SVC and STATCOM Application in Electric Arc Furnace Efficiency Improvement Mahsa Ghapandar Kashani Dept. of Electrical and Computer Engineering North Carolina State University
[email protected]
Subhashish Bhattacharya Dept. of Electrical and Computer Engineering North Carolina State University
[email protected]
Saman Babaei Dept. of Electrical and Computer Engineering North Carolina State University
[email protected]
Abstract — Electric Arc Furnaces (EAF) are high power industrial loads which cause power quality problems at all voltage levels due to their unbalanced and nonlinear characteristics. The rapid, stochastic large swings in real and reactive power required by the arc furnace causes voltage drops, rapid voltage variation and distortion across the ac supply network. These voltage drops and fluctuations not only have negative impact on the power system quality and other loads, but also have an effect on the arc furnace operation, power output and efficiency. Hence, some sort of reactive compensation is required to limit the voltage disturbances injected by arc furnace into the electric power system. In this paper, an accurate electric arc furnace model, whose parameters have been set according to a 80 MVA actual arc furnace, is studied. A Static VAR Compensator (SVC) is simulated in PSCad and Real Time Digital Simulation (RTDS)/RSCAD platform for the purpose of comparison comparison of voltage regulation at EAF bus. It is shown that t he SVC mitigates the reactive power fluctuations in addition to providing the fundamental reactive power, and regulates the Point of Common Coupling (PCC) bus voltage precisely during the arc furnace operation. To verify the PSCad simulation results and make a comparison, a real time simulation study based on Real Time Digital Simulation (RTDS)/RSCAD platform has been performed in this case. On the other hand, a 80 MVA static synchronous synchronous compensator (STATCOM) is simulated in PSCad. It is illustrated that the SVC is inherently limited in its ability to respond rapidly to the fluctuating arc furnace load. It is found that the transient performance of the EAF voltage in case which equipped with the STATCOM is better than the case equipped with SVC. It is also demonstrated that although the voltage regulation by the SVC compensates a portion of the reactive power fluctuation, it is completely unable to supply any portion of the fluctuating real power drawn by the arc furnace, while the STATCOM can supply those components of active and reactive power fluctuation. The STATCOM will not normally have a source of real power connected to its DC terminals. It is therefore unable to supply sustained real power or real power fluctuations. With suitable choice of DC capacitor, however, it is capable of supplying in large part the fluctuating real power requirement of the furnace.
Keywords—Electric Arc Furnace (EAF), Static VAR Compensator (SVC), SATACOM, voltage regulation and reactive power compensation compensation
I.
I NTRODUCTION NTRODUCTION
The electric arc furnace presents a complex and large load in a power grid, which has unbalanced, unbalanced, non-linear, and timevarying characteristics with a strongly fluctuating consumption of reactive and real power. [1]. Since the electric arc furnace does not have any built-in compensation for controlling voltage variations like an electrical motor or drive system, which consumes more current when voltage decreases in order to maintain the same torque, the power input to the furnace is very sensitive to voltage variations [2]. The inductive VARs drawn by the furnace has a major impact on the feeding voltage and creates a voltage drop at the primary side of t he arc furnace transformer during its operation. This reduces the active power to the arc furnace and also to the other loads connected to the same feeding bus bar. Thus, efficient operation of an electric arc furnace requires the voltage to be kept high and stable. This paper specifically studies the effect of SVC and STATCOM voltage regulation on the EAF operation, voltage regulation and efficiency improvement, and on the other hand studies the limitation of the SVC ability in compensating the active/real and reactive power fluctuation. In this work, an accurate model which takes into account the stochastic and chaotic characteristics of an electric arc furnace is used. All the parameters of this model have been set according to an 80MVA actual EAF. An actual SVC system model and a 80 MVA STATCOM are simulated separately in PSCad as compensators of reactive power required for the EAF. The rest of this paper is organized as follow: section II, presents the EAF model and its PSCad operation results. Section III, describes the AC system supplying the EAF. The characteristic of the SVC which is used for maintaining the EAF voltage in the acceptable operating range has been presented in section IV. STATCOM characteristics characteristics is presented in section V. PSCad simulation results of EAF operation with and without SVC and STATCOM under different conditions are presented in section VI., Section VII is illustrating the RTDS results. Finally section VIII draws the conclusion of this study. II.
