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simulation

VIEWS: 78 PAGES: 8

									                                                Electric Power Systems Research 77 (2007) 1124–1131




                             Distributed simulation for power system analysis
                                       including shipboard systems
                                             Jian Wu, Noel N. Schulz ∗ , Wenzhong Gao
             Department of Electrical and Computer Engineering, Mississippi State University, Box 9571, Mississippi State, MS 39762, United States
                                   Received 8 May 2006; received in revised form 8 August 2006; accepted 15 September 2006
                                                              Available online 20 October 2006



Abstract
   Power systems are distributed in nature. Often they can be divided into sections or groups and treated separately. Terrestrial power systems
are divided into separate utilities and are controlled by different regional transmission organization (RTO). Each RTO has detailed data for the
area under its control, but only limited data and boundary measurements of the external network. Additionally, shipboard power systems may be
divided into sections where local information is kept but not distributed to other parts of the system. Thus, performing a comprehensive power
system analysis in such a case is challenging. Also, simulating a large-scale power system with detailed modeling of the components causes a
heavy computational burden.
   One possible way of relieving this problem is to decouple the network into subsystems and solve the subsystems respectively, and then combine
the results of the subsystems to get the solution. The way to decouple the network and represent the missing part will affect the result greatly. Also,
due to information distribution in the dispatch or data centers, a problem of doing power system analysis with limited available data arises. The
equivalent for other networks needs to be constructed to analyze the power system.
   In this paper, a distributed simulation algorithm is proposed to handle the issues above. A history of distributed simulation is briefly introduced.
A generalized coupling method dealing with natural coupling is proposed. Distributed simulation models are developed and demonstrated in the
virtual test bed (VTB). The models are tested with different network configurations. The test results are presented and analyzed. The performance
of the distributed simulation is compared with the steady state and time domain simulation results.
© 2006 Elsevier B.V. All rights reserved.

Keywords: Distributed simulation; Shipboard power systems; Transient analysis; Time domain simulation; Resistive companion model; Virtual test bed (VTB)



1. Introduction                                                                   is installed into the ship power system. While tests with the
                                                                                  actual electric ship hardware are costly and risky, a virtual test
   The large-scale terrestrial power systems are composed of                      environment is more affordable and safer to perform a hardware
several utilities and controlled by different regional transmis-                  test in the prototype stage. Such hardware-in-the-loop tests can
sion organizations (RTO). Each RTO has detailed parameters                        be undertaken as distributed simulation with part of the system
for the area under control, but only limited data of the exter-                   simulated in software and part of the response originating from
nal network. Usually, each RTO has the right to read only the                     the hardware.
boundary measurements on the tie lines that connect its control                       Therefore, distributed simulation, which can decouple an
area to others. Thus, performing comprehensive power system                       entire system into multiple parts, is beneficial to a large-scale
analysis in such case is very difficult.                                           power system and shipboard power systems (SPS) analysis. Dis-
   Also, for an all-electric ship to ensure its survivability, a                  tributed simulation helps provide quick diagnosis of failures in
weakly meshed zonal network is used. In each zone an intelligent                  SPS and better understanding of the system status. An exten-
controller coordinates the zonal connection. In the development                   sion of distributed simulation could enable hardware to interact
stage, new equipment needs to be tested before the equipment                      remotely [1,2].
                                                                                      For the reasons above, five universities in the US have
                                                                                  teamed up for a Department of Defense Multiple University
 ∗   Corresponding author. Tel.: +1 662 325 2020; fax: +1 662 325 2298.           Research Initiative (MURI) project to develop remote testing
     E-mail address: schulz@ece.msstate.edu (N.N. Schulz).                        and measurement (RTM) models and procedures to virtually

