Application of Electromagnetic Transient- Transient ...

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Application of Electromagnetic TransientTransient Stability Hybrid Simulation to FIDVR Study Qiuhua Huang, Student Member, IEEE, Vijay Vittal, Fellow, IEEE

 Abstract—This paper deals with the development of a new electromagnetic transient (EMT)-transient stability (TS) hybrid simulation platform and its application to a detailed faultinduced delayed voltage recovery (FIDVR) study on the WECC system. A new EMT-TS hybrid simulation platform, which integrates PSCAD/EMTDC and the open source power system simulation software InterPSS has been developed. A combined interaction protocol with an automatic protocol switching control scheme is proposed. A multi-port three-phase Thévenin equivalent is developed for representing an external network in an EMT simulator. Correspondingly, the external network is represented in three-sequence, and a three-sequence TS simulation algorithm is developed. These techniques allow simulation of unsymmetrical faults within the internal network without the constraint of phase balance at the boundary. The effectiveness of the proposed techniques is first tested on the IEEE 9 bus system. Subsequently, the proposed hybrid simulation approach is applied to a detailed FIDVR study on a large WECC system. The study shows that a normally cleared single-line-to-ground (SLG) fault in the transmission system could lead to a FIDVR event, with compressor motors of the air conditioning units on the faulted phases stalling first, followed by a propagation of motor stalling to the unfaulted phase. Moreover, similar events are observed in simulations with a wide range of load compositions. Lastly, the effect of the pointon-wave (POW) at which a fault is applied on the occurrence of a FIVDR event is also analyzed. Index Terms--electromagnetic transient, fault induced delayed voltage recovery, hybrid simulation, interaction protocol, multiport three-phase Thévenin equivalent, transient stability

I. INTRODUCTION

W

ith the proliferation of converter based power electronic devices and small single-phase induction motors in power systems, the interaction of such fast responding elements with the power systems over time spans as long as 20 seconds has become a subject of significant interest [1]-[2]. The fault-induced delayed voltage recovery (FIDVR) phenomenon [3]-[5] falls into this category of events. Detailed modeling and simulation of single-phase compressor motors of air conditioners (A/Cs) and the distribution network is critical for the accuracy of FIDVR simulation results, especially under asymmetric fault conditions [5]-[7]. However, positive This work was supported by the National Science Foundation under the Grant EEC-9908690 at the Power System Engineering Research Center. Q. Huang, V. Vittal are with the Department of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85281 USA (email: [email protected]; [email protected]).

sequence transient stability (TS) simulators are unable to accurately model the A/C response to unbalanced faults. Simulation of large power systems with associated detailed modeling of large numbers of fast responding elements is too computationally burdensome for existing electromagnetic transient (EMT) simulators. While the scale of the system can be reduced by modeling a large portion of the system with a Norton or Thévenin equivalent, the drawback is that the nonlinear, dynamic response of the equivalenced portion of the system cannot be represented in the EMT simulation. The EMT-TS hybrid simulation approach has been found to be practically feasible to meet such a simulation demand [1][2], [8]-[15]. Alternative methods include dynamic phasor [16] and frequency adaptive [17] modeling approaches. The EMTTS hybrid simulation approach is adopted in this paper, as this approach allows the flexible integration of the existing and proven EMT and TS simulators without “reinventing the wheel”. The portion of the system with a high penetration of A/C loads, referred to as the internal network, is modeled in an EMT simulator, whereas the rest of the system is regarded as the external network and represented by a phasor domain model. Previous research on EMT-TS hybrid simulation mainly focused on interfacing techniques [11], including network equivalents on both sides [1],[12],[18] and interaction protocols [9],[13],[18]-[20] as well as the development of hybrid simulation programs [1]-[2], [10], [14]-[15]. The external network equivalents used in previous research, with the exception of [12], were developed based on positive-sequence network models. Consequently, if the resulting network equivalents were used in study cases with unbalanced conditions, the internal network would have to be extended substantially in the cases with a mesh network topology, in order to comply with the three-phase balanced assumption, which would undermine the merits of hybrid simulation. For the interaction protocol, either the serial or the parallel protocol was used in previous research. The serial protocol has been found to be a limiting factor of simulation speed, whereas the parallel protocol could lead to accuracy issues. Moreover, these programs, with the exception of [2] and [10] are designed to run all simulations on only one computer, thus they are potentially limited by the local computing resources. References [2] and [10], however, did not provide implementation details of the commercial solution.