ELECTRIC ARC FURNACE MODEL
Since the arc melting process is a stochastic process, process, making an exact model for an electric arc furnace is a difficult process.
1.
0.8
0.6
1
0.4 ) u p ( e g a t l o v F A E
0.5
) u p ( 0.2 e g a t l o v 0 e s a h p 3 -0.2 F A E
0
-0.5
-0.4
-1 -0.6
-1.5 -2
-1.5
-1
-0.5
0 EAFCurrent(pu)
0.5
1
1.5
2
-0.8 0.175
0.18
0.185
0.19
0.195
0.2
0.205
Time(sec)
Fig.1.
Electric arc furnace voltage versus current
Fig.2.
Electric arc furnace 3-phase voltages without addition of Gaussian noise to the model
0.8
2
EAF Voltage (pu) EAF current (pu)
0.6
1.5 0.4
1
) u p ( e 0.2 g a t l o v 0 e s a h p 3 F -0.2 A E
) u p ( t n 0.5 e r r u C / ) 0 u p ( e g a t l -0.5 o V
-0.4
-1
-0.6
-1.5
-0.8 8.36
-2 8.365
8.37
8.375
8.38
8.385
8.39
0.11
0.12
0.13
0.14
Fig.3.
Electric arc furnace 3-phase voltages with addition of Gaussian noise to the model
1.5
Fig.4.
0.16
0.17
0.18
0.19
0.2
Electric arc furnace voltage and current versus time without addition of Gaussian noise to the model
EAF Voltage (pu) EAF Current (pu)
1
) u p ( t n e r r u C / e g a t l o V
0.15 Time(sec)
Time(sec)
Table 1.EAF model parameters
0.5
PhaseA
0
-0.5
-1
-1.5 1.05
1.06
1.07
1.08
1.09
1.1
1.11
1.12
1.13
Time(sec)
Fig.5.
PhaseB
PhaseC
m
0
0
0
n
2
2
2
3500 2 12.5
3500 2 12.5
k 1 k 2 k 3
3500 2 12.5
Electric arc furnace voltage and current with addition of Gaussian noise to the model
In this regard, numerous models have been presented to describe the arc furnace [3]-[13]. Each of the referenced models produces results that are valuable under selected study conditions. In this work, an accurate model which has been presented in [14] is used. This model is designed as a custom component for use with the PSCad modeling software. The model is single-phase, which can be used in any configuration so that unbalanced situations can be easily simulated. The method used in this model is the Modified Euler Method, also known as Heun’s Method. The equations presented for the electric arc are as follows: [14] . . .
.
(1)
.
(2)
where: k 1,k 2 ,k 3 ,m, n are model constants, r is arc radius in centimeters, i is current through the arc in Amperes, and v is voltage across the arc in Volts. The inputs to the model are these five basic values used in the equations (k 1,k 2 ,k 3 ,m, n). The outputs from the model are the arc voltage and current. The value of each input is assigned such that the desired output can be obtained [14]. The model parameters have been set in such a way that EAF generates the 80 MVA arc power that perfectly matches with real EAF used
in this study. The model parameters used in this study are presented in Table.1. There is an additional capability of adding Gaussian noise to the model. The noise is added as a variation to the arc radius [14]. Fig.1-Fig.5, illustrate the operation of this EAF model with and without adding Gaussian noise. III.
SYSTEM DESCRIPTION
The single line diagram of the system is shown in Fig.6. In this model all the values and parameters have been selected according to an actual plant which has a 100-ton furnace with a nominal rating of 80 MVA. This plant is supplied with a 138 kV transmission line. A step-down transformer (138/15.24 kV) feeding the furnace transformer at approximately 15 kV. For many years a conventional SVC was used for power factor correction and voltage regulation of this plant. The ±80 MVA compensator is connected to the 15 kV furnace bus with a shunt coupling transformer. There is a fixed 60 MVA AC capacitor bank in conjunction with this compensator [1].
Fig.6.
Single Line Diagram of the System
KI S
Fig.7.
I.
