A Novel Inverter Based Resource Control Strategy to 
Facilitate Utility-Scale Renewable Integration and Retain 
Existing Transmission Protection Infrastructure 
 
 
 
A THESIS 
SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL 
OF THE UNIVERSITY OF MINNESOTA 
BY 
 
 
 
Daniel James Kelly 
 
 
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS 
FOR THE DEGREE OF 
DOCTOR OF PHILOSOPHY 
 
Professor Ned Mohan, Advisor 
October, 2022 
  
 
 
 
 
 
 
 
 
© Daniel James Kelly 2022 
ALL RIGHTS RESERVED 
i 
 
 
 
Acknowledgements 
 
To my parents Ann and Jim, and my brother Tommy. Your love and support mean the 
world to me, and I could not have done this without you. 
 
To my advisors Ned Mohan and Pratap Mysore, your mentorship and kindness were 
invaluable, and I greatly appreciate the opportunity to learn from you while collaborating 
on this research project. 
 
  
ii 
 
 
 
Abstract 
 Renewable generation capacity in the North American electric grid is expected to 
expand considerably over the next few decades. Photovoltaics and type-4 wind turbines 
connected to the grid via power electronic inverters have a significantly different fault 
response than conventional synchronous generators. The existing protection infrastructure 
for the North American transmission network was not designed with the behavior of these 
Inverter Based Resources (IBR) in mind. As IBR penetration continues to increase, the 
overall system behavior under faulted conditions may change to the point where protective 
relays may fail to accurately detect the location of a fault. 
This thesis proposes a novel control strategy for utility-scale inverter-based 
resources designed to ensure proper operation of the existing transmission-line protection 
infrastructure. The fault response of an IBR depends on its control logic which varies 
between manufacturers, but typically will resemble its pre-fault behavior of generating 
balanced three-phase currents. Transmission-line protective relays rely upon the 
unbalanced currents produced by synchronous generators to accurately determine the fault 
location. By controlling IBRs to emulate synchronous generator fault behavior, protective 
devices see the quantities they expect and require for proper operation. This will allow 
electric utilities to retain their existing protection infrastructure, eliminating the need for 
any costly equipment upgrades and operational downtime.  
iii 
 
 
Contents 
 
 
Acknowledgements .............................................................................................................. i 
Abstract ............................................................................................................................... ii 
List of Tables ..................................................................................................................... vi 
List of Figures ................................................................................................................... vii 
1 Introduction ...................................................................................................................... 1 
1.1 Motivation ................................................................................................................. 1 
1.1.1 Renewable Generation Trends & IBR Fault Response ...................................... 1 
1.1.2 Impact on Transmission Network Protection ..................................................... 2 
1.2 Relevant Electrical Standards.................................................................................... 3 
1.2.1 VDE-AR-N-4120 - Technical Connection Rules for High-Voltage (Germany) 3 
1.2.2 P2800 – IEEE Standard for Interconnection and Interoperability of Inverter-
Based Resources (IBRs) Interconnecting with Associated Transmission Electric 
Power Systems ............................................................................................................. 5 
1.3 Proposed Control Strategy ......................................................................................... 6 
1.4 Thesis Outline ............................................................................................................ 6 
2 Transmission Protection................................................................................................... 8 
2.1 Distance & Directional Protection ............................................................................ 8 
2.1.1 Zones of Protection ............................................................................................. 9 
2.1.2 Distance Element ................................................................................................ 9 
2.1.3 Directional Element .......................................................................................... 11 
2.2 Differential Current Protection................................................................................ 12 
iv 
 
3 Benchmarking Synchronous Generator Behavior ......................................................... 13 
3.1 System Model in CAPE with Synchronous Generator ........................................... 13 
3.2 Synchronous Generator Fault Response ................................................................. 14 
3.2.1 Low side response (13.8 kV) ............................................................................ 14 
3.2.2 High voltage response (345 kV) ....................................................................... 16 
4 Inverter Based Resource Model ..................................................................................... 18 
4.1 System Model in Simulink with IBR ...................................................................... 18 
4.1.1 Transmission Network ...................................................................................... 18 
4.1.2 Inverter Design ................................................................................................. 19 
4.2 Fault Identification .................................................................................................. 25 
4.2.1 High Side (345 kV) Fault Detection ................................................................. 25 
4.2.2 Low Side (690 V) Fault Detection ................................................................... 26 
4.3 IBR Reference Current Modification ...................................................................... 27 
5 Simulation Results ......................................................................................................... 32 
5.1 Mid-line Faults ........................................................................................................ 32 
5.1.1 Fault Detection at IBR ...................................................................................... 32 
5.1.2 IBR Current Modification ................................................................................ 37 
5.1.3 Voltage & Current Phase Relationship at Relay .............................................. 42 
5.1.4 Response Time Summary ................................................................................. 45 
5.2 Evolving Faults ....................................................................................................... 46 
5.2.1 Test Procedure .................................................................................................. 46 
5.2.2 Evolving Fault Response Time Summary ........................................................ 48 
6 Relay Hardware Verification ......................................................................................... 50 
6.1 Relay Testing Process ............................................................................................. 50 
6.1.1 COMTRADE File Preparation ......................................................................... 51 
v 
 
6.1.2 Doble Protection Suite Testbench Setup .......................................................... 51 
6.1.3 Relay Settings ................................................................................................... 51 
6.2 Mid-line & End-line Results ................................................................................... 52 
6.3 Evolving Fault Results ............................................................................................ 58 
7 Conclusions and Future Work ....................................................................................... 60 
7.1 Conclusions ............................................................................................................. 60 
7.2 Future Work ............................................................................................................ 61 
Appendix A Relay Operation Times................................................................................. 64 
 
 
  
vi 
 
 
 
List of Tables 
 
Table 1-1: P2800 IBR performance requirements .............................................................. 5 
Table 3-1: Synchronous generator & transmission network parameters .......................... 14 
Table 3-2: Synchronous generator fault response on low side of transformer, 13.8 kV .. 15 
Table 3-3: Voltage & current phasors at 345 kV relay ..................................................... 16 
Table 3-4: Angular relationship between 345 kV faulted phase voltage and current ....... 17 
Table 4-1: Summary of IBR parameters ........................................................................... 24 
Table 4-2: Inverter reference currents to emulate synchronous generator fault response 28 
Table 5-1: Fault detection & step response times relative to fault inception.................... 37 
Table 5-2: Summary of response times of proposed IBR control strategy ....................... 46 
Table 5-3: Summary of fault identification and step response times during evolving faults
........................................................................................................................................... 49 
Table 6-1: Distance & directional relay settings ............................................................... 52 
Table 6-2: Summary of relay operation times for mid-line and end-line faults ............... 57 
Table 6-3: Evolving fault relay operation times ............................................................... 59 
Table A-1: Comprehensive relay fault operation times .................................................... 64 
  
vii 
 
 
 
List of Figures 
 
Figure 1-1: VDE-AR-N-4120 IBR negative sequence injection requirements [10]........... 4 
Figure 2-1: Relay zones of protection ................................................................................. 8 
Figure 3-1: Two-bus transmission network with 100 MVA synchronous generator ....... 13 
Figure 4-1: System model with 100 MW inverter ............................................................ 19 
Figure 4-2: Inverter control block diagram ....................................................................... 20 
Figure 4-3: PLL output Theta with Va (not to scale)........................................................ 21 
Figure 4-4: Inverter connected via LC filter to 100 MVA step-up transformer ............... 24 
Figure 4-5: IBR pre-fault phasor diagram ........................................................................ 29 
Figure 4-6: IBR post-fault A-G phasor diagram ............................................................... 29 
Figure 4-7: IBR post-fault B-C phasor diagram ............................................................... 30 
Figure 4-8: IBR post-fault B-C-G phasor diagram ........................................................... 30 
Figure 4-9: IBR post-fault A-B-C-G phasor diagram ....................................................... 31 
Figure 5-1: A-G fault detection using 690 V line-to-line voltages ................................... 33 
Figure 5-2: B-C fault detection using 690 V line-to-line voltages ................................... 34 
Figure 5-3: B-C-G fault detection using 690 V line-to-line voltages ............................... 35 
Figure 5-4: Three-phase fault detection using 690 V line-to-line voltages ...................... 36 
Figure 5-5: Inverter currents during A-G fault ................................................................. 39 
Figure 5-6: Inverter currents during B-C fault .................................................................. 40 
Figure 5-7: Inverter currents during B-C-G fault ............................................................. 41 
Figure 5-8: Inverter currents during three-phase fault ...................................................... 42 
Figure 5-9: 345 kV phase relationship between faulted voltage and current, A-G fault .. 43 
Figure 5-10: 345 kV phase relationship between faulted voltage and current, B-C fault 44 
Figure 5-11: 345 kV phase relationship between faulted voltage and current, B-C-G fault
........................................................................................................................................... 44 
viii 
 
Figure 5-12: 345 kV phase relationship between faulted voltage and current, three-phase 
fault ................................................................................................................................... 45 
Figure 5-13: Fault detection & step response times during evolving fault (A-G to A-B-G 
to Three-phase) ................................................................................................................. 48 
Figure 6-1: Relay hardware verification workflow .......................................................... 50 
Figure 6-2: Relay event record for A-G mid-line fault, Zone 1 operation ....................... 53 
Figure 6-3: Relay event record for A-G end-line fault, Zone 2 operation ........................ 54 
Figure 6-4: Relay event record for B-C mid-line fault, Zone 1 operation ........................ 55 
Figure 6-5: Relay event record for B-C end-line fault, Zone 2 operation ........................ 56 
Figure 6-6: Zone 1 overreach during three-phase end-line fault ...................................... 58 
 