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The issues identified above are addressed in this paper with the development of a new hybrid simulation platform integrating PSCAD/EMTDC [21] and an open source power system simulation software InterPSS [22], based on a decoupled architecture. A socket-based communication framework is developed to support this architecture. A combined interaction protocol with an automatic protocol switching scheme is proposed to increase the speed of hybrid simulation while maintaining accuracy. A multi-port three-phase Thévenin equivalent is proposed for representing the external network in PSCAD. Correspondingly, a three-sequence TS simulation algorithm is developed based on InterPSS for simulating the external network. With these techniques, any type of fault within the internal network can be analyzed without the threephase balance constraint at the boundary. The remainder of this paper is organized as follows. In section II, the details of the development of the proposed hybrid simulation platform based on PSCAD/EMTDC and InterPSS are presented. Results of testing on the proposed approaches on a modified IEEE 9-bus system are given in Section III. A detailed FIDVR study on a large WECC system model is conducted based on the developed hybrid simulation platform in Section IV. The conclusions are provided in Section V. II. DEVELOPMENT OF A NEW HYBRID SIMULATION PLATFORM BASED ON PSCAD AND INTERPSS A. Architecture of the Hybrid Simulation Platform The architecture of a hybrid simulation platform not only affects the selection of the communication method and interaction protocol, but also its extendibility in the future. A decoupled architecture for integrating an EMT and TS program is proposed and implemented using the pipe technology in [13]. A similar decoupled architecture is employed in this paper, as shown in Fig.1, but implemented using a socket-based communication framework, which is more flexible and enables distributed simulation over a local area network (LAN). PSCAD/EMTDC is adopted as the EMT simulator, and InterPSS is chosen for TS simulation. InterPSS not only provides models and algorithms for power flow, short circuit analysis and positive-sequence based transient stability simulation, but also defines the corresponding application programming interfaces (APIs). The socket communication framework, consisting of a socket component developed as a user-defined model in PSCAD and a socket server on the InterPSS side, is specially developed for data exchange between the two simulators. The socket client in PSCAD is developed based on the socket component developed in [23], which has been enhanced to realize programming-language-neutral data exchange and facilitate data export and import through the same socket. It should be noted that with this architecture, only existing user interface functions of PSCAD and APIs of InterPSS are used for the development and no modification of the PSCAD program itself is required. Therefore, the proposed approach and algorithms discussed in the following subsections can be seamlessly extended to other similar EMT or TS simulators.

InterPSS Core Engine

PSCAD/EMTDC

Socket Component

Socket Communication

I120 EMT (t ) V abc T (t )

Hybrid Simulation Manager

Socket Server

Network Equivalent Helper Sub-Network Helper

Fig.1 Schematic diagram of the architecture of the hybrid simulation platform

B. A Combined Interaction Protocol The interaction protocol relates to how the two simulators interact with each other in exchanging the necessary network equivalent parameters. There are mainly two types of interaction protocols used in previous research, i.e., the serial and parallel protocol [11]. With the serial protocol, one simulator must wait until the other completes the simulation of one interaction time step and transfers the equivalent data. To overcome this performance issue, several types of parallel protocols have been proposed [11]. The parallel protocol proposed in [9] requires data exchange for each iteration within one TS simulation time step. This requirement not only makes the data exchange process complicated, but is also impractical for most existing commercial EMT simulators as the iteration times required are unknown a priori. The parallel protocol proposed in [10] is relatively easy to implement. However, it could cause significant errors when the internal system experiences large disturbances, as the equivalents of the external network are not updated in a timely fashion to reflect the disturbances within the internal network. In an effort to combine the advantages of both types of protocols, a combined interaction protocol is proposed based on the following observation: fast dynamics and significant system changes usually occur during the faulted period and last for up to tens of cycles after the fault is cleared; in order to reflect the fast dynamic response of the internal network in the external network, or vice versa, in a timely manner, the serial protocol should be used. For the rest of the simulation period, the parallel protocol can be used to achieve good efficiency, as the system mainly experiences slow dynamics. First, both serial and parallel interaction protocols are implemented as shown in Fig. 2 and Fig. 3 respectively. In both figures, t denotes the start time for the processing step, ∆𝑇 is TS simulation time step as well as the EMT-TS interaction 120 120 time step, 𝐼𝐸𝑀𝑇(𝑡) and 𝐼𝐸𝑀𝑇(𝑡−∆𝑇) are the three-sequence current injection vectors sent from the PSCAD side at the present and previous interaction time step, respectively. If a fast transient phenomenon within the internal network is detected, the serial protocol is used for this time step. As shown in Fig.2, the operation involved is divided into 5 steps. The first step is data transfer via a socket and pre-processing. 120 Then, in step (2), 𝐼𝐸𝑀𝑇(𝑡) is used as the input for the threesequence TS simulation and the three-sequence voltages of the 120 boundary buses 𝑉𝑇𝑆(𝑡+∆𝑇) are updated. Subsequently, the 𝑎𝑏 three-phase Thévenin equivalent voltages 𝑉𝑇(𝑡+∆𝑇) are derived