Single Line Diagram of the SVC
STATIC VAR COMPENSATOR A NALYSIS
The SVC is a mature and reliable technology, which has been used predominantly in arc furnace and transmission applications [15]. The huge amount of the reactive power drawn by furnace leads to significant voltage drop at the furnace transformer. The worst condition occurs when the furnace electrodes are shorted. The purpose of the static VAR compensator (SVC) is to supply capacitive VARs to offset the inductive VARs drawn by the furnace system and, therefore, to minimize the voltage drop on the system. The maximum useful MVAR size of the SVC would generally be the maximum VARs drawn by the furnace system [2]. In this work a ±80 MVA closed-loop control system SVC with two Thyristor Controlled Reactors (TCRs), and three Thyristor Switched Capacitors (TSCs) is used. The simplified block diagram of the SVC control structure is depicted in Fig.8. In this block diagram the actual voltage signal (Vactual ) is the magnitude of the 15.24kV bus voltage. This signal must be accurate, insensitive to system harmonics and system frequency deviations. The reference voltage (Vreference) is generated by a ramp-function generator in the PSCad where the set points are raised and lowered in steps. The slope of the steady-state voltage/current characteristic is adjustable between 0.1% and 5% based on 80 MVAR. The voltage control regulates the system voltage quickly and accurately. The PI-regulator output signal represents the required SVC reactive power to correct the voltage error signal ΔV [16].
Fig.8.
II.
Simplified PI Controller Block Diagram
STATCOM A NALYSIS
The conventional SVC based compensator has inherently some limitation, which restricts its ability to respond rapidly to the fluctuating arc furnace load, so that the compensator is completely unable to supply any portion of the fluctuating real power drawn by the furnace. Real power fluctuation produces phase angle variations at the bus voltage that do in fact contribute to flicker. By appropriately controlling the STATCOM voltage source, any desired current can be forced to flow through the tie reactance. The voltage-source inverter based STATCOM is appropriately designed with high bandwidth control capability, then it can be used to force three phase currents of arbitrary wave shape through the tieinductance into the power line. This unique capability makes the STATCOM an ideal candidate for arc furnace compensation. Connected to the ac supply bus for an arc furnace, the STATCOM can thus be made to supply those components of the arc furnace load comprising non-sinusoidal, unbalanced, randomly fluctuating currents, in addition to the fundamental reactive power. The STATCOM will normally not have a source of real power connected to its DC terminals. It is therefore unable to supply sustained real power or real power fluctuations. With suitable choice of DC capacitor, however, it is capable of supplying in large part the fluctuating real power requirement of the furnace [1]. In this paper, a 80MVA STATCOM is simulated as a compensator for the EAF system.
1.01
80
) W 75 M ( r e w70 o p e65 v i t c a F60 A E
1
0.99
Capacitor Bank & SVC on
0.98
) u p ( e g0.97 a t l o V l 0.96 a u t c A
Cap1,2,3 on
Capacitor Bank on CapacitorBank & SVC off
55
Capacitor Bank & SVC on
0.2
0.3
0.4
0.5
0.6
0.7
Time (Sec) ) 75 R A V M70 ( r e w65 o p e60 v i t c a e r 55 F A E50
Cap1,2 on
0.95
Cap1 on
Capacitor Bank & SVC off
0.94
0.93
0.92 0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Time (Sec)
Capacitor Bank on Capacitor Bank & SVC on CapacitorBank & SVC off
0.2
0.3
0.4
0.5
0.6
0.7
Time (Sec)
Fig.9. Actual bus voltage in five different cases: 1-Capacitor ank and SVC off 2- 20MVA capacitor 1 on. 3- Capacitor 1, 2 on.4- capacitors 1, 2, and 3 on.5-Capacitor bank and SVC on
Fig.10.
90
EAF active and reactive power in three different cases: 1- capacitor bank and SVC off. 2- Capacitor bank on. 3- Capacitor bank and SVC on.
80 60
80
SVC is off
SVC is on
40
70
c a 20 P
Total active power of the System (Mw)
0
Total Ractive power of the System (Mvar)
60
-20
m e 50 t s y s Q - 40 m e t s 30 y s P
-40 0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1. 2
1.3
Time (Sec)
Capacitor Bank & SVC off
40
SVC is off
SVC is on
20
20 Capacitor Bank on
c a 0 Q
Capacitor Bank & SVC on
10
-20
0
-40 0.3
-10 0.2
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
Time (Sec)
0.4
0.6
0.8
1
1.2 Time (Sec)
1.4
1.6
1.8
2
Fig.11. Total active power of the AC-system is increased by the SVC. Total reactive power of the AC-system is compensated by the SVC.