 
 
1 
 
Chapter 1  
Introduction 
1.1 Motivation 
1.1.1 Renewable Generation Trends & IBR Fault Response 
The generation profile of the North American electric grid is moving towards a higher 
penetration of renewables, as many local and state governments set ambitious clean energy 
goals. States which comprise nearly 51% of the US population have committed to 100% 
renewable, carbon-free, or carbon-neutral electricity by 2050 [1]. Electric utilities such as 
Xcel Energy and MidAmerican Energy Company have also set goals for net-zero carbon 
emissions by 2050 [2,3]. Meeting these goals will require a large expansion in renewable 
generation capacity while simultaneously retiring fossil fuel generation. 
Many of these modern renewable generation sources, such as photovoltaics and 
type 4 wind turbines, are connected to the grid via a power electronics inverter, termed 
Inverter Based Resources (IBR). These IBRs are digitally controlled and have a 
significantly different fault response from the synchronous generators they are replacing. 
The magnitude of the IBR fault current is typically between 100-150% of its rated 
maximum output, with very low negative and zero sequence components [4,5]. The 
2 
 
transient response, which occurs immediately after a fault, can be difficult to precisely 
predict as it depends on the IBR manufacturer’s proprietary control logic and pre-fault 
system operating conditions.  
1.1.2 Impact on Transmission Network Protection 
Protective relays are used to monitor transmission lines for electrical faults and to promote 
reliability of the transmission network. Modern relays are programmable, microprocessor-
based devices. Commonly, a distance protection strategy is used to determine how far from 
the relay a fault is occurring, and whether the relay should take action to clear the fault. 
These relays can have relatively long lifetimes, and because the general principle of the 
distance element has remained the same throughout the evolution of protective relay design 
there is a wide variety of relay models in use today.  
Historically, relays have been programmed expecting the fault response of 
synchronous generators found in conventional fossil fuel power plants. During an 
unbalanced fault a synchronous generator produces negative sequence quantities which are 
not present during normal operating conditions. As the presence of these quantities 
indicates abnormal system behavior, they are utilized by the relay for fault detection. 
However, an IBR’s fault response has very low amounts of these negative sequence 
quantities, which can render the relay unable to accurately locate a fault.  
Phasor-based fault analysis programs are typically used by protection engineers to 
develop appropriate relay settings and can rapidly generate fault studies for transmission 
networks. These phasor-based programs are not well suited to modeling IBR behavior, 
which involves detailed time-domain control logic more suited to an electromagnetic 
transient (EMT) simulation, which requires significantly more time and effort to perform. 
3 
 
A study by Sandia National Laboratories characterized the fault response from multiple 
IBR manufacturers’ EMT models [6]. They discovered that IBR fault response varied 
greatly between manufacturers and concluded that without a standardization of IBR fault 
response these EMT simulations would be necessary to properly program transmission 
protective relays.  
Relay manufacturers such as General Electric and Schweitzer Engineering 
Laboratories are developing strategies to address issues related to high IBR penetration [7-
9]. They propose modifications to standard protection logic, for example using zero 
sequence quantities in the absence of negative sequence, or hardware upgrades such as 
replacing distance relays with current differential relays. However, any changes to existing 
protective infrastructure would have substantial capital and operational downtime costs. 
As electric utilities are already undertaking a large generation expansion to meet carbon-
free generation goals which requires significant financial investment, it is desirable to 
retain the existing protective relay assets. Considering the physical size of the North 
American electric grid, these replacement or upgrade costs could quickly become 
infeasible.  
1.2 Relevant Electrical Standards 
1.2.1 VDE-AR-N-4120 - Technical Connection Rules for High-Voltage 
(Germany)  
The VDE-AR-N-4120 standard defines requirements for IBRs connected to Germany’s 
bulk power system. This standard does not apply to IBRs connected to the North American 
4 
 
electric grid but has similarities to the recently published P2800 standard discussed in the 
following section. 
IBRs connected to the transmission network are required to inject negative 
sequence current proportional to a measured change in negative sequence voltage during 
faults as shown in Figure 1-1. The proportionality constant k is allowed to vary between 2 
and 6 [10]. 
 
Figure 1-1: VDE-AR-N-4120 IBR negative sequence injection requirements [10] 
 Note that this standard only refers to negative sequence current magnitudes and 
does not mandate any requirements related to the phase angle relationship of negative 
sequence voltage and current. During an unbalanced fault, relays are programmed with the 
expectation that a synchronous generator’s negative sequence current will lead the negative 
sequence voltage by a certain angle. If the appropriate phase angle relationship is not 
maintained, relay protective functions which expect such a relationship may not operate 
properly. 
5 
 
1.2.2 P2800 – IEEE Standard for Interconnection and Interoperability of 
Inverter-Based Resources (IBRs) Interconnecting with Associated 
Transmission Electric Power Systems 
This recently published IEEE standard provides guidance for IBR owners connected to the 
bulk transmission system, in an effort to standardize behavior during abnormal grid 
conditions. As it is a recent standard, IBRs connected to the North American electric grid 
today do not necessarily conform yet.  
Similar to VDE-AR-N-4120, IBRs are required to inject negative sequence current 
proportional to the measured negative sequence voltage. Additionally, P2800 requires that 
the negative sequence current leads the negative sequence voltage by between 90° and 100° 
for photovoltaic and type-4 wind turbine inverters [11]. 
 This standard also specifies performance requirements for IBRs replicated in Table 
1-1 below. The rightmost column for “all other IBR units” applies to the photovoltaic and 
type-4 wind turbine IBRs considered in this study and are used to evaluate the effectiveness 
of the proposed control strategy in later chapters. The step response time is defined as the 
period from when the fault occurs to when the IBR takes action to modify its control, and 
should be less than 2.5 cycles or 41.7ms for a 60 Hz system. After the step response there 
is a transient response, which should settle out within 4 cycles.  
Table 1-1: P2800 IBR performance requirements 
 Type III WTGs All other IBR units 
Step Response Time N/A 2.5 cycles 
Settling Time 6 cycles 4 cycles 
  
6 
 
1.3 Proposed Control Strategy 
The challenges to transmission protection posed by an increased penetration of renewable 
generation are largely due to the difference in fault response between IBRs and 
synchronous generators. By controlling an IBR to emulate the fault response of a 
synchronous generator, existing distance relays will see the quantities they expect and 
continue to operate properly as renewable penetration increases. The proposed control 
strategy can be summarized in the following three steps: 
1. Benchmark synchronous generator fault response for each type of fault. 
2. Use voltage magnitude measurements to classify the type of fault on a transmission 
line. 
3. Modify IBR current injection to emulate synchronous generator behavior. 
Once the inverter classifies the fault, a look-up table like implementation allows the 
IBR to emulate a synchronous generator by mimicking the relative magnitudes and angular 
relationships of the voltage and current signals. This strategy is simple in concept and 
intended to be easily implemented on any programmable IBR. 
1.4 Thesis Outline 
Some of the simulation results and surrounding discussion in the following chapters is 
reproduced from the published paper by Kelly, Mysore, and Mohan [12]. 
• Chapter 2 discusses principles of transmission protective relay elements, to 
provide context important for understanding the purpose of the proposed control 
strategy. 
7 
 
• Chapter 3 describes the process of benchmarking synchronous generator behavior, 
which is necessary to develop the desired IBR fault response. 
• Chapter 4 details how the IBR model was developed, fault identification strategies, 
and the details of IBR modification to emulate synchronous generator fault 
response. 
• Chapter 5 presents simulation results for the proposed IBR control strategy, and 
evaluates the performance compared to the benchmarks from P2800 shown in Table 
1-1. 
• Chapter 6 explains the process of validating simulation results on relay hardware. 
• Chapter 7 summarizes conclusions and potential avenues for future work. 
 
  
8 
 
 
 
 
Chapter 2  
Transmission Protection  
2.1 Distance & Directional Protection 
One of the most common protective relaying schemes uses a distance element to determine 
how far from the relay a fault is occurring, and a directional element to determine if the 
fault is in front of or behind the relay. If both elements assert, meaning they confirm that a 
fault is present, then the relay will take action to clear the fault. To better explain these two 
elements, first one should understand zones of protection. The following subsections will 
analyze the two-section transmission network shown in Figure 2-1.  
 
