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TRANSCRIPT
TRANSACTIONS
ON ELECTRICAL ENGINEERING
ERGO NOMEN
CONTENTS
Aleisawee Alsseid, Abdulrahman Emhemed, Alhade Algitta.:
DC Network Model Based on VSC-HVDC System . . . . . . . .
55 – 62
Gric, P.: Protection against the Effects of the Asynchronous
Operation of Synchronous Motors Based on the Principle of
Comparison of the Machine Power Factor . . . . . . . . . . . .
63 – 67
Pavelka, J., Šimek, J., Kobrle, P., Kokeš, P.: The Cause of
Mechanical Vibration of Palasher Synchronous Motors and its
Removal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
68 – 73
Vol. 8 (2019) No. 4 pp. 55 – 73
TRANSACTIONS ON ELECTRICAL ENGINEERING
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Transactions on Electrical Engineering, Vol. 8 (2019), No. 4 55
TELEN2019012 DOI 10.14311/TEE.2019.4.055
DC Network Model Based on VSC-HVDC
System
Aleisawee Alsseid 1), Abdulrahman Emhemed 2) and Alhade Algitta 3) 1) 3) College of Electronic Technology – Bani Walid, 38645 Bani Walid, Libya
2) College of Technical Sciences – Bani Walid, Libya, e-mail: [email protected]
Abstract — The recent developments in high power rated
Voltage Source Converters (VSCs) and the control strategies
have resulted in their successful application in HVDC
transmission systems, which have become an attractive
option for renewable energy applications or for distribution
power in large metropolitan areas. A 153th order multiple-
input multiple-output (MIMO) small-signal model of DC
network model based on VSC-HVDC system and controls is
developed in state-space form within MATLAB. The
optimum values of the controller gains are selected by
analyzing the root locus of the analytical model. The
developed small-signal detailed models are linearized and
implemented in MATLAB. The validity and accuracy of the
proposed models are verified against nonlinear PSCAD/
EMTDC and a summary of the model structure and controls
is presented in detailed. Confirmation of the effectiveness of
optimization gains is done by simulating the modelled system
in MATLAB and PSCAD software. There simulation results
performed with very good matching is confirmed in the time
domain. It is the most detailed model currently available.
Keywords – DC network model, voltage source converter,
high voltage direct current, DC voltage control, modelling multi
terminal VSC HVDC.
I. INTRODUCTION
High-Voltage Direct Current (HVDC) technology has been implemented in several places around the world particularly through the last six decades. From the historical point of view, HVDC technology first made its mark in the early subsea cable interconnections of Gotland (1954) and Sardinia (1967), and then for long distance transmission with the Pacific Intertie (1970) and Nelson River (1973) [1]. The application of high voltage (HVDC) transmission for integrating large scale and/or off-shore wind generation systems with the electric grid is attractive in comparison to extra high voltage (EHV) AC transmission systems due to a variety of reasons. HVDC is often the economic means for delivering power over long distances and/or for interconnecting two nonsynchronised AC networks, which may operate at different frequencies [2]. HVDC has better properties with underground/subsea cable transmission. The increasing use of HVDC transmission has made it as a competitive alternative for AC transmission. Due to social and political resistance, it has become very difficult to construct new overhead lines. Moreover, the overhead lines have significant environmental impact on areas such as land, water, vegetation, and cultural heritage [3]. The voltage source converter based High Voltage Direct Current (VSC-HVDC) technology, also named as HVDC light, is a new invention of HVDC transmission technology which uses self-commutated converters and DC power
transmission to interconnect two or more transmission networks. In contrast to the traditional thyristor based HVDC system, the VSC-HVDC system has many features such as: the ability to independently control active and reactive power flows at its terminal; the option to control its terminal bus voltage; and the potential to be connected to a very weak AC system. The main advantages of VSC power transmission are the high controllability and the possibility to make connections in or between networks by low weight extruded cables [4, 5, 6]. Voltage Source Converter based HVDC (VSC-HVDC) has attracted significant interest since the development of high speed, high voltage switches which enable the advantages of VSC-HVDC to be exploited commercially [7, 8]. These features make VSC transmission attractive in many applications like the emerging interconnections required by renewable energy sources [9]. With the benefits of the performance of DC links being recognised, interest is growing in extending existing HVDC links into multi-terminal HVDC systems [10]. The availability of ±300 kV DC enables VSC-HVDC system to transmit large amounts of power over long distances. Under restrictions in right-of-way, the VSC-HVDC system provides a solution for adding new transmission lines. VSC-HVDC will continue to provide solutions for many challenging issues associated with the modern deregulated power systems such as distributed power generation, power market, feeding remote isolated loads or city centers [11, 12]. VSC also has some disadvantages such as its high power losses and high capital costs compared with conventional HVDC. One of the key features of HVDC is through the opportunity to use underground DC cable which has a great advantage in comparison with overhead lines. The overhead lines change the landscape and constructions of new lines are often met by public resistance. Furthermore, HVDC cables also have lower losses than AC cables. The DC cables are used where overhead lines are unsuitable and due to environmental impacts or land use considerations, such as in high-density urban areas or ecologically sensitive areas. From an environmental point of view, the DC-cable technology has many advantages such as no alternating magnetic field and no risk for oil leakage [13] and is designed to be environmentally friendly [14]. In addition, HVDC cable system does not face the distance limitations or suffer the higher losses of AC cable systems. Extruded HVDC cables are lighter, more flexible, and easier to splice than the mass-impregnated, oil-paper cables (MIND) used for conventional HVDC transmission, thus making them more advantageous for land cable applications. The lower cost cable installations made possible by the extruded HVDC cables makes long-distance underground transmission economically feasible for use [13, 14]. Therefore, HVDC
Transactions on Electrical Engineering, Vol. 8 (2019), No. 4 56
TELEN2019012 DOI 10.14311/TEE.2019.4.055
systems increase the transmission capacity and system stability very efficiently and assist in prevention of cascading disturbances [15]. A multi-terminal HVDC transmission (M-HVDC-VSC) is an HVDC system with more than two converter stations. M-VSC-HVDC has the possibility of being an attractive alternative to AC transmission in city centers where underground cable transmission is preferred for safety and environmental reasons [16]. The M-VSC-HVDC system can be used for wind power integration [17], for urban area interconnection [18], the location and isolation of DC faults [19], and for power quality enhancement [20] are reported in the literature. A multiterminal VSC-HVDC system is economically competitive and technically practicable thereby increasing the scope of application of HVDC 1inks. The M-HVDC-VSC transmission is more complex than two terminal HVDC transmission systems. In particular, the control system is more complicated. The central cause of difficulty in modelling of M-VSC-HVDC systems can be review as: Higher order system, Discontinuous and non-linear nature of signal transfer through converters, Complexity of interaction equations between AC and DC variables, and Frequency conversion through AC-DC converters. However, such studies have been limited and further researches are required to fully exploit M-VSC-HVDC system capability. This paper presents a detailed analytical model for a multiterminal HVDC and uses this model to study system control under a range of operating conditions. A d-axis current control and a DC voltage droop control are implemented in the M-VSC-HVDC control system. The dynamics of the system are investigated and compared when the two different schemes are used. The detailed small-signal model of DC network model based on VSC-HVDC system and main control strategies is described and developed in MATLAB. A five terminal M-VSC-HVDC was modeled in PSCAD and its operation was investigation. Results obtained from simulation study on an M-VSC-HVDC test system using PSCAD /EMTDC are presented to verify the theoretical analytical model and the proposed control strategies. The M-VSC-HVDC systems in this research are based exclusively on voltage source converters. The model consists of five converters (VSC1- VSC5) systems, two sending AC systems (main grid), and three equivalent receiving AC systems. The detail model of the studied network is shown in Fig. 1 in Appendix.
Three terminals (T2, T3, and T4) are connected to different points in the receiving AC grid (large city). Each system has it is own equivalent impedance and Short-Circuit-Ratio. A Δ-Y transformer is connected with its corresponding impedance to each terminal. Terminal T2 is linked with terminal T1 by DC cable at length of 300 km the later is connected to receiving end AC2 system. Similarly, terminal T4 is tied with terminal T5 by DC cable at length of 200 km then connected to receiving end AC3 system. To ensure security of supply and reliability the voltage-source converter at terminal T3 is arranged in a ring and connected by a DC cable with (T2, T3) at length of 60 km and 40 km and (T5-T1) at length of 200 km. VSC multi-terminal HVDC (M-VSC-HVDC) systems, which consist of more than two voltage source converter stations connected together through DC cable to form a DC ring, can increase the flexibility and reliability of transmission systems. In such kind of configuration the faulted section can be isolated from the rest of network without disconnected any converter station. Therefore, power
continuously could be supplied to the connected parts of the DC network.
