The Impact of Detailed Distribution System Representation in Dynamic Sub-Transmission-Distribution Co-Simulation

There has been a significant growth in the distributed energy resources (DERs) connected to the distribution networks in recent years, increasing the need for modeling the distribution networks in detail in conjunction with the sub-transmission/transmission networks. This paper models a real distribution/ sub-transmission network using a three-phase/three-sequence co-simulation. One of the modeled distribution feeders has a high penetration of DERs with significant reverse power flow and is modeled including the secondary network. Custom user-defined models are used to represent the solar photovoltaic (PV) units on the feeder including advanced controls and abnormal voltage responses from IEEE 1547–2018 standard. The co-simulation framework developed supports power flow/steady state as well as dynamic analysis. Using this developed framework, this paper studies the impact of balanced and unbalanced faults applied to the distribution and sub-transmission networks. The impacts of the faults on the feeder with the high penetration of DERs are studied in terms of the solar PV units tripping due to under/overvoltages and the resulting change in the feeder-head flow. It is seen that the detailed modeling of the distribution network is needed for accurately capturing the response from the distribution-connected DERs during fault events both on the distribution as well as sub-transmission networks.


I. INTRODUCTION
D ISTRIBUTION systems are one of the key elements of the overall power system network. Historically, several approximations have been invoked when studying their behavior. Such approximations can be found in the distribution system modeling textbooks such as [1]. These approximations may not be appropriate with the increasing proliferation of distributed energy resources (DERs) connected to the distribution systems in the recent years. Some smaller grids like Hawaii can have an instantaneous penetration of DERs of more than 71% of their daytime demand, and supply 11% of annual energy [2]. Furthermore, even larger grids across the United States of America and the world expect the share of DERs to grow significantly in the near future.
Due to the increased penetration of distribution-connected DERs and smart devices, there has been a critical need for studies involving both distribution and subtransmission/transmission networks to examine the impact of the DERs on the sub-transmission system and transmission system. This need is highlighted by the differences observed between integrated transmission-distribution system simulations in terms of aspects such as voltage regulator operations [3], exchanged power at the transmission/distribution boundary in presence of voltage dependent loads [4], or time series voltage excursions [5]. The authors of [6] show that accurately capturing the response of DERs can impact bulk system events such as fault-induced delayed voltage recovery. Hence, for distribution networks, especially those with a high penetration of DERs, it is important to consider transmission/sub-transmission and distribution networks in an integrated fashion.
The authors of [6] adopt a coupled simulation approach for studying the impact of DERs on the fault induced delayed voltage recovery. The coupling approach entails recording the responses from one domain/simulation to update the other domain/simulation. The drawback of the coupled simulation approach is that due to the coupling process, each domain simulation has to be run multiple times before reaching convergence. Another approach for integrating the distribution and sub-transmission/transmission is to model the entire system using a single modeling framework [7] or using a single commercial software, such as ePHASORSIM [8]. However, a large number of available tools for transmission and distribution systems do not support integrated modeling of both systems in the requisite detail, hence, co-simulation is seen as a suitable approach which allows the use of existing established software with the domain-specific modeling capabilities, features and algorithms while analyzing the different systems in an integrated fashion.
Using either the co-simulation approach or the integrated modeling approach, several works have been published in recent years discussing dynamic simulations involving models of both transmission/sub-transmission and distribution grids. The authors of [9] model the entire network (transmission/sub-transmission and distribution) using dynamic phasors and validate the simulation results with detailed MATLAB/Simulink models for a small synthetic test case. On the other hand, the authors of [8] create a combined transmission-distribution (T&D) model for power flow and dynamic studies using ePHASORSIM for a real system. In [10] a scalable multi-timescale dynamic T&D co-simulation formulation is presented. The authors of [11] describe dynamic T&D co-simulation approaches with series and parallel solution schemes, and consider the impact of the integration time step on the T&D co-simulation for both approaches. The focus in these papers is on developing the integrated modeling framework rather than the examination of system response for specific disturbances or for examining the impact of DERs on system performance.
