply. By doing this, a more typical magnetization current waveform is observed in Fig. 53.

Comparing each coil’s magnetization current shows that coil B has a lower current magnitude

given the same flux excitation. This shows that each coil, especially coil B, operates on distinctly

different saturation characteristics.

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Fig. 52. Delta primary of the transformer broken into its constituent coils.

Fig. 53. During individual excitation, coil B shows much less saturation current magnitude

compared to coil A and coil C.

Standard 3-phase transformer blocks in Simscape power systems allow for one saturation curve

to be defined for all coils. To circumvent this, individual single-phase, saturable transformers are

utilized, each with a unique saturation curve. In this case, the transformer blocks use a flux and

65

current relationship to define saturation, as opposed to a flux density and magnetic field

relationship. These two relationships are functionally equivalent, so a flux and current relationship

will be used throughout the rest of this work. Once the saturation characteristics have been defined,

the individual single-phase transformers can be wired back into an equivalent 3-phase transformer

to complete the Simulink model, as shown in Fig. 54.

Fig. 54. Each transformer coil can be modeled independently as a saturable transformer, and

then be wired back into its original 3-phase transformer form.

By integrating the excitation voltage over time, the flux in the coil can be determined. The

calculated flux plotted against current shows standard hysteresis loops for each coil in Fig. 55.

Since we are limited to a saturation curve and not a hysteresis curve, we cannot define the coercive

current or residual flux of the hysteresis loop. Performing a DC saturation test of the coil could be

useful; however, this assumes the residual flux in the transformer is zero at the start of the test.

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Successive tests result in different curves due to residual flux, which may be unreliable for

developing high fidelity models.

It was proposed to approximate a saturation curve by finding a function that produces minimal

error in the modeled magnetization. Since a saturation characteristic must start at zero flux and

zero current in Simscape power systems, a function is needed that crosses the origin. In addition,

flux must be monotonically increasing with increasing current. Therefore, the chosen function

should also be monotonically increasing. It is proposed that a combination of an arctangent

function and a linear function be used to fulfill these requirements.

Fig. 55. Hysteresis curves are easily obtained but are unable to be implemented into the OPAL-

RT due to a restriction inherent to the simulator.

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The proposed saturation function is presented in Eq. 16 where the flux 𝛷 is the dependent

variable, and the current 𝐼 is the independent variable.

𝛷 = 𝛼 𝑎𝑟𝑐𝑡𝑎𝑛(𝛽𝐼) + 𝛾𝐼 (16)

The constant 𝛼 implicitly accounts the saturation flux of the coil, 𝛽 implicitly accounts for the

coil’s unsaturated permeability, and 𝛾 implicitly accounts for the coil’s saturated permeability. The

goal of this equation is to provide a saturation characteristic that best matches the simulated current

waveforms to that of the experimental waveforms without modeling hysteresis. These three

constants, 𝛼, 𝛽, and 𝛾, are optimized such that the error between the simulation current waveforms

and the experimental current waveforms is minimized.

A constrained optimization function ‘fmincon’ in MATLAB’s optimization toolbox was

utilized to iteratively determine the optimal value of the constants. Bounds were defined to keep

the saturation characteristic within reasonable expectation. The ‘fmincon’ function operates on a

principle of gradient descent to mathematically determine optimization. Since we are working with

physical hardware, there is no defined mathematical model from which to determine how to change

the constants to descend to the minimum point. The function ‘fmincon’ determines gradient

descent iteratively by perturbing the initial guess at the constants, and from those new altered

constants a new saturation flux is generated. This new saturation characteristic is implemented in

an open-secondary saturable transformer block in a Simulink model, shown in Fig. 56, to generate

a new simulation magnetization current waveform. A cost function is defined to determine how

close the simulation waveform is to the experimental. In this case, a mean-square-error cost

function was applied so large differences in the waveforms has a larger impact on the overall error.

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This was done to help force the simulation to follow the shape and inflection of the experimental

data, instead of just splitting the difference and resulting in a weak fit to the experimental data.

Note that the excitation voltage waveform in simulation was phase locked to the experimental

voltage waveform beforehand, so the excitation between the two was close to identical. The mean

square error cost function is defined below, where n is the sample number and N is the total number

of samples.