II. VSC-HVDC CONVERTER CONTROL
The control strategy of the VSC-HVDC is based upon a simplified mathematical model of the converter connected to the system as depicted in Fig. 2 in Appendix. An extended Park’s transformation [21, 22] is used to
transform the electrical variables from the abc reference frame into a synchronous rotating dq reference frame. The advantage of this transformation is that the controllable electrical variables are now DC values. This feature is useful for design, analysis, and for decoupled control of the two AC dq current components. The balanced three-phase system can be transformed into synchronously-rotating orthogonal system by applying Park’s transformation. The d-axis of the AC current component contributes to the instantaneous active power P(t) and the q-axis is always in quadrature with it, and represents the instantaneous reactive power Q(t). The overall test system of the VSC-HVDC converter control, using PID control method is depicted in Fig. 2 Appendix. For a multiterminal M-VSC-HVDC one converter is usually used to control the DC voltage. Terminal one (VSCT1) it has the role of providing controlled DC voltage [23, 24], the other terminals control their DC current/power [25]. The proposed control strategy consists of an outer control loops and an inner current control loops. Two inner fast proportional-integrator differential (PID) controllers ensure that the converter currents are bounded under all conditions. In the inner current control loops decoupled current compensation and voltage feed-forward compensation is adopted. The outer controllers include the DC voltage controller, the AC voltage controller and the DC current/power controller. Proportional-Integrator (PI) regulators are implemented in all these outer controllers to eliminate the steady state errors and generate a reference value for the inner. The choice among these different kinds of controllers to provide the reference values of the converter current will depend on the application. The output of the control system (MT1d, MT1q), after transformation, into magnitude (Mm) and phase shift (Mφ) represent the reference voltages for the pulse-width modulation (PWM). The phase looked loop is used to synchronised the converter firing angles with the AC system. PLL is currently in use in HVDC schemes worldwide and the latest type of PLL is D-Q-Z. The derivation of the PLL linearized model is obtained from [26].
A. AC Voltage Control
The equations describing the AC circuit linking the VSCT1 and ACT1-M stated in a dq reference frame synchronously rotating with the PCC AC voltage vector (VACT1) are:
DCdTqACTTdATTCdATdACTACT vmiLiRvi
dt
dL 11111111
2
1 (1)
DCqTdACTTqACTTqACTqACTACT vmiLiRvi
dt
dL 11111111
2
1 (2)
(3) 2
3
2
3
11111
11111
qACTdACTdACTqACTACT
qACTqACTdACTdACTACT
ivivQ
ivivP
(3)
Transactions on Electrical Engineering, Vol. 8 (2019), No. 4 57
TELEN2019012 DOI 10.14311/TEE.2019.4.055
where vDC is the DC voltage at VSCT1, RT1 represents converter losses, LT1 is transformer leakage inductance, iACT1d, and iACT1q are AC dq current components at ACT1-
M, is the frequency of the AC system and PACT1/QACT1 is the active and reactive power at the PCC bus. The VSCT1 reference frame is orientated with the VACT1 voltage vector employing a Phase Locked Loop, such that vACT1q = 0, and vACT1d = |VACT1|. Accordingly, the active and reactive power is controlled by independently controlling the AC current vector components using modulation control signals (MT1d, MT1q).
B. DC Voltage Control
In a VSC based HVDC system, the function of the DC voltage controller is to generate a DC voltage reference of the DC network and controlling the DC voltage to ensure that the power balance is satisfied. The DC voltage controllers adopt PI control to regulate the DC voltage. The output of DC voltage control is the active current (iACT1dref).
C. Converter Model
Linking between DC and AC voltages is achieved with the following linearised fundamental converter equations either at VSCT1 or VSCT2 [27]:
dTDCRDCTdTdACT MvvMV 1
0
11
0
12
1
2
1 (4)
qTDCTDCTqTqACT MvvMV 1!
0
11
0
12
1
2
1 (5)
Linking between AC and DC converter currents is similarly achieved by combining fundamental converter voltage equations, with AC/DC power balance equations, giving:
qACTqT
DCT
dACTdT
DCT
qTqACT
DCT
TdACT
DCT
DCT
IMC
IMC
MIC
MIC
Id
11
0
1
11
0
1
11
0
1
11
0
1
1
1
4
31
4
3
1
4
31
4
3
(6)
III. ANALYTICAL MODEL STRUCTURE
A 153rd order multiple-input multiple-output (MIMO) small-signal model of the VSC-M-HVDC system and controls Fig. 3 Appendix is developed in state-space form within MATLAB. It consists of the following three interlinked sub-system state-space models; AC system model terminal one (6th order), DC system model including (DC-cable, Control system, and PLL models), (123rd order) and AC system model terminal two (6th order). The two terminal VSC-HVDC model which includes AC models (ACT2 and ACT1), DC model and control configurations and the dynamics of the PLL are depicted in Fig. 3 Appendix in the form of block diagrams in order to highlight the interaction between subsystems. It shows the input signals that are entering into the DC model in addition to the output signal that is transferred into AC systems from the DC system model. The coupling between the respective sub-systems is achieved using selected variables, with d and q denoting the respective vector components. The input and output variables of the sub-systems are conditioned using linking matrices (LDCT1, LDCT2, PACT1, PACT2) that are developed using converter fundamental frequency modeling equations (4)–(6) [27]. Additional coupling matrices provide the measured and reference variables
required by the respective controllers. The state-space model of VSC-HVDC is written in standard matrix form as:
refrefss
refrefss
ux
ux
DCY
BAx
s
s
(7)
where the system matrix (As) incorporates the sub-
system and linking matrices, and the input/output vectors
(uref /Yref) are:
1111
2222
1212122
0
0
ACdqTDCTDCTACT
ACdqTDCTDCTACT
dqACTACTDCTdqACTACTDCTDCT
s
ACLB
ACLB
CPBCPBA
x (8)
refDCT
refACT
refACT
refDCT
ref
I
V
V
V
2
1
2
2
u, and
2
1
2
2
DCT
ACT
DCT
ACT
s
I
V
V
V
Y (9)
IV. CONTROLLER OPTIMIZATION
A. The Inner Fast Control Loops
The fastest current controllers can be designed using the differential equations for the converter in the d-q reference frame. The closed loop transfer function of the inner control loop can be derived. The resultant feedback loop is compared with the standard second order system. Using (1), and assuming fast DC voltage control (VDC = const), we derive the control signal MdT1 to include the PID control signal MdT1and decoupling compensation as:
DC
qACTTdT
dTv
ILMM
111
1 2
(10)
Substitution of (10) into (1) and re-arranging gives:
sT
k
sLRM
I
TTdT
dACT
11
1 1
111
1
(11)
where k1 = 1/RT1 and T1 = LT1/RT1. Consequently, a proportional gain (Kp), integral gain (Ki), and differential gain (Kd with time constant Td) controller combines in a feedback loop to give a second-order system:
pddpLSMddT
pddp
dACrefT
dACT
kskTKLLsTL
ksksTK
i
i
2
11
1)( (12)
Considering desired speed of response around 50 ms, and damping ratio = 0.7, the parameters Kp, Td and kd can be computed. A small integral gain Ki is also included to eliminate steady-state error caused by non-zero stator resistance RT1. The q-axis controller is designed in same manner using (2). The final controller gains are given in the Appendix.
B. The Outer Controllers
The response of the system depends upon the interaction of the outer loop controllers with the subsystems so the PI controller parameters cannot be calculated on their own. The model has four outer-loop controllers that monitor the following variables (VACT1, VDCT1, VACT2, and IDCT2). Identification of optimum PI zero location for outer-loop controllers is carried out using the root locus technique with the MATLAB model, where the location of the real poles
Transactions on Electrical Engineering, Vol. 8 (2019), No. 4 58
TELEN2019012 DOI 10.14311/TEE.2019.4.055
and the damping of the complex poles of the modelled system can be specified. In order to identify the optimized gains three designated zero locations are chosen and their influence on system behavior is investigated. Confirmation of the effectiveness of optimization gains is done by simulating the modelled system in MATLAB and PSCAD.
C. Design of PI Controller
There are two parameters for each outer-control-loop
Proportional gain Kp and integral gain Ki that can be
specified for a desired performance.
)/()( sKKKsG iPoPI (13)
Or, equivalently,
s
zsKK
s
KKKsKKsG Po
Poi
PoPI
/)( (14)
where the zero z = −Ki /KoKp which represent the controller zero and Ko is the open-loop gain.
The problem of tuning the controller parameters for a specific desired performance can be described as follows: find out the gains Ko, Kp and place the zero such that the modelled system satisfies the required performance criteria. The explanation to this task can be established with the aim of the root-locus technique and by using the participation factor. Initially, there are four outer loop controllers that monitor the following variables (VACT1, VDCT1, VACT2, and IDCT2) at both terminals sending and receiving ends.
The design procedure is iterative; therefore the locus in one diagram is dependent on the previous selection in the other loops. To achieve a satisfactory performance of designed controller for both schemes, the zero location for each individual sub-system is investigated for three different values. After the identification of zero location of the modeled system, the performance of the developed controllers can be investigated in the time-domain. The zero is firstly located close to the dominant real pole and then the gain is varied using root locus.