One application of T&D dynamic co-simulation is to enhance the load model representation of the distribution feeders. The authors of [12] use T&D dynamic co-simulation to estimate static load parameters representing the distribution feeders. The co-simulation formulation from [11] is utilized in [13] to determine the composite load model parameters for capturing response from a specific feeder. In [14] a three-phase/three-sequence dynamic T&D co-simulation algorithm is developed using multi-area Thévenin equivalent approach. This paper considers balanced as well as unbalanced faults. The authors of [7] model the entire transmission-distribution network using a three-phase formulation for a utility network and consider an unbalanced fault. However, these references do not consider the impacts of DERs connected to the distribution feeders.
The authors of [15] model the combined T&D system using MATLAB/Simulink and study the impact of aggregate DERs including protection settings on dynamic stability for load changes and balanced/unbalanced faults using small test networks. The authors of [16] simulate the combined T&D system using DIgSILENT PowerFactory to study the bulk system impact of DERs and dynamic motor loads and use the simulation to parameterize the equivalent models to be used instead of a detailed distribution feeder representation. They model the transmission system in positive sequence and use a small test system to represent each feeder. The authors of [17] consider the impact of solar PV units on stability using T&D co-simulation for different disturbances and different PV penetration levels. They consider a limited number of large (∼100kW) DERs -this may not be the case in a more residential area with a high number of small rooftop solar PV units. In [18], the load tap operations due to DER generation intermittency and the voltage recovery after a fault event in presence of DER ride-through are studied using T&D co-simulation. The authors represent a real transmission network in positive sequence and the distribution network in three phase detail, but the DER units are represented using an aggregate model. The authors of [19] develop a two-level Schur-complement based domain decomposition method including parallel processing to simulate the differential-algebraic equations corresponding to the combined transmission-distribution system. A case study on the expanded Nordic system showing a long term voltage instability after a fault event is presented using this algorithm. In [20], dynamic equivalents of distribution networks are formed though Monte-Carlo simulations using multiple disturbances to account for the uncertainty in the inverter based generation parameters. The performance of dynamic equivalents is compared with the detailed distribution system representation both with and without considering disconnections from inverter based generation. These inverter based resources are shown to provide transmission voltage support during and after clearing the fault. Here, the residential rooftop installations are considered to trip immediately after the inception of a fault, and sustained response from only larger installations is considered. The authors of [21] consider a dynamic T&D co-simulation using HELICS and study frequency regulation/response from the DERs including application to a large synthetic network. The considered disturbances do not lead to low voltages where DER over/undervoltage trip/no trip characteristics would be important.
This study aims to model a real sub-transmission and distribution network in detail (including the secondary network and detailed models for rooftop solar PV units existing at each residential location) using a three-phase/three-sequence co-simulation framework and study the behavior of the modeled network for different balanced and unbalanced faults, considering the solar PV trip/no trip characteristics and advanced controls. The study establishes the importance of VOLUME 10, 2023 modeling the distribution network in detail to capture the response of the T&D network to faults accurately. The contributions of this work can be summarized as follows: • A detailed model of a real sub-transmission and distribution network is created using the proposed subtransmission/distribution co-simulation formulation in three-sequence and three-phase domains respectively. The control features and the dynamic characteristics of solar PV units are represented in this framework using custom phasor domain models.
• The impact of the advanced control and trip/no-trip conditions from the IEEE 1547-2018 standard on the feeder response is studied for different faults.
• For an unbalanced fault on the distribution feeder with a very high penetration above 400% when comparing the load and solar PV generation, it is shown that the post-fault clearance current may trigger the ground protection installed at the feeder-head.
• It is shown that different feeders connected to the same substation can behave differently for a sub-transmission fault.
