Modulation Strategies for a Mutually Commutated Converter System in Wind Farms Stephan Meier, Staffan Norrga, Hans-Peter Nee ROYAL INSTITUTE OF TECHNOLOGY Teknikringen 33 100 44 Stockholm, Sweden Tel.: +46 8 7906598 Fax: +46 8 205268 E-Mail:
[email protected] URL: http://www.eme.ee.kth.se
Acknowledgements The authors would like to thank Vindforsk for financial support. Vindforsk is a research program of the Swedish Energy Agency for fundamental and applied wind power research.
Keywords Modulation strategy, Vector control, Wind energy, Adjustable speed generation system, HVDC.
Abstract A novel mutually commutated converter (MCC) system consisting of a voltage source converter (VSC) and a cycloconverter connected by a medium-frequency (MF) transformer is adapted for the power collection and conversion in large wind farms. Different modulation strategies based on space vectors are described and evaluated with regard to the very restrictive constraints on the modulation and commutation of the thyristor valves in the cycloconverter. This paper shows that a feasible and effective modulation strategy can be found in order to provide the desired reference voltage vector during every single modulation interval and under all operating conditions. The proposed current clamping control strategy is based on stopping the gate pulses of the conducting thyristor valve during a certain dead-time whenever the current in the corresponding phase leg becomes zero.
1. Introduction A novel power converter concept based on the mutual operation of a VSC and a cycloconverter connected by a single-phase MF transformer has recently been proposed [1]. Utilizing a transformer that operates above the grid frequency is beneficial considering both its weight and its losses. Furthermore, soft commutation of all semiconductor devices can be achieved by consistently commutating the two converters in alternation. However, the demand for soft switching imposes certain restrictions concerning the modulation of the cycloconverter. By adapting a method originally developed for quasi-resonant DC link converters [2], a new space vector modulation (SVM) scheme was derived [3]. A potential application of a distributed version of the above-mentioned converter concept is in large wind farms [4] as presented in Section 2. But the considered application entails certain additional and specific constraints for its modulation. These constraints concern mainly the particular operating conditions as well as the application of thyristors in the cycloconverter valves with their limited turn-off capability.
2. Proposed VSC transmission system for wind farms The proposed VSC transmission system is an integrated solution for large wind farms that provides both variable-speed operation for the individual wind turbine, the interconnection of the wind turbines, as well as an interface for HVDC transmission in an efficient and cost-effective way [4]. Figure 1 shows that the squirrel-cage induction generator of every wind turbine is connected to a single-phase MF collection grid via a cycloconverter and an MF distribution transformer. An HVDC cable is then connected to the collection grid via an MF transmission transformer and a single-phase VSC. By alternately commutating the cyclo-converters and the VSC it is possible to maintain soft commutations for all semiconductor devices. The modulation strategies discussed in this paper concern mainly the thyristor-based cycloconverters located in the nacelle of every wind turbine. Figure 1 shows how the cycloconverters are built up by valves consisting of anti-parallel thyristors.
+/− 150kV DC
150kV
33kV
500Hz
500Hz
Gearbox
3kV
1kV
500Hz
23.5−50Hz
Squirrel−cage induction generator Single−phase VSC Cycloconverter Single−phase MF transformer Circuit breaker Disconnector
Thyristor-based cycloconverter
Fig. 1: Simplified schematic of the proposed VSC transmission system for wind farms.
2.1 Operating conditions and control strategy of the wind turbine generator The proposed VSC transmission system should be able to operate over the same range as a state-of-the-art wind turbine, such as the V90-3.0MW from the Danish manufacturer Vestas Wind Systems A/S [5]. According to Figure 2, three important operating points are identified: 1: Low power generation at the cut-in wind speed. 2: Nominal power generation at the nominal wind speed. 3: Nominal power generation at the cut-out wind speed. The cycloconverter is not required to operate at a lower frequency than the one at operating point 1. During the start-up, the rotor of the wind turbine is unloaded and power generation does not start until the turbine has accelerated to its minimum operating speed. The cycloconverter is neither required to operate above nominal power generation or at a higher frequency than the one at operating point 3. Once the wind speed exceeds the cut-out wind speed, the turbine speed is limited and the wind turbine is eventually stopped with help of its pitching system and its mechanical break. The chosen control strategy of the induction generator is also pointed out in Figure 2. Up to nominal speed, the stator voltage is increased proportionally to the frequency in order to maintain nominal flux in the induction generator. This causes the induction generator to operate at a very low power factor at low frequencies. However, this is desirable from a modulation point of view as it helps to establish a sufficient fundamental stator current. Thus, multiple current direction reversals due to current ripple that may complicate the modulation of the cycloconverter valves can be reduced. Above nominal speed, both the
Generator voltage [p.u.]