Fig. 4. DC voltage control PI gain (KPdcT1, KIDCT1) optimization
(SCRT1=10).
Fig. 4a shows the root locus for DC voltage at terminal one, where Ko is varied between [0, 0.4] as marked by an asterisk () and diamond () with fixed nominal system configuration.
The design in Fig. 4a is also iterative, since the locus in one figure is dependent on the prior selections in the other loop. It shown that, as the open-loop gain increase the closed loop poles will get closer to the imaginary axis as presented in Fig. 4a. Therefore, the control system performance will have the worse relative stability margins as the gain increased. A 5% step response is applied on the reference value of VDCT1 in order to evaluate the control system performance as presented in Fig. 4b. Thus, varying Ko with keeping all other parameters constant is causing significant changes in speed and quality of system step response. The best performance is clearly confirmed in time domain response with respect to the selected eigenvalues Fig. 4a. Hence the achieved speed of the response is almost below 50 ms.
V. MODEL VALIDATION
In order to validate the analytical models against the detailed non-linear PSCAD/EMTDC (PSCAD1) and the simplified non linear PSCAD/EMTDC test system model (PSCAD 2) and to assess their accuracy, their performance is compared by conducting small-signal step tests in the detailed time-domain simulations on each of the analytical model external inputs of both sending and receiving ends. Fig. 5 shows the comparison between the linear small-signal model and PSCAD models. A set of figures are presented for the applied step input in order to confirm the validity of the modeling system. Fig. 5a – 5d show the response signals of the following variables at VSCT1 VACT1ref, VDC0T1, IdT1, IqT1 whereas Fig. 5e – 5h are illustrating the response signals of the following variables at VSCT2 VAC0T2, IDC0T2, IdT2, IqT2 respectively. The detailed PSCAD1 model responses exhibit greater noise content, and there is pronounced non-linear behaviour. The high noise content is attributed to the low switching frequency and also as a significance of the optimized value for the DC capacitors. However with use of the simplified PSCAD model it can be clearly appreciated from Fig. 5 that, despite significant linearization and continuous power converter system modelling, the analytical model demonstrates very good small signal accuracy. The results for a step change in AC voltage reference VACrefT1 are shown in Fig. 5a. The behavior of test system where the step change is applied is almost identical for both models. The reaction of the DC voltage to the applied step change is shown in Figure 5b. There is a very good correspondence between the models. The dq-axis current components at terminal one are shown in Fig. 5c – 5d. The response matching in those figures were also confirmed and found to be very good agreement. Fig. 5e illustrated the corresponding dynamic interaction on the AC voltage at terminal two VACT2. As it is illustrated in Fig. 5f the DC current controller behaves well, tracking the reference with accuracy, very good agreement is achieved. The dq-axis current components at terminal two are shown in Fig. 5f and 5h the same conclusion is observed as obtained from Fig. 5c and 5d. Accurate and fast regulation of monitored variables VACrefT2, VDC0T2, VAC0T2, and IDC0T2 is achieved in Fig. 5a, 5b, 5e and 5f respectively and the multivariable properties of the system (control interactions) are also modeled accurately.
-100 -80 -60 -40 -20 0-200
-100
0
100
200
Im
Re
Gain Increase
Selected eigenvalues
0 0.05 0.1 0.15 0.2 0.25300
309
318
327
Vd
cT
1 [
KV
]
Time [s]
O
O
Max. gain
Selected gain
)a
)b
Transactions on Electrical Engineering, Vol. 8 (2019), No. 4 59
TELEN2019012 DOI 10.14311/TEE.2019.4.055
Fig. 5. Analytical model verification strategy 1, following a – 10 % AC voltage reference step change (VACT1ref):
a ) AC voltage (VACT1ref), b) DC voltage (VDCT1),
c ) Direct current (IACT1d),d) Quadrature current (IACT1q), e ) AC voltage (VACT2), f) DC current (IDCT2),
g ) Direct current (IACT2d), h) Quadrature current (IACT2q).
VI. CONCLUSIONS
A test system of DC grid network is developed in PSCAD. A detailed and accurate analytical model of DC grid is presented in this paper. The dynamic analytical state-space model is built of subsystems to enable model application to a wide range of MIMO system dynamics investigation. The derived detailed models are linearized and implemented in MATLAB. The validity and accuracy of the proposed models are verified against non linear PSCAD simulations, and very good matching is confirmed in the time domain. It is the most detailed model currently available.
ACKNOWLEDGEMENTS
The author gratefully acknowledge support from professor D. Jovcic, School of Engineering, University of Aberdeen, Aberdeen.UK.
REFERENCES
[1] Prabha Kundur, Power System Stability and Control. McGraw-Hill, 1994.
[2] X.-P. Zhang, “Comprehensive modeling of the unified power flow controller for power system control,” Electrical Engineering, vol. 88, no. 4, pp. 241-246, April 2006.
https://doi.org/10.1007/s00202-004-0280-0
[3] Stijn Cole, Dirk Van, Leonardo Meeus, and Ronnie Belmans, “Technical development of the Future Transmission Grid”, in Power Engineering Society General Meeting, 2007. 24-28 June 2007, pp. 1-6.
[4] B. Jacobson, Y. J Iang-Hafner, P. Rey, and G. Aspund, “HVDC With Voltage Source Convectors and Extruded Cables for up to ±300 kV and 1000 MW,” B4-105, CIGRE 2006.
[5] G. Asplund, K. Eriksson, and H. Jiang, “DC transmission based on voltage source converters,” in Cigre Conference 14-302, France, 1998.
[6] N. Flourentzou, V. G. Agelidis, and G. D. Demetriades, “VSC-based HVDC power transmission systems: An overview,” IEEE Trans. Power Electronics, vol. 24, no. 3, pp. 592-602, 2009.
https://doi.org/10.1109/TPEL.2008.2008441
[7] K. Eriksson, “HVDC light and development of voltage source converters,” ABB review, 2002.
[8] F. Schettler, H. Huang, and N. Christl, “HVDC transmission using voltage sourced converters – Design and Applications,” in IEEE summer power meeting 2000, Seattle, July 2000.
[9] Lars Weimers, “HVDC Light – a new technology for a better environment,” IEEE Power Engineering Review, pp. 19-20, August 1998. https://doi.org/10.1109/MPER.1998.691411
[10] P. C. S. Krishnayya, S. Lefebvre, V. K. Sood, and N. J. Balu, “Simulator study of multiterminal HVDC system with small parallel tap and weak AC systems”, IEEE Trans. on Power Apparatus and Systems, no. 10, pp 3125-3132, October 1984.
https://doi.org/10.1109/TPAS.1984.318334
[11] Mojtaba Noroozian, Abdel-Aty Edrise, David Kidd, and Abrt J.F.Keri, “The Potential Use of Voltage-Sourced Convector-Based Back-to-Back Tie in Load Restorations,” IEEE Trans. On Power Delivery, vol.18, no.4, pp. 1416-1421, October 2003.
https://doi.org/10.1109/TPWRD.2003.817777
[12] K. R. Padiyar, Nagesh Prabhu, “Modeling, Control design and Analysis of VSC based HVDC Transmission Systems”, in International Conference on Power System Technology-POWERCON 2004, 21-24 November 2004. Singapore, pp.1351-1355.
[13] L. Weimers, “New markets need new technology,” in Proc. of 2000 International Conference on Power System Technology, vol. 2, Perth, Australia, pp. 873-877, December 2000.
[14] K. Eriksson, “Operational experience of HVDC Light,” in Seventh International Conference on AC-DC Power Transmission, London, U.K., November 2001. https://doi.org/10.1049/cp:20010543
[15] M. Bahrman and B. Johnson, “The ABCs of HVDC Transmission Technology,” IEEE Power Energy Magazine, Vol. 5, pp. 32-44, March/April 2007. https://doi.org/10.1109/MPAE.2007.329194
[16] Xiao-Ping Zhang, “Multi-terminal voltage-sourced converter-based HVDC models for power flow analysis,” IEEE Transactions on Power Systems, vol. 19, issue 4, pp.1877-1884, Nov. 2004.
https://doi.org/10.1109/TPWRS.2004.836250
[17] W. Lu and B.-T. Ooi, “Optimal acquisition and aggregation of offshore wind power by multiterminal voltage-source HVDC,” IEEE Trans. Power Delivery, vol. 18, no. 1, pp. 201-206, January 2003.