Fig.12.
Active and Reactive power fluctuation seen by the AC-system due to EAF operation
80
1.01
) 75 W M ( r e 70 w o P e v i t c 65 A F A E
1
Capacitor Bank & STATCOM on
0.99
0.98 ) u p0.97 ( e g a t l 0.96 o V l a u t 0.95 c A
Capacitor Bank on Capacitor Bank & STATCOM on
Capacitor Bank & STATCOM off
60
Cap 1,2,3 on
55 0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2
2.2
Time (Sec) 80
) 75 R A V 70 M ( r e 65 w o P 60 e v i t 55 c a e R 50 F A E 45
Cap 1,2 on
0.94
Cap 1 on 0.93
Capacitor Bank & STATCOM off 0.92
0.91
0.5
1
1.5
2
40 0.2
2.5
Capacitor Bank & STATCOM off
0.4
Capacitor Bank on Capacitor Bank & STATCOM on
0.6
0.8
Time (Sec)
Fig.13.
1
1.2
1.4
1.6
1.8
Time (Sec)
Actual bus voltage in five different cases: 1-Capacitor bank and STATCOM off 2- 20MVA capacitor 1 on. 3- Capacitor 1, 2 on. 4-capacitors 1,2, and 3 on.5-Capacitor bank and STATCOM on
Fig.14. EAF active and reactive power in three different cases: 1- capacitor bank and STATCOM off. 2- Capacitor bank on. 3- Capacitor bank and the STATCOM on. 60
100
40
STATCOM is on
STATCOM is off
20
c a P
80
Total active power of the System (Mw) Total Ractive power of the System (Mvar)
60 m e t s y s Q - 40 m e t s y s P
0
-20 -40 3.5
4
4.5
5
5.5
Time (sec)
Capacitor Bank on Capacitor Bank & STATCOM off
60
Capacitor Bank & STATCOM on
40
STATCOM is off
STATCOM is on
20
20
c a
0
Q
-20
0
-40 -60 3.5
-20 0.2
4
4.5
5
5.5
Time (sec)
0.4
0.6
0.8
1
1.2 Time (Sec)
1.4
1.6
1.8
2
2.2
Fig.15. Total active power of the AC-system is increased by the STATCOM. Total reactive power of the AC- system is compensated by the STATCOM.
Fig.16.
Active and Reactive power fluctuation seen by the AC-system due to EAF operation
III.
SVC AND STATCOM SIMULATION R ESULTS
As previously mentioned, the EAF causes voltage drops and fluctuation across the AC supply network. This issue is illustrated in Fig.9. When all the capacitor banks and SVC are isolated from the circuit the RMS value of the bus voltage measured from point B (Fig.6) is 0.91pu, which is considerably low. This voltage drop reduces the active power to the arc furnace as well as the other loads connected to the same feeding bus. By inserting the 60 MVA capacitor bank, this voltage drop can be improved and the RMS value of the bus voltage reaches to 0.95pu. However, with only capacitor compensation, the system voltage is still far below the nominal point. Having installed the SVC and setting the reference voltage at 1pu, the bus voltage reaches to nominal system voltage. These cases have also been studied with the STATCOM, and the results are shown in Fig.13. The change in active and reactive power consumption of the EAF corresponding to these voltage changes is shown in Fig.10 and Fig.14 for the SVC and STATCOM respectively. As it is illustrated, this voltage regulation by the SVC and STATCOM causes the EAF bus voltage to be 1.0 pu. The higher voltage level at the furnace bus gives higher active/real power to the furnace, which enables benefits such as shorter melting time, reduced energy losses, reduced electrode consumption and lower plant losses [17]. Reactive power support functionality of the SVC and STATCOM decrease the utility reactive power injection dramatically. Fig.11 and Fig.15 show the trend of total active and reactive power provided by the AC-system at point A (Point A is shown in Fig.6). As it is demonstrated when the SVC or STATCOM is on, the reactive power exchange between EAF and the utility is decreased. It is important to notice that fluctuations of the EAF reactive power decrease after installing the SVC. This compensation of EAF reactive power fluctuations has been il lustrated in Fig.12. Although the voltage regulation by the SVC compensate considerable portion of the reactive power fluctuations, it is completely unable to supply any portion of the fluctuating real power drawn by the arc furnace. This fact is also shown in Fig.12. By connecting the STATCOM to the ac supply bus, it can supply those components of the arc furnace load comprising non-sinusoidal, unbalanced, randomly fluctuating currents, in addition to the fundamental reactive power. As it is illustrated in Fig.16, the significant portion of the fluctuating real and reactive power is compensated by the STATCOM. With suitable choice of DC capacitor, the STATCOM is capable of supplying in large part the fluctuating real power requirement of the furnace. This is something that is fundamentally not possible with an SVC. IV.
