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Interaction Between a Superconducting Coil and the Power Electronics Interface on a 100 MJ SMES System Michael Steurer, Cesar A. Luongo, Paulo R. Ribeiro, and Steve Eckroad
Abstract—Although numerous studies have focused on the connection of SMES to the utility power grid, fewer have addressed in detail the interactions between the power electronics interface and the SMES coil. While electromagnetic transient models are available from classical transformer studies, little work has been done on how these models apply to SMES coils. This paper presents the computer modeling of the interaction between a 100 MJ/100 MW LTS SMES coil now under construction and its power electronics interface. It is concluded that frequency domain modeling methods are applicable to study SMES coil-converter interactions and to recommend preferred operating frequencies of the power converter provided that certain characteristics unique to SMES systems are accounted for. Index Terms—Frequency response analysis, SMES, superconducting cables.
I. INTRODUCTION
W
ITH the advent of the next generation of electric power conditioners and the emphasis on quality and security of power systems, superconducting magnetic energy storage (SMES) is expected to play an increasingly important role. The largest SMES coil currently under construction was designed for storing up to 100 MJ and providing up to 50 MW of real power (at 24 kV DC) to assist in damping low frequency oscillations on a transmission grid. The magnet will be installed at a test facility for utility/shipboard power systems at the new Center for Advanced Power Systems at Florida State University [1]. Despite the actual power capability of the coil, the supplying converter system will be rated initially for only up to 5 MW (at 2.5 kV DC). These less stringent requirements should not challenge the dielectric insulation of the coil. However, insulation failure during pulsed operation is a major design consideration for coils this large. The fact that this area has not received much attention in the past was the motivation for the present work. Fig. 1 shows the major components of the planned system, with the SMES coil connected to a voltage source converter Manuscript received August 6, 2002. This work was supported in part by the Electric Power Research Institute, Palo Alto, CA. M. Steurer and C. A. Luongo are with the Center for Advanced Power Systems at Florida State University, Tallahassee, FL 32310 USA (e-mail:
[email protected];
[email protected]). P. R. Ribeiro is with the Department of Electrical Engineering, Calvin College, Grand Rapids, MI USA, and also with CAPS, Florida State University, Tallahassee, FL USA (e-mail:
[email protected]). S. Eckroad is with the Electric Power Research Institute, Palo Alto, CA 94304 USA (e-mail:
[email protected]). Digital Object Identifier 10.1109/TASC.2003.812895
Fig. 1. Voltage source power converter connected to a SMES. The transient behavior of the sub-systems shaded in gray is the subject of this paper.
(VSC) via a DC-DC chopper. The latter consists of two and and two self-commutating power electronic switches and . The power flow in and out of the SMES diodes across is regulated via the DC component of the voltage V and the coil which in turn is controlled by switching on and off simultaneously at a constant base frequency and a variable duty cycle . The Fourier series contains even and odd harmonics, which may excite of coil resonances and cause standing voltage waves of high amplitudes within the coil and consequently cause additional insulation stress [2]. Few papers have actually addressed in detail the interaction between a superconducting coil and the power converter [3]–[5]. It was shown in [4] that the eddy current losses within the cable-in-conduit-conductor (CICC) provide sufficient damping to the resonances observed at several 10 kHz. However, it was suggested in [5] that large SMES coils are prone to potential resonance problems since resonance frequencies decrease with increasing coil size. This issue is important when higher chopper frequencies are employed in conjunction with a large SMES coil for faster response of the control and to reduce lower frequency harmonics. These increased stresses, which have not been fully understood and assessed in the past, may pose a high risk of coil failure or diminished performance, and need to be addressed in the design stage. II. MODEL A lumped parameter network model was developed, taking into account self and mutual inductances, turn-turn and turnground capacitances, as well as damping resistance. Frequency domain analysis was preferred for this work, because for a conis a periodic signal. This secstant duty cycle the voltage
1051-8223/03$17.00 © 2003 IEEE
STEURER et al.: INTERACTION BETWEEN A SUPERCONDUCTING COIL AND THE POWER ELECTRONICS INTERFACE
Fig. 2. Equivalent circuit in which the SMES coil structure model of variable complexity (different number turns lumped into one segment) was analyzed. Different grounding scenarios can be achieved by adjusting R and R . One (C ) or two (C and C ) surge capacitors can be modeled as well.
tion briefly describes the analysis method and discusses the need for modeling the frequency dependency of the series damping.
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Fig. 3. Magnitude of the terminal impedance for (a) the unbalanced and (b) the balanced setup, both consider a quasimetal shield on the coil surface.
(2) for each of the harmonic components the Fourier series of all nodal voltages are found.