𝐶𝑜𝑠𝑡 =∑ (𝐼𝐸𝑥𝑝(𝑛)−𝐼𝑆𝑖𝑚(𝑛))

2𝑁𝑛=1

𝑁 (17)

In simple terms, based on the resulting cost for a given perturbation, if the cost has increased

beyond the cost of the unperturbed constants the solver will try a new perturbation until the cost is

reduced. The optimization routine will then continue to change the variables in small steps until

the cost cannot be reduced any further, indicating a local minimum.

Fig. 56. A very simple plant was used to generate saturated magnetization currents for

comparison against data.

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Saturation curves were optimized for each coil in the transformer, shown in Fig. 57, with each

minimizing the error between the simulation generated waveform and its respective waveform

from experimental data. Since the simulation limited to saturation and cannot introduce hysteresis,

there is still some error between experimental and simulation data. The optimization routine does

its best to account for hysteresis by minimizing the error while being limited to a saturation

function.

Fig. 57. Minimization of error in the optimized magnetization current waveforms get close to

the waveshape but are unable to account for the residual magnetization and coercive current in

the true hysteresis characteristics.

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An open-secondary transformer model in Fig. 58 was built to test if modeling the saturation of

the individual coils translates effectively to a model of the unbalanced magnetization currents in

the physical transformer. Simulation data now begins to follow the shape of the unbalanced

magnetization currents in Fig. 59. This comparison shows promise in the effectiveness of the

proposed modeling technique, and further validation is performed in the next section.

Fig. 58. Using the optimized saturation characteristics, a 3-phase transformer with an open

secondary was constructed.

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Fig. 59. A promising comparison of experimental data to simulation data shows the individual

coils approximate the waveshape of the transformer’s unbalanced magnetization in each line

current.

Model Validation

A low-voltage and low-power hardware testbed that included the transformer in question

(presented abstractly in Fig. 60) was constructed to validate the models against. This test bed was

similar to the one used in the previous chapter, but with a purely resistive load. In order for the

proposed model to be valid, the %THD predicted by the simulation must match up closely to the

%THD of a real system.

The programmable power supply utilized in the last chapter was utilized to provide near ideal

sinusoidal 3-phase voltage for validating the transformer models. Using a near ideal source avoids

error introduced by some unmodeled rotating machine or distorted mains voltage. For the 6-pulse

rectifier, a LabVolt Power Thyristor module from Festo [38] was utilized, shown in Fig. 61. In this

module, thyristors can be individually controlled externally, such as from the OPAL-RT simulator.

A controller was developed in Simulink and deployed on OPAL-RT in Fig. 62 to control the

LabVolt 6-pulse rectifier and the simulated rectifier effectively the same.

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Finally, a Chroma 63804 programmable load in Fig. 63 [39] was used in a constant resistance

mode to load the rectifier at a percent of the rated power of the system. A resistive load was used

to best represent what the current waveforms might look line in an operation scenario. A constant

power or a constant current load profile would distort the line current waveforms to maintain the

right profile at the output, leading to results that may still be useful, but uncharacteristic of a typical

rectifier system.

Fig. 60. Efficacy of proposed model in predicting power quality in multi-pulse rectifier systems

will be determined by comparing experimental and simulation data of this system.

Fig. 61. A previously procured LabVolt 6-pulse thyristor module was used as the hardware 6-

pulse rectifier [38].

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Fig. 62. Simulink block diagram implemented in OPAL-RT was utilized as a controller to fire

both simulated and hardware rectifiers in the same way.

Fig. 63. A Chroma 63804 AC/DC programmable load was used in a constant resistance mode to

load the hardware testbed [39].

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The firing angle of the rectifier regulates the bus voltage of the commercial DC distribution

bus proposed by [1]. In addition, total continuous power draw from the bus may change over time

due to additional loads coming on or offline. These two variables act as independent parameters

that affect the power quality of the AC system. As mentioned before in the background, harmonic

distortion of 60 Hz systems is an important metric in determining power quality of an isolated DC

microgrid. In the case of an unfiltered 6-pulse rectifier, power quality standards for isolated DC

microgrids will not be met in general. The more important aspect of this work is showing that the

model will be able to predict what the %THD will be, all nonlinearities included. This way, real

designs may be validated at the simulation stage, so they have a greater chance of meeting power

quality standards for isolated DC microgrids when they are physically implemented.

Results: Input Power Quality

Simulations were run that varied the firing angle and the power draw of the load within

reasonable expectations of an isolated DC microgrid. Since bus voltage should not deviate far from

nominal, firing angle setpoints from 0 degrees to 60 degrees in increments of 5 degrees was tested.