Figure 2-1: Relay zones of protection 
9 
 
2.1.1 Zones of Protection 
Relay A has two zones of protection for which it is responsible. If a fault occurs within its 
Zone 1, relay A should attempt to clear the fault instantaneously. Typically, Zone 1 is set 
to protect around 85% of the total length of the line. Due to potential measurement errors 
in long transmission lines, the entire line is not protected by Zone 1 to avoid unnecessary 
loss of service. If Zone 1 is set to protect 100% of the line, such a measurement error could 
cause relay A to operate for a fault on the adjacent section 2, which should ideally be 
protected by Zone 1 of relay B.   
Zone 2 of relay A functions as a time-delayed backup for Zone 1 of relay B and is 
typically set to protect approximately 125% of the line impedance. If relay A detects a fault 
within its Zone 2, it will wait for a few electrical cycles to allow relay B’s instantaneous 
Zone 1 to operate. Each section of the transmission line is also protected by a mirrored 
relay monitoring for faults in the opposite direction, shown as unlabeled boxes in Figure 
2-1. 
2.1.2 Distance Element 
 The Zone 1 and Zone 2 values shown in Figure 2-1 correspond to “reach impedance” 
settings within the relay, defined as a percentage of the transmission line’s total impedance. 
The relay continuously calculates the impedance it sees via measured voltages and currents 
and compares it to the reach impedance. If the calculated impedance is less than the reach 
impedance, then the fault may be within its zone of protection. However, this also requires 
verification by the directional element to determine if the fault is in front of or behind the 
relay, which will be discussed in Section 2.1.3. 
10 
 
 The distance element calculates six “loop impedances” for comparison with the 
reach impedance setting. There are three ground loops (A-G, B-G, C-G) and three phase 
loops (A-B, B-C, C-A). Consider the phase-A to ground loop impedance calculation [13-
15]: 
𝑍𝐴𝐺 =
𝑉𝐴𝐺
𝐼𝐴+(𝑘0∗3𝐼0)
    (2.1) 
 where: 
  𝑍𝐴𝐺 = A-ground loop impedance 
  𝑉𝐴𝐺 = A-ground voltage 
  𝐼𝐴 = A-phase current 
  3𝐼0 = 3*zero sequence current 
  𝑘0 = Zero sequence compensation factor 
𝑘0 =  
𝑍0−𝑍1
3∗𝑍1
     (2.2) 
 where: 
  𝑍0 = Zero sequence line impedance 
  𝑍1 = Positive sequence line impedance 
 If the calculated loop impedance ZAG is less than the reach impedance setting, then 
the distance element asserts, meaning it declares that there might be a fault within its zone 
of protection. However, the distance element alone is not enough to determine if the fault 
is in front of or behind the relay, which is the responsibility of the directional element. To 
11 
 
simplify this discussion, it is assumed that distance and directional elements are the only 
two elements required to declare a Zone 1 fault. In practice, modern relays are highly 
customizable and involve multiple other logic functions designed to avoid mis-operation 
and unnecessary operational downtime. 
2.1.3 Directional Element  
The directional relay element is used to determine if a fault is occurring in front of or behind 
the relay. Negative sequence voltage and current measurements are often used for these 
calculations as they are not typically present during normal operating conditions, yet 
abundant during unbalanced faults in systems with predominantly synchronous generation. 
An impedance based directional element uses the following equation to calculate the 
negative sequence apparent impedance Z2 [13,16]: 
𝑍2 =
𝑉2
𝐼2
     (2.3) 
 The calculated Z2 is then compared to forward & reverse threshold settings Z2F and Z2R, 
which depend on the system configuration. Additionally, there is a minimum negative 
sequence current threshold setting required to facilitate this protection logic in both the 
forward and reverse direction. If the directional relay declares a forward fault at the same 
time the distance element asserts, the relay will take action to clear the fault. 
• If 𝑍2 < 𝑍2𝐹 & 𝐼2 > 𝐼2𝐹_𝑚𝑖𝑛  – Forward fault    (2.4) 
• If 𝑍2 > 𝑍2𝑅 & 𝐼2 > 𝐼2𝑅_𝑚𝑖𝑛  – Reverse fault 
  Herein lies the vulnerability of these relays in transmission networks with high 
penetrations of IBRs. As IBRs typically produce very low negative sequence current during 
12 
 
faults the minimum I2 thresholds are not met. The directional relay is unable to determine 
if the fault is within its zones of protection, even if the distance element asserts properly. 
2.2 Differential Current Protection 
Differential current protection, an alternative to the distance & directional strategy, 
compares a relay’s current measurement at both ends of a transmission line. Each relay is 
measuring the current flowing into the transmission line, which during normal operating 
conditions should be equal and opposite. Thus, if the sum of the currents does not equal 
zero (within some tolerance tuned to the system conditions) then the relay declares a fault 
on the transmission line.  
This requires communication between the relays because each relay perform this 
calculation independently. Additionally, because these relays are monitoring inward from 
either end of a one transmission line segment, they do not provide backup protection to 
adjacent line segments, akin to the Zone 2 of distance protection [17]. 
 Transmission networks employing differential current protection are not as 
susceptible to the negative-sequence reliance of the distance & directional protection 
scheme and should operate properly in transmission networks with high penetrations of 
IBRs [7-9]. However, due to the required communication infrastructure, differential 
current protection is more expensive and as such less common. Replacing existing distance 
relays with differential current relays would require capital and operational downtime costs, 
as well as additional design considerations to provide appropriate backup protection 
without Zone 2 distance elements.  
 
13 
 
 
 
 
Chapter 3  
Benchmarking Synchronous 
Generator Behavior 
3.1 System Model in CAPE with Synchronous Generator 
To determine appropriate inverter reference currents during fault conditions, the first step 
is to benchmark synchronous generator behavior using the two-bus transmission network 
shown in Figure 3-1. A 13.8 kV, 100 MVA synchronous generator is connected to a 345 
kV transmission line via a delta-wye step-up transformer, with the delta side lagging the 
wye side by 30°. At the remote end, a 1000 MVA equivalent source represents the bulk 
power system.  
 
Figure 3-1: Two-bus transmission network with 100 MVA synchronous generator 
100MVA
Generator
345 kV Transmission line, 50 km
345 kV
1000MVA 
System
Mid-line fault
14 
 
PSS@CAPE, a phasor-based fault analysis program, is selected for this study due 
to availability of realistic system impedances and ease of generating output data. Relevant 
system parameters are included in Table 3-1.  
Table 3-1: Synchronous generator & transmission network parameters 
Parameter Values 
Generator Voltage / Power 13.8 kV 100 MVA 
Generator Impedances Xd” = 0.148 p.u. X2 = 0.141 p.u. 
Xfmr Windings 13.8 kV Delta 345 kV Wye-Gnd 
Xfmr Impedance / Rating Z1 = 0.126 p.u. 100 MVA 
Line Impedance Z1 = 2 + j19 Ω Z0 = 16 + j65 Ω 
Line Length 50 km  
Eq. Source Voltage / Power 345 kV 1000 MVA 
Eq. Source Impedances Z1=10.5+j117 Ω Z0=15.6+j136 Ω 
 
3.2 Synchronous Generator Fault Response 
3.2.1 Low side response (13.8 kV) 
There are four categories of faults, and one example from each category is considered 
throughout this study.  
• Single-line to ground (A-G) 
• Line-to-line (B-C) 
• Double-line to ground (B-C-G) 
• Three-lines to ground or Three-phase (A-B-C-G) 
15 
 
A fault is created in the middle of the transmission line for each of the fault types 
listed above. The synchronous generator fault response is recorded in Table 3-2. Prior to 
fault inception, the system is generating at unity power factor with the angle of phase-A on 
the 345 kV transmission line at 0°, and the angle of phase-a at the generator at -30°. Note 
that the subscript case denotes the location of the measured signal relative to the step-up 
transformer. For example, Ia indicates the low side 13.8 kV phase-a current, while IA  
represents the high side 345 kV phase-A current. 
Table 3-2: Synchronous generator fault response on low side of transformer, 13.8 kV 
Fault Type Ia  
(p.u.) 
Ib  
(p.u.) 
Ic   
(p.u.) 
A-G 2.1 ∠ -85° 2.1 ∠ 95° 0.04 ∠ -113° 
B-C 1.8 ∠ -177° 1.8 ∠ -175° 3.6 ∠ 4° 
B-C-G 2.1 ∠ -146° 2.1 ∠ 153° 3.6 ∠ 4° 
A-B-C-G 3.6 ∠ -117° 3.6 ∠ 123° 3.6 ∠ 3° 
 
The synchronous generator fault currents are used as a basis for determining 
appropriate inverter reference currents for each type of fault. These reference currents 
indicate the desired IBR output at any given time and are the control mechanism by which 
IBR behavior is modified.  This process is fully detailed in Chapter 4.  
Note that these synchronous generator fault currents are a function of the various 
system impedances which vary between transmission networks. The inverter currents need 
not identically replicate Table 3-2, but more so serve as a guideline for developing a control 
strategy to ensure proper operation of distance and directional relay elements.  
16 
 
3.2.2 High voltage response (345 kV) 
To evaluate the success of the proposed control strategy later in Chapter 5, it is important 
to understand the relationship between voltage and current phasors expected by the 345 kV 
relay. In particular, the phase angle relationship between the faulted phase voltage and 
current should be maintained. The faulted phase current should lag the faulted phase 
voltage by approximately the line impedance angle, which in this system is 85°. Voltage 
and current measurements at the 345 kV relay for each type of fault are shown in Table 3-
3.  
Table 3-3: Voltage & current phasors at 345 kV relay  
Fault VA  
(p.u.) 
VB 
(p.u.) 
VC 
(p.u.) 
IA 
(p.u.) 
IB 
(p.u.) 
IC 
(p.u.) 
A-G 0.1 ∠ -7° 0.9 ∠-118° 0.9 ∠ 116° 3.5 ∠ -85° 0.8 ∠ -85° 0.8 ∠ -87° 
B-C 1 ∠ 0° 0.5 ∠-177° 0.5 ∠ 177° ~0  2.4 ∠-176° 2.4 ∠ 4° 
B-C-G 0.93 ∠ -1° 0.1 ∠-167° 0.1 ∠ 152° 0.8 ∠ 98° 3.3 ∠ 143° 3.1 ∠ 45° 
A-B-C-G 0.1 ∠ -3° 0.1 ∠-123° 0.1 ∠ 117° 2.7 ∠ -87° 2.7 ∠ 153° 2.7 ∠ 33° 
 
During an A-G fault in a system with predominantly synchronous generation, IA 
should lag the faulted phase voltage VAG by 85°. For a B-C and B-C-G fault, IBC should 
lag VBC by 85°. For three-phase faults, all three currents should lag their corresponding 
voltage by 85°. Table 3-4 reproduces the data from Table 3-3 in a format to highlight that 
these relationships do indeed hold within a few degrees. 
 