stator voltage and the active power are kept constant, which causes the induction generator to operate in field weakening mode. 1
2
1 0.8
0.6 0.5 Turbine speed [rpm] 1) 8.6 Wind speed [m/s]
1)
Active power [p.u.]
3
1)
Rotor frequency [Hz]
16.1
4 0.04 p.u.
15 1.0 p.u.
25 1.0 p.u.
44.07
50.36
23.54 1)
18.4
Data from the wind turbine Vestas V90-3.0MW.
Fig. 2: Operating conditions of the wind turbine Vestas V90-3.0MW and control strategy of the generator. For the three operating points of the wind turbine, it is possible to find the corresponding operating conditions of the induction generator as shown in Table I (considering generator parameters according to Figure 7). Furthermore, it is assumed that the cycloconverter should be operated with an effective pulse number of at least 20, which will be the case in operating point 3. The pulse number is then successively increasing when the wind turbine frequency decreases, as a result of the fixed VSC switching frequency of 500 Hz. The normalization is based on the active power at operating point 2 and half the DC-link voltage being 1 p.u. Therefore, the maximum output voltage of the cycloconverter in linear operation is 1.15 p.u. (2/√3). With regard to a safety margin (e.g. due to the thyristor turn-off time tq as discussed in Section 3.3), the cycloconverter output voltage is deliberately limited to 1.0 p.u. in all operating conditions.
Table I: Operating conditions of the induction generator Operating point Active power [p.u.] Reactive power [p.u.] Power factor Stator voltage |us| [p.u.] Stator current |is| [p.u.] Stator frequency [Hz] Effective pulse number Slip [%]
1
2
3
-0.04 0.30 -0.13 0.53 0.38 23.52 42.53 -0.11
-1.0 0.68 -0.83 1.0 0.80 43.76 22.85 -0.71
-1.0 0.62 -0.85 1.0 0.79 50 20 -0.72
3. Modulation constraints from a space vector perspective A description based on space vectors offers many advantages for analyzing the constraints and possibilities regarding the modulation and commutation of the cycloconverter valves. SVM has gained popularity as it is relatively simple to implement and inherently compatible with modern current and torque control schemes. Thereby, the three phase quantities are transformed into their space vector equivalents. Figure 3 shows how the line current directions and their magnitude relations vary depending
on the location of the current vector. It is also shown that the space vectors corresponding to the switching states of the cycloconverter (base vectors) form a hexagon, with two zero vectors in its center, in which all the phase legs are switched to the same DC link terminal. jβ |i1| < |i2|,|i3| |i3| < |i1|,|i2|
i1 < 0 i2 > 0 i3 > 0
i1 > 0 i2 > 0 i3 < 0
III II IV I V VI i1 < 0 i2 < 0 i3 > 0
|i2| < |i1|,|i3|
V3 (−+−)
|i2| < |i1|,|i3| i1 < 0 i2 > 0 i3 < 0
i1 > 0 i2 < 0 i3 > 0
i1 = 0
jβ
jβ V3 (−+−)
V2 (++−)
V2 (++−)
i2 = 0 i1 > 0 i2 < 0 i3 < 0
α
V4 (−++)
i3 = 0 |i3| < |i1|,|i2|
|i1| < |i2|,|i3|
us
V0 (−−−) V7 (+++)
α
is First and last base vector are zero vectors V5 (−−+) VSC SVM
V1 (+−−)
V6 (+−+)
V0 (−−−) V7 (+++) Last base vector α V4 (−++) is First base vector V1 (+−−) us V5 (−−+)
V6 (+−+)
MCC SVM
Fig. 3: Space vector modulation. Left: Current sectors. Middle and Right: Location of voltage vectors during a modulation interval for VSC SVM and MCC SVM, respectively. The modulation strategy should also be specially adapted to the wind turbine operation at low wind speeds, which contributes a considerable part to the total electric energy production. Another important issue for the modulation scheme is its capability to handle emergency events. An event outside the normal operation scheme may occur for instance due to inaccuracies in the current measurement or component failures. In such a case, the modulation scheme is required to avoid fatal emergencies causing damage to the equipment (e.g. short circuits) and should, if possible, restore normal operation with a minimum deviation in terms of applied voltage-time area.