Load power may vary widely depending on the operational scenario of the isolated DC microgrid,

so average rated load was tested from 10% to 100% in 10% increments. %THD is calculated from

the below equation, where h is the magnitude of the harmonic and n is the order of the harmonic.

The resulting %THD is presented as a function of firing angle and load power in Fig. 64.

%𝑇𝐻𝐷 = 100% ∗√∑ℎ𝑛

2

ℎ1 (18)

𝑛 ∈ 2,3,4, …

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Fig. 64. Experimental data shows that the %THD in a 6-pulse rectifier system varies smoothly

for a given firing angle and rated resistive load.

Using the proposed model, the same tests and calculations were performed in simulation. The

resulting %THD produced by the simulation in Fig. 65 appears to match most of the magnitudes

and contours of the experimental data. In order to quantitatively evaluate the performance of the

model, the percent error between the simulation %THD and the experimental %THD is calculated

and plotted in Fig. 66. This surface shows that the error over a large majority of the region is below

5% error. Unfortunately, there is one area of operation that does not predict the %THD well with

a percent error around 15-20%. In a practical sense, this region of operation is unlikely to be used

for any extended period of time, though additional improvements to the proposed model are

desired. Otherwise, this error shows a limitation in the proposed reduction of hysteresis

characteristics to saturation characteristics in the model and improvements may be negligible.

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Fig. 65. Simulation data shows a distinctly similar characteristic in %THD profile compared to

experimental data.

Fig. 66. Error in the predicted %THD is minimal across variations in both firing angle and load,

with the exception of a small region in low firing angle and load.

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Since %THD is a calculation resulting from the aggregate of harmonic magnitudes, it is also

relevant to examine the individual harmonic magnitudes and time domain waveforms to address

their validity and conformity to potential power quality standard for isolated DC microgrids. First,

in a low error region, it is observed that all individual harmonics in simulation are very close to

experimental data. Even harmonics uncharacteristic to 6-pulse rectifier circuits, such as the slight

3rd harmonic shown in Fig. 67, show good matching. The time domain waveform in Fig. 68 shows

similar pulse shape, including different inflections.

Fig. 67. At one of the lowest error operation points, it is observed that individual line current

harmonics are modeled to high degree.

Fig. 68. The time domain waveforms at this operation point show superb matching between

experimental and simulation data.

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Harmonic fidelity at high load with variations in firing angle is mostly maintained, with some

slight deviations from the experimental data. Fig. 69 shows an example of high-power draw with

high firing angle. Fortunately, overall %THD is maintained due to all harmonics being roughly

balanced in being either greater or lower in magnitude. The time domain waveforms, though

largely different in shape than in Fig. 70, maintains predictability.

Fig. 69. Increasing the firing angle at high load shows good matching in harmonic content,

though slight deviations in individual harmonics are apparent.

Fig. 70. Time domain waveforms of the simulation at a higher firing angle operation point still

show the characteristic waveshape of the experimental data.

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In one of the worst areas of performance at low load and high firing angle, all lower order

harmonics observed in experimental data are at least represented in the simulation data, as shown

in Fig. 71. Unfortunately, harmonic magnitudes are not nearly as consistent as in other operational

regions, such as Fig. 67 and Fig. 69. This variation poses a challenge in predicting power quality

accurately in some areas of operation.

The waveforms in Fig. 72 exemplifies what small deviations in harmonic magnitudes can cause

in the time domain. While the general shape of the waveforms is maintained, some transient

aspects of the experimental waveforms are not represented, which may have to be addressed by

other portions of power quality standards for isolated DC microgrids.

Fig. 71. In the worst performing region in terms of error in %THD, harmonics are still predicted

to a fair degree.

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Fig. 72. Time domain waveforms at this operation point fit the rough shape of experimental data

but lacks the ability to predict the highly nonlinear and transient nature of line currents at such a

low load and high firing angle.

Chapter 5: Low Voltage PHIL Implementation of the Multi-Pulse Rectifier Model

Now that a PHIL compatible model of a 6-pulse rectifier is validated, the model can be

implemented in PHIL, while still accurately predicting power quality in simulation. This chapter

will quantifiably show the efficacy of implementing multi-pulse rectifier circuits, including

magnetics, in PHIL on the OPAL-RT system at a low-voltage.

