Harmonic Mitigation in Single Phase Mutually Commutated Converter Systems Tommy Kjellqvist
Staffan Norrga
Royal Institute of Technology SE-100 44 Stockholm, Sweden Email:
[email protected]
ABB AB SE-721 78 Västerås, Sweden Email:
[email protected]
Abstract— An AC/DC converter comprising a cycloconverter and a capacitively snubbered voltage source converter (VSC), coupled by a medium frequency transformer, offers significant advantages. Bidirectional AC/DC power flow as well as voltage transformation and isolation can be achieved. By mutual commutation of the converters, soft switching can be achieved for all semiconductors, thus, link frequency can be increased, allowing smaller transformer and reduced filter components. However, the mutual commutation scheme imposed by the soft switching requirement puts constraints on the PWM pattern causing low frequency harmonics in certain operating points. It is shown that the low frequency harmonics can be eliminated for all points of operation, both in a single bridge configuration and interlaced configuration, common in AC-fed propulsion. A sub-optimal harmonic mitigation method based on a regularly sampled modulator is proposed. By proper oversampling of the reference waveforms substantial reduction of the low frequency harmonic contents can be achieved. The mitigation method is verified by circuit simulation and the feasibility to propulsion is demonstrated.
Lline
Uq iac
i tr
uac
utr
Uq
Fig. 1.
Basic converter cell of the studied topology.
I. I NTRODUCTION An AC/DC converter comprising a cycloconverter and a capacitively snubbered voltage source converter (VSC), coupled by a medium frequency transformer, as shown in Figure 1, offers significant advantages. Bidirectional AC/DC power flow as well as voltage transformation and isolation can be achieved. By mutual commutation of the converters, soft switching can be achieved for all semiconductors. Therefore, transformer frequency can be raised considerably, reducing the size and weight of the transformer. However, the mutual commutation scheme imposed by the soft switching requirement puts constraints on the PWM pattern. These restrictions have been found to cause low frequency harmonics not present in a conventional PWM pattern [1]. The investigated topology is proposed as a good candidate for the line side conversion stage in AC-fed propulsion systems where the weight and volume of the line transformer is a concern. Loss reduction in the VSC by employing soft switching [2] in combination with modern magnetic materials [3] allow for transformer frequency in the 4 kHz range. It offers a clean interface to conventional propulsion systems since the secondary side converter can be reused with the only modification of added capacitive snubbers. EMI is an important issue in track bound systems where track circuits are sensitive to certain low frequencies and harmonics in the audio band may couple to telephone lines and
Cd
Fig. 2. Proposed dual bridge MF transformer bases line rectifier for AC-fed propulsion.
a common practice in AC fed propulsion is to use multiple converter bridges, connecting to multiple secondary transformer windings, increasing the number of voltage levels at the primary terminals. Interlacing the operation of the converters, i. e. phase shifting the carrier waveforms, harmonic cancellation can be achieved. An analytical description of harmonic cancellation by interlacing for the conventional traction PWM converters is given in [4]. This concept can be adapted for the MCC by cascading to converter cells as shown in Figure 2. This would allow for the reuse of the designs of the present line converters. In the following, methods to mitigate low frequency harmonics in single bridge and interlaced dual bridge configu-
utr T
C
D
Z
T
C
D
Z
u∗ac
T
t itr
t
uac
t uac
t
utr
t
Fig. 3. Commutation sequence during power flow from the DC to the AC side. Letters designate the conducting component of the VSC; (T) corresponds to IGBT, (D) diode, (C) snubber capacitor and (Z) zero current.