17 
 
Table 3-4: Angular relationship between 345 kV faulted phase voltage and current 
Fault Faulted Voltage Faulted Current Phase Difference 
A-G VA = 0.1∠ -7° IA = 3.5 ∠ -85° 78° 
B-C VBC = 0.05∠ -90° IBC = 4.8 ∠ -176° 86° 
B-C-G VBC = 0.07∠ -98° IBC = 4.8 ∠ -178° 80° 
A-B-C-G VA = 0.1∠ -3° IA = 2.7 ∠ -87° 84° 
 
 
  
18 
 
 
 
Chapter 4  
Inverter Based Resource Model  
4.1 System Model in Simulink with IBR 
4.1.1 Transmission Network 
A 100 MW inverter is modeled in place of the synchronous generator from Chapter 3 and 
connected to the same transmission line and remote end equivalent source as shown in 
Figure 4-1. Simulink is selected as the analysis software due to its capability to model 
inverters and power systems in the time-domain, which facilitates implementation of the 
proposed control strategy. Simulink is also able to be integrated with Opal-RT, a program 
that can import Simulink models and with perform real-time hardware-in-the-loop 
simulations. Opal-RT can also easily generate COMTRADE files, which are used to export 
the simulation results for testing on distance relays, as discussed in Chapter 6.  
19 
 
 
Figure 4-1: System model with 100 MW inverter  
An additional 3-winding transformer is added to represent the configuration of a 
utility-scale IBR generation facility more accurately. The output of many inverters is 
collected from multiple feeders at a medium voltage (34.5 kV) before connecting to the 
high-voltage transmission network. The 2-winding transformer impedance is 5.75%, and 
the 3-winding transformer impedance between the two wye-connected windings is 10%. 
The delta tertiary winding is left unconnected. Unless otherwise specified, the system 
parameters are the same as shown in Table 3-1.  
4.1.2 Inverter Design 
The 100 MW inverter is an aggregated inverter model, which represents the generation 
from an entire solar or wind farm. Aggregating the contribution of all IBR in a generation 
facility allows for testing the efficacy of the proposed control strategy while reducing 
simulation time. Figure 4-2 depicts a block diagram of the inverter model, and the 
following subsections detail various parts of the design much of which is based on the DQ 
current control modeling techniques described in Mohan [18].  
20 
 
 
Figure 4-2: Inverter control block diagram 
Phase-Locked Loop  
A phase-locked loop (PLL) is used to synchronize the inverter output with the established 
grid voltage. This is accomplished by tracking the phase-A voltage angle. When the voltage 
crosses zero and is increasing in magnitude, the phase angle output 𝜃 = 0 resulting in the 
sawtooth waveform shown in Figure 4-3. 
 
21 
 
 
Figure 4-3: PLL output Theta with Va (not to scale) 
The output 𝜃 of the PLL is then used in a mathematical operation called Park’s 
transformation, which translates signals from the phase ABC domain to the DQ domain. 
This is shown as an input arrow to each ABC/DQ, or DQ/ABC transform block in Figure 
4-2.  
                      [
𝑉𝑑
𝑉𝑞
] =
2
3
[
cos (𝜃) cos (𝜃 −
2𝜋
3
) cos (𝜃 +
2𝜋
3
)
−sin (𝜃) −sin (𝜃 −
2𝜋
3
) −sin (𝜃 +
2𝜋
3
)
] [
𝑉𝑎
𝑉𝑏
𝑉𝑐
]    (4.1) 
Park’s transformation is useful for this control application because when the system 
is in balanced steady-state, time-varying AC voltage and current signals in the ABC 
domain become DC signals in the DQ domain, simplifying the mathematical analysis of 
system dynamics.  
22 
 
Current Control 
The inverter output is controlled by specifying “reference currents” (Ia*, Ib*, Ic*), which 
correspond to the leftmost block in Figure 4-2. These are specified in the ABC domain 
before being transformed into DQ (Id*, Iq*). This allows a straightforward implementation 
of the synchronous generator fault response, detailed in Section 4.3.  
The current controller has two proportional-integral (PI) feedback loops which 
compare the measured inverter output current to the reference current setpoints in the DQ 
domain. The output of each PI controller is summed with the measured voltage and the 
feed-forward terms, defined by the following equations: 
𝑉𝑑𝑐𝑛𝑡𝑟𝑙 = [𝐾𝑝(𝐼𝑑
∗ − 𝐼𝑑) + 𝐾𝑖 ∫(𝐼𝑑
∗ − 𝐼𝑑)𝑑𝑡] + 𝑉𝑑 − (𝐼𝑞 ∗ 𝜔𝑔𝑟𝑖𝑑 ∗ 𝐿𝑓𝑖𝑙𝑡𝑒𝑟), 
 𝑉𝑞𝑐𝑛𝑡𝑟𝑙 = [𝐾𝑝(𝐼𝑞
∗ − 𝐼𝑞) + 𝐾𝑖 ∫(𝐼𝑞
∗ − 𝐼𝑞)𝑑𝑡] + 𝑉𝑞 + (𝐼𝑑 ∗ 𝜔𝑔𝑟𝑖𝑑 ∗ 𝐿𝑓𝑖𝑙𝑡𝑒𝑟)  
             (4.2) 
where: 
 𝐾𝑝 = PI controller proportional constant 
 𝐾𝑖 = PI controller integral constant 
𝐼𝑑
∗ , 𝐼𝑞
∗ = Inverter reference current setpoints 
𝐼𝑑 , 𝐼𝑞= Measured inverter output currents 
𝜔𝑔𝑟𝑖𝑑 = Grid frequency  
𝐿𝑓𝑖𝑙𝑡𝑒𝑟 = Filter inductance 
23 
 
Space Vector Pulse Width Modulation 
The Space Vector Pulse Width Modulation (SVPWM) logic generates PWM control 
voltages for an average model inverter. The outputs from equation 4.2 are transformed back 
into the ABC domain and used in the following equations to generate these signals, derived 
in Mohan [18]: 
𝑉𝑎𝑏𝑐_𝑃𝑊𝑀 =
𝑉𝑎𝑏𝑐_𝑐𝑛𝑡𝑟𝑙−𝑉𝑘
𝑉𝑑𝑐
2⁄
     
𝑉𝑘 =
max(𝑉𝑎,𝑉𝑏,𝑉𝑐)+min (𝑉𝑎,𝑉𝑏,𝑉𝑐)
2
    (4.3) 
The three outputs from equation 4.3 are scaled between 0 and 1, which correspond 
to the PWM “duty ratio” for each phase (ratio of the phase voltage to the DC bus voltage). 
This correlates to the output voltage by the following equation: 
𝑉𝐿𝐿𝑜𝑢𝑡(𝑅𝑀𝑆) =
𝑉𝑃𝑊𝑀∗𝑉𝐷𝐶
√2
    (4.4) 
LC Filter 
The output of the inverter is passed through an LC filter before connecting to the first step-
up transformer, as shown in Figure 4-4. The filter is designed to minimize the allowable 
ripple in the inverter output current below 5% and the filter capacitor voltage ripple below 
2% for an IBR switching frequency of 50 kHz. However, since an average model inverter 
is used for the simulations in Chapter 5, the effect of the filter on the total harmonic 
distortion of the output current and voltage is not apparent. The parameters are listed in 
Table 4-1 for completeness, but a derivation of these parameters is omitted. 
24 
 
 
 
Figure 4-4: Inverter connected via LC filter to 100 MVA step-up transformer 
Summary of IBR Parameters 
A summary of relevant IBR parameters is shown in Table 4-1 below. 
Table 4-1: Summary of IBR parameters 
Parameter Value 
DC Voltage 1 kV 
Rated Line-to-Line Voltage 690 V (RMS) 
Rated Power 100 MVA 
Frequency 60 Hz 
Lfilter 14.3 uH 
Cfilter 6.6 mF 
Rc 3.3 mΩ 
25 
 