Low Voltage PHIL Experimental Setup

The full model described in chapter 4 is implemented in the OPAL-RT system in parallel with

the operating hardware system the model is based on, abstractly represented Fig. 73. First, the

model is made fully compatible with the OPAL-RT system by wrapping the model with the OPAL-

RT specific blocks needed by the simulator, seen in Fig. 74. The output voltage of the rectifier is

measured and sent out to the OPAL’s analog output block. The analog output peripheral signal is

connected to ‘phase A’ of the high slew rate power supply in order to emulate the rectifier’s DC

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output with ripple. The power supply’s output is connected directly to the programmable load. The

programmable power supply is commanded to draw load current at a constant resistance for each

tested power level from both DC output from the hardware testbed and the emulated DC output

from the programable power supply. This way, the hardware load current and the simulation load

current will be almost identical. Special care must be taken to provide limits on the range and slew

rate the OPAL-RT’s analog outputs can have. For example, the analog control input of the high

slew rate power supply has an input voltage range of ±5 volts. A saturation block should be placed

before the OPAL analog output block in the simulation with an upper limit of 5 and lower limit of

-5 to prevent the analog outputs from damaging the power supply’s control input. This is just one

example of proactive protection of equipment, and not all scenarios can be predicted. However,

because of the wide range of possible operational scenarios, the careful inclusion of rate-limit and

saturation blocks are critical in the safe implementation of PHIL. Fig. 75 shows the experimental

setup for validation of a PHIL implemented multi-pulse rectifier. Since the load is known in this

experiment, feedback of the load current back into the OPAL-RT is not necessary.

Fig. 73. Abstract diagram of PHIL implementation of a modeled power system.

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Fig. 74. 6-Pulse rectifier model implemented in OPAL-RT for output voltage validation.

Fig. 75. Experimental setup for validating the emulated PHIL rectifier output against the

hardware rectifier output.

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Low Voltage PHIL Results

Similar to the input line currents in Chapter 4, %THD calculations were performed across the

same region of operation on the output voltage waveforms. While not particularly needed to meet

any power quality standard, %THD given a good overall indication of the performance of output

voltage harmonic content. The harmonic contents of the output voltage waveforms are examined

here at a low-voltage to compare their performance compared to the harmonic content performance

at the MV level. The %THD for each operation point in the experimental data is presented in Fig.

76. In this case, %THD varies considerably given a change in firing angle; however, variations in

load power have relatively low effect on a change in %THD. Next, in Fig. 77, the %THD of the

PHIL emulated rectifier shows a very similar curvature and magnitude to the experimental data.

Since the PHIL is based on simulation, the plot is noticeably smoother and uniform between data

points, as compared to some slight variations between points in the experimental data in Fig. 76.

Fig. 76. %THD calculated from the hardware rectifier’s output voltage.

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Fig. 77. %THD calculated from the PHIL emulated rectifier show a very similar contour to

experimental data.

As expected from the overall %THD plot in Fig. 76 and Fig. 77, the individual harmonic

magnitudes between the hardware rectifier and the PHIL emulated rectifier are well matched in

Fig. 78. As the firing angle is increased, the harmonic magnitudes increase overall. These results

show that, given the bandwidth of the equipment used, PHIL emulation of a 6-pulse rectifier is

effective at generating accurate output voltage harmonics.

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Fig. 78. Comparison of the harmonic spectrums between the experimental and PHIL data at

various operation points.

Calculating the absolute error between the experimental %THD and the PHIL %THD in Fig.

79 shows that the PHIL emulated rectifier effectively models the harmonic content of the hardware

rectifier system overall. Most error points are less than 5% with a few exceptions. Notably, the

area of 20% error in the line currents seen back in Fig. 65 is not present, meaning that the output

voltage waveforms are relatively immune to error in transformer magnetization modeling.

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Fig. 79. Percent error overall between experimental %THD and the PHIL %THD.

The waveforms in Fig. 80 show a comparison between the output voltage of the simulation,

the hardware testbed, and the PHIL emulated rectifier in the time domain at the same selected

operation points from Chapter 4. The mean absolute error (MAE) is calculated in Fig. 81 to show

the discrepancy between the hardware rectifier and the PHIL emulated rectifier quantifiably. Both

time domain and frequency domain results show that the output voltage of the PHIL rectifier

properly emulates the output voltage of a real hardware rectifier system at low-voltage. All the

while, the input power quality of the rectifier system is being predicted in the real-time simulation

as the rectifier’s output characteristics are emulated with the high slew rate power supply.