• It is shown that a detailed distribution feeder modeling including the secondary network is needed to accurately capture the response from the solar PV units. The rest of the paper is organized as follows: Section II describes the distribution-sub-transmission co-simulation framework used in this work, and Section III describes the custom model created to represent the solar PV units installed in the distribution network. The network data and model are discussed in Section IV. The behavior of the distribution feeder with high penetration of solar PV generation under balanced and unbalanced faults on the distribution and sub-transmission network is studied in Section V. This section also discusses the impact of different controls and abnormal voltage responses on the feeder behavior during these faults. Section VI establishes the importance of modeling the secondary network by comparing the simulations with and without having a detailed secondary network model. Section VII concludes the paper.

II. CO-SIMULATION FRAMEWORK
There are four aspects of the dynamic co-simulation framework: • The transmission/sub-transmission network model • The distribution network model • Representation of the sub-transmission and distribution systems in the other network • The coordination and information exchange during the co-simulation. The sub-transmission system for this project is modeled in InterPSS [22]. InterPSS, an open-source software, was selected because it supports modeling in three-sequence detail for power flow as well as dynamic simulations. The distribution systems are represented as equivalent loads in positive sequence and equivalent current injections in negative and zero sequence circuits during the power flow, while during the dynamic simulation for all three sequence circuits, the distribution systems are represented using equivalent current injection. The three sequence networks are considered to be decoupled in the InterPSS network model. The positive sequence dynamic simulation is performed using a differential-algebraic equation formulation, whereas the negative and zero sequence effects are represented by sequence impedances. More details of the three-sequence dynamic simulation approach followed are available in [14] and [23]. A three-sequence model allows for applying balanced as well as unbalanced faults on the sub-transmission system to examine the impact on the integrated sub-transmission and distribution system.
The distribution system is modeled in three-phase unbalanced detail using OpenDSS [24]. OpenDSS is selected as a well-supported open-source software which allows for flexible and detailed modeling of distribution networks. The distribution networks modeled include the substation transformer as well as several feeders. One of the feeders is modeled in detail including the primary as well as secondary networks, described further in Section IV. The loads and solar PV inverter units for this feeder are modeled at their residence/user location on the secondary network. The solar PV inverters are modeled as a custom user model in OpenDSS, described in Section III. The sub-transmission system is represented using an unbalanced voltage source for both power flow and dynamic simulation modes.
Helics [25] is selected for the time synchronization and the data coordination/information exchange between the two software packages. Helics is an open-source software designed to facilitate co-simulation between different software and supports connections to different software. For this work, the Java and Python language bindings of Helics were used while interfacing Helics software with InterPSS and OpenDSS, respectively.
The overall schematic of the different models and data exchange is shown in Fig. 1. In each iteration, the voltages for the boundary buses from InterPSS are sent to the distribution systems and the currents injected at the boundary buses from the distribution network are measured and sent back to the sub-transmission system. Here, the sub-transmission model is in three-sequence domain and the distribution systems are in three-phase domain. The currents in three-phase domain from the distribution networks are converted to three-sequence values before being sent to the sub-transmission systems, while the sub-transmission boundary voltages are sent to the distribution network in three-sequence domain and converted to three-phase values before being updated in the network model. Note, since the sub-transmission system is modeled using all three sequence networks, unbalances in voltages and currents are allowed/retained across the boundary.
At the start of the simulation, the software packages, and the Helics connections are initialized and the networks are loaded. During the power flow, the boundary values are iterated between the software packages until convergence  is attained in the distribution and sub-transmission systems as well as for the boundary bus values. Once the steady-state power flow is successfully solved, the dynamic models are initialized. The loads in the distribution system are represented using a constant impedance model during the dynamic simulation, while the solar PV units are represented using custom user models. In each time step, the dynamic co-simulation is performed in a serial manner: the different subsystems are solved sequentially, providing updated values to the next subsystem, and moving to the next time step once all subsystems have been solved. A schematic of this serial solution process during the dynamic simulation is shown in Fig. 2.