3 Positive-sequence network solution and integration step

(1) I EMT (t )

x(t )

0  g1 ( x(t  T ), y

socket server

(1) ( t  T )

I

Step (1)

TS (t  T )

)

(0) 0  g 0 ( y((0) t  T ) , I EMT ( t ) )

Step (2)

x(t  T )

V 120

(2) 0  g 2 ( y((2) t  T ) , I EMT ( t ) )

(0) I EMT (t )

120 EMT ( t )

,I

(1) EMT ( t )

Negative- and zerosequence network solver

(2) I EMT (t )

VTS120(t )

(1)

VTS ( t T )

x(t )  f ( x(t ), y((1)t ) ) x(t  T )  x(t )  x(t ) T

120 I EMT (t )

VTS(2)(t T )

Calculate the multi-port three-phase Thévenin equivalent ( for details, see the subsection D)

VTS(0)(t T )

V abc T (t  T )

socket server

VTS120(t T )

Step (3)

V abc T (t  T )

Three-sequence TS simulation

Step (4) 120 I EMT (t )

120 I EMT ( t T )

socket client

EMT step 1

EMT step 2

Step (5)

EMT step 3

EMT step N-1

……………………………………..

EMT step N

t  T

t Fig. 2 The implementation of EMT-TS hybrid simulation with the serial type of interaction protocol

x(t  T ) VTS120(t )

Calculate three-phase socket 120 Thévenin server I EMT (t ) equivalent

x(t ) 120 TS ( t )

V

120 I EMT (t )

Step (b) Step (a)

socket server

Threesequence TS simulation Step (d)

Step (c)

V abc T (t )

120 I EMT ( t T )

Step (e)

120 I EMT (t )

socket client

t

EMT step 1

EMT step 2

...

VTS120(t T )

EMT step N-1

EMT step N

t  T

Fig. 3. One interaction step of the developed EMT-TS hybrid simulation with the parallel type protocol.

by the network equivalent helper in step (3) and sent back to 120 PSCAD in step (4). On receiving 𝑉𝑇(𝑡+∆𝑇) , PSCAD continues to step (5), which usually consists of hundreds of EMT simulation steps. Considering the computational complexity of each step, it is obvious that step (2) and step (5) are the two most time-consuming steps. Otherwise, the parallel protocol shown in Fig. 3 is used. The step for calculating the Thévenin equivalent (step (b)) is executed right after step (a), while the time-consuming step (d) is the last step on the TS simulation side. With this execution sequence, the Thévenin equivalent is calculated using the voltages obtained from the previous step and sent back to PSCAD immediately, such that step (d) and step (e) can be run simultaneously. One of the challenges in this combined protocol design is to identify an appropriate protocol switching time for general applications. To address this challenge, a protocol switching control scheme is proposed for selecting the processing step interaction protocol based on the last step protocol and detection of any large transient event within the internal network. The details of the design of the scheme are as follows: 1) Detection of Fast Dynamics within the Internal Network There are basically two options for detecting disturbances: one is the rate of change, the other is the change of magnitude. The change of magnitude fails to provide the information for determining whether the system is undergoing a fast transient or a slow dynamic condition. In contrast, the rate of change, or

the maximum rate of change for multiple monitored variables, can provide the necessary information. Thus the rate of change is adopted for controlling the protocol switching. 2) Variable Selection for Detecting Fast Dynamics In principle, current, voltage and power are good candidates for detecting transient events within the internal network. Considering that the sequence current injections at the boundary have been used as the interfacing variables, reusing them for protocol switching control can reduce the communication overhead and simplify the interfacing design. Therefore, the three-sequence current injections are adopted for detecting fast dynamics. 3) Implementation The detection is based on the maximum rate of change of the three-sequence current injections at the boundary, which is 120 denoted by 𝑅𝐼𝐸𝑀𝑇(𝑡) and defined by (1). I RI