0378-7796/$ – see front matter © 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.epsr.2006.09.009
                                       J. Wu et al. / Electric Power Systems Research 77 (2007) 1124–1131                              1125

connect power system laboratories over a distributed network.             the potential to extend to CORBA and allow for more clients
The MURI project targets setting up a large-scale power sys-              and a securer connection. Therefore, these properties provide the
tem laboratory to carry advanced, non-destructive testing and             development tools to make an application adjustable within dif-
measurement of power systems [1].                                         ferent network environments easily and not limit the distributed
                                                                          simulation algorithm only within VTB.
2. Literature survey                                                          In this paper, our research has extended the decoupling sim-
                                                                          ulation method for dc link to ac systems and explored the
2.1. Distributed simulation                                               decoupling method for a power system simulation. The algo-
                                                                          rithm’s capability to deal with three-phase coupling will be
   Distributed Simulation makes use of the computer network               demonstrated with different kinds of networks with different
and computes the overall power system solution through sepa-              power sources and power load configurations. In this paper,
rately and concurrently computing units. One of the most devel-           a distributed simulation algorithm is proposed. The models
oped techniques in distributed simulation is parallel processing.         dealing with the natural coupling were developed in VTB and
This method requires the information of a whole power system              demonstrated with different network configurations, including
matrix. The advanced techniques divide the computation load               a shipboard power system-an 18-bus icebreaker. The distributed
based on the partitions of system matrix [3,4]. This method can           simulation performance is analyzed in time domain and steady
greatly improve the computation speed for a large-scale power             state. The results, when compared to published work, demon-
system and has been used in simulation software such as the real          strate how the new models for distributed simulation expand the
time digital simulator (RTDS).                                            simulation toolbox in VTB.
   The other technique in distributed simulation is based on
graphically decoupling. This method is used for dc circuit anal-          3. Decoupling method
ysis such as VLSI circuit analysis and large power electronic
system analysis, where the dc link is selected as the coupling               This section describes the algorithm extended from the dc
point [5–7]. This method is attractive when some component                coupling method to distributed simulation of power system. The
models are unavailable but a response of the models is avail-             problem starts with the entire power system network. Suppose
able. It also conforms to the nature of the power system network,         that two sub-networks connect via a tie line as shown in Fig. 1.
which is composed of a number of sub-networks and allows a                The key issues for distributed simulation include decoupling
simplified problem formulation for each sub-network.                       the circuit and representing the missing subsystem. The choices
                                                                          of the decoupling point and subsystem model will affect the
2.2. Simulation environment                                               stability and accuracy of the solution.
                                                                             Using the VI overlap decoupling method described in paper
   The virtual test bed (VTB) is a time domain simulation soft-           [11], the whole system can be decoupled into two subsystems
ware package and provides multidisciplinary simulation envi-              with the transmission line present in both, as the two circles
ronment including electrical, thermal, chemical and mechanical            indicate in Fig. 1.
engineering [8,9]. Its open architecture allows users to develop             When solving subsystem A, the subsystem B is treated as the
their own models [8]. Its extension to real-time VTB matches the          “missing system.” A stabilizing resistor and a current source in
MURI final project goal of the hardware-in-the-loop test. VTB              parallel represent the missing subsystem, subsystem B in this
uses the resistive companion form (RCF) to model each compo-              case, as shown in Fig. 2(a). The corresponding point in the part-
nent and get a solution through nodal analysis. RCF discretizes           ner subsystem B controls their values. Similarly, when solving
the device differential equations and describes the electrical            subsystem B, the subsystem A is treated as the “missing system.”
component based on its instantaneous response to its terminals’           A stabilizing resistor and a current source in parallel represent
voltage inputs. The independency allows the models to be devel-           the missing subsystem, subsystem A in this case, as shown in
oped separately and interconnect with each other easily. This             Fig. 2(b).
technique is widely used in time domain simulation software                  Fig. 3 shows the general workflow of the algorithm. For
such as Pspice, PSIM, and PSCAD [8,9].                                    detailed implementation, if the inner loop runs once, this
   In this work, VTB is selected as the simulation environ-               algorithm is called a linear method. For nonlinear methods,
ment. However, the application of the proposed algorithm for
distributed simulation is not limited to VTB. It is applicable
to all time domain simulation software using RCF techniques.
Remote procedure call (RPC) [10] is selected as the protocol for
communication since it can invoke a function remotely through
a standard interface. The functions interface called by RPC is
defined by the interface definition language (IDL), which is a
standard language used to describe the interface to a routine or
function. RPC can further migrate to common object request
broker architecture (CORBA), since objects in the CORBA are
defined by an IDL. So, with simplified programming, RPC has                                   Fig. 1. Whole system without decoupling.
1126                                   J. Wu et al. / Electric Power Systems Research 77 (2007) 1124–1131

                                                                          if the stabilizing resistor is static, this algorithm is called a
                                                                          non-adjusted stabilizing method. If the stabilizing resistor is
                                                                          varying, this algorithm is called adjusted stabilizing method.
                                                                              Here are the detailed steps for solving subsystem A. In this
                                                                          workflow, the superscript, n, indicates the number of the inner
                                                                          iteration step.