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Fig. 80. Comparisons of simulation, hardware, and PHIL emulated 6-pulse rectifier output

voltage waveforms at various power draws and firing angles.

Fig. 81. Mean absolute error calculation between the hardware rectifier and PHIL rectifier’s

output voltage waveforms across the investigated range of operation.

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Chapter 6: Medium Voltage PHIL Implementation of the Multi-Pulse Rectifier Model

Realizing a power amplifier on the order of thousands of volts and tens of kilowatts of power

is no trivial matter. Much like in the low voltage experiments, a high slew rate power supply was

needed to act as the power amplifier to emulate the rectifier’s output. In order to achieve a similar

effect, a state-of-the-art medium voltage power supply (MVPS) was commissioned to act as the

high slew rate power supply for medium voltage PHIL. A commercially available medium voltage

representative power supply is shown in Fig. 82. Since these power supplies are commercial

products, much of their exact power electronic and control topologies are proprietary.

Fig. 82. Commercially available medium voltage power supply [7].

89

The MVPS has a ‘DC mode’ in which the MVPS will output a DC voltage and current. Due to

a proprietary topology, these power supplies must always have some load at the MVPS output or

the MVPS might be damaged during operation. The DC mode along with analog control allows

for the MVPS output to be regulated into dummy loads. This way, arbitrary voltage, current, or

power profiles may be generated if the MVPS can slew as fast as the analog control input. The end

goal is to quantifiably show the viability of implementing the discussed rectifier model in PHIL at

medium voltage by observing the harmonic content present in the MVPS output. There has been

published work on this type of implementation; however, no data has been presented quantifiably

showing if PHIL can implement the dynamics and harmonic content of multi-pulse rectifier

systems at a medium voltage level [40]. The first section of this chapter discusses the

commissioning of the MVPS for use in an MVDC testbed implemented at UTA. The second

section presents data on the PHIL implementation of the multi-pulse rectifier model at medium

voltage and discusses its validity.

Commissioning of a 1 kV to 6 kV DC/DC Power Supply for MVDC PHIL

Control of the MVPS in the ‘DC mode’ is performed through two DB-25 connections and two

single-mode fiber connections, pictured partly in Fig. 83. Each DB-25 connector uses a mix of

analog and digital inputs and outputs to interface with the testbed’s controller. One fiber

connection is used by the MVPS to tell the testbed controller that the MVPS is ready to engage the

output. The second fiber is used by the testbed controller to engage the MVPS’s output to produce

output voltage and power.

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Fig. 83. Dual DB-25 connections are utilized in the commercially available MVPS.

The bulk of the control system used in the testbed is implemented with National Instruments

(NI) cDAQ and data acquisition hardware [41]. An example of this hardware is shown in Fig. 84.

Considering that most of the NI hardware interfaces use DB-37 connections for their peripheral

IOs, an elegant way of interfacing the controller to the MVPS was needed.

Fig. 84. Portion of the custom PLC realized through National Instruments hardware [41].

In order to achieve the system integration, a controller interface, seen in Fig. 85, was

implemented. The operator of the testbed uses a host PC that interfaces with the NI cDAQ over

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the network. The NI cDAQ utilizes hardware ‘cards’ that slot into a chassis. Each card has a unique

function, such as acting as digital input or outputs, or acting as analog input or outputs. Relevant

cards are connected to PCB breakouts with DB-37 cables and are accessed with screw terminals

from a DB-37 breakout PCB. Signals are mapped from the three DB-37 breakouts to their

respective terminals on a DB-25 breakout PCB, shown abstractly in Fig. 86. Though many pieces

of MV equipment share cDAQ cards in the overall testbed, only a select few signals from each 37

terminal card are dedicated to the MVPS and are combined to a single DB-25 connection. Next in

the chain, a DB-25 cable is used to pipe the signals from the breakout PCBs to a custom designed

interface PCB that provides signal conditioning and routing, shown in Fig. 87. The interface PCB

takes the incoming bundled DB-25 cable and reroutes the signals to their respective end location

on the two DB-25 connections on the front panel of the MVPS. In addition to rerouting the signals,

simple digital and analog signal conditioning techniques are used to shift the cDAQ system voltage

from 24 V to a 15 V level required by the MVPS, as well as passing analog control signals

appropriately. Diagnostics and test terminals were in included in the design such that the system

could be monitored directly from the diagnostic DB-25 connector. Lastly, the interface PCB

converts the two digital signals into single-mode optical fibers for engaging the MVPS with the

PLC, and for the MVPS to indicate a ‘ready’ state to the PLC.