https://doi.org/10.1109/TPWRD.2002.803826
[18] H. Jiang and A. Ekstrom, “Multiterminal HVDC systems in urban areas of large cities,” IEEE Trans. Power Delivery, vol. 13, no. 4, pp. 1278-1284, October 1998. https://doi.org/10.1109/61.714496
[19] L. Tang and B. Ooi, “Location and Isolating DC Faults in Multi-terminal DC Systems,” IEEE Trans. Power Delivery, vol. 22, no. 3, pp. 1877-1884, 2007. https://doi.org/10.1109/TPWRD.2007.899276
[20] W. Lu and B. Ooi, “Premium quality power park based on multi-terminal HVDC,” IEEE Trans. Power Delivery, vol. 20, no. 2, pp. 978-983, April 2005. https://doi.org/10.1109/TPWRD.2004.838633
[21] I. Papic, P. Zunko, D. Povh, and M. Weinhold, “Basic control of unified power flow controller,” IEEE Trans. Power System, vol. 12, pp. 1734-1739, Nov. 1997. https://doi.org/10.1109/59.627884
[22] C. Schauder and M. Mehta, “Vector analysis and control of advanced static VAR compensators,” IEE Proceedings - Generation, Transmission and Distribution, 140(4), July 1993.
https://doi.org/10.1049/ip-c.1993.0044
[23] Weixing Lu and Boon-Teck Ooi, “DC Overvoltage control during loss of converter in multi-terminal voltage-source converter-based HVDC (M-VSC-HVDC),” IEEE Transactions on Power Delivery, vol. 18, issue 3, pp.915-920, July 2003.
https://doi.org/10.1109/TPWRD.2003.813888
[24] B R Andersen, L Xu, and K T G Wong, “Topologies for VSC transmission,” Seventh International Conference on AC-DC Power Transmission (IEE Conf. Pub. No.485). IEE, 2001 London, UK, pp. 298-304. https://doi.org/10.1049/cp:20010559
195
205
215
225
Vacre
fT1 [
KV
]
265
285
305
325
Vdc0T
1 [
KV
]
-1.5
-1.3
-1.1
-0.9
IdT
1 [
KA
]
0 0.05 0.1 0.15 0.2 0.25-2.2
-1.2
-0.2
0.8
IqT
1 [
KA
]
Time [s]
107
110
113
Vac0T
2 [
KV
]0.95
1
1.05
Idc0T
2 [
KA
]
0 0.05 0.1 0.15 0.2 0.25-0.4
-0.2
0
0.2
IqT
2 [
KA
]
Time [s]
1.8
2
2.2
2.4Id
T2 [
KA
]
a)
b)
c)
d)
e)
f)
g)
h)
PSCAD1
MATLAB
PSCAD2
PSCAD1
MATLAB
PSCAD2PSCAD1
PSCAD1
PSCAD2MATLAB
Ref
Ref
PSCAD1
PSCAD2
MATLAB
PSCAD1
MATLAB
PSCAD2Ref
Ref PSCAD1MATLAB
PSCAD2
MATLAB
PSCAD2
PSCAD1MATLABPSCAD2
Transactions on Electrical Engineering, Vol. 8 (2019), No. 4 60
TELEN2019012 DOI 10.14311/TEE.2019.4.055
[25] D. Jovcic, “Interconnecting Offshore Wind Farms Using Multiterminal VSC-based HVDC,” IEEE PES general meeting, Montreal, pp. 1-7, June 2006.
https://doi.org/10.1109/PES.2006.1709326
[26] D. Jovcic, Control of High Voltage DC and Flexible AC Transmission Systems. PhD Thesis, University of Auckland, New Zealand, December 1999.
[27] D. Jovcic, N. Pahalawaththa, and M. Zavahir, “Analytical modelling of HVDC-HVAC interactions,” IEEE Trans. Power Del., vol. 14, no. 2, pp. 506-511, Apr. 1999. https://doi.org/10.1109/61.754095
DC
-Lin
e 1, (T
1-T
2),
200 k
m
VSC2-T2
L ac2
R ac2
V ac2
110KV
AC
L
110 KV
+150KV C
VSC4-T4
L ac3
L ac4
R ac3
R ac4
VSC3-T3
R
R
L
VSC5-T5
CDCL2
C
V DCT2
CCC
CCCC
DCT2
L
R
R
L
Transformer-T2Transformer-T4
IDCT2
DCT2
DC2T3
DC2T2
DC2T3
DC2T2DCL2
V DCL2
DCT3 DCT3
V DCT3 IDCT3IDCT4V DCT4
DCT4DCT4
DC3T3
DC3T4
DC3T4
DC3T3
DCL3 DCL3
V DCL3
Transformer-T3e ac4
+150KV +150KV-150KV-150KV
-150KV
110 KV 110 KV
110 KV
300 MW300 MW300 MW
DC
-Lin
e 2, (T
1-T
2),
40 k
m
DC
-Lin
e 3, (T
1-T
2),
60 k
m
DC
-Lin
e 4
, (T
1-T
2),
60 k
m
DC-L 3 DC-L 2
Receiving
area
e ac3
e ac2
AC
+150KV-150KV
C
R ac5
L ac5
CC
C
V ac5
Transformer-T5
DC-L 4
R
R
L
L
DC4T4
DC4T5
DC4T5
DCL4
DCL4
V DCL4
DCT5DCT5
e ac5
110 KV
300 MW
Sending
area
AC
+150KV-150KV
R
R ac1
L
DC1T2
L
L ac1
C
DCL1C
CDCT1
C
VSC1-T1
V ac1
Transformer-T1
DC-L1
DC1T2
DC1T1
RDC1T1
DCL1
V DCL1
V DCT1
DCT1
e ac1
220 KV
600 MW
CDC_DCN
CDC_DCN
RDC_DCN
LDC_DCN L
DC_DCNR
DC_DCN
DC_DCNV
DC-Line 5, (T1-T5), 200 km
APPENDIX
Fig. 1. Detailed model of studied network.
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Fig. 2. Diagram circuit and overall control block of two stations of VSC-HVDC model.
Outer-loop controllers
AC voltage controller
+-+
4pk
ski /4
++-
qrefi
DC current controller
+-+5pk
ski /5++-
drefi
VDC
1
VDC
1
Inner-loop controllers
dqabc
Filter
dACTI
2
qACTI
2
2ACTV
refACTV 2
refDCTI 1
1DCTI
2aACTV2bACTV2cACTV
MM m
DQ
+ +dqabc PLLPLL
I
11LDCTL1TR 1TL
1TR 1TL
1TR 1TL
VSC
T1
VSC
T2
2TL
2TL
2TL2TR
2TRCDCT1
CDCL1
VDCL1
VDCT2
CDCT2
DCT2
12LDCTL
VDCT1
IDCT12TR
IcT1
IaT1
IbT1
IaT2
IbT2
IcT2
11LDCTR
eaT1
ecT1
bT1e
Outer-loop controllers
AC voltage controller
+-
+1pk
ski /1
++-
qrefi
DC voltage controller
+-
+2pk
ski /2++-
drefi
VDC
1
VDC
1
Inner-loop controllers
MM m
DQ+ +
PLL1aACTV
1bACTV
1cACTV
dqabc
1aTM1bTM
1cTM
Filter
Filter
dqabc
dACTI
1
Filter
PLL
PLL
1ACTV
refACTV 1
refDCTV 1
1DCTV
Filter
eaT2
bT2e
ecT2
2aTM2bTM 2cTM
Filter
Filter
Filter
T1dM
T1qM
T2qM
T2dM
12LDCTR
Schematic Controller of VSCT1
Schematic Controller of VSCT2
m
e
t
s
y
S
t
s
e
T
dACTI
2
dACTI
2
qACTI
2
qACTI
2
+-
+3pk
ski /3++
sT
sk
d
d
1 L
+-
+3pk
ski /3++
sT
sk
d
d
1 L
L+3pk
ski /3++
sT
sk
d
d
1
++
L+3pk
ski /3++
sT
sk
d
d
1
++
qACTI
1
dACTI
1
qACTI
1
qACTI
1
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Controller
Model
&PLL
Model
LinkingDC to AC
outputs
1DCTV
Linking AC to DC
ACT1 Model
inputs
outputs
dTV 1
qTV 1
dACTV 1
qACTV 1
dACTI 1
qACTI 1
dACTI 1
qACTI 1
dACTI 1
qACTI 1
DC Model
outputs
inputsinputs
VSCT1
Side
VSCT2
Side
outputs
1ACTV
1ACT
qTM 1
dTM 1
dTM 1
dTM 1
qTM 1
qTM 1
inputs
refDCTV 1
refACTV 1
1DCTV
1DCTV
dACTI 2
qACTI 2
2ACTV
2ACT
dTM 2
qTM 2
Linking AC to DC
ACT2 Model
inputs
outputs
dTV 2
qTV 2
LinkingDC to AC
2DCTV
dACTV 2
qACTV 2
dACTI 2
qACTI 2
Controller
Model
&PLL
Model
outputs
inputs
refACTV 2
DCTrefI2DCTI
dTM 2
qTM 2
dTM 2
qTM 2
Fig. 3. Schematic diagram of linking subsystems models.
Transactions on Electrical Engineering, Vol. 8 (2019), No. 4 63
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DOI 10.14311/TEE.2019.4.063
Protection against the Effects of the
Asynchronous Operation of Synchronous Motors
Based on the Principle of Comparison of the
Machine Power Factor
Petr Gric
PEG s.r.o., Praha, [email protected]
Abstract — This paper deals with the possibility of using
the principle of comparison of the operational power factor
for evaluation of the asynchronous operation of synchronous
motors. This way of definition of the asynchronous operation
is possible to use for motors protection and other protective
systems of drives with synchronous motors.