3.1 Conventional SVM for VSC In conventional SVM for VSC (VSC SVM), a modulation interval is always starting and ending with zero vectors. The switching sequence is chosen such that the active base vectors are the ones adjacent to the reference voltage vector, refer to Figure 3. The switching instants are determined such that the average of the base vectors during the modulation interval corresponds to the reference voltage vector.
3.2 Constrained SVM for MCC with cycloconverter turn-off capability The modulation of a MCC (MCC SVM) differs from the modulation of a conventional VSC in several aspects. Firstly, as the VSC and the cycloconverters are alternately commutated, one of the edges of each voltage pulse will coincide with the switching of the VSC. This defines a constant modulation interval in which the other edge of the voltage pulse may be arbitrarily placed by commutating the corresponding cycloconverter phase leg. A second modulation constraint is the fact that the sign of each phase voltage has to be opposite to the sign of the corresponding line current after the VSC commutation in order to allow the cycloconverter phase legs to be naturally commutated. This implies that the modulation interval begins and ends with active vectors of opposite directions (unless one of the line currents is changing sign), determined by the instantaneous direction of the current vector, see Figure 3. Figure 4 shows all possible base vector sequences with the current vector located in sector I. Each phase leg commutation corresponds to a transition along one of the three directions in the voltage hexagon. If the current is located in any other sector, the possible vector sequences are shifted so that they are located as in Figure 4 with respect to this sector. The vector sequences consist of four base vectors. In practice, either the first or last base vector is suppressed (moved to the immediate beginning or end of the modulation interval) so that a three-vector sequence is obtained. This is attractive as it reduces the current ripple by avoiding voltage vectors of opposing direction during the same modulation interval. A more
comprehensive description as well as a method for finding the optimum vector sequence in any operating point can be found in [3]. S1.
V2 (++−) 3
2
V3 (−+−)
S2.
2
is
V1 (+−−)
V4 (−++)
S5.
S4.
is
V1 (+−−)
V4 (−++) 2
V4 (−++) V0 (−−−)
3
V6 (+−+)
3
V1 (+−−)
S6.
is
V7 (+++)
1
2
1
is
V1 (+−−)
V4 (−++)
V3 (−+−)
S3.
3
1
is
V7 (+++)
1
V2 (++−)
V4 (−++)
V0 (−−−)
V1 (+−−)
1
3
V5 (−−+)
2
V6 (+−+)
V4 (−++) 1
is 3
V1 (+−−) 2
V5 (−−+)
Fig. 4: Possible base vector sequences with the current vector located in sector I. If one of the line currents changes sign, the conditions for a natural commutation of the corresponding phase leg are no longer fulfilled. However, a cycloconverter equipped with IGBTs has the capability to force the turn-off of its valves, which allows the commutation scheme to maintain the desired pulse pattern regardless of a probable zero-crossing of the line currents. If one of the line currents has changed sign during a modulation interval, an additional phase leg commutation is required at the end of this modulation interval in order to establish the conditions for continuous natural commutations.
3.3 Constrained SVM for MCC without cycloconverter turn-off capability The modulation strategy proposed in the previous section is not suitable and adapted for cycloconverters equipped with thyristors due to the fact that their valves lack turn-off capability. Switching off a thyristor is only possible when its anode current tries to go negative under the influence of the external circuit. A forced turn-off would need to be enabled by complex, cost- and loss-intensive commutation circuits, which is no viable solution. Figure 5 shows an example where the current vector moves out of the initial sector during the modulation interval (i.e. one of the line currents changes sign). After a current sign reversal, the corresponding phase leg can no longer be commutated and one of the directions in the voltage hexagon will be inhibited. Once a line current is approaching zero and the corresponding phase leg commutation is still pending, the controller has the choice between commutating it just before the zero-crossing, or to refrain from doing any commutation during this modulation interval. For the first choice, the corresponding phase leg can be re-commutated at the end of the modulation interval (corresponding to a transition from base vector V1 to V2) in case the line current changes sign. However, the zero-crossing is more likely to be delayed to the subsequent period in this case.