                                                                          1. At initialization, assume v2 = 0 and i2 = 0.
                                                                          2. Construct equivalent circuit for subsystem B, set stabilizing
                                                                             resistor RS A = R0 A , where R0 A is a user defined value.
                                                                                                  S              S
                                                                             Set the current source i0 A = (v2 (t − h)/RS A ) + i2 (t − h).
                                                                                                       S
                                                                          3. Solve for sub-system A and send v0 and i0 to subsystem B.
                                                                                                                    1      1
                                                                          4. Receive vn and in from subsystem B.
                                                                                        2      2
                                                                          5. Construct equivalent circuit for subsystem B, for non-
                                                                             adjusted static stabilizing resistance, RS A will keep static;
                                                                             for adjusted static stabilizing resistance RS A will be adjusted
                                                                             according to history data. The next section presents a detailed
                                                                             explanation about RS A selection in A = (vn (t))/(RS A +
                                                                                                                       S      2
                                                                             in (t)).
                                                                              2
                                                                          6. Solve for subsystem, get vn+1 and in+1 .
                                                                                                           1         1
       Fig. 2. Decoupled system with equivalent circuit.
                                                                          7. Check convergence of i1 . If convergence, proceed to next time
                                                                             step. If not convergence, send vn+1 and in+1 to subsystem B
                                                                                                                1        1
                                                                             and go step 4.

                                                                              Similarly, this process goes through subsystem B:

                                                                          1. At initialization, assume v1 = 0 and i1 = 0.
                                                                          2. Construct equivalent circuit for subsystem B, set stabilizing
                                                                             resistor RS B = R0 B , where R0 B is a user defined value.
                                                                                                  S              S
                                                                             Set the current source i0 B = (v1 (t − h)/RS B ) + i1 (t − h).
                                                                                                       S
                                                                          3. Solve for sub-system B and send v0 and i0 to subsystem A.
                                                                                                                    2      2
                                                                          4. Receive vn and in from subsystem A.
                                                                                        1      1
                                                                          5. Construct equivalent circuit for subsystem A, for non-
                                                                             adjusted static stabilizing resistance, RS B will keep static;
                                                                             for adjusted static stabilizing resistance RS B will be adjusted
                                                                             according to history data. The next section presents a detailed
                                                                             explanation about RS B selection. in B = (vn (t)/RS B ) +
                                                                                                                      S        1
                                                                             in (t).
                                                                              1
                                                                          6. Solve for subsystem B, get vn+1 and in+1 .
                                                                                                             2        2
                                                                          7. Check convergence of i2 . If convergence, proceed to next time
                                                                             step. If no convergence, send vn+1 and in+1 to subsystem A
                                                                                                               2         2
                                                                             and go step 4.

                                                                              At each time step, for high accuracy simulation, the inner loop
                                                                          executes and stops when the current on the transmission line con-
                                                                          verges. For low accuracy or future hardware-in-the-loop tests,
                                                                          the inner loop executes only once (linear method). The outer
                                                                          loop executes to increase the simulation time until it reaches the
                                                                          total simulation time.
                                                                              To test the distributed simulation algorithm, two models
                                                                          were developed in VTB to collect/send information to a remote
                                                                          site and receive/reproduce the information at a local site. The
                                                                          server model sends boundary measurements to other clients, and
                                                                          the client model receives boundary measurements from other
                                                                          servers. Fig. 4 shows the client/server’s symbols. The three-
          Fig. 3. Workflow of distributed simulation.                      phase client/server models decouple a three-phase system, and
                                          J. Wu et al. / Electric Power Systems Research 77 (2007) 1124–1131                                  1127