III. SOLAR PHOTOVOLTAIC MODEL
In distribution feeders with a high penetration of solar photovoltaic generation, the solar PV units in the system need to be represented in detail to capture the accurate behavior of the distribution system under various disturbances. A userdefined model for OpenDSS is created to represent the solar PV units including the controls. A schematic of the modeled controls is shown in Fig. 3. Here, without loss of generality  the dc-side of the unit is represented as a constant dc voltage source. The pulse-width modulation is represented using an average model. However, via a user defined model, the phase locked loop and proportional resonant current control as well as the active/reactive power control are modeled in detail. Different active/reactive power control modes as defined in the IEEE 1547-2018 Standard [26] are supported by the userdefined model. In addition, the abnormal voltage trip settings according to the inverter category as defined in [26] are also supported.
For the active/reactive power modes, the setpoints are assumed to be equal to the default settings given in [26] for Category B inverters. The abnormal voltage trip/no trip settings used are given in Table 1. These settings represent the most conservative settings for each of the three categories from [26] (i.e. the mandatory ride through settings are considered and the permissive ride through is not considered). Note, the clearing times given in the table are maximum values, for the results presented in Sections V and VI it is assumed that the inverters trip within one cycle if the corresponding clearing time is 0.16 s (∼9.6 cycles).
The user model represents the solar PV unit as a system of differential-algebraic equations. Using these equations, the user-defined model requires the user to define various functions as a part of solving the power flow and performing dynamic simulations. The dynamic equations corresponding to the filter as well as the current control and phase locked loop are modeled as phasor dynamics equations using the procedure from [27]. The created model is previously validated in [28]. Different advanced controls and abnormal voltage responses described in this section are implemented building on the version from [28].

IV. NETWORK MODEL
The network modeled is based on a real substation and the connected feeders in Arizona. The selected substation from the utility feeds five feeders via two substation transformers. The substation transformers and the five feeders are modeled as two distribution systems, divided between two substation transformers. The high voltage bus at this distribution substation is considered to be the boundary between the distribution and sub-transmission systems. This substation is connected to two other substations via 69 kV level lines. These two substations in turn connect to the bulk transmission network. Hence, the bulk transmission system and the rest of the network is represented at these two substations using equivalent Thévenin source model including the transfer impedance. A schematic diagram of the modeled network is given in Fig. 4. The figure also shows the location of the faults applied to the sub-transmission network as discussed in Section V.
The single line diagrams with some key elements of the feeders are shown in Fig. 5, and some of the key characteristics for these feeders are given in Table 2. From this table, it is observed that Feeder 1 has a high level of penetration of the solar PV generation (and hence peak reverse power flow) compared to the other feeders -Feeder 1 also has one of the higher penetrations of solar PV generation for the feeders controlled by the partner utility. Feeders 2-5 are modeled in detail, but the secondary networks are not modeled for these feeders. On the other hand, Feeder 1 is modeled in detail with  the secondary network included. Utilizing the detailed model of Feeder 1, the dynamic co-simulations and results discuss the impact of various fault events on it.
The initial feeder models are created by converting the feeder models obtained in CYME format from the utility to OpenDSS circuit models using a tool developed for this purpose [29]. The Feeder 1 model is further tuned by combining other data from various sources such as the geographic information system (GIS) data and advanced metering infrastructure (AMI) meters -the procedure followed for creating the feeder models is described in previous publications [30], [31]. The sub-transmission model contains two voltage sources -the active power and voltage references are created based on the sub-transmission active power and voltage magnitude measurements and feeder-head measurements of active and reactive powers from the feeders. The operating point is selected to correspond to a high reverse active power flow case, at 1 PM on March 15, 2019. This operating point corresponds to light load and high solar PV generation, resulting in a reverse power flow of over 2 MW from Feeder 1. It is found that the feeder-head active and reactive powers for all five feeders and the active power flows in the two sub-transmission lines have errors less than 5% compared to the field measurements. The voltages obtained for Feeder 1 also match closely with the voltage measurements from AMI meters connected to this feeder, as shown in Fig. 6.  The boundary values in the different systems are provided in Table 3 as an illustration of the unbalance across the T&D boundary during the co-simulation. It is observed that distribution system D2 comprised of Feeder 2 and Feeder 3 has a very high ratio of negative to positive sequence currents -this corresponds to a very low power exchanged for these feeders at the feeder-head at the peak reverse power flow scenario selected (643 kW and 333 kVAr).