4.2 Fault Identification 
4.2.1 High Side (345 kV) Fault Detection 
Before inverter reference currents can be changed, the fault type must be correctly 
identified. This can be accomplished by measuring 345 kV phase (A-G, B-G, C-G) and 
line-to-line (A-B, B-C, C-A) voltage magnitudes at the relay location, and classifying the 
fault according to the following criteria:  
• Single-Line to Ground 
o Faulted phase below 0.8 p.u. 
o Healthy phases above 0.8 p.u.  
• Line-to-Line 
o Both faulted phases below 0.8 p.u. 
▪ But above 0.4 p.u. 
o Faulted line-to-line below 0.8 p.u. 
• Double-Line to Ground 
o Both faulted phases below 0.4 p.u. 
o Faulted line-to-line below 0.8 p.u. 
• Three-Lines to Ground 
o All phases below 0.8 p.u. 
The 0.8 per-unit threshold is selected because it is significantly below normal 
operating voltage conditions, and the 0.4 per-unit threshold is selected to differentiate 
between a line-to-line and double-line to ground fault.  
26 
 
4.2.2 Low Side (690 V) Fault Detection 
While fault identification at the 345 kV relay is ideal due to the minimal impedance 
between the measurement and fault locations, it is unlikely that the IBR will have access 
to these signals. There is not usually communication between the point of connection to 
the bulk transmission system and individual inverters on a fast enough time scale to be 
used in making control logic decisions, especially in large generation facilities where many 
IBRs are spread over a large area. 
It is more likely that the inverter will need to use local measurements for fault 
detection. Voltage magnitude thresholds were developed using the line-to-line voltage 
magnitudes at the inverter step-up transformer 690 V terminals (A-B, B-C, C-A) 
classifying the fault according to the following criteria: 
• Single-Line to Ground (A-G) 
o A-B < 0.8 p.u. 
o B-C > 0.8 p.u. 
o C-A > 0.6 p.u. 
• Line-to-Line (B-C) 
o A-B > 0.8 p.u. 
o B-C < 0.8 p.u. 
o 0.4 p.u. < C-A < 0.8 p.u. 
• Double-Line to Ground (B-C-G) 
o 0.4 p.u. < A-B < 0.8 p.u. 
o B-C < 0.4 p.u. 
o C-A < 0.8 p.u. 
27 
 
• Three-Lines to Ground 
o All line-to-line voltages below 0.4 p.u. 
The 0.8 per-unit threshold is selected because it is significantly below normal 
operating conditions. Other thresholds are chosen to ensure selectivity between fault types. 
Voltage classification was verified in simulation for all types of faults. 
The RMS voltage magnitudes used for fault detection are calculated over a one 
cycle (60 Hz) moving window. This has potential for a misclassification for fault types 
other than single-line-to ground. For example, during a B-C-G fault, the voltage 
magnitudes briefly meet the B-C fault criteria. These misclassifications necessitate adding 
a delay after a fault is first detected but before the inverter reference currents are changed, 
to allow for the voltage magnitudes to reach appropriate levels for accurate fault detection. 
A delay of one cycle (16.67ms) was verified in simulation as sufficient to avoid any 
misclassification and will be explored in further detail in Chapter 5.  
4.3 IBR Reference Current Modification 
To protect the IBR power electronic components from damage, the magnitude of the output 
current should not exceed its rated value. As shown in Chapter 3, the synchronous 
generator fault current magnitudes exceed this limit, reaching as high as 3.6 per unit.  
When emulating synchronous generator fault behavior, inverter reference currents 
are limited to 1.0 per-unit and mimic the relative magnitudes and phase relationship of the 
synchronous generator currents. Consider the magnitude of fault currents shown in Table 
3-2 for a B-C fault. The C-phase magnitude is double the magnitude of the other two phases. 
The IBR maintains this relative magnitude between phases while staying within its 
28 
 
maximum current limit by injecting Ia = Ib = 0.5 per unit, and Ic = 1 per unit. After a fault 
is detected using the criteria described in Section 4.2, the inverter reference currents are 
changed from their normal balanced, unity power factor operation to those shown in Table 
4-2.  
Table 4-2: Inverter reference currents to emulate synchronous generator fault response 
Fault  
Type 
Ia  
(p.u.) 
Ib  
(p.u.) 
Ic  
(p.u.) 
A-G 1∠ -85° 1∠ 95° 0 
B-C 0.5 ∠ 180° 0.5 ∠ 180° 1 ∠ 0° 
B-C-G 0.5 ∠ -150° 0.5 ∠ 150° 1 ∠ 0° 
A-B-C-G 0.9 ∠ -115° 0.9 ∠ 125° 0.9 ∠ 5° 
 
When modifying inverter reference currents, the phase angles shown in Table 4-2 
are relative to the pre-fault phase-A voltage angle (0° at 345 kV). For all simulations, it is 
assumed that the pre-fault current injection is 1.0 per unit, balanced, at unity power factor. 
Example phasor diagrams of the pre-fault and post-fault IBR currents for all fault types are 
shown in Figures 4-5 through 4-9. 
29 
 
 
Figure 4-5: IBR pre-fault phasor diagram 
 
Figure 4-6: IBR post-fault A-G phasor diagram 
-1
0
1
-1 0 1
IBR Pre-Fault Current Injection
Ia Ib Ic
-1
0
1
-1 -0.5 0 0.5 1
IBR Post-Fault A-G Current Injection
Ia Ib Ic
30 
 
 
Figure 4-7: IBR post-fault B-C phasor diagram 
 
Figure 4-8: IBR post-fault B-C-G phasor diagram 
 
-1
0
1
-1 -0.5 0 0.5 1
IBR Post-Fault B-C Current Injection
Ia Ib Ic
-1
-0.5
0
0.5
1
-1 -0.5 0 0.5 1
IBR Post-Fault B-C-G Current Injection
Ia Ib Ic
31 
 
 
Figure 4-9: IBR post-fault A-B-C-G phasor diagram 
Reference currents for faults in the same category (e.g., A-G, B-G), are determined 
by maintaining the relative difference between each phase current angle, as well as the 
difference between the pre-fault angle and post-fault angle. For example, a B-G fault shifts 
Ib by -85° (-120° - 85°) = -205°, with Ic = -Ib, and Ia = 0.  
Note that the magnitude of reference currents is reduced to 0.9 for an A-B-C-G 
fault. A relay element known as Loss of Potential, or Fuse Failure, blocks the distance 
element from operating when a drop in voltage is detected without a change in current. By 
reducing the current magnitude, this undesirable blocking of distance operation can be 
avoided. 
 
 
 
-1
-0.5
0
0.5
1
-1 -0.5 0 0.5 1
IBR Post-Fault A-B-C-G Current Injection
Ia Ib Ic
32 
 
 
 
 
Chapter 5  
Simulation Results 
5.1 Mid-line Faults 
To simulate the effectiveness of the control strategy, a fault of each category is created at 
the middle of the transmission line. This fault should be cleared by the instantaneous Zone 
1 protection; however, Simulink cannot model the protection logic for a distance relay. 
Therefore, success in this chapter is defined using the following criteria: 
1. The fault type is properly detected, and IBR reference currents modified within 2.5 
cycles, which is the P2800 step response time requirement. 
2. Relationship between the voltage and current signals at the 345 kV relay resemble 
the synchronous generator response within 4 cycles, i.e., the faulted current lags the 
faulted voltage by the line impedance angle of 85°.   
5.1.1 Fault Detection at IBR 
Before the reference currents can be modified, the IBR must properly detect the type of 
fault. As previously mentioned in Chapter 4, it is unlikely that the IBR will have access to 
the 345 kV voltage and current measurements. As such, this subsection will use the line-
to-line voltages at 690 V to identify the fault.  
33 
 
 A mid-line fault is created 0.05s into the simulation, which will remain true for all 
mid-line scenarios in this chapter. A one cycle moving RMS average for all three line-to-
line voltages is monitored. For each fault type, the total time from fault inception to 
accurate detection is determined as shown in Figures 5-1 to 5-4, with results summarized 
in Table 5-1.  
 
Figure 5-1: A-G fault detection using 690 V line-to-line voltages 
The highlighted point in Figure 5-1 shows the moment where the criteria for 
identifying an A-G fault is met, 4.81ms after fault inception. However, the reference 
currents cannot be modified immediately due to the potential misclassification for other 
types of faults as discussed in Chapter 4, which is also shown in Figures 5-2 through 5-4.  
 
A-G 
34 
 
 
Figure 5-2: B-C fault detection using 690 V line-to-line voltages 
The first highlighted point in Figure 5-2 shows where the fault detection logic 
incorrectly identifies a B-G fault. As the RMS moving averages continue to drop, the B-C 
fault is correctly identified at the second highlighted point 7ms later, which is a total of 
14.3ms from fault inception.  
 