Fig. 85. Block diagram of the solution to interfacing a NI-based custom PLC with the MVPS.

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Fig. 86. Block diagram showing the signal breakdown of the DB-25 cables that bridge the PLC

and the MVPS

Fig. 87. Final assembly of the interface PCB, providing signal rerouting, digital and analog

signal conditioning, diagnostic and monitoring, and conversion to optical fiber.

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A LabVIEW ‘virtual instrument’ (VI) program was developed to control the MVPS. The VI

acts as a digital graphical user interface (shown in Fig. 88) that runs on a standard Windows PC.

The program, coded graphically in Fig. 89, communicates with the NI cDAQ hardware in real-

time, updating control signals and feeding back analog diagnostic data provided by the MVPS.

Data collection was integrated into this controller to record the diagnostic data for post-operation

analysis. Once the MVPS has been supplied its auxiliary voltage and its 1 kVDC input voltage

(shown as the DC/DC converter back in Fig. 2), the MVPS starts in a faulted state. Pressing and

then releasing the ‘reset faults’ button clears all faults in normal circumstances. If all faults have

been successfully cleared by MVPS, then the fault indicator on the front panel will go dark. In

addition, the MVPS will assert a ‘ready’ fiber signal to the interface PCB. This fiber is converted

to a digital electrical signal by the interface PCB, read by the cDAQ’s digital input card, imported

to the LabVIEW digital interface, and appears as a lit ready indicator on the VI front panel. Next,

an ‘HV on’ digital signal is sent to the MVPS and puts the MVPS into a standby mode. Finally,

the output of the MVPS is engaged and disengaged by asserting a digital signal to the interface

PCB, which is converted to an optical fiber signal and read by the MVPS. When the MVPS’s

output is active and is loaded resistively, adjusting the current analog control set point allows the

operator or an external controller to modulate the MVPS’s output voltage, current, or power. An

example of this analog following is shown in a manual ramp test in Fig. 90. This figure shows that

both the voltage, current, and power of the MVPS will follow the dynamics of the control input.

The ability of this medium voltage supply to quickly slew with analog control shows good potential

for PHIL.

94

Fig. 88. A relatively simple LabVIEW program (front panel pictured here) was developed to

operate the MVPS.

Fig. 89. Graphical code of the LabVIEW program.

95

Fig. 90. Analog control of the MVPS in test mode shows that voltage, current, and power follow

the contours and rapid transients of the control signal, lending this supply to potential in medium

voltage PHIL.

Implementation of PHIL for medium voltage levels

A similar OPAL-RT block diagram used in the low voltage PHIL emulation was used to

control the output voltage of the MVPS during PHIL emulation, shown in Fig. 91. The model

developed in earlier chapters was scaled for an input voltage of 4160 VAC and a transformer

secondary output voltage of 3500 VAC. The system power was also scaled to be 80 kW, which is

the maximum power allowed by the MVPS. This change in secondary voltage (instead of a 1:1

ratio) was made to allow for the full ripple of the DC output voltage to be in the operation range

of the MVPS, which is 3500-7000 VDC. Otherwise, due to the static testbed load resistance, the

MVPS would be operating out of range. Despite this change to the transformer turns ratio, the

MVPS is still operating in a valid medium voltage range, which is the main goal of these

experiments. The simulation output voltage that is sent to the MVPS was, at first, bandwidth

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limited by passing it through a software low-pass filter. Gradually, as seen in Fig. 91, higher and

higher cutoff frequencies were implemented until the unadulterated simulation output voltage was

being sent to the MVPS. This was done as a precaution in the event that ever-increasing control

ripple caused the MVPS to become unstable. In the end, no erratic behavior was observed from

the MVPS from any applied filter, all the way through to the no filtering case.

Fig. 91. OPAL-RT block diagram used to control the MVPS for MV PHIL emulation.