Keywords — synchronous motors, asynchronous operation,
power factor evaluation.
I. INTRODUCTION
Synchronous machines are used in many applications thanks to the defined rotor speed of synchronous machines to stator frequency and the possibility of control the reactive part of energy. Asynchronous operation is a nonstandard state when the rotor of a synchronous machine is not rotating synchronously with the rotating field of the stator. This state can occur when the machine is overloaded, the rotor is under exited, due to the fluctuation of power supply voltage or combination of these bearings. Long term asynchronous operation is an inadmissible state. Perhaps we could say an emergency state of synchronous machines.
II. ASYNCHRONOUS OPERATION
Start-up winding, so-called damper (amortisseur) winding, is the most strained part during asynchronous operation. Machine, especially rotor winding, can be permanently damaged during long term asynchronous operation. For example, the rotor rod can be unsoldered, or the couplings (screws) of the damper winding could be overheated and destroyed. These parts can consequently damage the stator winding of the synchronous machine.
The time that the synchronous motors can operate in asynchronous mode differs according to the nature of the load and construction of the machine. The rotors of the synchronous machines are designed for asynchronous start-up, so they are dimensioned for short term asynchronous operation. I have encountered a case where the synchronous drive of a mining ventilator with a power rating of 3250 kVA was working in an asynchronous mode approximately for 8 hours because of an excitation problem. The drive could not be shut down because of the safety of the miners. Only the power was reduced to approximately one-third of PN. After the drive was shut
down, the revision of the rotor and stator winding was made, but no adverse effect of the long-term operation was discovered.
On the other side, the synchronous motor of 4000 kW that drives the piston compressor was destroyed after 30 s of asynchronous operation at 0.75 Pn. The cause was a meltdown of a damper coupling and, consequently, the destruction of the stator winding.
Synchronous machines need to be protected against the consequences of the asynchronous operation due to the possibility of a crash.
The asynchronous operation of synchronous motor occurs, of course, during start-up when the motor is connected directly or indirectly through a start-up reactor to the power grid. After start-up to almost synchronous rotations (and short-circuit of start-up reactor), the excitation is connected, and the rotor is pulled to synchronous rotations. This procedure is considered for normal operation and the motor is designed for it. Rotor winding cannot be an open circuit during start-up. It must be short-circuited either directly or through a resistor or some other device that will limit the voltage inducted to the excitation winding during start-up. If the excitation is constant and the load is getting higher, than the machine goes to the inductive (under-excited) part of the operation area. With further increasing of the load (or decreasing of the excitation or a stator voltage), the inductive power factor is getting lower to the limit of stable operation of the machine. The limit is at cos φ lower than 0.5 ind. at machines with salient poles, and cos φ is less than one at machines with a cylindrical rotor. Copy of capability diagram of stability for synchronous generator with a cylindrical rotor with a power rating of 31 MVA is shown in Fig. 1. The operational limit can be seen in the inductive part under cos φ = 0.99, which practically excludes operation in under-excitation state with a nominal load. The operation in the over-excitation part is not dangerous for a synchronous machine, and it is only limited by the value of phase stator current that cannot be higher than IN. The value of the phase current is equal to the vector product of the real and imaginary part of the phase current.
𝐼𝑓 = 𝐼𝑎 + 𝐼𝑟
If – phase stator current of synchronous motor
𝐼𝑎 – the real part of phase current
𝐼𝑟 – the imaginary part of phase current
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At the listed values of cos φ, the machine falls out of
synchronism and rotor slip up for a pole span with regard
to the rotating magnetic field of the stator. This
phenomenon cyclically repeats, and asynchronous
operation occurs unless there is not a rise of excitation
current (e.g., due to the influence of under-excitation limit
of excitation source) or the power of the load is not
lowered.
This process is described in Fig. 2 and Fig. 3.
Fig. 1. Capability diagram of synchronous generator 31 MVA.
Fig. 2. Slip up for a pole span with regard to torque angle of the machine.
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Torque angles for each state of the machine (motor operation) are shown in Fig. 2.
δmin – torque angle for P = 0, Ibn and Un (idle operation, nominal excitation current), torque angle minimal
δ – operational torque angle, motor works at nominal load, operational value of excitation current and nominal stator voltage
δmax – maximal torque angle that corresponds to stability limit, when this angle is exceeded the magnetic bond is torn and the rotor slips up for a pole span
When the magnetic bond between the rotor and stator magnetic field is torn, the slip up occurs. It goes through a stage of instability (magnetic poles with the same polarity are repelled) back to the working area. If there is no change
either torque (the load torque does not change) or electrical (an increase of stator voltage, an increase of excitation current), the rotor will not hold in the working area and the slip-up cycle repeats itself.
Torque angle is proportional to the load, stator voltage and excitation current:
δ ~ Ib; P2, (Mz), Un
If we neglect linearity of waveforms, we could say that the same that holds for torque angle δ also holds for power factor (cos φ):
cos φ ~ Ib; P2, (Mz), Un
Fig. 3. Slip up for a pole span with regard to power factor of the machine.
Fig. 4. Comparison of waveforms of torque angle and power factor during slip up.
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The process of slip up in relation to the power factor is shown in Fig. 3.
cos φc lim – power factor for P = 0, Ibn a Un (idle operation, nominal excitation current), power factor has the lowest value in the capacitive area
cos φ – normal operation power factor, the motor works with nominal load, normal operation value of power factor and nominal stator voltage
cos φi lim – power factor that corresponds to the stability limit, has the lowest value in the inductive area. When this value is exceeded the magnetic bond is torn, and the rotor slips up for a pole span.
A comparison of the previously stated bonds between torque angle δ and power factor cos φ (with neglection of linearity and nonlinearity of both waveforms) is shown in figure 4.
In figure 5, the same process is shown at the circle diagram.
This diagram corresponds to the view on an analog meter for measurement of power factor with the electromagnetic system without directive torque estimating the power factor from line voltages L1, L2, L3 and phase current. The process of slip up for a pole span shown with bold arrow corresponds to the movement of a pointer of the meter. We can also observe the dynamics of the movement on the pointer where the transit through the unstable part is quick against the transit through the normal working part.
The principle of evaluation of asynchronous operation and design of the appropriate protection for the synchronous machine against this phenomenon is derived from the process described above.
The synchronous machines can be protected against the creation of the asynchronous operation and against the consequences of the asynchronous operation. The former is an operational matter and it is usually one of the functions of the excitation systems. If the machine is getting to the stability limit, we can prevent it by an increase of the stator
voltage, lower the load or increase the excitation current. The first two options are very difficult to implement, so the best option is to regulate the excitation current of the machine. This function has many names. It depends on the philosophy of the regulation and the manufacturer. In most cases, it is solved as a “limit of under-excitation,” so the parameter is the limit of the power factor.
This parameter can be changed based on the active machine load at advanced regulations, where is the need to use the power and current values of the machine fully. At some machines with low load due to the reluctance torque of the machine (machine with salient poles), the transfer to the synchronous operation will not happen even with zero excitement, so it is not necessary to limit the value of excitation current firmly set by the limit of under excitation.
Under excitation limits also protects the machine against sudden supply voltage drops, short term power shocks, and other transients. Some of the excitation systems can, for some limited time, increase the excitation current to approximately 1.5 Ibn when the machine may fall from synchronism. This short-term increase of excitation current makes it possible to contain the magnetic bond between the stator and the rotor.
III. PROTECTION AGAINST THE CONSEQUENCES OF THE
ASYNCHRONOUS OPERATION
Incorrectly (semantically), they are called “protection against the asynchronous operation.” However, these protections do not protect against the creation of asynchronous operation, but they protect only against consequences when it already happens.
These protections are always part of the electric protection of the machine, and their activation means that the drive is shutdown.
Most of these protections work on the impedance principle. Parameter for setting these protections is the reactance of the machine (per unit value of transverse reactance of the machine in excited state Xqsat to the nominal value of reactance of the machine).
The value of Xqsat is hard to obtain. One of the possibilities is prototype measurements and then change the settings based on the tests of the motor with protection.
Based on experiences, the protections, which function is based on the impedance principle (see above), do not work reliably, and they cannot be used for all types of synchronous machines. That is why I later describe the possibility of how to derive the asynchronous operation from the comparisons of the threshold limits power factor.
Based on a general slip up for a pole span that is described above, it is possible to uniquely define the asynchronous operation without the need to know the impedance, power, and construction parameters of the synchronous machine. Protection working on this principle will reliably evaluate asynchronous operation for every type of synchronous and powered machines.
Fig. 5. Circle diagram of a slip up for a pole span.