rations are presented and evaluated by circuit simulation. II. M UTUALLY C OMMUTATED I SOLATED C ONVERTER S YSTEM The investigated converter topology, illustrated in Figure 1, comprise a conventional VSC, fitted with capacitive snubbers, connected via a medium frequency transformer to a cycloconverter. By alternately commutating the cycloconverter and the VSC it is possible to always operate the cycloconverter by natural commutation and zero voltage switching for the VSC, i. e. the converters are mutually commutated. The commutation cycle is outlined below and is described in detail in [5]. The commutation sequence, illustrated in Figure 3, is as follows. The cycle is initiated in a state where the power flow is from the DC to AC side. By commutating the VSC power flow is reversed, setting up the conditions for natural commutation of the cycloconverter. Due to the capacitive snubbers, the IGBTs will turn off at zero voltage. By commutating the first cycloconverter leg, current through the transformer is forced to zero, resulting in zero power flow. Commutating the second cycloconverter leg reverse the transformer current and the power flow is now again from the DC to the AC side, thus, the conditions are again set up for zero-voltage turn-off of the IGBTs and the next cycle may commence. By varying the duration of the various states, it is possible to produce a three-level PWM pattern at the output. To ensure soft switching of both VSC and cycloconverter all states must occur in the specified order, resulting in a short deviation from the desired output voltage during the commutation of the VSC. If power flow from the DC to the
t
Fig. 4. Typical PWM sequence during a power flow reversal with carrier shift synchronized to cycle boundary.
AC side is desired, the first cycloconverter leg is commutated immediately after the commutation of the VSC as illustrated in Figure 3. If power flow in the opposite direction is desired, the commutation of the first cycloconverter leg is delayed until the desired pulse width is achieved. The VSC is then commutated right after the commutation of the second cycloconverter leg, reducing the power flow in the undesired direction to a minimum. Furthermore, the VSC should be commutated at constant frequency and phase to avoid saturation of the transformer. The constraints can be accounted for in a carrier-based modulator by alternating between trailing and leading edge sawtooth carriers depending on the instantaneous power flow. Figure 4 shows the PWM pattern generation during a reversal of the power flow. The change of carrier during the fundamental cycle imposes certain asymmetries in the pattern and, particularly, there is no quarter wave symmetry. These asymmetries may cause low frequency harmonics depending on the position of the carrier shift in the commutation cycle. The resulting harmonic content in a severe operating point is illustrated in Figure 5. The switching function can be expressed as a double Fourier series expansion where the time dependency is given by two variables x(t) and y(t). f (x, y) =
∞ X
∞ X
Cmn ej(mx+ny)
(1)
m=−∞ n=−∞
x(t)
= ωc t + θ c
(2)
y(t) = ω0 t + θ0
(3)
and the complex Fourier coefficients are calculated from a
The magnitude is reduced in proportion to the pulse number and the square of the carrier multiple. The last term indicate a relationship to the operating point defined by the modulation index and the load angle. A single harmonic component is a superposition of the contribution from all carrier multiples. Therefore, it is possible that contribution from multiple carrier multiples may sum to zero under certain operating conditions.
0
Harmonic Magnitude (p.u.)
10
WTHD0=1.5%
−1
10
−2
III. M ITIGATION OF LF H ARMONICS
10
0
Fig. 5.
20
40 60 Harmonic Number
80
100
Low frequency harmonic content in a worst-case operating point.
double integral Cmn =
1 4π 2
Z
π
−π
Z
π
f (x, y)e−j(mx+ny) dxdy.
(4)
−π
The solution of the Fourier coefficients for the single-phase three level MCC system is given in [6] and repeated in equations (7-10). For integer pulse numbers, p, the harmonic component at multiples, k, of the fundamental can be derived by summation Dk =
∞ X
(5)
Cm,k−mp
m=−∞
where Cm,k−mp
Uq (1 − (−1)k )j k e−jkφ pπ 2 (−1)m −mp jmpφ × j e m2 × [1 − cos(2πmM sin φ)]
•
•
A. Single Bridge Systems The proposed carrier based modulation scheme allows for one degree of freedom, namely the phase of the carrier can be chosen independently of the fundamental. This can be accounted for by phase shifting the Fourier coefficients. Cmn (θc , θ0 ) = ej(mθc +nθ0 ) Cmn (0, 0)
≈ −
where (6)
2Uq k j k e−jkφ f (α, β) 1 − (−1) pπ 2
(12)
∞ m X (−1) f (α, β) = cos (mβ) (1 − cos(mα)) (13) m2 m=1
and
α
=
β
= θc + pφ.
2πM sin φ
(14) (15)
Baseband harmonics (m = 0, n 6= 0): C0n = M Uq , for n = ±1 and zero otherwise.