Medium Voltage Results

Unfortunately, the MVPS is observed as not able to keep up with the large ripple of the applied

simulation voltage, as seen in Fig. 92. The MVPS appears to be attempting to track the control

signal, but is bandwidth limited well below the first major harmonic of the 6-pulse rectifier. Further

inspection of the harmonic spectrum in Fig. 93 shows that the MVPS waveform begins to show

the correct harmonic spectrum for the 6-pulse rectifier but is severely limited in bandwidth. This

is likely due to a control input filter that is inherent to the MVPS and is unavoidable. In addition,

the main component of the ripple observed in Fig. 93 is a harmonic at 60 kHz. The topology of the

commercially available MVPS is proprietary to the manufacturer, but it is likely that this ripple is

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due to an IGBT based topology (perhaps a type of series resonant converter) where switching

frequency of the inverter IGBTs are individually limited to an upper frequency of around 30 kHz

with current state-of-the-art technology. When this 30 kHz waveform is rectified at the MVPS

output, the fundamental frequency of the MVPS output voltage ripple becomes 60 kHz, which is

consistent with the harmonic content observed. However, this is only speculation to serve as a

caution for future efforts.

Fig. 92. MVPS fails to follow the wide ripple of the simulation voltage.

Fig. 93. Characteristic harmonics are present in the MVPS waveform but are significantly

reduced in magnitude compared to the theoretical values.

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Though unable to perform high frequency MV PHIL, the average voltage of the simulation

and MVPS is well emulated. In Fig. 94, the blue and orange bands represent the simulation and

MVPS output voltages, respectively, much like in Fig. 92. During the test the firing angle of the

simulation rectifier was linearly increased from 5 degrees to 30 degrees over 1 second, lowering

the average output voltage and increasing the magnitude of the output voltage ripple. The linear

change in firing angle results in a characteristic cosine shape of the decreasing average output

voltage informed by equation (13). Next, the firing angle was decreased back down to 5 degrees

linearly over 1 second, and the average voltage and ripple voltage returns to its initial operation.

The scaled control voltage and MVPS voltage are passed through a moving average filter to

determine their average value over time. These averaged waveforms are very closely matched with

a mean absolute error of 10.2 V. This low error relative to the medium system voltage between the

averaged waveforms indicates that PHIL is better suited for more macro-scale system changes at

a MV level than emulating individual converter output harmonics. The test shown in Fig. 94 shows

that, though PHIL emulation of harmonic content may not be a currently viable technology, the

ability of PHIL to emulate the average DC characteristics of a modeled power system topology

can be done accurately.

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Fig. 94. The MVPS cannot properly emulate the significant voltage ripple of the 6-pulse rectifier

but is able to accurately model the average magnitude of the rectifiers output voltage given a

change in firing angle control.

A final test was performed where the simulation rectifier was step loaded with an 80 kW

resistive load in simulation. The MVPS load remained at its constant value of 314.5 ohms. This

causes a sag in the simulation’s output voltage shown in the blue waveform in Fig. 95. This is

reflected in the MVPS output voltage in orange in Fig. 95 as it follows the change in the control

signal, demonstrating that the MVPS can emulate step changes in the simulation rectifier’s average

output voltage. An enhanced version of Fig. 95 is presented in Fig. 96 showing that, while not

perfect in transient performance, the MVPS is able to make the quick transition in following the

average output voltage of the control signal when the simulation load is applied. Despite the quick

transition of the simulation voltage and the bandwidth limitations of the MVPS, the average of

both control and MVPS voltage signals are nearly identical. Calculating the mean absolute error

between the two averaged signals in this experiment results in an error of 6.43 V. This experiment

shows that if the MVPS is being used to source a real hardware load, other system conditions, such

as additional simulation loads or even fault conditions, can occur in simulation and affect the

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MVPS output. This lends to the ability of MV PHIL technology to consider many different power

systems with many different operation conditions during the design process, all while interfacing

with existing hardware and understanding how the existing hardware will be affected by those

design choices and operational conditions.

Fig. 95. MVPS is able to emulate variations in average DC output when step loaded.

Fig. 96. Closer inspection of the MV output waveforms shows the transient capability of the

MVPS for PHIL emulation.