120 EMT ( t )

 max( i

max s  (1, 2, 0)

(

(s) EMT (i , t ) I

I

(s) EMT (i , t  T )

)) / T

(1)

(1) EMT (i , t  T )

where i denotes one of the boundary buses, s represents one of (𝑠) the three sequences; 𝐼𝐸𝑀𝑇(𝑖,𝑡) is the current injection of sequence s at the boundary bus i at time t. 120 It is observed that 𝑅𝐼𝐸𝑀𝑇(𝑡) generally becomes smaller or 120 settles down after reaching the peak. If only 𝑅𝐼𝐸𝑀𝑇(𝑡) were used for decision-making, the scheme would sometimes switch the protocol back to the parallel type even during the fault period. To address the issue, a delay function is intro120 duced. With this delay function, 𝑅𝐼𝐸𝑀𝑇(𝑡) must be consecutively less than the threshold for at least a period defined by the delay setting before switching from the serial protocol to the parallel protocol, otherwise the serial protocol is used. The logic of the final protocol switching control scheme is 120 illustrated by Fig. 4. When 𝑅𝐼𝐸𝑀𝑇(𝑡) is larger than the threshold  , the serial protocol is used; otherwise, the decision is made based on the protocol used in the last interaction step. When the protocol is switched from the serial type to the parallel type, the delay function becomes active.

4 120 I EMT (t )

I120 EMT (tT )

Maximum rate of change

RI

120 EMT

Y

120 RI EMT ?

N

time step

1 series N

last step used series?

Y

Delay

0 parallel

T

Fig. 4. The logic of protocol switching control algorithm.

4) A Guide for Parameter Selection The choice of the threshold is based on the characteristic of the power system transient, specifically the characteristic of 120 120 𝑅𝐼𝐸𝑀𝑇(𝑡) . Typically, 𝑅𝐼𝐸𝑀𝑇(𝑡) is very small under a steady state or a slow dynamic condition, while it becomes notably larger under the fast-transient condition of a fault. Thus, the threshold here, to a large extent, is analogous to the threshold setting for over-current protection. But the threshold selection in this scheme is much simpler, as the reference value is almost irrelevant to the operating conditions. Thus, a 2-10% step change for each interaction time step is recommended as the threshold. The interaction time step ∆𝑇 is usually the same as the TS time step, thus 1-10 ms can used depending on the integration method of the TS simulation and the phenomenon studied. For the delay time setting, based on the characteristics of power system transients and simulation experience, the delay time should be at least half of the fault period. 5) Potential Applications If the study is concentrated on the fast transient period, the 120 𝑅𝐼𝐸𝑀𝑇(𝑡) can be used to assist in the early termination of the hybrid simulation. For study cases where a longer term simulation (e.g. 5-20 s) is needed, it is desirable to switch from hybrid simulation to quasi-steady-state dynamic simulation after the fast transients settle [18]. With the availability of 120 𝑅𝐼𝐸𝑀𝑇(𝑡) , a priori knowledge of the study case is no longer required. C. Extension of InterPSS for hybrid simulation Within the box on the right hand side in Fig.1, three Java classes, i.e., hybrid simulation manager, sub-network helper and network equivalent helper, are specially developed to enhance InterPSS for hybrid simulation. The core functions of the hybrid simulation manager include the protocol switching control discussed in the previous section and managing data conversion and interchange. The sub-network helper mainly defines the boundary between the internal and external networks and provides the boundary information to the network equivalent helper. The primary objective of the network equivalent helper is to calculate/update the Thévenin equivalents of the external system. In accordance with the use of the three-phase Thévenin equivalent in the internal network, all components in the external system, including the generators, transmission elements and loads, are represented in three-sequence detail. For the generator modeling, rotor dynamics are considered only in the positive sequence, with the effects of the negative- and zerosequence represented by sequence impedances. Correspondingly, a three-sequence based TS simulation algorithm is developed, as depicted in Fig. 2. The algorithm is composed of

the conventional positive-sequence TS algorithm and a sequence network solver for calculating the negative- and zerosequence voltages with the sequence current injections at the buses of the external system. The equation 𝑔2 and 𝑔0 in the three-sequence TS simulation block in Fig. 2 can be described by (2) and (3). (2) (2) (2) 𝑔2 : 𝑰𝑒𝑥𝑡(𝑡) = 𝒀𝑒𝑥𝑡 𝑽𝑒𝑥𝑡(𝑡) (2) (0)