In the other case, the current changes sign prior to the commutation of the corresponding phase leg. An example of such a sequence is shown in Figure 5. The desired sequence with the given reference voltage vector is V4 - V5 - V7 - V1 with an additional commutation at the end of the modulation interval to V2 in order to re-establish the conditions for continuous soft-switching. However, after the current direction reversal in the second phase leg, the transition from V4 to V5 is not possible any more. The only two possible sequences are shown in Figure 5, of which the latter (T2.) is the most attractive with regard to the given voltage reference vector. Both possible vector sequences have also the advantage that an additional phase leg commutation at the end of the modulation interval can be avoided. However, in most cases the commutation scheme cannot provide the desired pulse pattern during the zero-crossing of a line current. V2 (++−)
T1.
2
V3 (−+−)
Last base vector
T2.
V2 (++−)
is
1
First base vector
V2 (++−)
2
is 1
is
V7 (+++)
V4 (−++)
V4 (−++)
V4 (−++)
us
us
us
Fig. 5: Possible base vector sequences when the current is moving from sector I into sector II. The application of thyristors in the cycloconverter imposes certain additional restrictions on the timing of the commutation scheme. After turning off a thyristor, a reverse voltage must be maintained across it during the turn-off time tq. If a thyristor gets forward biased before the time tq has elapsed, it may unintentionally be re-triggered. This implies that the last base vector in every modulation interval has to be maintained during at least the time tq in order to prevent the thyristors from accidentally turning on during the subsequent VSC commutation. This is especially critical for an MCC in the considered application, where the power flow is directed from the AC side to the DC side. Consequently, the commutation instants are located towards the end of the modulation interval. In order to avoid any problems, a safety margin corresponding to tq should be kept at the end of the modulation interval. This reduces somewhat the maximum possible amplitude modulation ratio and slightly increases the current ripple. Today, fast thyristors are available from the major manufacturers with turn-off times tq around 20 μs, which corresponds to 2% of the intended modulation interval.
4. Current clamping control strategy for MCC As seen in the previous section, the limited controllability of the thyristor valves calls for a new modulation strategy whenever one of the line currents approaches zero. Due to the relatively low pulse number, a certain current ripple is inevitable. Especially during low power generation, the current ripple may imply that the current vector repeatedly moves back and forth between two sectors, which is highly undesirable. The proposed current clamping control strategy is based on stopping the gate pulses in the phase leg where the current is close to zero during a certain interval. A similar dead-time control strategy, where the gate pulses of the thyristors are stopped if the output current is lower than a threshold value, was previously described [6]. However, in contrast to the proposed current clamping control strategy for MCC, the dead time was constant and not adjusted during every modulation interval. Basically, the same modulation strategy as in Section 3.2 is used in order to determine the base vector sequence and the commutation instants. A predictor with a simple transient model of the squirrel-cage induction generator (refer to Section 5.1 for further details) then determines the trajectory of the current
vector for the calculated base vector sequence. In this way it can be predicted in advance at what exact instant the current vector leaves the initial sector, i.e. even before a certain commutation cycle has begun. In case of an imminent change of current sector, there is enough time to alter the base vector sequence as described subsequently. E1.
E2.
V2 (++−)
V2 (++−)
Vi1=0 V (++−) 2
E3.