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IV. DESCRIPTION OF PROTECTION AGAINST THE EFFECT OF
THE ASYNCHRONOUS OPERATION
Protection against the effect of asynchronous operation must fulfill these requirements:
a) Reliability of operation
a. The protection must always turn off the machine at the failure events.
b. The protection cannot turn off the machine at normal operation or at transient that does not directly threaten the operation of the drive.
c. The protection must signalize fault warning messages and emergency states.
b) The protection must contain blocking circuits that ensure deactivation of the protection during start-up and turning off the drive.
c) It must have a diagnostic of the excitation state of the machine (over-excitement, under excitement, cos φ = 1).
d) It must have signalization of operational and faulty states.
a. The protection must signalize fault warning messages and emergency states.
b. It must signalize the actual operating area of the motor (over excited, under excited)
Ad a)
The principle of evaluating a fault state (asynchronous operation, so the slip up for a pole span) must ensure reliable identification of the fault state. It cannot react at the so-called swinging of the rotor (change of torque angle δ). On the other side, it must safely evaluate the slip up (loss of pole coherence). Reliability of operation of any component of regulation and control is the basic required attribute.
Ad b)
The synchronous machine is start-up by asynchronous method, so the protection must be disabled during the start until synchronization is completed.
Ad c), d)
The diagnostic of excitation state is suitable for both setting up protection and for maintenance and prophylactics of the protection. It is necessary to realize that the protection as a superior safety part must be regularly controlled, and revision must be done according to valid standards (ČSN in the Czech Republic) and operational regulations.
Also, it is necessary to visualize operational states (presence of voltage, blocking, unblocking, slip up, TRIP). The TRIP function must be signalized even after fault ends (memory with reset).
V. PROTECTION FUNCTIONALITY
The functionality principle is derived from machine behavior during slip up for a pole span. The value of power factor change from normal operation (capacitive) power factor through cos φ = 1 to inductive part and through cos φ = “0” (unstable state) go back to the capacitive area during slip up for a pole span (Figure 5). We can say for sure that if the actual power factor changed from inductive
area through limit state cos φI lim to unstable area cos φC lim ≥ cos φm ˄ cos φm ≤ cos φI lim (Figure 5 – area of instability) and from unstable area through limit state cos φC lim to capacitive area that this transient is slip up for a pole span and so it is asynchronous operation. This area is indicated in Figure 5 as an area of instability. The area of instability is an area where the motor cannot operate and gets through it to an over excited state – the area of capacitive cos φ.
cos φC lim – border of instability in capacitive state of the machine
cos φm – operational point – instantaneous power factor of the machine
cos φI lim – border of instability in inductive state of the machine
The limit values cos φC lim, and cos φI lim cannot be specified generally. They depend on machine construction (cylindrical rotor / salient pole rotor, number of poles, air gap, etc.), nominal values and active load.
Nevertheless, we can say that a magnetic bond is torn at a higher power factor at machines with cylindrical rotors than with salient rotors.
Cylindrical machines can slip up at power factor under 0.9 inductive. Machines with saline rotors have the stability limit at cos φ approx.. under 0.4 inductive.
The exact limits value definition is not so much important. If we use the algorithm described above, the definition of the asynchronous operation is safely defined. We can choose limit values that the machine cannot reach, e.g.:
cos φC lim = 0.4 cap. [-]
cos φI lim = 0,4 ind. [-]
Slip up for a pole span alone is not an emergency state for the machine. It is necessary to realize that most of the synchronous machines are constructed for asynchronous start-ups, so it must be designed for short-term asynchronous operation.
Generally, we can say that a limited number of slips in a specified time is not an emergency state for a machine. It is useful to use this fact for the design of machine protection with the possibility to set “n” possible slips in time “T.” With this, we eliminate unnecessary emergency shutdowns of drives during transients, short-term voltage drops, short-term overloads, and so.
VI. CONCLUSION
Asynchronous operation is a dangerous state of a synchronous machine. During asynchronous operation, the start-up (damping, amortisseur) winding can be damaged a stator winding can get overload by a current that leads to machine destruction.
The protections against asynchronous operation often works incorrectly and unreliable. Either they react in moments that are not dangerous for synchronous machines and cause unnecessary weaning of the drive or they do not respond at real asynchronous operation. It is necessary to set them up complicatedly (often not available parameters are needed), and it is difficult to test and do a revision.
The described detection principle of asynchronous operation clearly defines this state and it is possible to evaluate it reliably.
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The Cause of Mechanical Vibration of Palasher
Synchronous Motors and its Removal
Jiří Pavelka 1), Josef Šimek, Pavel Kobrle 1) and Petr Kokeš 2)
1) Czech Technical University in Prague, Faculty of Electrical Engineering, Department of Electric Drives and Traction,
Prague, Czech Republic, e-mail: {pavelka,kobrlpav}@fel.cvut.cz 2) The Czech Academy of Sciences, Institute of Thermomechanics, Department D 6 - Electrical Engineering and
Electrophysics, Prague, Czech Republic, e-mail: [email protected]
Abstract — The paper describes the procedure and the
result of the analysis of mechanical vibrations of mining
machines at the Palasher mine in the Russian Federation.
The cause of these vibrations was the change in the
magnitude of the magnetic flux in the air gap. The
simulations showed the possibility of eliminating these
changes in magnetic flux by injecting suitable voltages into
the stator windings. The implementation of this injection is
further described by torque variable component feed-direct
compensation. Finally, oscillography records are presented
before and after injection.
Keywords — mining machine, synchronous machine, indirect
frequency converter, Maxwell’s force, resonant frequency,
feedforward compensation, voltage injection.
I. INTRODUCTION
The Czech company ELEKTROTECHNIKA, a. s., (earlier ČKD Elektrotechnika, a. s.) is, besides other things, a long-term supplier of electric drives for high power hoisting (mining) machines. These are controlled drives with specific requirements for their design, implementation and control. The development of power electronics converters made it possible to replace the original supply of DC mining motors from rotating Ward Leonard sets with the supply from thyristor rectifiers and later to replace the DC motors with the synchronous motors supplied from high-voltage frequency converters with the voltage DC-links.
A hoist tower with an electric drive is a complex mechanical system whose natural vibration frequencies are dependent on its stiffness. These frequencies may be close to the resonant frequency occurring at some operating speed or at some speed during the start up or breaking when the machine remains there for a longer time. It may cause the unacceptable vibration of the hoist tower. [1] describes in detail the problem of mechanical oscillation of a 4 MW DC motor supplied from a thyristor rectifier. The paper contains an analysis of possible causes of this vibration and also the description of the implemented method leading to reducing the vibrations to the permissible limit.
This article is the English version of the Czech article [6]. It contains the description of the mechanical vibrations of the mining machines that are driven by the slow running synchronous motors 5T404-40H 1800kW, 6000V, speed 58 rpm, and 5T448-40H 5800kW, 6000V, speed 51 rpm in the mine Palasher in Russia. It also contains an analysis of the causes of the vibration, a proposal of the method of its elimination, the results of
simulation verification, and the results of the implementation of the proposed method on real drives in Palasher.
II. THE BASIC PARAMETERS OF THE DRIVES
IN THE PALASHER MINE
The Czech company ELEKTROTECHNIKA, a. s., supplied one electric drive for 1.8 MW hoisting machine and two electric drives for 5.8 MW hoisting machines in the Palasher mine in the Russian Federation to the company INCO Engineering, spol. s r.o.
The basic parameters of the 1.8 MW drive for the hoisting machine are the following:
- Slow running synchronous motor 5T404-40H 1 800 kW, 6 000 V, 186 A, speed 58 rpm, cos φ 1 from the company ČKD Kompresory, a. s. (now Howden ČKD Compressors, s. r. o.);
- Multilevel frequency converter 6 kV/6 kV, 50 Hz/19.33 Hz from the company ČKD Elektrotechnika, a. s. (now ELEKTROTECHNI-KA, a. s.);
- Control system EMADYN F from the company ČKD Elektrotechnika, a. s. that uses the system of the company Beckhoff for the superior control.
After the production at the end of 2013, the complete drive was tested in no-load operation in the test room of the company ČKD Kompresory, a. s. Already during the tests, the engine vibrated excessively when passing some speed.
Due to the fact that the motor was fastened to the temporary foundation of the test room and its rotor was on spare bearings, the solution of the problem of mechanical vibration was postponed until commissioning in the customer's mine. At the beginning of April 2016, speed tests of the drive were carried out in the Palasher mine. During the speed tests, the motor was assembled with traction wheels of the hoisting machine, but without ropes and has not yet concreted its foundation. During the acceleration and deceleration, the mining machine passed through two bands of mechanical resonance.
The basic parameters of the 5.8 MW drives for the hoisting machine are the following:
- Slow running synchronous motor 5T448-40H 5 800 kW, 6 000 V, 585 A, speed 51 rpm, cos φ 1 from the company ČKD Kompresory, a. s. (now Howden ČKD Compressors, s. r. o.);
- Multilevel frequency converter 6 kV/6 kV, 50 Hz/17 Hz from the company ČKD
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Elektrotechnika, a. s. (now ELEKTROTECHNI-KA, a. s.);
- Control system EMADYN F from the company ČKD Elektrotechnika, a. s. that uses the system of the company Beckhoff for the superior control.