(7)
Cm0 = 0
(8)
Carrier harmonics (m 6= 0, n = 0): Sideband harmonics (m, n 6= 0):
Cmn
1 J0 (2πmM ) − n n −jnφ jπJn (2πmM ) Uq n m e (1 − (−1) ) (−1) j n − = ∞ P 2 Jk (2πmM ) mπ 2 −2 (jk sin kφ + n cos kφ) 2 2 n −k k=2,4...
•
(11)
As mentioned in previous section, the observed low frequency harmonic content is composed from sidebands to carrier multiples. Considering the contribution from every carrier multiple, (5) can be rewritten, Dk |k≪p =
for k ≪ m·p, i.e. harmonics far away from the corresponding carrier. It is observed that the contribution from each sideband takes a constant magnitude and only differs in phase, for harmonic numbers far away from the corresponding carrier. •
The possibility to mitigate low frequency harmonics is investigated. The analysis is based on the analytical approximated expression for the side band harmonics in equation (6). Mitigation techniques developed for both single bridge and interlaced dual bridge are evaluated. The effect of sampling in a practical modulator is discussed.
(9)
For large values of n, i. e. far away from the carrier frequency equation (9) can be approximated: Cmn ||n|≫0 ≈
Uq n (1 − (−1) ) (−1)m j n e−jnφ [1 − cos (2πmM sin φ)] . mnπ 2
(10)
1
1
0.8 0
0.6
0.2
0.8
0.40.6
0.8
0.2
0.8
0.4
0
0.4
−0.4
−0.2
0.2
−0. 6
0.2
−0.
0
0.4 0 0.2
0.4
0.6
0.8
1
0
0.2
α/π
0.2 0.6
0.8
0 0
8
0
−0.4
β/π
−0.2
0
0.4
−0.6
β/π
0
0.6
−0.2
−0.4 0.6
0.4
0.6
0.8
1
α/π
Fig. 6. The magnitude of the low frequency components for a single bridge, as a function of the operating point α and the carrier shift β, normalized to the maximum value.
Fig. 7. The magnitude of the low frequency components for two interlaced bridges, as a function of the operating point α and the carrier shift β, normalized to the maximum value.
Angle α takes a value from −2π to 2π and is defined by the operating point of the converter, while angle β, represents the phase shift between AC current and the carrier ranging from −π to π. The low frequency sidebands extend down to the fundamental frequency and have a constant magnitude. The magnitude is defined by the summation in (13). A maximum value, for any operating point defined by α and carrier shift β, can be derived.
Similar to the single bridge case, an angle β that zero function f (α, β), i.e. eliminating all low frequency harmonics can be found for any operating point α, as seen in Figure 7. Due to the interlacing contribution from odd carrier multiples and multiples of four in the sum are eliminated and the max value for any operating point and carrier shift becomes
max |Dk |k≪p =
Uq p
(16)
A carrier shift that zeros the low order harmonics can be found for any operating point. Figure 6 shows the magnitude of the low frequency component normalized to the maximum value. Choosing a constant carrier shift equal to β = π/2 result in significantly reduced harmonics over the complete range of possible operating points. By evaluating the sum (13) results in a maximum value Uq (17) max |Dk |k≪p = 4p
max |Dk |k≪p =
Uq . 2p
(20)
A constant relation between carrier and load angle, β = π4 , yields small amounts of low frequency harmonics for any operating point. The first contributing sideband becomes the fourth and the maximum amplitude max |Dk |k≪p =
Uq . 8p
(21)
due to the elimination of contributions from odd carrier multiples.
Interlacing does not significantly reduce the amount of low frequency harmonics by itself due to the remaining contribution from the dominating harmonics originating from the first carrier multiple. However, if the contribution from the first carrier multiple is eliminated, by proper choice of carrier phase shift, all sidebands originating from up to the forth carrier multiple are eliminated.