uref
uref
uref
V0 (−−−)
Vi2=0 Vi1=0
V1 (+−−)
V1 (+−−) Vi1=0
V1 (+−−)
is is V5 (−−+)
current reversal avoided
is V6 (+−+)
V6 (+−+)
Voltage vector sequences i2 = 0
c2
c2
i1 = 0
i1 = 0 c2
current reversal delayed
start
(c1) avoided
(c1) avoided
current reversal delayed
c1 start
c3 end
c3 end
start
end
c3
Current trajectories
Fig. 6: Examples of base vector sequences and corresponding current trajectories with current clamping control strategy for MCC (the current vector is initially located in sector V). If the current trajectory is only temporarily leaving the initial current sector during a modulation interval as for instance in example E1 in Figure 6, the arising current reversal should be avoided. This is done by not gating on the anti-parallel thyristor in the conducting valve of the corresponding phase leg. This implies that the line current through the initially conducting device is turned off once it gets zero and the phase outlet is getting isolated from the DC link terminals. When choosing the commutation instant of the corresponding phase leg accordingly, it is still possible to provide the desired reference voltage during the modulation interval. In example E1, the commutation of the second phase leg (c2) is delayed to the instant when the current would originally have re-entered the initial current sector. It should be mentioned that the example E1 in Figure 6 is only the most common and basic case. Especially at low power generation (corresponding to a high pulse number and low current), different other current trajectories may occur. For instance, a phase leg commutation may be necessary while the current in another phase is clamped (similar to example E3) or the current trajectory may pass through both neighboring current sectors. However, all these cases can be treated in a similar way as in example E1. The examples E2 and E3 in Figure 6 represent two different cases where the current vector is actually required to change into a neighboring current sector. As discussed in the previous section, it is in this case not possible to maintain the desired voltage sequence in a conventional manner due to the fact that the phase leg in which the current is changing sign is either not at all commutated or not at the desired instant. The proposed current clamping control strategy compensates this drawback by controlling the dead-time
during which the corresponding line current is kept to zero. Once the anti-parallel thyristor to the previously conducting thyristor in the same valve is gated on, the current will start flowing into the new current sector. In this way we regain the control over the phase leg in which the current is changing sign and it is therefore possible to provide the desired reference voltage during every modulation interval. The example E3 differs from E2 in the way that a phase leg commutation takes place while the current in another phase is actually clamped. Figure 6 shows also the voltage vector sequences, which now contain voltage vectors during the current clamping that differ from the eight base vectors. Therefore it is not trivial to determine the exact timing for the phase leg commutations as well as the release of the current clamping. The switching instants have to be determined prior to the start of the modulation interval with the aid of a predictor.
5. Evaluation of modulation strategies In order to evaluate the discussed modulation strategies, a simulation model was implemented in Matlab/Simulink. The evaluation is limited to the three different operating points described in Section 2.1 which are assumed to be representative for all operating conditions.
5.1 Induction generator model A transient model of the squirrel-cage induction generator was implemented according to Figure 7. The normalized generator parameters used in the simulations correspond to those of a multi-megawatt wind turbine [7]. Based on the equivalent circuit in Figure 7, the basic equations for the stator current is (1) and rotor flux Ψr (2) forming the Matlab/Simulink model can be extracted. As all simulations are done in steady-state, the angular rotor frequency ωr was assumed constant as a function of the generator slip and stator frequency. is +
us
Rs
Lsl
Lrl im Lm
ir Rr +
jωrΨr
Normalized wind turbine generator parameters: magnetizing inductance Lm: 3.0 p.u. stator leakage inductance Lsl: 0.1 p.u. rotor leakage inductance Lrl: 0.08 p.u. stator resistance Rs: 0.01 p.u. rotor resistance Rr: 0.01 p.u.
Fig. 7: Equivalent circuit of the induction generator and normalized generator parameters. 2 ⎡ ⎛ Lm Rr ⎞ Lm Lm + Lrl di s ⎟+ = ⋅ ⎢u s − i s ⋅ ⎜⎜ Rs + 2 ⎟ L dt Lm (Lsl + Lrl ) + Lsl Lrl ⎣⎢ (Lm + Lrl ) ⎠ m + Lrl ⎝
RL dΨ r Rr = jωr Ψ r − Ψ r ⋅ + is ⋅ r m dt Lm + Lrl Lm + Lrl
⎛ Rr ⎞⎤ ⋅ ⎜⎜ ⋅ Ψ r − jωr Ψ r ⎟⎟⎥ L L + lr ⎝ m ⎠⎦⎥
(1)
(2)
5.2 Current and flux trajectories The stator current and flux trajectories at steady-state for both conventional SVM for MCC and the proposed current clamping control strategy are shown in Figure 8. As expected, the stator flux is at its nominal value in operating point 1 and 2, whereas the generator operates in field-weakening in operating point 3. Similarly, the current is at its nominal value in the operating points 2 and 3, whereas it is lower at operating point 1 directly after start-up. Looking closer at the current trajectories, it can be observed that
they only differ around the zero-crossings of the line currents for the two different modulation strategies. This becomes especially apparent at operating point 1, where the current ripple is considerable. Nevertheless, the proposed current clamping control strategy handles all three operating points smoothly. 1
2
3
MCC SVM 1
2
3
Current clamping MCC SVM
Fig. 8: Trajectories of current (solid) and stator flux (dotted) at steady-state in the three operating points. Looking at the line currents of operating point 1 in Figure 9, it is apparent how the current clamping control strategy works and how multiple zero-crossings of the current are avoided. This is also reflected in the harmonic content of the line currents. From the right side of Figure 9, it can be seen that in this specific operating point all major harmonics except the 5th harmonic are reduced considerably for the current clamping MCC SVM compared to MCC SVM, which results in a reduced total harmonic distortion THD0. The reduction of the harmonic content in the generator current is also reflected in a slightly reduced rms-value of the torque ripple according to Table II. The torque ripple is diminished in accordance with the decreasing effective pulse number after the start-up of the wind turbine.