A. Analysis Method
B. Damping due to Skin Effect
For the phenomena studied here in the frequency domain ) plus the chopper shown analysis, the DC-link capacitor ( in Fig. 1 together behaves like a voltage source to the SMES coil. This is illustrated in the equivalent circuit in Fig. 2. The vacuum impregnated coil is represented by a lumped parameter network model of sufficient complexity (indicated as coil structure). The latter is embedded in an outer circuit to model various grounding conditions, addition of surge capacitors, and damping effects due to the conductive paint applied to the outside coil. The coil can be balanced with respect to ground by k . An unbalanced choosing for example condition (one terminal grounded) is achieved by k and m . By calculating self and mutual inductances, as well as capacitances of the coil on a turn-to-turn basis from material and geometrical data given in [1, Table I], all parameters are found to formulate the nodal impedance matrix of the electrical network shown in Fig. 2 and relate the nodal to the nodal voltages by current injection
The conductor of the CAPS-SMES coil is a cable in conduit conductor (CICC) assembled from a NbTi superconductor em, both surrounded by bedded in a copper matrix with an L310 stainless steel (SS) conduit [1]. In order to assess the damping this CICC adds due to the skin effect, a 2D finite element analysis (FEA) was carried out. The results are in agreement with [4]. However, in contrast, it was found that the SS conduit did not carry any current at 5 kHz, since the CICC of the CAPS-SMES differs significantly from the one analyzed in [4]. As a result of the FEA, an equivalent frequency dependent has been included in the analysis. It apdamping resistor and is connected in series to the inducpears in Fig. 2 as tors in each of the segments.
(1) ( Since only a single current injection exists at node is the reference and the node “ground” is included in ), all . By nodal voltages are easily found from one column of such that becomes the terminal ordering the elements of impedance – leads to (2) as outlined in more detail where [ ] is the first column of gives the voltage amplificafor example in [6]. Here, vector is frequency dependent in tion factors for each node. Since general, it must be computed for each frequency of interest sepand evaluating arately. After finding the Fourier series of
III. RESULTS A. Resonance Phenomena Within the Coil First a coil with a low resistive outside surface is analyzed. provides the only damping, thus leading to In this case, the worst case. Fig. 3 shows the magnitude of the terminal for the most important range of frequencies impedance between 100 Hz and 30 kHz. From Fig. 3, two significant facts appear: 1) The series resistance of the CICC provides only very low damping in this frequency range. Therefore, any series resonance leads to extreme small residual impedances around 1 . (Note that only few of all the resonances in Fig. 3 have been scanned with high resolution to actually reveal the low residual impedance in the plot.) 2) The first parallel resonance frequency is shifted toward higher values (390 Hz) in the balanced case, and so are the odd count series resonances. Furthermore, the damping at those resonances is orders of magnitudes higher which in turn makes them less problematic. Finally, neither the
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frequency nor the residual impedance at even-count series resonance change between the two cases. Fig. 3 also shows the total of the series-damping resistor at kHz 4.2 K based on the FEA of the skin effect. For the Cu-matrix still carries 99% of the current, thus providing a maximum total series damping resistor of only 2 for the entire coil. Above 10 kHz, the skin effect causes the current to flow partly in the SS conduit, which above 50 kHz finally carries the total current. The damping at room temperature between 1 kHz and 10 kHz is more than one order of magnitude larger. The proximity effect, which according to [5] further increases the apparent resistance of the CICC by typically a factor of less than 10, will be incorporated in the model once frequency response measurements are available in the near future. B. High Resistive Paint To model the effect of the high resistive paint applied to the external surface of the coil, originally required to minimize ground fault currents, a resistance was inserted in series with in Fig. 2). Fig. 4(a) each of the turn-ground capacitances ( upon the terminal impedance for illustrates the effect of three different values, while Fig. 4(b) shows the corresponding – across the first segment. It can voltage amplification be seen that the damping of the series resonances increases with and consequently reduces the voltage amplification factors and the stress on the insulation. A quasimetal (low resistive) leads to high amplification of voltages shield with 200 kHz, reaching in the whole frequency range between 1 k reduces them more than 10 at 2.2 kHz. A value of k even further to less than to less than 0.8 and 0.1. The high resistive paint thus provides the only significant damping of series resonances to such a large superconducting coil. This important fact has not been explicitly addressed in the past.
Fig. 4. Magnitude of (a) the terminal impedance and (b) voltage amplification across the first segment for three different cases of resistive paint: (1) quasimetal R 10 , high resistive (2) R = 2 k , and (3) R = 20 k .
=
C. Surge Capacitor to In order to prevent surges with steep voltage rise enter any type of apparatus, so called surge capacitors are sometimes connected in parallel to the main terminals. Since the line resistance between the DC-link capacitor and the coil is in the across the terrange of m ( in Fig. 2), a single capacitor minals of a resistively balanced coil does not change the voltage amplification significantly. Such a setup only limits the rise time . The of voltage surges steeper than the time constant 1 s which is latter will typically be on the order of 0.1 in the range of the switching times of semiconductor devices. and are used (each However, when two capacitors between terminal and ground) the voltage amplification is indeed changed throughout the entire frequency spectrum. Fig. 5(a) shows the magnitude of the terminal impedance and Fig. 5(b) shows the voltage amplification – of node #47 (which is at a quarter of the total conductor length) against ground over frequency for three different scenarios: 1) F, and 3) no surge capacitor, 2) F. It can clearly be seen that although the terminal impedance characteristic changes dramatically between (a1) and (a2)–(a3), – does not change between (b1) and (b2) and only
Fig. 5. Magnitude of (a) the terminal impedance and (b) voltage amplification against ground for three different scenarios: (1) no surge capacitor, (2) C = 5 F across the terminals, and (3) two capacitors C = C = 5 F from each terminal to ground.