B. Multiple Bridge Systems
C. Regular sampling
The harmonic content at the output is the sum of the harmonic components from each converter cell. The carriers are phase shifted by an angle θc , with respect to the voltage reference and additionally an angle π with respect to each other. ∞ X (18) (ejmθc + ejm(θc +π) Dk =
A limiting factor with naturally sampled PWM is the difficulty of implementation in digital hardware since the commutation instance is described by a transcendental equation. This is commonly solved by sampling the reference at regularly spaced instances. To avoid multiple commutations per cycle, the sampling instances are generally chosen to coincide with the carrier peak. The most pronounced effect of reference sampling is the introduction of low order baseband harmonics. For moderate pulse numbers the amplitude is low and roll off quickly with increased harmonic order. In the studied topology, sampling of the current has significant effect on the harmonic contents. In fact, sampling the current at the carrier edge is equivalent to the most unfavourable
m=−∞
Equation (18) can be expanded into (12) where,
f (α, β) =
∞ m X 1 + (−1) cos (mβ) (1 − cos(mα)) . m2 m=1 (19)
u∗ac
M=0.7, p=48 1.6
WTHD0 [%]
1.5
uac
1.4 1.3 1.2 1.1
ik−1
ik
0
0.1
0.2
Fig. 8. PWM generation process during carrier shift occurring at suboptimal current sampling instance for interlaced dual bridge. Upper: Carrier and reference voltage waveforms. Lower: Resulting output voltage.
alignment between carrier and current in the naturally sampled case. For low pulse numbers, a natural sampling approach is attractive due to better harmonic performance and higher bandwidth in a closed loop control. A convenient approximation of the natural sampling system can be achieved by oversampling. If the bidirectional switches are implemented using turnoff capable devices the switching pattern is not restricted by natural commutation of the cycloconverter. If occasional hard commutation of the cycloconverter can be accepted, at least at low currents, proper pattern for harmonic cancellation can be applied without actually aligning the carrier to the fundamental current. By proper sampling of the current reference, the carrier can be forced to change only at suitable instances without actually changing the carrier phase. Figure 8 indicate the suitable sampling instances for an interlaced bridge and resulting switching pattern during a current reversal at sampling instance ik . A similar approach can be taken for the single bridge case. IV. E VALUATION OF M ETHODS A. Figures of Merit Calculating the THD requires knowledge of the frequency dependent impedance of the line and filters. As the filter as well as the line generally show inductive behaviour, the weighted THD can be used. The weighted THD is normalized to the maximum available fundamental, i.e. v u ∞ 2 u X Vk 1 t . (22) W T HD0 = V1 |M =1 k k=2
The weighted total harmonic distortion (W T HD0) is chosen as the figure of merit in the comparison between modulation methods. WTHD0 figures has been derived by FFT calculations on the ideal switching waveform, i. e. Non zero transition times and other non ideal circuit and modulation properties has not been considered.
0.3
0.4
0.5
φ/π
ik+1
Fig. 9. Calculated WTHD0 with no LF harmonics mitigation (cross), carrier aligned to current waveform (circle), and optimum LF harmonics mitigation (plus). M=0.7, p=24 0.75 0.7 WTHD0 [%]
ik−2
0.65 0.6 0.55 0.5
0
0.1
0.2
0.3
0.4
0.5
φ/π
Fig. 10. Calculated WTHD0 in a dual bridge configuration with no LF harmonics mitigation (cross), carrier aligned to current waveform (circle), and optimum LF harmonics mitigation (plus).
The normalized weighted THD has been calculated for every load angle while the modulation index and fundamental phase are kept constant. Figure 9 shows the result for a single bridge converter while Figure 10 shows similar curves for interlaced dual bridge converter. Three modulation techniques are evaluated. First, the carrier is aligned to the fundamental. This technique results in significant increase of the harmonic content at certain operating points. Second, an optimum phase of the carrier relative to the current fundamental is chosen. The resulting harmonics coincide perfectly with the minimum value of the the first method for any operating point. Third, a constant sub-optimal phase relation, suitable for the proposed oversampling technique, is used. The sub-optimal method shows only a slight distortion increase in certain operating points. B. Verification by Circuit Simulation The proposed harmonic mitigation technique has been verified by simulation in the circuit simulator SABER, by which the effects of non-ideal switching waveforms can be
C. Railway Propulsion The investigated topology is pointed out as a good candidate for line side rectification in AC-fed propulsion in railway traction. Therefore, an effort has been made to show the feasibility of the proposed mitigation technique in this context. For the high pulse numbers considered for railway traction, where the weight of the transformer is the primary concern, THD is not considered to be a problem. However, harmonic currents generated by the propulsion equipment may interfere with telecommunication lines close to the tracks. A measure on the severity of the disturbance is given by the psophometric current, which is a filtered version of the line current, sZ f2
(p(f )I(f ))2 df
Ipso =
Harmonic Magnitude (p.u.) Harmonic Magnitude (p.u.)