B-G 
B-C 
35 
 
 
Figure 5-3: B-C-G fault detection using 690 V line-to-line voltages 
The leftmost point in Figure 5-3 shows where the fault detection first incorrectly 
identifies a B-G fault 6.12ms after fault inception, before correctly identifying the B-C-G 
fault 8.74ms later which is a total of 14.86ms after fault inception. 
B-G 
B-C-G 
36 
 
 
Figure 5-4: Three-phase fault detection using 690 V line-to-line voltages 
A similar misclassification is observed in Figure 5-4 during a three-phase fault. An 
A-G fault is first identified 4.44ms after fault inception, before all three voltages drop 
below the 0.4 per unit threshold 11.17ms later to appropriately classify the three-phase 
fault. The fault is correctly identified 15.61ms after fault inception, within one cycle. 
To avoid changing the reference currents inappropriately, a one cycle delay is added 
between when any fault is identified and when the reference currents are allowed to change. 
This results in the step response time being equal to the sum of the initial fault detection 
time and the one cycle additional delay, shown in the rightmost column of Table 5-1.  
A-G 
A-B-C-G 
37 
 
All fault types are properly identified within one cycle and inverter reference 
currents are modified within 2.5 cycles (or 41.67ms), meeting the step response 
requirement. 
Table 5-1: Fault detection & step response times relative to fault inception 
Fault  
Type 
Initial Fault 
Detection 
(ms) 
Accurate 
Detection 
(ms) 
Step Response  
(Initial Detection  
+ 1 Cycle Delay) 
 (ms) 
A-G 4.81 4.81 21.48 
B-C 7.3 14.3 23.97 
B-C-G 6.12 14.86 22.79 
A-B-C-G 4.44 15.61 21.11 
 
The added one cycle delay may be slightly longer than necessary based on these 
simulation results, as the greatest time difference between initial and accurate fault 
detection is 11.17ms during the three-phase fault. However, waiting one cycle from initial 
detection still meets the desired step response benchmark, so remaining somewhat 
conservative with this delay is prudent. 
5.1.2 IBR Current Modification 
As mentioned in Chapter 1, the transient response of an IBR immediately following a fault 
depends on proprietary control logic unique to each manufacturer’s design. The magnitude 
of the current during this transient response can vary between 1.0 and 1.5 per unit. The IBR 
model studied in this chapter is focused on understanding the proposed control strategy and 
does not attempt to mimic the complexity and variety of control functionality found in a 
38 
 
real-world IBR, and as such cannot easily or accurately replicate the transient response. 
The IBR control will attempt to always limit the magnitude of the IBR current to 1.0 per 
unit. 
 Pre-fault, the IBR is injecting 1.0 per unit current at unity power factor. Once any 
type of fault is detected, the inverter will wait for one cycle before taking any action. At 
the end of this delay period, if a fault is still present the IBR will modify its reference 
currents according to Table 4-2. Once the reference currents are modified, there is some 
transient period where the output of the inverter stabilizes to the new desired output. The 
end of this transient period is defined as the “Settling Time” benchmark and should resolve 
within 4 cycles from fault inception. Figures 5-5 through 5-8 will show the IBR response 
for each fault category. The desired settling time metric of less than 4 cycles is met for all 
types of faults. 
 
39 
 
 
Figure 5-5: Inverter currents during A-G fault 
An A-G fault is simulated in Figure 5-5. The A-G fault is detected 4.8ms after 
inception, with the step response occurring one cycle later at 21.48ms from inception. 
There is a brief transient period ending at approximately 5.5ms after the step response and 
27ms from fault inception. At this point the IBR currents resolve to the desired behavior 
of Ia = -Ib (as shown by their intersecting zero crossings and identical magnitudes) with Ic 
≈ 0.  
40 
 
 
Figure 5-6: Inverter currents during B-C fault 
In Figure 5-6 a B-C fault is simulated. A fault is initially detected 7.3ms after its 
inception, with the step response occurring 24ms after the fault. There is a brief 5ms settling 
period, ending 29ms after fault inception. The IBR currents resolve to the desired behavior 
of Ia = Ib with Ic at double the magnitude and 180° out of phase. 
41 
 
 
Figure 5-7: Inverter currents during B-C-G fault 
In Figure 5-7, a B-C-G fault is simulated. A fault is initially detected 6.12ms after 
inception, and the step response occurs 22.8ms after inception. There is a brief settling 
period of 4.2ms, ending 27ms after fault inception. The desired IBR current injection is 
achieved, Ia leads Ib by 60° with equal 0.5 per unit magnitudes, and Ic lagging Ib by 150° 
with a 1.0 per unit magnitude. 
42 
 
 
Figure 5-8: Inverter currents during three-phase fault 
A three-phase fault is simulated in Figure 5-8. A fault is initially detected 4.44ms 
after fault inception, and the step response occurs 21.11ms after the fault. There is a brief 
settling period of 4.6ms, ending 24.7ms after fault inception. The desired IBR behavior is 
achieved, reducing the magnitude to 0.9 per unit but maintaining 120° between the phases.  
5.1.3 Voltage & Current Phase Relationship at Relay 
As distance relay logic is not implemented in these Simulink simulations, it is necessary to 
use another metric for determining if the control strategy is successful. If the phase 
relationship between the faulted voltage and current is similar to the synchronous generator 
fault response detailed in Chapter 3, it is reasonable to expect the distance relays to operate. 
43 
 
 To make an easier comparison between voltage and current magnitudes, a reference 
signal of 1.0 per unit with the pre-fault voltage phase angle is used for the appropriate 
faulted phase voltage and compared to the post-fault current. For example, for an A-G fault 
VA_pre-fault = 1.0 at 0°. The voltage phase angle does not shift more than a few degrees from 
pre to post fault, thus providing a good comparison to determine if synchronous generator 
behavior is emulated. The faulted phase current should lag the faulted voltage by 
approximately 85°, which is the phase angle of the transmission line impedance.  
Figures 5-9 through 5-12 show the voltage & current phase relationship at the relay 
for each type of fault. This relationship is achieved within 3 cycles for each scenario, with 
the phase relationship displayed on each of the figures.  
 
Figure 5-9: 345 kV phase relationship between faulted voltage and current, A-G fault 
44 
 
 
Figure 5-10: 345 kV phase relationship between faulted voltage and current, B-C fault 
 
Figure 5-11: 345 kV phase relationship between faulted voltage and current, B-C-G fault 
 
45 
 
 
Figure 5-12: 345 kV phase relationship between faulted voltage and current, three-phase fault 
5.1.4 Response Time Summary 
The fault type is accurately detected within 1 cycle (16.7ms), the step response within 2 
cycles (33ms), and the settling time within 3 cycles for all types of faults as shown in Table 
5-2. This meets the benchmark step response time of 2.5 cycles and settling time of 4 cycles. 
All times are relative to fault inception. 
 
 
46 
 
Table 5-2: Summary of response times of proposed IBR control strategy 
Fault  
Type 
Accurate Fault 
Detection  
(ms) 
Step Response  
Time  
(ms) 
Settling  
Time 
(ms) 
A-G 4.81 21.48 27 
B-C 14.3 23.97 29 
B-C-G 14.86 22.79 27 
A-B-C-G 15.61 21.11 24.7 
 
5.2 Evolving Faults 
It is possible for a fault on a transmission line to “evolve”, or transition between fault 
categories. This occurs when a fault on one phase conductor propagates to one or more 
other conductors. For example, after a short time an A-G fault may become an A-B-G fault, 
and then evolve again to a three-phase fault. The following sections will investigate how 
evolving faults affect accuracy and responsiveness of the proposed control strategy.  
5.2.1 Test Procedure 
It is difficult to comprehensively study evolving faults, as the time between evolutions 
varies. Considering that the Zone 1 instantaneous protection of distance relays should clear 
faults with evolution stages lasting for more than a few cycles, this study will focus on 
intervals of 1.5 and 2 cycles between evolution stages. The following 6 fault sequences 
were considered: 
• A-G to A-B-G to three-phase 
• A-G to A-B-G 
47 
 
• A-G to three-phase 
• B-C to B-C-G to three-phase 
• B-C to B-C-G 
• B-C to three-phase 
These 12 fault scenarios are created at the middle of the transmission line. In each 
evolution stage, the time to accurately detect the fault type is recorded, as well as the time 
it takes for inverter reference currents to be modified. The one cycle artificial delay 
between when a fault is first identified, and the reference currents are modified is 
maintained for these simulations. Figure 5-13 below shows an example of this process of 
classifying response times. 
48 
 
 
Figure 5-13: Fault detection & step response times during evolving fault (A-G to A-B-G to 
Three-phase) 
The fault sequence studied in Figure 5-13 is A-G to A-B-G to three-phase, with 2 
cycles between each evolution. The detection and step response times for each stage are 
shown with arrows on the horizontal axis. This illustrates that the fault detection logic can 
accurately detect and inject appropriate currents during an evolving fault. The fault 
detection and step response times are recorded in the following section.  
5.2.2 Evolving Fault Response Time Summary 
A summary of the response times for each of the scenarios is listed in Table 5-3 below. 
The fault ID columns specify how long it takes to accurately identify the fault time. All 
49 
 
times are relative to the fault evolution of the current stage. For example, the A-B-G fault 
is identified correctly 11.4ms after the fault evolves from A-G to A-B-G. 
Table 5-3: Summary of fault identification and step response times during evolving faults 
Fault 
Sequence 
Stage 1 Stage 2 Stage 3 
Fault 
ID 
(ms) 
Step  
Response 
 (ms) 
Fault  
ID  
(ms) 
Step  
Response 
 (ms) 
Fault  
ID 
(ms) 
Step  
Response  
(ms) 
AG-ABG-3Ph 4.81 21.48 11.4 19.3 9.8 24.67 
AG-ABG 4.81 21.48 11.4 19.3   
AG-3Ph 4.81 21.48 11.81 18.91   
BC-BCG-3Ph 14.3 20.67 12.13 23.67 13.35 24.57 
BC-BCG 14.3 20.67 12.13 23.67   
BC-3Ph 14.3 20.67 14.93 23.67   
 
These details are included for completeness and to illustrate that the fault detection 
& injection logic are functioning as intended. However, the ultimate success metric for 
evolving faults is determined by proper operation of the distance relay. As Simulink does 
not implement the relay protection logic it is possible that the distance element would 
operate before the evolving fault finishes its sequence. This requires validating simulation 
results on relay hardware, discussed in Chapter 6. 
  