                                                                              and in+1 is a function of v1 n and i1 n . Similarly, vn+1 and in+1 is
                                                                                   2                                                1        1
                                                                              a function of vn and in . Their relationship is expressed in the Eq.
                                                                                             2      2
                                                                              (1) with the changing portion decoupled from the fixed portion.
                                                                                             ⎡                      R L − RS A ⎤
                                                                                 n+1                   0
                                                                                i1 (t)       ⎢                     Req 1 + RS A ⎥
                                                                                 n+1
                                                                                          =⎢ ⎣ RS − R S B
                                                                                                                                   ⎥
                                                                                                                                   ⎦
                                                                                i2 (t)                                    0
                                                                                               Req 2 + RS B
                 Fig. 4. Server/client models in VTB.                                                  in (t)
                                                                                                        1            J1
                                                                                                  ×             +                              (1)
                                                                                                       in (t)
                                                                                                        2            J2
the single-phase client/server models decouple a single-phase
system.                                                                       where
                                                                                                  RL                  Req 1
4. Numerical analysis                                                         J1 = −                      iL (t) +              ieq 1 (t)
                                                                                           RS   A + Req 1          RS A + Req 1

    This section establishes the mathematical model of the dis-                                   RS                  Req 2
tributed algorithm through circuit analysis and analyzes the                  J2 = −                      iS (t) +              ieq 2 (t)
                                                                                           RS   B + Req 2          RS B + Req 2
convergence of different methods.
    In each time step, after the original system is decoupled, the
two subsystems can be represented in the RCF model, as shown                                  Req 1                    RS A
                                                                              i0 (t) =
                                                                               1                        ieq 1 (t) −             i0
in Fig. 5.                                                                                 RS A + Req 1             RS A + Req 1 S     A

    For subsystem A (Fig. 5(a)), no matter how complex the
known subsystem is, at each time step, it can be simplified into                               Req 2                    RS B
                                                                              i0 (t) =
                                                                               2                        ieq 2 (t) −             i0
a Norton equivalent and represented by a current source iS and a                           RS B + Req 2             RS B + Req 2 S     B
resistor RS . Following the RCF modeling, the transmission line
is represented by a current source, iT , and a resistor, RT . The                          v2 (t − h)
missing subsystem is represented by a current source iS A and a               i0
                                                                               S   A   =              + i2 (t − h)
                                                                                             RS A
stabilizing resistor RS A . Similarly, for subsystem B (Fig. 5(b)),
no matter how complex the known subsystem is, at each time
                                                                                           v1 (t − h)
step, it can be simplified into a Norton equivalent and repre-                 i0
                                                                               S   B   =              + i1 (t − h)
sented by a current source iL and a resistor RL . Following the                              RS B
RCF modeling, the transmission line is represented with iT and
                                                                                           vn (t − h)
RT . The missing subsystem A is represented by a current source               in
                                                                               S   A   =    2
                                                                                                      + in (t − h)
                                                                                                         2
iS B and a stabilizing resistor RS B .                                                       RS A
    Following the algorithm described in Fig. 3, the relationship
between the voltage and current of each iteration in the inner                             vn (t − h)
                                                                              in
                                                                               S   B   =    1
                                                                                                      + in (t − h)
                                                                                                         1
loop can be determined through nodal analysis. According to                                  RS B
the algorithm, vn and in controls the value of iS A , vn and in
                  2       2                                1      1
controls the value of iS B . All other elements, like resistors and                    2Lload
current source, are known and fixed at this time step. Thus, vn+1              RL =            + Rload
                                                                2                        h




                                  Fig. 5. RCF equivalent circuit for subsystems. (a) Subsystem A and (b) subsystem B.
1128                                                       J. Wu et al. / Electric Power Systems Research 77 (2007) 1124–1131

           2Ltrans     line
                                                                                                 With such a stabilizing resistance selection, the solution
RT =                          + Rtrans   line                                                 is guaranteed to converge to the true solution, which can be
                h
                                                                                              obtained from nodal analysis of the non-distributed simulation.
                                      1                                                       In Fig. 5(a), after replacing RS A with RL and iS A with iL , and
Req−1 =                                                                                       in Fig. 5(b), replacing RS B with RS and iS B with iS , the true
                1/(RS + RT ) − 1/(RS + RT )(RT /RS )(iT (t)/iS (t))
                                                                                              solution can be expressed in the equations below:
                                      1                                                                   RL                 Req 1
Req    2   =                                                                                  i1 = −              iL (t) +            ieq 1 (t)
                1/(RL + RT ) + 1/(RL + RT )(RT /RL )(iT (t)/iL (t))                                    RL + Req 1          RL + Req 1