(0)

(0)

𝑔0 : 𝑰𝑒𝑥𝑡(𝑡) = 𝒀𝑒𝑥𝑡 𝑽𝑒𝑥𝑡(𝑡) (3) where the subscript ext denotes the external network, (2) (0) 𝑽𝑒𝑥𝑡(𝑡) and 𝑽𝑒𝑥𝑡(𝑡) are vectors of negative and zero sequence (2)

(0)

voltages, respectively; 𝒀𝑒𝑥𝑡 and 𝒀𝑒𝑥𝑡 are the bus-admittance matrices of the negative and zero sequence network, respec(2) (0) tively; 𝑰𝑒𝑥𝑡(𝑡) and 𝑰𝑒𝑥𝑡(𝑡) are vectors of the negative- and zerosequence current injections. If the faults are applied within the internal network, the bus-admittance matrices are constant during the whole simulation, thus the matrix factorization is required only once. In addition, only entries corresponding to boundary buses in both (2) (0) 𝑰𝑒𝑥𝑡(𝑡) and 𝑰𝑒𝑥𝑡(𝑡) are non-zero and are obtained from 120 𝐼𝐸𝑀𝑇(𝑡) .The three sequence networks are decoupled and can be solved independently.

D. Multi-Port Three-phase Thévenin Equivalent A multi-port three-phase Norton equivalent is proposed in [12] in order to consider unsymmetrical faults. However, actual modeling of this equivalent in an EMT simulator could be limited by the available controllable current source components. For example, the phase of the single-phase current source in PSCAD is not adjustable, while the single-phase voltage source is controllable for both the phase and magnitude. Therefore, a three-phase Thévenin equivalent is proposed to represent the external network. The Thévenin equivalent is formed based on a three-phase Norton equivalent [12] using the following three major steps: 1) Calculate multi-port three-sequence Norton equivalents First, the three sequence networks of the external network are formed. The three-sequence equivalent admittance matrix 𝒀120 𝑁 can be calculated based on the method proposed in [12]. 120 𝒀120 is a block matrix and the submatrix 𝑌𝑁𝑖𝑗 representing 𝑁 120 the entry at the row i, column j of 𝒀𝑁 is as follows (1) 𝑌𝑁𝑖𝑗 0 0 120 𝑌𝑁𝑖𝑗 =

0

(2)

𝑌𝑁𝑖𝑗

0 .

(4)

(0) 𝑌𝑁𝑖𝑗 ]

0 [ 0 A three-sequence Norton equivalent can then be obtained as 120 120 𝑰120 − 𝑰120 𝑁 = 𝒀𝑁 𝑽 𝐸𝑀𝑇

(5)

120 where 𝑰120 𝑁 and 𝒀𝑁 are the three-sequence Norton equivalent current source vector and admittance matrix, respectively; 𝑽120 is a vector representing the three-sequence voltages of the boundary buses; 𝑰120 𝐸𝑀𝑇 is a vector of current injections from the internal network into the external network. 2) Three-sequence to three-phase transformation The primitive self-admittances of each boundary bus and the primitive mutual admittances among the boundary buses

5

are obtained from 𝒀120 𝑁 first. These admittances and the entries in 𝑰120 are transformed to a three-phase form in an element𝑁 wise manner: 𝑎𝑏𝑐 120 𝐼𝑁𝑖 = 𝑺𝐼𝑁𝑖 (6) 𝑦𝑖𝑎𝑏𝑐 = 𝑺𝑦𝑖120 𝑺−1

(7)