changes for specific frequencies between (b2) and (b3). The consequence of a reduced terminal impedance at the chopper operation frequency in case (2) and (3) is a nonnegligible increase in AC current through the power electronics and the DC-link capacitor for high voltage applications. D. Chopper Operating Frequency From the previous sections it is evident that the chopper voltage signal (the fundamental and harmonics) must not excite series resonances of the coil in order to avoid continuous over voltage conditions. Fortunately, the negative effects of the harmonic decrease faster than the inverse of the harmonic order because of the residual resistance increases with frequency (skin effect). Therefore, it is reasonable to require that harmonics only up to a specific order should not excite resonances (e.g., up to the 6th harmonic which at 75% duty cycle appears
STEURER et al.: INTERACTION BETWEEN A SUPERCONDUCTING COIL AND THE POWER ELECTRONICS INTERFACE
Fig. 6. (a) Chopper operating frequencies which will excite series resonances of a balanced coil with either their fundamental or one of their harmonics. The bar width represents a safety margin around those frequencies while the bar height indicates the harmonic number that will be excited. The hatch-marked bars show the preferred frequency ranges. For comparison (b) shows the terminal impedance.
with an amplitude of 0.26 pu). Not only must the resonance frequencies be avoided exactly but also within a safety margin. Fig. 6 shows those frequencies [for case (2) in Fig. 4] with bars indicating the harmonic number matching a coil resonance by their height (e.g., height 3 means third harmonic of this frequency excites a resonance), while the bar width represents the safety margin in frequency. Consequently, the hatch-marked bars give bands of operating frequencies which meet the above requirements and are therefore considered as “allowed.” While other requirements such as size of the DC-link capacitor, current ripple within the coil, and capabilities of the power electronic switches may also influence the choice of the chopper operating frequency, the criteria shown in Fig. 6 gains importance for large SMES coils since their resonance frequencies are much lower than those of small coils. IV. CONCLUSIONS AND FUTURE WORK The interaction phenomena investigated here are especially important for applications involving large SMES coils, since they have very low resonance frequencies which can easily be excited by low order harmonics of the DC-DC chopper voltage signal. • The control strategy (i.e., the operating frequency) of any power converter interface between a large SMES coil and the power system must be based upon a comprehensive and detailed modeling of the coil’s resonance behavior.
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• The influence of the resistive paint upon the damping of resonances shall be included in the requirements for the choice of its resistivity. In addition, the subject must be investigated further to allow for enhanced development of the modeling. • Validation of the theoretical coil model by means of frequency response measurements of the coil as it is fabricated will improve the model, especially in the medium frequency characteristics of the CICC, which has been modeled here based on a simplified 2D FEA. • Harmonic branch currents flowing in the Cu-matrix and the SS conduit produce additional heat losses, which are not covered by the classical AC loss calculations. The analysis shall be expanded to address this issue properly. • As an alternative to the VSC/Chopper configuration studied the SMES may be connected to the AC side directly via other topologies. While the principal findings regarding resonance phenomena within the coil remain valid, the differences in the control requirements for alternative interfaces must be addressed separately. ACKNOWLEDGMENT The authors would like to thank Dr. J. Toth of the National High Magnetic Field Laboratory, Tallahassee, FL for providing the FEA of the eddy current phenomena and C. Weber from BWXT in Lynchburg, VA for providing additional data for the model. REFERENCES [1] C. A. Luongo, T. Baldwin, P. Ribeiro, and C. M. Weber, “A 100 MJ SMES demonstration at FSU-CAPS,” in Applied Superconductivity Conference, Houston, TX, August 4–9, 2002, Paper no. 1LB01. [2] H. Brandes and J. A. Allison, “Breakdowns between phases and coils are much more frequent than ground failures,” IEE Power Engineering Journal, pp. 158–163, August 2000. [3] A. B. Arsoy, Z. Wang, Y. Liu, and P. F. Ribeiro, “Transient modeling and simulation of A SMES coil and the power electronics interface,” IEEE Transactions on Applied Superconductivity, pp. 4715–4724, December 1999. [4] A. M. Miri, C. Sihler, M. Droll, and A. Ulbricht, “Modeling the transient behavior of a large superconducting coil subjected to high voltage pulses,” in The Proceedings of International Conference on Power System Transients, September 1995, 563, pp. 57–62. [5] A. M. Miri, C. Sihler, H. Salbert, and K.-U. Vollmer, “Investigation of the transient behavior of a superconducting magnetic energy storage (SMES) generating high power pulses,” European Transactions on Electrical Power Engineering, vol. 8, no. 1, pp. 13–19, Jan./Feb. 1998. [6] R. C. Degeneff, “A general method for determining resonances in transformer windings,” IEEE Transactions on Power Apparatus and Systems, vol. 96, no. 2, pp. 423–430, March/Apr. 1977.