                           1                                                                              RS                 Req 2
iL (t) = −                            v2 (t − h)                                              i2 = −              iS (t) +            ieq 2 (t)
                 (2Lload / h) + Rload                                                                  RS + Req 2          RS + Req 2
                 (2Lload / h) − Rload                                                         Here, i1 and i2 are of the same magnitude and are the opposite
            −                         i1 (t − h)
                 (2Lload / h) + Rload                                                         of each other.
                                      1
iT (t) = −                                                 v2 (t − h)                         5. Test cases and performance analysis
                 (2Ltrans      line / h) + Rtrans   line
                 (2Ltrans      line / h) − Rtrans line                                           To demonstrate the distributed simulation algorithm, corre-
            −                                              i1 (t − h)
                 (2Ltrans      line / h) + Rtrans line                                        sponding models are developed in VTB using C++ language and
                                                                                              tested with different network configurations. The models perfor-
                   RS                RT                                                       mance is analyzed in time domain and steady state simulation.
ieq 1 (t) =               iS (t) −          iT (t)
                 RS + R T          RS + R T
                                                                                              5.1. Test case #1
                   RL         RL                RT
ieq 2 (t) =               =          iL (t) +          iT (t)                                     The first test case is a two-bus system, as shown in Fig. 6,
                 RL + R T   RL + R T          RL + R T
                                                                                              and the system specification comes from the MURI project as
Here, h is the time step size. All the variables at time t–h are                              shown in Table 1.
known. For the linear VI coupling model, i0 (t) and i0 (t) are the
                                            1         2                                           Distributed simulation is carried out on a different connected
solutions for that time step.                                                                 number of loads with different step sizes. The adjusted sta-
   To make the solution stable and converging, the eigen-                                     bilizing resistance algorithm is compared with non-adjusted
value of the iteration matrix must be within the unit circle.                                 stabilizing resistance and the linear algorithm. The results of all
However, the eigenvalues λ, (RL − RS A )/(Req 1 + RS A ) and                                  distributed test cases are compared with a single simulation with
(RS − RS B )/(Req 2 + RS B ), are related to state variables and                              the same time step to evaluate the performance of distributed
time step size sensitive. To make | | within 1, the best choice is                            simulation. The mean absolute percentage error (MAPE) mea-
to approximate RS A = RL and RS B = RS .                                                      sured its performance in the transmission line current as show
   But, as stated in the algorithm, only boundary voltage and                                 in Eq. (6). Table 2 shows the test results.
current measurements are available for the unknown subsys-
                                                                                                        |inon−distributed − idistribued |
tem, RL and RS are unknown. To estimate RL and RS from the                                    APE =                                       × 100%               (6)
measurement, the following relationship between voltage and                                                    inon−distributed
current in iterations is used:                                                                             1
                                                                                              MAPE =               APE                                         (7)
           vn                 vn−1                                                                         N
in
 S   =      1
                + in
                   1   =       1
                                     + in−1                                          (2)                       N
           RS                 RS        1
                                                                                              Here, N is the number of sample points in the simulation.
           vn                 vn−1                                                                This comparison shows quicker convergence and higher
in =
 L
            2
                + in =
                   2
                               2
                                     + in−1                                          (3)      accuracy for the adjusted stabilizing resistance algorithm. In
           RL                 RL        2
                                                                                              each time step, the adjusted stabilizing resistance method can
   Note that in and in are fixed at a specific time step in Eqs.
              S      L                                                                        find the solution within tolerance in two iterations, whereas the
(2) and (3). Thus, RL and RS can be calculated through the                                    non-adjusted stabilizing resistance method needs three to four
boundary voltage and current measurement. Make RS A = RL                                      iterations to reach the solution for converged cases.
and RS B = RS , and that creates the following equation for esti-
mation of RS A and RS B :                                                                     Table 1
                                                                                              System specifications for test case #1 [1]
                 vn    − vn−1
RS    A    =−     2       2
                                                                                     (4)      Voltage source                      RMS: 120 V, RS = 0.02
                  in
                   2   − in−1
                          2                                                                   Load #1                             R = 12.3 , L = 0.03138 H
                                                                                              Load #2                             R = 14.52 , L = 0.031468 H
                 vn − vn−1                                                                    Load #3                             R = 14.52 , L = 0.031468 H
RS    B    =−     1    1
                                                                                     (5)
                 in − in−1
                  1    1
                                                                                              Transmission line                   R = 0.34 , L = 0.005913 H
                                        J. Wu et al. / Electric Power Systems Research 77 (2007) 1124–1131                                   1129




                                                             Fig. 6. Two bus system.