𝑎𝑏𝑐 120 −1 𝑦𝑖𝑘 = 𝑺𝑦𝑖𝑘 𝑺 (8) where and denote the Norton equivalent current source of boundary bus i in three-sequence and three-phase, respectively; 𝑦𝑖120 and 𝑦𝑖𝑎𝑏𝑐 are the primitive self-admittance of the boundary bus i in three-sequence and three-phase representations, respectively, and a generic topology of 𝑦𝑖𝑎𝑏𝑐 is 120 𝑎𝑏𝑐 shown in Fig. 5(a); 𝑦𝑖𝑘 and 𝑦𝑖𝑘 are the three-sequence and three-phase mutual admittance between bus i and k, respectively; S is the three-sequence to three-phase transformation matrix. 3) Source transformation After the steps 1) and 2) are completed, a source transformation process for each phase of the boundary buses is performed to obtain the Thévenin equivalent, 𝑝 𝑝 𝑝 𝑉𝑇𝑖 = 𝐼𝑁𝑖 /𝑦𝑖 (9) 𝑎𝑏𝑐 𝐼𝑁𝑖

120 𝐼𝑁𝑖

𝑝

𝑝

𝑧𝑖 = 1/𝑦𝑖 (10) 𝑝 where p stands for one of the three phases, 𝑦𝑖 is the primitive self-admittance of phase p of boundary bus i, , 𝑝 and 𝑧𝑖 is the corresponding impedance for the single-phase 𝑝 Thévenin equivalent, 𝐼𝑁𝑖 is the Norton equivalent current 𝑝 source of phase p at bus i and 𝑉𝑇𝑖 is the corresponding phase p Thévenin voltage source. Subsequently, the phase-to-phase primitive mutual impedances of a boundary bus and the three-phase primitive mutual impedances among the boundary buses are obtained from the corresponding admittances based on (11) and (12), 𝑝𝑞 𝑝𝑞 𝑧𝑖 = 1/𝑦𝑖 (11) 𝑎𝑏𝑐 𝑎𝑏𝑐 𝑧𝑖𝑘 = 𝑦𝑖𝑘

−1

(12) 𝑝𝑞 𝑦𝑖

where q stands for one of the three phases and 𝑝 ≠ 𝑞; and 𝑝𝑞 𝑧𝑖 are the phase-to-phase primitive mutual impedances and admittances, respectively, between the phase p and q of 𝑎𝑏𝑐 boundary bus i; 𝑧𝑖𝑘 is the three-phase primitive mutual impedance between the boundary buses i and k. The desired three-phase Thévenin equivalent is shown in Fig. 5(b). III. TEST RESULTS A. Metric to quantify the simulation differences Besides visual comparison of the simulation results, the accuracy of the proposed hybrid simulation approach is also quantified by the average and maximum differences in simulation results with respect to that of the EMT simulation[19]. The maximum difference 𝐷𝑚𝑎𝑥 is defined as 𝐷𝑚𝑎𝑥 = max(‖𝑥ℎ𝑠,𝑖 − 𝑥𝑒𝑚𝑡,𝑖 ‖) (13) where 𝑥ℎ𝑠,𝑖 and 𝑥𝑒𝑚𝑡,𝑖 are the ith sample of the monitored variable x by the hybrid simulation and the EMT simulation, respectively. The average difference 𝐷𝑎𝑣𝑔 is calculated by (14) 1 𝐷𝑎𝑣𝑔 = ∑𝑁 (‖𝑥ℎ𝑠,𝑖 − 𝑥𝑒𝑚𝑡,𝑖 ‖) (14) 𝑁 𝑖=1 where N is the total number of the samples for comparison.

(a) (b) Fig. 5 Three-phase network equivalent: (a) the primitive self-admittance of the boundary bus i; (b) three phase multi-port Thévenin equivalent