0
10
WTHD0=1.4%
−2
10
0
20
40 60 Harmonic Number
80
100
0
10
WTHD0=1.3%
−2
10
0
20
40 60 Harmonic Number
80
100
Harmonic Magnitude (p.u.) Harmonic Magnitude (p.u.)
Fig. 11. Theoretical spectra (top) and spectra from SABER simulation (bottom) with current sampling at the cycle boundary
0
10
WTHD0=0.94%
−2
10
0
20
40 60 Harmonic Number
80
100
0
10
WTHD0=0.95%
−2
10
0
20
40 60 Harmonic Number
80
100
Fig. 12. Theoretical spectra (top) and spectra from SABER simulation (bottom) with proposed current oversampling technique Harmonic Magnitude (p.u.) Harmonic Magnitude (p.u.)
studied. In the analysis, voltage transients has been assumed to be instantaneous. However, due to the soft-switching, voltage transients have a significant duration affecting the output voltage. The commutation of the VSC does not result in any loss of voltage-time area at the output. However, it does result in a phase shift of the resulting harmonics. During the commutation of the cycloconverter, the output voltage is zero during the whole process, resulting in a loss of voltage-time area. These effects can, to some extent, be accounted for. This has not been done in the presented simulations. However, a low pulse number is used and, thus, the effect of non-ideal switching transients are diminished. In the simulations, a particularly severe operating point has been selected to clearly demonstrate the effect of applied mitigation technique. Figure 11 shows theoretical and simulated harmonics in a worst-case operating point when sampling at the cycle boundary is employed. The simulation result show unexpected uneven harmonics. This indicates a disturbance of the half wave symmetry. However, the amplitude of the harmonics conformers well to the theoretical worst case value of 2% and the weighted total harmonic distortion show fair agreement. Figure 12 shows theoretical and simulated harmonics in the same operating point as in Figure 11 but with the proposed over sampling technique implemented. Both the simulated individual harmonics as well as the weighted THD are in excellent agreement with the theoretical values. Figure 13 shows theoretical and simulated harmonics in with the proposed over sampling technique for the dual bridge implemented. The amplitude of the low frequency harmonics are reduced to a value in the order of 0.1% which is higher than the theoretical value but much lower than the worst-case value of 0.6% for the investigated operating point. A slight increase of the low order harmonics as well as around the pulse number can be observed. However, the weighted THD is completely dominated by the harmonics around twice the pulse number.
0
10
WTHD0=0.21%
−2
10
0
20
40 60 Harmonic Number
80
100
0
10
WTHD0=0.21%
−2
10
0
20
40 60 Harmonic Number
80
100
(23)
f1
where the filter, defined in [7], describe how severe a disturbance of a specific frequency is experienced in the
Fig. 13. Theoretical spectra (top) and spectra from SABER simulation (bottom) with proposed current oversampling technique in a dual bridge configuration.
TABLE I I NVESTIGATED T RAIN S ET Line voltage Line frequency Rated power per drive unit Line filter Multiple drive units Transformer frequency Configuration
Un fn Pn Xl N ftr -
15 kV 16 2/3 Hz 1.1 MW 20 % 6 1000 Hz - 4000 Hz Single bridge / Interlaced
2
Psophometric current [A]
10
1
10
Regular, Non−interlaced Regular, Interlaced Oversampled, Non−interlaced Oversampling, Interlaced
0
10
−1
10
−2
10
1000
1500 2000 2500 3000 3500 Transformer frequency [Hz]
4000
Fig. 14. Psophometric current plotted versus transformer frequency for interlaced and non-interlaced modulation and regular and over sampling.