Table 2
MAPE for distributed simulation
Case                    Step size (s)        Linear (%)              Non-adjusted stabilizing resistance       Adjusted stabilizing resistance (%)

One load                1e-6                   0.3312                0.0248%                                   0.0248
                        1e-5                   2.741                 0.0248%                                   0.0248
                        1e-4                  15.733                 Did not converge                          0.0248
                        1e-3                 422.338                 Did not converge                          0.0248
Three load              1e-6                   0.322                 0.0323%                                   0.0323
                        1e-5                   3.774                 0.0928%                                   0.0928



   Fewer iterations lead to less computation time. The adjusted            linear method can have better performance when the correction
stabilizing resistance method always converges and is not time             based on the previous calculation is introduced for next step sim-
step sensitive. For the linear method, the MAPE keeps grow-                ulation, using a state estimator. The accuracy decreases when
ing exponentially when the time step size increase, because the            the number of components in simulation increases for all three
larger the step size reduces accuracy of the discretized RCF               methods. This decrease occurs because the VTB solver only has
model for the components in simulation. Without the correction             control over the voltage profile, while the currents are calculated
in the minor step for the non-linear method, the error accumu-             based on individual device model; thus the truncation error can
lates and finally makes the simulation results inaccurate. The              accumulate.




                                             Fig. 7. 18-Bus ship power system distributed simulation.
1130                                     J. Wu et al. / Electric Power Systems Research 77 (2007) 1124–1131

Table 3
Power flow solution from VTB
Bus no.             Voltage magnitude (pu)              Voltage angle (degree)               Real power                      Reactive power
                                                                                             generation, P (MW)              generation, Q (MVar)

 1                  1.02                                 0                                   5.722                           1.292
 2                  1.02                                 0                                   6.329                           0.1424
 3                  1.02                                 0                                   6.112                           0.1391
 4                  1.02                                 0                                   5.896                           0.1335
 5                  1.0199                              −0.0054
 6                  1.0199                              −0.0053
 7                  1.0197                              −0.0136
 8                  0.9866                             −10.5502
 9                  0.9865                             −10.5638
10                  1.0198                              −0.0111
11                  0.9873                             −10.6174
12                  0.9872                             −10.6311
13                  1.0196                              −0.0167
14                  0.9872                             −10.4745
15                  0.9870                             −10.4911
16                  1.0197                              −0.015
17                  0.9851                             −10.7343
18                  0.9849                             −10.7502


5.2. Test case #2                                                           demonstrate the capability of natural level coupling agent model.
                                                                            Generally, a smaller time step makes the distributed simulation
   In this section, a more complicated test case is developed               more accurate than it is with non-distributed simulation. With
based on a new benchmark test system of a ship’s distribu-                  a small enough time step, little difference exists between non-
tion network described in paper [13]. This system is an 18-bus              adjusted stabilizing element and adjusted stabilizing element
shipboard power system. It has six polynomial loads and four                methods. However, when the time step increases, an inappropri-
generators. This shipboard power system is configured in two                 ate stabilizing element will make the simulation diverge. Since
zones. The two zones are weakly coupled through transmission                limited information about the external system is available, it
lines 5 and 6. Therefore this line is selected as the decoupling            is difficult to guess an appropriate stabilizing element. At this
point. Here single-phase client/server models are used for the              point, the advantage of adjusted stabilizing element is obvious.
distributed simulation in VTB, shown in Fig. 7.                             It can identify the optimal stabilizing element for the system to
   Here, the PQ load model is a non-linear model dependent                  make the simulation converge. This characteristic is especially
on the terminal voltage’s RMS value, as described in detail in              useful when the system is nonlinear or there is a time varying
paper [12]. Its performance has been validated. The transformers            element.
and lines are represented by an inductor since reference [12]                   Also, as noticed from the two-bus test cases for natural cou-
provides only R and L parameters. This test, besides comparing              pling model, a single load test has better performance than
the MAPE of current flowing through the tie line (from bus 5                 multiple loads. This difference is caused by the VTB solver,
to bus 6), also compares the power flow solution between the                 where voltage is taken as the state variable and is controlled
distributed simulation and non-distributed simulation.                      within a given tolerance. The current of each element is com-
   After data processing, the MAPE is within 0.5% deviation                 puted separately. However the truncation error can make the sum
from the non-distributed simulation. Table 3 shows the power                of the current mismatch bigger. So the number of branches at the
flow solution using VTB. Compared to the result from the power               coupling point causes the simulation to converge with different
flow solution in paper [13], the voltage magnitude is the same               accuracies.
while the voltage angle deviation is within 0.014 degree. This                  For a steady state test, satisfactory results are achieved for the
error diminishes because in steady state, the error integrated to           developed electric ship test case. This demonstrates the natural
zero. The steady state solution in distributed simulation matches           coupling model’s capability to work with multiple sources and
the solution in non-distributed simulation [13]. The close voltage          multiple loads. Testing the natural coupling model further with
match indicates the simulation confirms power flow analysis and               a larger scale power system will be possible when VTB-Pro is
can be used for transient analysis.                                         released, as it can accommodate more nodes and is more stable.