The present penetration of solar PV generation in Feeder 1 (approx. 237 % when comparing the hourly load and solar PV generation at the chosen operating point) does show impacts on the feeder fault responses, however, these impacts are expected to be even more prominent for higher penetrations of solar PV generation. Hence, several cases of higher solar PV penetration of up to 400% penetration level are created for Feeder 1 by random allocation. The procedure for this allocation was developed by the National Renewable Energy Laboratory during their LA100 study [32].

V. RESPONSE OF THE T&D SYSTEM TO FAULTS
With the accurate network model and the T&D dynamic co-simulation formulation described in this paper, this section discusses the response of the combined T&D system for balanced (three-phase to ground -3pG) and unbalanced (single line to ground -SLG) faults on the distribution and subtransmission network. These responses highlight the impact of the faults on the combined system and the need for modeling the distribution network in detail. The response of

Feeder 1 is studied closely when applying various faults since Feeder 1 is modeled in detail and has a high penetration of solar PV generation.
For all the studies in this section, the selected base operating point is described in Section IV. In each case, the chosen fault is applied for five cycles (fault on the sub-transmission network) or fifteen cycles (fault on the distribution network) and cleared after the fault duration. The fault locations on the distribution and sub-transmission networks are shown in Fig. 4 and Fig. 7. For the sub-transmission faults, the fault location is selected to be at the middle of one of the sub-transmission lines. For distribution system faults, the fault location is selected near the middle of Feeder 1 on a three-phase bus on the main three-phase trunk of Feeder 1.
The solar PV inverters are assumed to have the trip/ no-trip response corresponding to the Category I inverters from Table 1 and are assumed to trip for voltages below 0.45 p.u. and above 1.2 p.u. within one cycle. The tripped inverters are assumed to not automatically reconnect after the fault is cleared. Furthermore, unless otherwise mentioned, the results correspond to solar PV inverters operating at unity power factor mode. However, the impact of different inverter abnormal categories as well as advanced inverter controls (volt-VAr, with the reactive power-voltage curve taken from the default values given in IEEE 1547-2018 standard) is also discussed for these faults. The inverter current is limited to twice the rated current when experiencing low voltage magnitude. The inverter model scales down the original active and reactive power references according to the selected control mode to satisfy the current limit while retaining the ratio of the active/reactive power references. For example, if the current limit is enforced for an inverter following unity power factor control, then the active power reference will be scaled down to satisfy the current magnitude limit, but for an inverter following volt-VAr control, both the active and reactive power references will be scaled down to satisfy the current magnitude limit.

A. UNBALANCED FAULT ON THE DISTRIBUTION NETWORK
When a SLG fault is applied on Feeder 1, the boundary currents in the distribution system (added together for both systems D1 and D2) and the sub-transmission system are plotted in Fig. 8 as a validation for a successful dynamic T&D co-simulation. Fig. 9 and Fig. 10 show the voltage profile for the feeders 1,4, and 5 connected to the substation transformer for the faulted feeder.