50 
 
 
 
Chapter 6  
Relay Hardware Verification 
6.1 Relay Testing Process 
This chapter describes how the proposed control strategy was verified on relay hardware. 
A file format called Common format for Transient Data Exchange for power systems 
(COMTRADE) allows for the export of 345 kV voltage and current signals from Simulink 
into a form that can replayed in a relay testing environment. A signal generator is connected 
to relays and utilizes the COMTRADE files to replay the simulation data. The relays under 
test are programmed as if they were deployed in the 345 kV transmission network used in 
simulation and generate event records which are used to analyze the fault operation times. 
A diagram of this workflow is shown in Figure 6-1. 
 
Figure 6-1: Relay hardware verification workflow 
 
51 
 
6.1.1 COMTRADE File Preparation 
The mid-line fault simulations from in Chapter 5 are used to evaluate the Zone 1 
instantaneous protection logic for distance relays. COMTRADE files were also generated 
for the 12 evolving fault scenarios discussed in Section 5.2. 
An additional set of simulations were created where the transmission line fault 
occurs at the remote end of the line, outside of Zone 1. These end-line simulations test for 
a type of mis operation called “Zone 1 overreach”, meaning it takes action to clear a fault 
that is outside of its zone of protection. Only the time-delayed Zone 2 backup protection 
should operate for end-line faults.  
6.1.2 Doble Protection Suite Testbench Setup 
A Doble signal generator in combination with its Protection Suite software is used to 
import the 345 kV simulation data in the COMTRADE file format. The signal generator is 
connected to each relay under test. The software instructs the signal generator to inject 
voltages and currents from the simulation data scaled to the relay’s rated input values. The 
relay will then generate an event record based on how these voltage and current signals 
interact with its programmed protection logic. The event record details all protective 
element operations for that simulation.  
6.1.3 Relay Settings  
Each relay tested was programmed with the distance settings shown in Table 6-1 below. 
These settings are typical for distance relays in a 345 kV transmission network. Refer to 
Chapter 2 for details on the purpose of these settings. Note that these settings are referred 
to the secondary of the relay current and voltage transformer ratings. 
52 
 
Table 6-1: Distance & directional relay settings  
Parameter Value 
Line Impedance 0.64 ∠ 85° 
Zone 1 Reach 85%  
Zone 2 Reach 125% 
Zone 2 Delay 5 cycles 
Forward Directional Threshold -0.3 Ω 
Reverse Directional Threshold +0.3 Ω 
Minimum I2 Forward Current 2.4 A 
Minimum I2 Reverse Current 1.2 A 
 
6.2 Mid-line & End-line Results 
The mid-line and end-line fault COMTRADE files were replayed on five relays from two 
different manufacturers. The goal is for all mid-line faults to be cleared by Zone 1 within 
3-5 cycles. End-line faults should be cleared by Zone 2 approximately 5 cycles after Zone 
1 would have operated, somewhere in the range of 7-10 cycles.  
As discussed previously, if synchronous generator behavior is not emulated the lack 
of negative sequence current (corresponding to the minimum I2 settings in Table 6-1) will 
prevent the relay’s directional elements from operating. If the relay can accurately detect 
the fault type and take appropriate action within the desired response time range, the IBR 
control strategy is successful. This section will explore four event records in detail, an A-
G mid-line fault, A-G end-line fault, B-C mid-line fault, and B-C end-line fault. The 
remaining results are summarized in tabular format.  
53 
 
 
Figure 6-2: Relay event record for A-G mid-line fault, Zone 1 operation 
Figure 6-2 shows the relay event record after replaying the COMTRADE 
simulation data from an A-G mid-line fault. The top two panels show the three-phase 
current and voltage waveforms recorded by the relay. The bottom panel shows the relevant 
relay Boolean operators that are triggered by the input voltage and currents. The Z1G 
operator asserts when a Zone 1 ground fault is detected. Since Zone 1 operates without 
delay, the TRIP operator asserts simultaneously. The left orange vertical bar denotes the 
fault inception point, and the right magenta vertical bar denotes when Zone 1 operates, 
31ms later. The relay TRIP occurs merely 4ms after the IBR settling period ends and is 
within the realm of expected relay response time with primarily synchronous generation. 
The event record also shows that the Z1G operator de-asserts very briefly before 
re-asserting. However, this occurs after TRIP asserts, so it has no effect on the relay 
operation time. 
54 
 
 
Figure 6-3: Relay event record for A-G end-line fault, Zone 2 operation 
 Figure 6-3 shows an event record for an A-G end-line fault. The relay operators 
shown in the bottom panel differ from the mid-line fault in Figure 6-2. The Z1G operator 
is not shown, meaning that it does not assert and there is no Zone 1 overreach, thus the 
fault location is accurately detected. When the Zone 2 ground fault element Z2G asserts, a 
5-cycle delay timer begins. Once the timer finishes counting the Zone 2 ground trip (Z2GT) 
operator asserts, simultaneously asserting the relay TRIP equation.  
After the fault is detected by the relay, Z2G de-asserts very briefly before re-
asserting. This de-assertion causes the Zone 2 timer to restart, resulting in a slightly longer 
relay TRIP time. The total time from fault inception to TRIP is 123ms, or approximately 
7.4 cycles.  
 
55 
 
 
Figure 6-4: Relay event record for B-C mid-line fault, Zone 1 operation 
 Figure 6-4 shows an event record for a B-C mid-line fault. For detecting line-to-
line and double-line to ground faults this relay uses the M1P operator for Zone 1, and M2P 
for Zone 2. These operators utilize the phase distance loop-impedance calculations 
described in Chapter 2. The phase Zone 1 element correctly locates and clears the fault. 
The total time from fault inception to TRIP is 50ms, which is 21ms after the IBR settling 
period ends.  
  
56 
 
 
Figure 6-5: Relay event record for B-C end-line fault, Zone 2 operation 
 Figure 6-5 illustrates time-delayed Zone 2 operation for a B-C end-line fault. Zone 
1 (M1P) does not assert during this simulation, indicating that the fault location was 
correctly identified. After a five cycle delay from when the fault is detected the Zone 2 
phase element (M2P) causes the TRIP element to assert, 140ms after fault inception.  
 
  
 
 
 
 
57 
 
Table 6-2 below summarizes the average and maximum relay operation times for 
the five relays under test: 3 from manufacturer 1, and 2 from manufacturer 2. A 
comprehensive table of relay operation times is shown in Appendix A.  
Table 6-2: Summary of relay operation times for mid-line and end-line faults 
Fault  
Type 
Mid-Line 
(Zone 1) 
End-Line  
(Zone 2) 
Avg 
(ms) 
Max 
 (ms) 
Avg 
(ms) 
Max  
(ms) 
A-G 37.6 48 119.2 125 
B-C 49 56 140.4 151 
B-C-G 42.4 46 136 140 
A-B-C-G 39.8 44 122.75 129 
 
Overall, the desired relay operation time benchmarks were achieved. The average 
Zone 1 operation time for mid-line faults is within 3 cycles for all fault types, with the 
worst-case maximum operation time being only a few milliseconds longer than 3 cycles. 
The average end-line fault operation times are between 7 and 9 cycles, with the worst-case 
maximum operation time being 9 cycles for a B-C fault.  
58 
 
 
Figure 6-6: Zone 1 overreach during three-phase end-line fault 
There was one instance of Zone 1 overreach observed during a three-phase end-line 
fault on one of the relays, as shown in Figure 6-6. The other four relays operated properly 
for the same COMTRADE file. The Zone 2 pickup element (PH_DIST_Z2_PKP) asserts 
to start the five cycle delay timer, but a few milliseconds later Zone 1 causes the relay to 
trip incorrectly. To determine the precise cause of this mis-operation, further investigation 
and discussion with the relay manufacturer is necessary. This outlier response time was 
omitted from the three-phase Zone 2 average shown in Table 6-2. 
6.3 Evolving Fault Results 
The 12 evolving fault scenarios described in Section 5.2 were played back on the same 5 
relays. A similar event record analysis process as shown in Section 6.2 was followed to 
determine the relay operation times. As all the evolving faults are mid-line faults, they 
59 
 
should be cleared by Zone 1 instantaneous protection. The results are summarized in Table 
6-3 below.  
Table 6-3: Evolving fault relay operation times 
Fault  
Sequence 
Time  
Between  
Stages  
(cycles) 
Mfr. 1 Mfr. 2 Average  
Operation 
Time 
(ms) 
R1 
(ms) 
R2 
(ms) 
R3 
(ms) 
R1 
(ms) 
R2 
(ms) 
AG-ABG-
3Ph 
2  61 56 42 46 26 46.2 
1.5 64 66 56 93 27 61.2 
AG-ABG 2 61 70 40 47 26 48.8 
1.5  57 69 58 75 44 60.6 
AG-3Ph 2  64 70 42 72 27 55 
1.5 57 67 50 63 26 52.6 
BC-BCG-3Ph 2 44 50 40 46 40 44 
1.5 38 57 36 47 38 43.1 
BC-BCG 2 48 51 40 46 40 45 
1.5 37 57 38 42 38 42.3 
BC-3Ph 2  59 49 40 46 39 46.6 
1.5 36 45 32 46 40 39.8 
 