Table II: Torque ripple in percent of nominal torque TN for the three operating points Torque ripple rms [%]
Operating point 1 (T = 0.085 p.u.)
Operating point 2 (TN = 1.135 p.u.)
Operating point 3 (T = 0.993 p.u.)
VSC SVM MCC SVM Current clamping MCC SVM
21.0 21.7 18.7
15.2 15.1 14.3
13.1 13.3 12.6
Phase current amplitude [p.u]
Phase current [p.u.]
0.6 0.4 0.2 0 −0.2 −0.4 0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
Time [s]
0 −0.2 −0.4 0.015
0.02
0.025
Time [s]
0.2 0.15 0.1 0.05 0 0
Phase current amplitude [p.u]
Phase current [p.u.]
0.2
0.01
0.25
5
10
15
0.03
0.035
0.04
0.045
20
25
30
35
40
45
50
Harmonic number
MCC SVM
0.4
0.005
THD0 = 24.0 %
0.3
0.045
0.6
0
0.4 0.35
0.4 0.35
THD0 = 17.6 %
0.3 0.25 0.2 0.15 0.1 0.05 0 0
5
Current clamping MCC SVM
10
15
20
25
30
35
40
45
50
Harmonic number
Fig. 9: Line currents and harmonic spectrum (averaging over one period) in operating point 1.
6. Conclusions A novel modulation strategy for MCC systems without cycloconverter turn-off capability has been proposed and verified by simulations. The described current clamping control strategy is based on blocking the switches in the phase leg where the current is close to zero during a certain interval. Based on a predictor, the desired voltage reference can be provided in any modulation interval under all operating conditions. The proposed modulation strategy does not only allow the replacement of IGBT valves in the cycloconverter with comparably cheap and well-established fast thyristors. In addition, it offers also a better performance than conventional SVM for MCC with regard to the current and torque ripple. As a consequence, the application of VSC transmission for the grid connection of large wind farms becomes far more attractive.
References [1] Norrga S., Meier S., Östlund S.: A Three-phase Soft-switched Isolated AC/DC Converter without Auxiliary Circuit, IAS 2004, Vol 3, pp. 1768-1775 [2] Malesani L., Tomasin P., Toigo V.: Space Vector Control and Current Harmonics in Quasi-Resonant SoftSwitching PWM Conversion, IEEE Transaction on Industry Applications, Vol 32 no 2, pp. 269-278, 1996 [3] Norrga S.: Modulation Strategies for Mutually Commutated Isolated Three-Phase Converter Systems, PESC 2005, pp. 2736-2743 [4] Meier S.: Novel Voltage Source Converter based HVDC Transmission System for Offshore Wind Farms, Licentiate thesis, Royal Institute of Technology, Stockholm, Sweden, 2005 [5] V90-3.0MW - An efficient way to more power. Available from the Vestas web site, http://www.vestas.com [6] Iturriz F., Ladoux P.: Phase-Controlled Multilevel Converters Based on Dual Structure Associations, IEEE Transactions on Power Electronics, Vol 15 no 1, pp. 92-101, 2000 [7] Ackermann T., ed.: Wind Power in Power Systems, John Wiley & Sons, Ltd, 2005