B. Test case The proposed hybrid simulation approach is first tested with the IEEE 9 bus system [24], as shown in Fig. A1 in the Appendix. For hybrid simulation, the internal/external interface comprises of bus 5 and bus 7. Thus, the external network is represented by a two-port three-phase Thévenin equivalent. In addition, the load at bus 5 is replaced by the detailed model as shown in Fig. A2. The composite load model mimics the WECC composite load model [6] except for the A/C motor that is represented by the detailed single-phase induction motor model developed in [7]. The composition and parameters of the detailed load model are provided in Table. A1, in the Appendix. The entire system is also modeled in PSCAD and solved to provide a benchmark result. The EMT simulation time step is set to 20 µs due to the requirement of the detailed A/C model. Both the TS simulation and interaction time steps are 5 ms. A single-line-to-ground (SLG) fault is applied on phase A of the 69 kV bus at 2.0 s and cleared after 4 cycles. C. The Combined Interaction Protocol The behavior of the combined protocol with ε = 0.004 and a two-cycle setting for the delay function is shown in Fig. 7. 120 The proposed index 𝑅𝐼𝐸𝑀𝑇(𝑡) correctly reflects the changes in the internal system and thereby the protocol switching control scheme promptly switches to a suitable protocol. The sensitivity analysis results shown in Fig. 7 illustrate that the protocol switching scheme is robust with respect to the threshold if the threshold is within the recommended range (i.e., 2%-10% change per each interaction step). The behavior of the parallel protocol under a fault condition is highlighted by large spikes in the Thévenin voltage shown in Fig. 8. The reason is that, with the parallel protocol, the TS program still uses the prefault voltage to calculate the Thévenin voltages for the first data exchange right after the fault, which results in erroneous (and much larger) equivalent voltages, and in turn produces a larger current injections in the subsequent steps. Moreover, the comparison results shown in Fig. 9 suggest that the performance of the proposed combined interaction protocol is more robust with respect to the interaction time step, compared to the parallel protocol.

6 1.5 2

1

Voltage (pu)

0

-2 120

log (RIEMT(t))

-4

log (threshold) protocol -6 1.95

2

2.05

0.5

0.28 0.26 2.053

2.15

-0.5

-0.5

Fig.6 The behavior of the combined protocol (ε

-1 2.076 2.078 2.08 2.082

2.2

time (s)

= 0.004)

2.055

0

-1

2.1

2.054

-1.5 1.98

2

2.02

2.04

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2.14

(a) time (s)

2 Threshold = 0.004 Threshold = 0.01 Threshold = 0.02 Threshold = 0.04

1

Voltage (pu)

Protocol signal

1.5 1 0.5

-1

0

1.98 2

2.05 2.1 time (s)

2.15

Voltage (kV)

Fig.7 Sensitivity of the protocol switching with respect to the threshold. 230

EM T-TS(combined)

220

EM T-TS(parallel)

2

2.02

2.04

2.2

2.06

2.08

(b) time (s) 1

Voltage (pu)

1.95

0

0 -1

210

1.98

200 190 1.95

2

2.02

2.04

2.06

2.08

(c) time (s) 2

2.05 2.1 time (s)

2.15

Fig. 8 The magnitude of the phase A Thévenin voltage source of bus 5

PSCAD

2.2

EMT -T S(parallel)

EMT -T S(combined)

Fig. 10. Three-phase voltages of bus 5: (a) phase A; (b) phase B; (c) phase C

4 PSCAD EMT -T S(parallel) EMT -T S(combined)

2

protocol signal

Current (pu)

0

-2 2.8 -4

2.6

2.4 -6 2.032 2.033 2.034 2.035 -8 1.95

Fig.9. The reactive part of the total load of bus 5 with different interaction protocols and interaction time step lengths.

2

2.05

2.1 2.15 2.2 time (s) Fig. 11. The phase A current injection at bus 5 into the external network

7 TABLE I SIMULATION RESULT DIFFERENCES OF THE PHASE A VOLTAGE AND CURRENT OF BUS 5 WITH DIFFERENT PROTOCOLS Interaction protocol parallel combined

𝐷𝑎𝑣𝑔 (𝑉𝑎) /pu 0.041 0.015

𝐷𝑎𝑣𝑔 (𝐼𝑎) /pu 0.068 0.050

𝐷𝑚𝑎𝑥 (𝑉𝑎) /pu 0.416 0.354

𝐷𝑚𝑎𝑥 (𝐼𝑎) /pu 1.029 0.541

TABLE II CASE SUMMARY OF THE WECC SYSTEM Buses 15750

Transmission lines 13715

24156 26105

1 Speed (pu)

24042

NORTH

14005

15061

15021

sub

EM T-TS(parallel)

0.6

Loads 7787

24086

PSCAD 0.8

24097

Generators 3074

sub

EM T-TS(combined)

15090

24092

24236 EAST

24801

0.4

24138

sub

0.2

28040

0 2

2.1

2.2 time (s)