Overall, the proposed control strategy handled evolving faults well enough for Zone 
1 to operate properly, in some cases even before the fault evolution was able to complete. 
The evolving faults beginning with a A-G fault are delayed by approximately 1-2 cycles 
compared with a non-evolving fault, but still within 4 cycles from fault inception. Evolving 
faults beginning with a B-C fault are relatively unaffected compared to the operation times 
for non-evolving faults.  
60 
 
 
 
Chapter 7  
Conclusions and Future Work 
7.1 Conclusions 
The profile of the electric grid will continue to move towards a higher penetration of IBRs, 
as municipalities and electric utilities set more ambitious renewable energy generation 
targets. Existing distance & directional relays in transmission networks are susceptible to 
failure as IBR penetration continues to increase, due to their reliance on negative sequence 
current produced by synchronous generators during unbalanced faults. By simply 
modifying inverter reference currents after a fault is detected, synchronous generator 
behavior expected by existing relays is emulated, effectively eliminating any costs that 
would otherwise be necessary to upgrade the existing protection infrastructure. 
The proposed novel inverter control method proved successful in the transmission 
network under study. All types of unbalanced faults were accurately detected within 1 cycle, 
inverter currents modified within 2-3 cycles, and synchronous generator behavior 
replicated within 3.5 cycles, resulting in accurate fault distance measurements by the relay 
with no Zone 1 overreach. These performance metrics were verified on five different relays.  
61 
 
The control strategy can be implemented in existing inverters and has the potential 
to be a de-facto standard in all future inverters.  
7.2 Future Work 
Opportunities for future work currently under consideration include but are not limited to 
the following areas: 
• Real-time simulation using OPAL-RT, which could connect the simulated 
transmission network to inverter hardware. 
• Multiple interconnected inverters simultaneously implementing the control strategy, 
rather than an aggregated inverter.  
• Vary the pre-fault IBR current injection, as it was assumed that IBR was always 
injecting 1.0 per unit pre-fault.  
• Investigate cause of unexpected relay behavior in outlier cases. This may lead to 
insights that would help improve the control logic. 
  
62 
 
 
 
References 
 
[1] W. Leon, “100% Clean Energy Collaborative”, Clean Energy States Alliance, 
https://www.cesa.org/projects/100-clean-energy-collaborative, retrieved Sept 2022. 
[2] “Destination Net Zero”, MidAmerican Energy Company, 
https://www.midamericanenergy.com/net-zero-greenhouse-emissions, retrieved Sept 2022. 
[3] “Xcel Energy commits to net-zero carbon goal by 2050”, Xcel Energy, November 1, 
2021. https://mn.my.xcelenergy.com/s/about/newsroom/press-release/xcel-energy-
commits-to-net-zero-carbon-goal-by-2050-MCZE7IKJSPUBEI5K3MZ5D3AZ74UQ, 
retrieved Sept 2022. 
[4] G. Kou, L. Chen, P. VanSant, F. Velez-Cedeno and Y. Liu, "Fault Characteristics of 
Distributed Solar Generation," in IEEE Transactions on Power Delivery, vol. 35, no. 2, pp. 
1062-1064, April 2020, doi: 10.1109/TPWRD.2019.2907462. 
[5] C. Li and R. Reinmuller, "Fault Responses of Inverter-based Renewable Generation: 
On Fault Ride-Through and Momentary Cessation," 2018 IEEE Power & Energy Society 
General Meeting (PESGM), 2018, pp. 1-5, doi: 10.1109/PESGM.2018.8585978. 
[6] Sandia National Laboratories. “Impact of inverter based resource negative sequence 
current injection on transmission system protection,” 2020, 
https://www.osti.gov/servlets/purl/1595917, retrieved Sept 2022. 
[7] V. Chakrapani and I. Voloh, "Impact of renewable generation resource on the distance 
protection and solutions," 16th International Conference on Developments in Power 
System Protection (DPSP 2022), 2022, pp. 238-243, doi: 10.1049/icp.2022.0946. 
[8] R. Chowdhury and N. Fischer, "Transmission Line Protection for Systems With 
Inverter-Based Resources – Part I: Problems," in IEEE Transactions on Power Delivery, 
vol. 36, no. 4, pp. 2416-2425, Aug. 2021, doi: 10.1109/TPWRD.2020.3019990. 
63 
 
[9] R. Chowdhury and N. Fischer, "Transmission Line Protection for Systems With 
Inverter-Based Resources – Part II: Solutions," in IEEE Transactions on Power Delivery, 
vol. 36, no. 4, pp. 2426-2433, Aug. 2021, doi: 10.1109/TPWRD.2020.3030168. 
[10] VDE Forum Network Technology/Network Operation in the VDE, 2018, Technical 
Connection Rules for High-Voltage (VDE-AR-N 4120).   
[11] "IEEE Standard for Interconnection and Interoperability of Inverter-Based Resources 
(IBRs) Interconnecting with Associated Transmission Electric Power Systems," in IEEE 
Std 2800-2022 , vol., no., pp.1-180, 22 April 2022, doi: 10.1109/IEEESTD.2022.9762253. 
[12] D. Kelly, P. Mysore and N. Mohan, "A Novel Control Scheme for Utility-Scale 
Inverter-Based Resources to Emulate Synchronous Generator Fault Response and Retain 
Existing Protection Infrastructure," 2021 74th Conference for Protective Relay Engineers 
(CPRE), 2021, pp. 1-7, doi: 10.1109/CPRE48231.2021.9429836. 
[13] E. O. Schweitzer, III and J. Roberts, “Distance relay element design,” in Proc. 19th 
Annu. Western Protective Relay Conf., Oct. 1992, pp. 3–25. 
[14] J. Roberts, A. Guzman, and E. O. Schweitzer, III, “Z = V/I Does Not Make a Distance 
Relay”, in 48th Annual Georgia Tech Protective Relaying Conf., May 1994. 
[15] "IEEE Guide for Protective Relay Applications to Transmission Lines," in IEEE Std 
C37.113-2015 (Revision of IEEE Std C37.113-1999) , vol., no., pp.1-141, 30 June 2016, 
doi: 10.1109/IEEESTD.2016.7502047. 
[16] B. Fleming, “Negative-Sequence Impedance Directional Element”, Schweitzer 
Engineering Laboratories, Inc., Feb. 1998, https://selinc.com/api/download/2475?id=2475, 
retrieved Sept 2022. 
[17] The Trajectories of Line Current Differential Faults in the Alpha Plane, Gabriel 
Benmouyal, Schweitzer Engineering Laboratories, Inc., 2014. 
https://cdn.selinc.com/assets/Literature/Publications/Technical%20Papers/6210_Trajector
iesLine_GB_20110627_Web.pdf?v=20160502-230243, retrieved Sept 2022. 
[18] Ned Mohan, 2014, Advanced Electric Drives: Analysis, Control, and Modeling Using 
MATLAB / Simulink, John Wiley & Sons 
64 
 
Appendix A 
Relay Operation Times 
The mid-line and end-line COMTRADE files were tested on 5 relays from 2 different 
manufacturers, denoted M1R1, M1R2, M1R3, M2R1, and M2R2. The relay operation 
times are shown in Table A-1 below, with the corresponding relay operator which cleared 
the fault in parenthesis. The Zone 1 overreach described in Chapter 6 is highlighted in red. 
Table A-1: Comprehensive relay fault operation times 
Fault 
Type 
M1 
R1 
 
M1 
R2 
 
M1 
R3 
 
M2 
R1 
 
M2 
R2 
 
A-G 
Mid-line 
36ms 
(Z1) 
48ms 
(Z1) 
31ms 
(Z1) 
36ms 
(Z1) 
37ms 
(Z1) 
A-G 
End-line 
121ms 
(Z2) 
125ms 
(Z2) 
123ms 
(Z2) 
122ms 
(Z2) 
105ms 
(Z2) 
B-C 
Mid-line 
56ms 
(Z1) 
50ms 
(Z1) 
48ms 
(Z1) 
47ms 
(Z1) 
44ms 
(Z1) 
B-C 
End-line 
151ms 
(Z2) 
140ms 
(Z2) 
140ms 
(Z2) 
137ms 
(Z2) 
134ms 
(Z2) 
B-C-G 
Mid-line 
42ms 
(Z1) 
42ms 
(Z1) 
40ms 
(Z1) 
46ms 
(Z1) 
42ms 
(Z1) 
B-C-G 
End-line 
137ms 
(Z2) 
140ms 
(Z2) 
140ms 
(Z2) 
137ms 
(Z2) 
126ms 
(Z2) 
A-B-C-G 
Mid-line 
36ms 
(Z1) 
44ms 
(Z1) 
38ms 
(Z1) 
42ms 
(Z1) 
39ms 
(Z1) 
A-B-C-G 
End-line 
122ms 
(Z2) 
129ms 
(Z2) 
129ms 
(Z2) 
48ms 
(Z1) 
111ms 
(Z2)