From Fig. 10, it is observed that for the other feeders connected to the substation transformer, only a small voltage dip at the feeder-head is experienced for faulted Phase A, corresponding to the voltage drop across the substation transformer. Hence, the voltage profiles for the other feeders do not indicate a high voltage drop or swell similar to the faulted feeder. However, it is seen that for Feeder 1 the faulted Phase A voltages are very low while Phase C experiences a high voltage swell. For this feeder, the highly unbalanced fault current flowing through underground cables with mutual coupling and the effective phase/ground impedances at the fault location result in such a voltage swell. This aspect of voltage swell is discussed in [33].  As a result, within one cycle after the fault is applied, a large number of solar PV units trip for Phases A and C. This results in a loss of approximately 1099 kW generation for Phase A and 1314 kW generation for Phase C. It was previously discussed in [33] that even with the volt-VAr control the voltage profiles (and the loss of generation) remain very similar. However, it should be noted that instead of inverter abnormal response Category I from IEEE 1547-2018, a more aggressive Category III implementation would result in the Phase A inverters remaining connected though the fault. Hence, there would be a reduction in the solar PV generation lost and no generation would be lost for Phase A. However, even the most aggressive Category III mandates the solar PV units disconnect for voltages of more than 1.2 p.u., and the loss of generation from Phase C would be the same even for Category III inverters. The disconnection of the solar PV generation for only the Phases A and C is reflected by the feeder-head active power flow for Feeder 1, as shown in Fig. 11, and the corresponding feeder-head current is plotted in Fig. 12.
When the fault is cleared, this results in Phases A and C with forward active power flow while the Phase B still has a reverse active power flow because the solar PV units 496 VOLUME 10, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.   connected to Phase B are not tripped -thus creating an unbalance in the post-fault clearance condition. This unbalance is noteworthy since this is a steady-state unbalance in the post-fault clearance condition. When calculated, the ground current measured at the feeder-head for this state would be approximately 190.45 A. For this feeder, there are phase and ground protection relays installed at the feeder-head. The ground current in the post-fault clearance condition being comparable to the ground relay pickup current of 300 A is a significant concern, since it will persist for a much longer period compared to the fault duration as long as no solar PV units connect back automatically. A similar SLG fault was also applied to the modeled T&D network by increasing the penetration of solar PV resources on Feeder 1. It is seen from Fig. 13 that at 418% penetration level the post-fault clearance ground current goes above the pickup current and would result in the relay tripping the feeder in steady-state even when the fault is already successfully cleared, resulting in a loss of connection for all the customers on this feeder.

B. BALANCED FAULT ON THE DISTRIBUTION NETWORK
For the balanced fault on the distribution system, the voltage profile for Feeder 1 is shown in Fig. 14, and the voltage profile   for Feeder 4 and Feeder 5 is shown in Fig. 15. It is seen that all three phases for the faulted Feeder 1 experience very low voltages, with the voltage near the fault location being nearly zero (Fig. 14) while the other feeders do not experience such low voltages (Fig. 15).
This results in most of the solar PV units on the faulted feeder experiencing very low voltages at the terminal, and hence a large amount of solar PV generation trips within one cycle for this fault. This can also be seen in Fig. 16, which shows the feeder-head active power for the faulted feeder and  Fig. 17, which shows the feeder-head current for the faulted feeder. In these figures, before the fault was applied there is substantial reverse active power flow at the feeder-head for all three phases. However, assuming that the tripped solar PV units do not automatically reconnect after the fault is cleared, there is a forward active power demand seen from the feeder in the post-fault clearance condition due to the loss of generation from the solar PV units. Overall, there is a loss of approximately 1171 kW generation on Phase A, 1341 kW on Phase B and 1314 kW on Phase C for Feeder 1.
While for the selected operating point, the resultant extra net demand may not be a significant issue since the operating point corresponds to a low load scenario, a similar increase in demand would be more significant for a near-peak demand operating point. For this fault, even if volt-VAr control is implemented instead of unity power factor for the solar PV units, the loss of generation is not significantly impacted. Note, however, that using category III inverters instead of category I inverters would result in the inverters not disconnecting due to the low voltages caused during the short-duration fault considered and no generation would be lost in such a case.