2.3

2.4

D. The three-phase Thévenin Equivalent Phase voltages and current injections at bus 5 with hybrid simulation and full-blown EMT simulation are compared and shown in Fig. 10 and Fig. 11. A quantitative comparison of the simulation results is provided in Table. I. The speed of the AC units connected to the phase C of a feeder is shown in Fig. 12 to illustrate the response of the A/C compressor motor to the SLG fault. From Fig. 10, it can be observed that the voltages obtained by the hybrid simulation deviate from the benchmark for a short period after the fault is cleared. Specifically, threephase voltages at bus 5 in the PSCAD simulation are distorted by the harmonics generated by the fault clearing and the nonlinear response of induction motor loads, while the curves obtained by the hybrid simulation are less distorted. The main reason is that the linear network equivalent is derived based on the fundamental frequency representation of the external system, while the properties of other frequencies of the external system are not adequately modeled. Despite a severe unbalanced condition at the boundary, the average differences of the simulation results obtained with the proposed hybrid simulation and combined protocol are within 0.05 pu, demonstrating the effectiveness of the proposed network equivalents and the three-sequence TS simulation. In addition, the hybrid simulation results obtained with the combined protocol are consistently closer to that obtained by PSCAD compared to the parallel protocol. IV. APPLICATION TO A DETAILED FIDVR STUDY ON THE WECC SYSTEM A. Overview of the WECC system A summer peak case of the WECC system is used, and its basic information is summarized in Table. II. In this study, a region which is known to experience FIDVR events in recent years is chosen for detailed study. A one-line diagram of this region and surrounding area is depicted in Fig. 13. For the sake of simplicity, the details of the sub-systems below 500 kV are not presented in Fig. 13.

24151

115 kV

2.5

Fig.12 Speed of the AC units connected to the phase C of a feeder

15093

sub

sub

M M M

Load

Load

500 kV sub

sub

Sub-system below 500 kV

Fig. 13. One-line diagram of the study region

B. Scope of the Internal Network The buses 24138 and 24151 in Fig. 13 correspond to two 500 kV substations, where a large percentage of the loads are induction motors, and a majority of them are single phase A/C induction motors, particularly, for the bus 24151. Thus both buses are of primary intestest in this study. As faults of concern are applied in the internal network, the areas where credible faults could potentially cause stalling of these A/C compressor motors should be included in the internal network. A sensitivity analysis based procedure is proposed to identify the voltage dip at a transmission bus that will result in stalling of A/C motors in the underlying distribution systems. Details of the approach are provided in Appendix. Based on the derived voltage dip threshold, a bus is included in the internal system if a SLG or three-phase (3Ф) fault at that bus cause a phase-toneutral voltage at buses 24151 and 24138 to go below 0.75 pu. SLG and 3Ф faults at the 500 kV buses in this region are analyzed and the fault voltages at bus 24138 and bus 24151 are recorded and shown in Fig. 14. Based on the short circuit voltages and the threshold of 0.75 pu, the area encircled by the dashed-dot line in Fig. 13. is chosen as the internal network. Bus 26105 is excluded from the detailed system although this bus meets the criterion above, since it is relatively far from the A/C loads served by bus 24151 and including it would significantly complicate the interface. A summary of the internal network is provided in Table. III. C. Distribution Network and Load Modeling The subtransmission and distribution systems that are supplied from the buses 24151 and 24138 are modeled down to the feeders where the loads are connected to. The distribution feeders are modeled in two sections, i.e., the total load is divided into two portions. Two thirds of the total loads are connected at a quarter of the distance along the line, with the rest one third of the load connected at the end of the feeder [25], as shown in Fig. 15. The parameters of the A/Cs are provided in [7] with the scale specially chosen to match the target

8

0.9

Voltage(pu)

Bus-24151 () Bus-24151 (SLG) Bus-24138 () Bus-24138 (SLG)

1.0

0.75 pu

0.5 0 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

0.7

(a) time(s) 0.6

Speed(pu)

Voltage (pu)

0.8

1

0.5 0.4 0.3

1 0.5 0

24801 24092 24086 24236 15021 26105 24156 15093 24042 24097

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

Faulted bus

(b) time(s)

TABLE III STATISITICS OF THE INTERNAL NETWORK MODEL INCLUDING SUBTRANSMISSION BUSES NOT SHOWN IN FIG.13 Total number of buses Number of buses shown in Fig.13

238 500 kV 230 kV 161 kV

Number of buses of different voltage levels (not shown in Fig.13)

Total Load Number of interface buses

1 Z 4 feeder

A B

115 kV 92 kV