6. Summary                                                                  7. Conclusion

   This paper compares three methods to represent the external                 In this paper, a distributed simulation algorithm using the
network, linear, non-adjusted stabilizing element and adjusted              generalized VI coupling method is proposed to handle natu-
stabilizing element. Numerical analysis techniques demonstrate              ral coupling. With a VI coupling model developed in VTB,
the convergence of the algorithm. Test cases are developed to               numerical analysis for convergence and computational stabil-
                                              J. Wu et al. / Electric Power Systems Research 77 (2007) 1124–1131                                              1131

ity is performed. The adjusted stabilizing resistance method is                    [8] G. Cokkinides and B. Beker, VTB Model Developer’s Guide. Vir-
proposed to achieve better convergence and stability. Test cases                       tual Test Bed Project, Department of Electrical Engineering, Univer-
with different network configurations are developed. The dis-                           sity of South Carolina, Columbia, SC, 29208, Available at http://vtb.
                                                                                       engr.sc.edu/modellibrary/modeldev.asp, Mar. 2001.
tributed simulation performance is analyzed in time domain and                     [9] W. Gao, E.V. Solodovnik, R.A. Dougal, Symbolically aided model devel-
steady state. The results demonstrate good performance of this                         opment for an induction machine in Virtual Test Bed, IEEE Trans. Energy
technique.                                                                             Convers. 19 (1) (2004).
    On the other hand, current models for distributed simulation                  [10] Remote Procedure Call, http://www.microsoft.com/technet/prodtechnol/
are developed based on RPC techniques, which are used for peer-                        windowsserver2003/library/TechRef/4dbc4c95-935b-4617-b4f8-
                                                                                       20fc947c7288.mspx.
to-peer communication and suitable for simple networks. While                     [11] J. Wu, N.N. Schulz, Generalized three phase coupling method for dis-
VTB is progressing to provide a COM server, a more promising                           tributed simulation, in: Proceedings of North America Power System Con-
feature is coming. Therefore, in the next step in our research we                      ference, Iowa, October 2005.
will migrate the models from RPC to a COM server and test it                      [12] J. Wu, Y. Huang, W. Gao, N.N. Schulz, Power system load modeling in vir-
with different system configurations.                                                   tual test bed, in: Proceedings of IEEE Power Engineering Society General
                                                                                       Meeting, Montreal, Canada, June 2006.
                                                                                  [13] T.L. Baldwin, S.A. Lewis, Distribution load flow methods for shipboard
Acknowledgments                                                                        power systems, IEEE Trans. Indus. Appl. 40 (5) (2004) 1183–1190.

   This research work has been made possible through the sup-                     Jian Wu is a Ph.D. candidate in electrical and computer engineering at Mis-
port of the DoD MURI Fund # N00014-04-1-0404 and ONR                              sissippi State University (MSU). She received B.S.E.E. and M.S.E.E. from
                                                                                  ZheJiang University, China. She has worked with HangZhou Municipal Power
Fund #N00014-02-1-0623.                                                           Company. She received another M.S.E.E. from MSU in 2004. Her fields of
                                                                                  interest include the power system modeling and simulation, common informa-
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                                                                                  Noel N. Schulz received her B.S.E.E. and M.S.E.E. degrees from Virginia
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