Production of complete drives, their no-load tests in the testing room of the production company ČKD Kompresory, a. s. and commissioning in the Palasher mine took place only a few months after the commissioning of 1.8 MW drive, and the similar vibrations of the hoisting machines were found as well.
In April 2016, the technical director of ČKD Elektrotechnika, a. s. asked the authors of the paper [1] for the preparation of an analysis of the causes of this mechanical vibration, the determination of the drive component causing it and the submission of any proposal for how to eliminate the mechanical vibration. The authors of the paper [1] prepared such an analysis in the form of a technical report based on the received technical background and data and they submitted it in May 2016 as [2]. The proposed measure was elaborated in detail, supplemented and implemented by Ing. Kokeš from the Czech Academy of Sciences. At present, the drives of all hoisting machines are in full operation.
III. THE HYPOTHESIS OF THE CAUSE OF MECHANICAL
VIBRATION
The following paragraphs give a physical explanation of how the excitation force causing the vibration is originated.
Fig. 1 shows the oscillogram of 1.8 MW synchronous motor rundown from the rated speed to zero without being supplied from the frequency converter.
It is apparent from the record that mechanical vibration occurs at 9.28 rpm, i.e. 16 % of the nominal speed, and 18.54 rpm, i.e. 32 % of the nominal speed, during the rundown of the excited synchronous motor and when the stator current is zero. This eliminates the effect of the frequency converter that supplies the stator winding on this vibration. Another test showed that the vibration does not occur when the synchronous motor is not excited during the rundown. This implies that the cause of the vibration is the mechanical forces that occur in the air gap of the rotating excited rotor of the synchronous motor.
Fig. 1. Recorded oscillogram of the rundown of 1.8 MW excited motor;
speed (green), stator current (blue), excitation current (red).
A. Lorentz’s and Maxwell’s Power in the Air Gap
It is known from the theory of electrical machines that two forces are created in the air gap of any type of rotary electric machine:
a) Lorentz’s force FL, which acts on an electric conductor of length L moving at velocity v in a magnetic field B. The sum of all these forces creates an electromagnetic torque Te on the circumference of the air gap.
For a salient poles synchronous motor with an excitation winding:
e M a M δ aˆ ˆ ˆˆk kT I B S I , (1)
where kM is the constant of the motor, represents the
space vector of the magnetic flux, aI is the space vector
of the stator current, δB is the space vector of the
magnetic field in the air gap and S is the area through which passes the field lines of the magnetic field.
b) Maxwell's attractive FM force, which acts in the air gap between the pole extensions of the stator and rotor. The following can be written for it:
2
M δ
1
2F B S
, (2)
where μ is the permeability of the air.
It can be seen from the record in Fig. 1 that the oscillation occurs even at zero stator current Ia and therefore the Lorentz’s force can be unequivocally eliminated as the cause of the vibration. But what is the magnitude of Maxwell's attractive force in the air gap?
In salient poles synchronous motor with an excitation winding, the excitation (field) current controller determines its magnitude so that the magnetic field in the air gap Bδ is constant. The following applies:
f
δ
m
f IB
R
, (3)
where ff I is the magnetomotive force of the
excitation winding of one pole and Rm is the magnetic reluctance of the magnetic circuit of one pole.
Maxwell’s force of one pole to the stator FM is obtained by substituting (3) to (2). This power is always attractive.
In a synchronous motor with equally large air gaps between the poles and the stator bore surface, the forces of the opposite pole extensions are identical, the direction of their action is opposite in space, and therefore their sum is theoretically zero.
In fact, however, the position of the rotor axis relative to the stator has always a certain eccentricity, which is the result of inaccurate positioning of the rotor in the center of the stator bore and deflection of the rotor due to its weight. This eccentricity causes the force ΔFM, which acts between the stator and the rotor in the direction of this eccentricity.
B. Influence of the Air Gap Size Variation on Force in the
Eccentricity Axis
Both 1.8 MW and 5.8 MW motors have the same number of stator slots Nd 240 and their rotors have the
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same number of poles 2p 40. Then the number of slots per pole Np is:
d
p
2406
2 40
NN
p (slots/pole). (4)
The stator of 1.8 MW synchronous motor has the bore Dvr 2 860 mm. The stator slot span τd is:
vr
d
d
2860 898537.44
240 240
D
N
(mm). (5)
The stator slot width is bd 18.4 mm and the slots are open. The ratio bd/τd 18.4/37.44 0.49 is therefore normal. The width of the pole extension bpn is 165 mm. Thus, under one pole extension there is a total of Npn slots:
pn
pn
d
1654.4
37.44
bN
(slots/pole ext.) (6)
Thus, when the rotor is rotating, the number of slots under the pole extension varies between four slots and five slots. This results in a periodic change of the magnetic reluctance Rmδ in the air gap due to the stator slotting, which is replaced by the sinusoidal waveform according to (7):
mδ mδ0 mδ dr1 k sin 2R R f t , (7)
where kmδ is the coefficient of the air gap varying due to the stator slotting and fdr is the slotting frequency.
At a constant magnetomotive force of the no-load excitation current F0, the fluctuation of the magnetic flux in the air gap Φδ will be described by:
0δ
mδ0 mδ dr
δ0 mδ dr
1 k sin 2
1 k sin 2
F
R f t
f t
. (8)
Substituting into (2) we get
2 222 δ δ0
M δ mδ dr
2mδ drδ0
2 2
mδ dr
Mpn0 mδ dr
11 k sin 2
2 2 2
1 2 1 k sin 2
2 k sin 2
1 2k sin
F B S f tS S
f t
S f t
F t
(9)
C. Determining the Frequency of the Forced Magnetic
Flux Variation
The change in magnetic reluctance is caused by changing the number of slots under the pole extension. In one revolution, this change occurs Nd times. Both types of motors have the same number of stator slots and the number of poles. Therefore, the relation between the supply frequency fs and the excitation frequency since the change of the magnetic flux fdr in both motors is the same:
d
dr s s s
24012
20
Nf f f f
p . (10)
For the operation of the hoist machine, it is important, that the mechanical resonance does not occur at the speed
at which the drive rotates for a longer time, or that the hoist machine or some of its parts must not inadmissibly vibrate when passing through the resonant zone during the start up or breaking.
IV. POSSIBILITIES TO ELIMINATE THE CAUSE OF THE
EXCITATION FORCE OF MECHANICAL VIBRATIONS
The actual cause of the excitation force is therefore the slotting on the internal diameter of the stator of the synchronous motor. Medium and large low-voltage electric rotary machines and all high-voltage electric rotary machines have in the stator open slots because of technological reasons, that concern the manufacturing of the winding. This causes a relatively large change in the magnetic reluctance of the air gap. Therefore, it is important that its magnitude, and especially the frequency, do not adversely affect the function of the entire mechanical system. It is known from the mechanics that every complex mechanical system has its resonant frequencies.
This results in the following options for reducing or eliminating the cause of the excitation force:
1. To select the fractional number of stator slots per pole per phase when designing the motor. As a result, the slot frequency and the excitation force frequency are shifted to a higher value outside the resonant frequencies of the mechanical system. However, this cannot be done on an already manufactured machine.
2. To tune the mechanical system of the hoisting machine so that its resonant frequencies are beyond the excitation frequencies. While there are many known methods for tuning the system to other resonant frequencies, they are usually hard to do on an already completed system.
3. To use magnetic slot wedges to close the stator slots of the synchronous motor. These considerably reduce the magnetic unevenness of the air gap and thereby also substantially reduce the magnitude of the excitation force due to fluctuations of the magnetic reluctance in the air gap. Replacing the magnetic slot wedges on the already manufactured machine is also usually difficult to perform.
4. To inject AC voltages of appropriate frequency, amplitude and phase into the excitation or stator windings so that the generated currents counteract the change in magnetic flux in the air gap, thereby reducing or eliminating this change. This fourth option has been used and will be described in more detail in the following text.
A. Method of Injection of AC Voltage Component
Let’s use a simplified model of the generation of the excitation force. The effects of the individual windings in the longitudinal axis of the synchronous motor can be described on the basis of the notion of magnetic fluxes and their paths according to Fig. 2. Similarly, assuming zero magnetic flux in the transverse axis Ψsq, it is possible to draw an equivalent diagram of the electrical circuits and their interconnections for the longitudinal axis of the synchronous motor (Fig. 3).
According to the equivalent diagram in Fig. 3, four equations can be written in which there are six variables:
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usd, isd, im, iD, uf, if. For an unambiguous solution, two variables must be chosen as independent variables.