Fig.22 shows how the voltage controller regulates the system voltage quickly and accurately such that the actual voltage of the bus follows the reference voltage precisely when the reference changes from 0.98 to1.02 pu. The change in active power consumption of the EAF when the SVC is Off and On is shown in Fig.23. As it is illustrated, this voltage regulation by the SVC causes the EAF bus voltage to be 1.0 pu. The higher voltage level at the furnace bus gives higher active/real power to the furnace, which enables benefits such as shorter melting time, reduced energy losses, reduced electrode consumption and lower plant losses [17]. Earca vs Iarc 2
1
0
-1
-2 -1
-0.5
Fig.17.
0
0.5
1
Electric arc furnace voltage versus current Earca Earcb Earcc
1
0.5
0
-0.5
-1 0.1 9152
0. 2005 7
Fig.18.
0.20961
0.21866
0. 22771
0 .2367 5
0.245
Electric arc furnace voltage versus time IL2EAFC IL2EAFA IL2EAFB
2
1
0
-1
R EAL TIME DIGITAL SIMULATION (RTDS) R ESULTS
To verify the PSCAD simulation results and make a comparison, a real time simulation study based on Real Time Digital Simulation (RTDS)/RSCAD platform has been performed. Fig .17-Fig.19, illustrate the operation of this EAF model without adding Gaussian noise.
-2 .20393
0.21375
Fig.19.
0.22356
0.23338
0.2432
0.25302
Electric arc furnace current versus time
0.2628
TCR1a
TCR1b
TSC1a TSC1b TSC1c
TCR1c
4
2 1
2
0 0
-1 -2
-2
TSC2a TSC2b TSC2c 2
-4
1 TCR2a
TCR2b
TCR2c
0.003
0
0.002
-1
0.001
-2 TSC3a TSC3b TSC3c
0
0.004 -0.001
0.002 -0.002
0 -0.003 2. 53 815
2. 54 244
2 .5 46 72
2. 55 101
2. 55 53
2 .55 95 9
2 .5 63
-0.002 -0.004 2. 685 65
Fig.20.
TCR1 & TCR2 Current. TCR1 is on and TCR2 is off
2 .69 027
Fig.21.
2 .6 94 9
2. 69 953
2 .7 041 5
2. 70 87 8
2. 713 4
TSC1, TSC2, TSC3 Current. TSC1,2 on and TSC3 off
Vact Vref
Parc
80
1.04 75
1.02 70
1 65
0.98 SVC is off
60
SVC is on
0.96 55
0.94 50
0.6
0.8
Fig.22.
1
1.2
1.4
1.6
1.8
2
2.2
Actual and reference bus voltage
V.
CONCLUSION
Electric Arc Furnaces are high power industrial loads which causes power quality problems at all voltage levels due to their unbalanced and nonlinear characteristics. The rapid, stochastic large swings in real and reactive power required by the arc furnaces causes voltage drops, rapid voltage variation and distortion across the AC supply network. This voltage drop significantly decreases the EAF efficiency. This paper specifically studied the voltage regulation issues of the ACsystem connected to the EAF, and on the other hand studies the limitation of its ability in compensating the active and reactive power fluctuation. In this paper, an accurate electric arc furnace model, whose parameters have been set according to an 80 MVA actual arc furnace, was studied. A SVC was simulated in PSCad and Real Time Digital Simulation (RTDS) for the purpose of voltage regulation of the EAF bus. It was shown that the SVC controller regulates the PCC bus voltage precisely during the arc furnace operation, and this voltage regulation improves the productivity and efficiency of the electric arc furnace, while it is completely incapable to compensate real power fluctuation which contributes to flicker. Also by modeling a 80 MVA STATCOM in the PSCad, it was shown that the STATCOM can also supply fluctuation components of the active and reactive power. The STATCOM will normally not have a source of real power connected to its DC terminals. It is therefore unable to supply sustained real power or real power fluctuations.