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Conclusions

Initial rectifier studies interested in directly charging capacitors with multi-pulse rectifiers

revealed an issue with modeling unbalanced transformer magnetics in the OPAL-RT real-time

modeling paradigm. A novel approach was taken that uses an established iterative optimization

algorithm to approximate the magnetization of each of the three coils in the low-voltage testbed

transformer with a saturation characteristic for simulation. This method resulted in a large

improvement over previous models in predicting both the total harmonic distortion and the

individual harmonic magnitudes over a wide range of rectifier operation. It was shown explicitly

that while most operation points have a percent error less than 5%, there is a portion of explored

operation where the model shows a less-effective percent error of around 20%. Fortunately, due

to the rectifier’s increased DC ripple and deviation from nominal bus voltage as firing angle is

increased, it is not expected for rectifiers in isolated DC microgrids to be operating in this region

of high firing angle (greater than 30 degrees). In addition, the models predict power quality at low

firing angle across loading conditions, which is important considering the multitude of operational

scenarios a commercial isolated DC microgrid may experience.

The results show that an accurate multi-pulse rectifier switching model can be generated for

PHIL emulation, or even just for design validation and prototyping. These models and results

thereof were developed on the basis of experimental data, giving them an extra edge in terms of

being valid representations of hardware. No extensive theoretical methods for the development of

the models or computationally complex implementations of the models were used. All

developments utilized standard Simulink Simscape Power Systems toolboxes compatible with the

OPAL-RT real-time simulation platform, MATLAB optimization toolbox, and experimental data.

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This simplicity shows a high ease of use and ease of access for future engineers to be able to

implement accurate models in a real design setting.

PHIL has been implemented effectively in a low-voltage rectifier testbed with good quantified

results. The programmable power supply is capable of following the analog control signal from

the OPAL-RT due to its high slew rate. The PHIL emulated rectifier is able to generate waveforms

accurate in both time and frequency domains across a wide range of rectifier operation. Notably,

the area of more significant error in the line current %THD investigation does not appear to affect

the output voltage analysis in simulation, hardware, or in PHIL. While modeling the unbalanced

transformer magnetics was crucial for input power quality consideration, it is fortunate that there

is little effect on the fidelity of the output voltage waveforms for PHIL emulation of multi-pulse

rectifiers.

For MV PHIL, it was determined that even with state-of-the-art equipment, emulating higher

frequency harmonics of a 6-pulse rectifier is not currently feasible. The control or topology

bandwidth of the MVPS was much more limited than expected. Even the first harmonic of the

rectifier output at 360 Hz is barely present in the MVPS output during PHIL emulation. Tests

looking at macro-scale changes in the system operation point show that the MV PHIL is better

suited for emulating average changes in the simulated power system or load profile. The MVPS

has inherent harmonic content and output ripple likely due to the limitations in switching frequency

of IGBTs internal to the MVPS. At these voltage and power levels, it is unfeasible to use another

type of power electronic switch without excessive complication of the power supply topology.

Further developments in semiconductor technology may allow for faster switching frequencies at

rated medium voltage and power levels, and thus allow for faster transient response times for MV

PHIL emulation.

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Future work on MV PHIL in the testbed at UTA could involve utilizing the MVPS and OPAL-

RT to emulate particular load profiles that may be common in isolated DC microgrids. Also, load

profiles or equipment topologies that may be unique cases to isolated DC microgrids can be studied

without further equipment procurement if good models can be developed. All in all, MV PHIL

shows great potential to explore endless designs choices and possible operational scenarios in the

UTA isolated DC microgrid testbed that can make larger contributions to the development of

microgrids in a world of constantly evolving and improving power systems.

Sponsorship Acknowledgement

I would like to thank the US Office of Naval Research (ONR) for their sponsorship of this

work under grant numbers N00014-17-1-2801, N00014-16-1-2248, N00014-18-1-2286, N00014-

18-1-2206, N00014-17-1-2288, and N00014-16-1-3001. Any opinions, findings, and conclusions

or recommendations expressed in this publication are those of the author and do not necessarily

reflect the views of the US Office of Naval Research.

104

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Biography

Brian J. McRee was born in San Diego, CA, USA in 1992. He received a B.Sc. in electrical

engineering from The University of Texas at Arlington, Arlington, TX, USA, in 2016, and received

a Ph.D. in electrical engineering from the University of Texas at Arlington, Arlington, TX, USA,

in 2019 under the direction of Dr. David Wetz.

His work at UTA includes developing real-time models of power electronic converters and

microgrids, performing model validation against hardware testbeds, and developing medium-

voltage power hardware-in-the-loop technology. His research interests include modeling and

simulation, hardware-in-the-loop, microgrids, power electronic converters, power quality, power

transformers, magnetics, analog signals, and intelligent/adaptive controls.