Another important aspect observed for the balanced (this Subsection) as well as unbalanced (previous Subsection V-A) faults on the distribution feeder is that the other distribution feeders connected to the same substation transformer do not experience similar abnormal voltage values as the faulted feeder, indicating that modeling the feeders separately is important to accurately capture the fault response for the distribution faults. Further, modeling the faulted feeder in sufficient detail is needed to appropriately apply the fault and capture the voltages at the DER and load terminals.

C. UNBALANCED FAULT ON THE SUB-TRANSMISSION NETWORK
When a SLG fault is applied on the sub-transmission system, assuming the fault is applied on Phase A, it is seen that at the boundary bus, the voltage for the faulted Phase A is approximately 0.56 p.u. voltage, whereas the other two phases have voltages between 0.95 and 1.06 p.u. However, these voltages  are on the high voltage/delta side of the substation transformer. Due to the delta-wye transformer at the substation, two of the phases (A and B) on the feeder experience low voltages between 0.75 and 0.85 p.u. while the Phase C voltage is between 1 and 1.1 p.u., as shown in Fig. 18 and Fig. 19.
These voltages are not so low or high as to cause any generation to trip. However, due to the low voltages on Phases A and B of the feeder, there is an increased reverse active power flow at the feeder-head for these phases, as shown in Fig. 20. The corresponding feeder-head current is plotted in Fig. 21. Fig. 18 also shows some locations with a significant voltage rise/drop across the secondary network, indicating the need to model the distribution feeders in detail to accurately capture the voltage at the loads/DERs.

D. BALANCED FAULT ON THE SUB-TRANSMISSION NETWORK
When a balanced fault is applied at the middle of the subtransmission network, the boundary bus experiences a low voltage of approximately 0.41 p.u. This results in all three phases on all the feeders experiencing a low voltage. The   Phases A, B and C respectively for Feeder 1. The feeder-head current magnitude for Feeder 1 is plotted in Fig. 24.
After clearing the fault, the active power flow is still in the reverse direction, the magnitude is somewhat less due to the loss of some solar PV generation. However, it is seen from Fig. 16 that while several solar PV units experience a voltage above 0.45 p.u., the voltage at the feeder-head is approximately 0.413 p.u. and there is a significant voltage rise along the feeder which allows the solar PV units connected to have voltages higher than 0.45 p.u. However, the other feeders do not have such a high reverse active power flow and corresponding voltage rise, hence, the solar PV units connected to the other feeders would all trip for this case. Hence, for this case it is seen that different feeders may behave differently -this behavior would not be captured by aggregating all the feeders together as a single load while studying this sub-transmission fault.
For this fault, it is observed that the voltages for Feeder 1 are close to 0.45 p.u. threshold below which the category I inverters would trip. In this case, if all the solar PV units on Feeder 1 operate in volt-VAr mode, there is a larger voltage rise owing to the extra reverse reactive power from the inverters, as seen in Fig. 25. This results in a majority of the solar PV units that would experience a voltage below the threshold of 0.45 p.u. for unity power factor control not experiencing such voltages below the threshold. Hence, the solar PV generation lost in this case is reduced to 137 kW for Phase A, 81 kW for Phase B and 40 kW for Phase C. This example shows that the advanced control modes such as volt-VAr mode could have an impact in terms of generation tripped due to certain sub-transmission events. For this fault, it is also observed that the response to the fault without the detailed distribution feeder model can be inaccurate -this is discussed in Section VI.