Fig.23.
0.8
1
1.2
1.4
1.6
1.8
EAF active power in two different cases: 1- SVC is off. 2- SVC is on
With suitable choice of DC capacitor, however, it is capable of supplying in large part the fluctuating real power requirement of the furnace [1]. This capability makes the STATCOM an ideal candidate for the voltage regulation at EAF bus. VI.
R EFERENCES
[1] C. Schauder, "STATCOM for Compensation of Large Electric Arc Furnace Installation", Power Engineering Society Summer Meeting, 1999. IEEE [2] I.A Erinmez, “Static Synchronous Compensator (STATCOM)” Report prepared Working Group 14, published by CIGRE as “Technical Brochure No 144” in Feb 2003 [3] J.-C. Baurnert, et al., "Dynamic modeling of the electric arc furnace process using artificial neural networks," La Revue de Metallurgie-CIT, pp. 839- 849, 2002. [4] L. F. Beites, et al., "Harmonics, interharmonics and unbalances of arc furnaces: a new frequency domain approach," in Harmonics and Quality of Power, 1998. Proceedings. 8th International Conference on, 1998, pp. 1071-1078 vol.2. [5] N. G. Bliss, et al., "Neural networks for the high voltage EAF," in Fifth European Electric Steel Congress, Paris, 1995, pp. 240-247. [6] R. F. Burch, "Thoughts on improving the electric arc furnace model," in Power and Energy Society General Meeting Conversion and Delivery of Electrical Energy in the 21st Century, 2008 IEEE2008, pp. 1-5 [7] F. Chen, et al., "Function space valued Markov model for electric arc furnace," Power Systems, IEEE Transactions on, vol. 19, pp. 826-833, 2004 [8] W. Fenghua, et al., "Modeling the DC electric arc furnace based on chaos theory and neural network," in Power Engineering Society General Meeting, 2005. IEEE, 2005, pp. 2503-2508 Vol. 3.
[9] Go, et al., "A New Field-Data-Based EAF Model for Power Quality Studies," Industry Applications, IEEE Transactions on, vol. 46, pp. 1230-1242, 2010. [10] R. Horton, et al., "A Time-Domain AC Electric Arc Furnace Model for Flicker Planning Studies," Power Delivery, IEEE Transactions on, vol. 24, pp. 1450- 1457, 2009. [11] H. Mokhtari and M. Hejri, "A new three phase timedomain model for electric arc furnaces using MATLAB," in Transmission and Distribution Conference and Exhibition 2002: Asia Pacific. IEEE/PES, 2002, pp. 2078-2083 vol.3 [12] A. R. Sadeghian and J. D. Lavers, "Application of adaptive fuzzy logic systems to model electric arc furnaces," in Fuzzy Information [13] J. G. Mayordomo, et al., "A new frequency domain arc furnace model for iterative harmonic analysis," Power Delivery, IEEE Transactions on, vol. 12, pp. 1771-1778, 1997. [14] L. W. White and S. Bhattacharya, "A single phase PSCad electric arc furnace model," in IECON 2012 - 38th Annual Conference on IEEE Industrial Electronics Society, 2012, pp. 5352-5356 [15] Go, et al., "A New Field-Data-Based EAF Model for Power Quality Studies," Industry Applications, IEEE Transactions on, vol. 46, pp. 1230-1242, 2010. [16] R.M. Mathur and R. K. Varma, "Thyristor-Based FACTS Controllers For Electrical Transmission Systems", IEEE Press [17] ABB, "Static Var Compensator, The key to better arc furnace economy" available online at: http://www05.abb.com/global/scot/scot221.nsf/veritydisplay/6 c4608703c0e7760832577bb004faee9/$file/A020102%20E.pdf, [18] PSCAD version 4.2.1. Winnipeg, Manitoba, Canada: Manatoba HVDC Research Centre, 2006 [19] FORTRAN 95 version 5.40. Rochester Hills, Michigan: Absoft Corporation, 1998