Fig. 2. Equivalent diagram of the magnetic circuits in the d-axis
(indices: s – stator, D – damper, f – excitation (field), σ – leakage,
m - main)
Usually, it is usd and uf. Similarly, according to the equivalent diagram in Fig. 2, six equations can be written in which there are eight variables: usd, isd, Ψsd, iD, ΨD, uf, if, Ψf. For an unambiguous solution, two variables must be chosen as independent variables. Usually, it is usd and uf again. In mathematical models of electric machines, it is commonly assumed that the parameters Rs, RD, Rf, Lm, Lσs, LσD, Lσf are constants. In this case, however, the main magnetic flux Ψm periodically changes due to the variable air gap, and it results in the time varying magnetizing inductance Lm. This can be described by the following equation:
m m0 m drΔ sin 2L L L f t . (11)
If the main magnetic flux Ψm is to be constant, its derivative must be zero:
m
m m
m m
m m
d d
d d
d d0
d d
tL t i t
t t
L t i ti t L t
t t
. (12)
B. Simulation of the Injection
The equivalent scheme in Fig. 3 and the derived equations were programmed in MATLAB-Simulink. Simulation calculations were made on this model to inject a suitable compensating voltage into both the excitation winding and the stator winding.
Fig. 3. Equivalent diagram of the electric circuits in the d-axis
These calculations confirmed the possibility of suppressing magnetic flux variations due to slotting. While the required magnitude of the injected voltage into the excitation winding determined by simulation has an unrealizable tenfold value of the nominal excitation voltage, the value of the injected voltage into the stator winding has a real magnitude of less than a tenth of the nominal stator voltage. A more detailed description and results are presented in [5].
C. Realization of the Injection on Drives in Palasher
Ing. Kokeš from the Czech Academy of Sciences developed three methods of voltage injection into the stator winding:
1. To add the basic vector regulation of the magnetic flux and the machine torque with a resonant controller of the stator current.
2. To add a resonant element to PI speed control.
3. To add the feedforward compensation of the alternating torque component using a mathematical model of the synchronous machine winding.
The undesired alternating torque component was
compensated by adding the compensating signal *
12e CT at
the torque regulator input in Fig. 4. R is the resonant element, which together with the PI controller in the superior system forms the PIR speed controller. At the
output of R is the compensating torque *
12e CT , which is
added to the required torque value *
eMT from the superior
controller. The required value for control by the part R is
zero. Therefore, the output *
12e CT of controller R
suppresses the unwanted component 12ωr (twelvefold of the rotational speed). The part R is continuously tuned to a resonant frequency of 12ωr according to the measured actual speed ωr, which is filtered by the low pass filter LPF, so that tuning R is not negatively affected by component 12.
Fig. 4. Compensation of unwanted AC torque component using
the resonant speed controller
Fig. 5. Feedforward compensation of the AC torque component
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Fig. 6. The speed (blue) and torque *eT (red) during run up of the drive 5.8 MW with maximal torque - without compensation
Fig. 9. AC component of the instantaneous speed during run up of the 5.8 MW drive with maximal torque - without compensation
Fig. 8. The speed (blue) and torque *eT (red) during run up of the drive 5.8 MW with maximal torque - with feedforward compensation
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Fig. 9. AC component of the instantaneous speed during run up of the 5.8 MW drive with maximal torque - with feedforward compensation
Each resonant controller is very sensitive to the transport delay of the controlled variable. Therefore, this controller worked stably only at very low speeds up to 0.025ωrn. The signal quality of the measured velocity ωr deteriorates with increasing value due to vibration disturbances. Another disadvantage is the relatively long stabilization of the control at higher speed changes, which can reach several tens of seconds. With the help of the resonant velocity controller, it was only possible to remove the vibrations from the ropes at very low speeds, and it was necessary to look for another method that would work satisfactorily in the entire speed range ωr.
This showed method number 3. Method number 2 was used only in the auxiliary measurements, in which the parameters of each synchronous machine needed for the third method were obtained. All three methods are described in more detail in [5].
The basis of the feedforward compensation is the direct
calculation of the torque component *
12e CT from the
instantaneous values of the stator current components isd, isq, excitation current if and the rotor position angle θr in the mathematical model of the machine, which was created using so called winding functions [3]. Such a model makes it possible to respect the spatial arrangement of the slots and the winding wires. The most general model requires knowledge of twelve parameters. Some of them may be zero. Detailed measurements on all machines showed that for each machine, it is appropriate to use a different number of non-zero parameters in the
TE12COMP model in Fig. 5. The calculated *
12e CT
component is added to the torque value *
eMT from the
torque controller to the resulting torque *
eT as in Fig. 4 in
the resonant controller.
The result of the use of the feedforward compensation is shown in the recorded oscillograms of the instantaneous
speed ωr and the required torque *
eT . Fig. 6 shows the run
up of the 5.8 MW motor without compensation and Fig. 7 shows only the AC component of the instantaneous speed. Fig. 8 and Fig. 9 show the same situation with feedforward compensation. From their comparison, it is evident that the compensation significantly reduced the resonance bands of the vibration in the speed, and at the
required torque an AC component with an amplitude of 0.15Ten appeared.
V. CONCLUSION
The paper shows how the modern control and computer technology make it possible to solve a problem which has appeared during the drive commissioning after it was manufactured and assembled. Further, it demonstrates how the theoretical knowledge of electrical machines is important for the creation of the necessary mathematical model. It also shows how important it is to follow the recommendations for the electromagnetic design of electric machines, in this case the recommended number of slots per pole per phase of slow running machines.
REFERENCES
[1] J. Pavelka, P. Pavelka, and J. Šimek, “Kmitání těžního stroje na dole Kirovsk,” (in Czech), 34th Conference on Electric Drives (ELPO), Pilsen, June 2015, pp. 44-49.
[2] J. Pavelka, J. Šimek, P. Kobrle, “Posudek a analýza příčin mechanického rozkmitání synchronního motoru 1,8 MW, 6 kV na zakázce Malý Palašer,” (in Czech), unpublished.
[3] P. Krause, O. Wasynczuk, S. Sudhoff, S. Pekarek, Analysis of Electric Machinery and Drive Systems, 3rd ed., John Wiley&Sons, Inc., Hoboken, New Jersey, 2013.
https://doi.org/10.1002/9781118524336
[4] A.H. Toliyat, N.A. Al-Nuaim, “Simulation and Detection of Dynamic Air-Gap Eccentricity in Salient-Pole Synchronous Machines,” IEEE Trans. Ind. App., vol. 35, pp. 86-93, January/February 1999. DOI: 10.1109/28.740849
https://doi.org/10.1109/28.740849
[5] J. Pavelka, J. Šimek, P. Kobrle and P. Kokeš, “Příčina mechanického chvění těžních synchronních motorů Palašer a jeho odstranění,” (in Czech), 36th Conference on Electric Drives (ELPO), Pilsen, June 2019, pp. 1-21.
[6] J. Pavelka, J. Šimek, P. Kobrle, P. Kokeš, “Příčina mechanického chvění těžních synchronních motorů Palašer a jeho odstranění,” (in Czech), Elektro, vol. 11, November 2019, pp. 6-9.
Transactions on Electrical Engineering, Vol. 8 (2019), No. 4
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TRANSACTIONS ON ELECTRICAL ENGINEERING VOL. 8, NO. 4 WAS PUBLISHED ON 31TH OF DECEMBER 2019
Aleisawee Alsseid, Abdulrahman Emhemed, Alhade Algitta.: DC Network Model Based on VSC-HVDC
System
The recent developments in high power rated Voltage Source Converters (VSCs) and the control strategies have
resulted in their successful application in HVDC transmission systems, which have become an attractive option
for renewable energy applications or for distribution power in large metropolitan areas. A 153 th order multiple-
input multiple-output (MIMO) small-signal model of DC network model based on VSC-HVDC system and
controls is developed in state-space form within MATLAB. The optimum values of the controller gains are
selected by analysing the root locus of the analytical model. The developed small-signal detailed models are
linearized and implemented in MATLAB. The validity and accuracy of the proposed models are verified against
nonlinear PSCAD/ EMTDC and a summary of the model structure and controls is presented in detailed.
Confirmation of the effectiveness of optimization gains is done by simulating the modelled system in MATLAB
and PSCAD software. There simulation results performed with very good matching is confirmed in the time
domain. It is the most detailed model currently available.
Gric, P.: Protection against the Effects of the Asynchronous Operation of Synchronous Motors Based on
the Principle of Comparison of the Machine Power Factor
This paper deals with the possibility of using the principle of comparison of the operational power factor for
evaluation of the asynchronous operation of synchronous motors. This way of definition of the asynchronous
operation is possible to use for motors protection and other protective systems of drives with synchronous
motors.
Pavelka, J., Šimek, J., Kobrle, P., Kokeš, P.: The Cause of Mechanical Vibration of Palasher Synchronous
Motors and its Removal
The paper describes the procedure and the result of the analysis of mechanical vibrations of mining machines at
the Palasher mine in the Russian Federation. The cause of these vibrations was the change in the magnitude of
the magnetic flux in the air gap. The simulations showed the possibility of eliminating these changes in magnetic
flux by injecting suitable voltages into the stator windings. The implementation of this injection is further
described by torque variable component feed-direct compensation. Finally, oscillography records are presented
before and after injection.