VI. IMPACT OF SECONDARY NETWORK MODEL
It is seen throughout the voltage profiles shown in the previous section that there is a significant voltage rise across the network due to the reverse active power flow, and some of this voltage rise is across the secondary network. In this section, the importance of modeling the secondary network is assessed. For this purpose, two models of Feeder 1 are considered. The ''secondary'' model is described and used so far, where the secondary network is modeled in detail for Feeder 1, and the loads and the solar PV units are located at the household/user locations. Another model, called ''primary'' model in this section, models Feeder 1 similar to the models of other four feeders, with the load and solar PV units represented in an aggregate manner at the secondary terminal of the distribution transformers, and there is no representation of the secondary network. For the aggregated solar PV units, the voltage at the secondary terminal of the distribution transformer is used for the volt-VAr curve, and the reactive power limits are equal to the summation of the corresponding limits of the connected inverters. A schematic describing these models can be found in Fig. 27.
It was found that at steady state, for both unity power factor control and volt-VAr control, the voltages along the feeders as well as the active and reactive powers seen at the   head of the feeder for the feeder modeled with the secondary networks were similar between the primary and secondary models, however, it is noted that there are certain overvoltages observed in the secondary model not observed in the primary model because the voltage rise across the secondary network is not captured, as seen in Fig. 28.
Due to this voltage difference, the reactive power from the inverters absorbed/injected at the transformer can have a significant difference for volt-VAr control (up to 44% difference for certain transformers) when comparing the two models. This difference between the reactive powers injected/absorbed by the inverters connected to that  transformer is shown as a bar chart in Fig. 29 for three transformers connected to Feeder 1. Considering all the solar PV units, the combined reactive power injected from all the solar PV units is different by 68 kVAr for the selected operating point (∼10% of the total reactive power from all the inverters or 14% of the feeder-head reactive power for this operating point).
For several balanced/unbalanced faults applied on the distribution and sub-transmission systems, the response for both the models is similar. However, for certain faults, the voltage at the inverter terminal is above 0.45 p.u. after capturing the voltage rise across the secondary network whereas it is below 0.45 p.u. for the primary model -resulting in a difference in the number of solar PV units which are registered as tripped in both models. For one such case, where a balanced three-phase to ground fault on the sub-transmission system is applied in the middle of one of the sub-transmission lines, the Feeder 1 voltage profile and the feeder-head active power are shown in Fig. 30 and Fig. 31, respectively.
Note that for this study the inverters are kept at unity power factor mode. For this fault, in the primary model, the solar PV generation tripped in Phases A, B and C are 1219 kW, 1335 kW and 1175 kW respectively, while in the secondary model, the tripped generation are much less, 1065 kW, 751 kW and 742 kW respectively. Hence, it is important to model the secondary network in detail and not modeling the secondary network can lead to an inaccurate response from the distribution model.

VII. CONCLUSION
This paper models a real sub-transmission-distribution network in three-sequence/three-phase detail using a T&D co-simulation formulation. The formulation is utilized to study the impacts of different faults on the network. The modeled network has a high penetration level of residential rooftop solar PV generation. It is seen that under faults, a large portion of these DERs may disconnect due to low or high voltage trips. Such trips may result in the active power flow at the feeder-head changing from reverse direction to forward direction. If two of the three phases experience low/high voltages that cause solar PV generation trips, it is seen that at higher penetration levels the feeder may trip even after the fault is cleared with the ground protection at the feeder-head with the present settings. Further, it is seen that advanced controls (such as volt-VAr) and advanced abnormal voltage responses as defined in the IEEE 1547-2018 standard may alleviate some of the loss of solar PV generation. It is observed that different feeders at the same substation may have very different responses for the same fault, indicating the need to model different feeders at a substation separately. By comparing two different network models, with and without the secondary network modeled in detail, it is found that without modeling the secondary network, some overvoltages may not be captured in steady state, and that there may be an error in the estimated the reactive power from the inverters operating in advance control modes such as volt-VAr. Furthermore, by comparing the fault response for the distribution feeder with and without modeling the secondary network, it is shown that the loss of solar PV generation may be estimated incorrectly if the secondary network is ignored. project, and the team at the National Renewable Energy Laboratory for their contributions in creating the high penetration scenarios.