telephone system. Standards prescribe a maximum value of the psophometric current for a complete train set and is in the order of 2A [8]. The investigated train set is outlined in Table I. Since a weight reduction of the propulsion system is desired a small line filter is considered. It should be noted that harmonic voltages in the grid may induce excessive harmonic currents in the filter. However, the potentially high bandwidth, due to high pulse number, may increase the possibility to do active filtering to draw only sinusoidal currents. The psophometric current resulting from a complete train set according to Table I has been calculated. The train set is operated at maximum load at unity power factor and the drive units are assumed to be non-interlaced, i.e. the psophometric current through the train set is equal to the sum of the current through each drive unit. The psophometric current is assumed to increase with increased load, which is true for the regularly sampled system. Figure 14 show the resulting psophometric current at rated load. The transformer frequency span from 1000 Hz, which is in the range of what is feasible for a transformer made from conventional magnetic steel, to 4000 Hz, which is considered to be in the range of what is achievable with regard to semiconductor switching losses. For the single bridge configuration, the psophometric current is dominated by the harmonics around the switching frequency. However, for frequencies around 4 kHz, the psophometric current is completely dominated by the low frequency harmonics. The figure shows that
interlacing does not significantly reduce the harmonic low frequency contents, due to the dominating remaining contribution from the first carrier multiple. However, significant reduction of the low frequency harmonics are achieved when the interlaced dual bridge configuration is combined with the proposed mitigation technique. V. C ONCLUSIONS The Mutually Commutated Converter (MCC) system are a promising alternative where bidirectional ac to dc conversion with galvanic insulation is necessary, where the MCC guarantee soft switching for all semiconductors without auxiliary switches. However, the topology has been found to generate substantial low frequency harmonics. The harmonics have been studied by double Fourier series expansion, and the low frequency harmonics have been found to be carrier side bands reaching an asymptotically constant amplitude at low frequency. A method to mitigate these side bands has been developed. If the carrier shift, imposed by the soft switching strategy, can be chosen freely in the cycle the low frequency harmonics can be eliminated. However, this solution may prove difficult to implement in a practice. A more practical mitigation technique, based on current oversampling, is proposed. For this method, maximum amplitude of the resulting low frequency spectra has been derived. The results have been verified by circuit simulations in SABER. The simulation results are in good agreement with the theoretical spectra. The mitigation technique is evaluated in the context of AC-fed traction. It has been concluded that an interlaced dual bridge configuration in combination with the proposed mitigation technique offers significant reduction of the low frequency harmonics. It is shown that the psophometric currents, driven by the converter harmonics, can be reduced to an order of magnitude below the value specified in standards. R EFERENCES [1] S. Norrga, “Modulation strategies for mutually commutated isolated three-phase converter systems„” 2005 IEEE 36th Annual Power Electronics Specialists Conference, 2005. [2] T. Kjellqvist, S. Norrga, and S. Östlund, “Switching frequency limit for soft-switching mf transformer system for ac-fed traction,” 2005 IEEE 36th Annual Power Electronics Specialists Conference, 2005. [3] ——, “Design considerations for a medium frequency transformer in a line side power conversion system,” 2004 IEEE 35tg Annual Power Electronics Specialists Conference, vol. Vol.1, pp. 704 – 10, 2004. [4] J. Shen, J. A. Taufic, and A. D. Mansell, “Analytical solution to harmonic characteristics of traction pwm converters,” IEE Proc.-Electr. Power Appl., vol. 144, pp. 158–168, Mar. 1997. [5] S. Norrga, “A soft-switched bi-directional isolated ac/dc converter for ac-fed railway propulsion applications,” in International Conference on Power Electronics, Machines and Drives, 2002, June 2002, pp. 433– 438. [6] ——, “On soft-switching isolated ac/dc converters without auxiliary circuits,” Ph.D. dissertation, KTH, Stockholm, Sweden, 2005. [7] ITU-T, Psophometer For Use on Telephone-Type Circuits, International Telecommunications Union Std. ITU-T O.41, 1994. [8] Banverket, EMC requirements for trackbound vehicles regarding telecommunication, radio and signalling disturbancess, Swedish Railway Administration Std. BVS 560.1201, 2002.
