Open-loop Approach for Control of Multi-terminal DC systems based on Modular Multilevel Converters
HAIDER Arif
Open-loop Approach for Control of Multi-terminal DC systems based on Modular Multilevel Converters Arif Haider, Noman Ahmed, Lennart Ängquist, Hans-Peter Nee Electrical Machine and Power Electronics Laboratory (EME) Royal Institute of Technology (KTH) Teknikringen 33, 100 44 Stockholm, Sweden Tel.: +46 765829649 E-Mail:
[email protected],
[email protected],
[email protected],
[email protected]
Keywords «Converter Control», «Multilevel Converters», «Multiterminal HVDC», «Power Transmission»
Abstract In this paper a multi-terminal direct current (MTDC) system with modular multilevel converters (M2Cs) is suggested. An open loop control method is used for the control of the converters. Each converter is modeled with 36 sub-modules per arm with a total of 216 sub-modules consisting of half bridges. Power-synchronization control is used instead of a phase-locked loop (PLL) for synchronization. Thus, the short circuit capacities of the ac systems are no longer limiting factors and the instability caused by the PLL in weak ac systems is avoided [10]. A direct voltage controller is implemented with power-synchronization control as an inner loop in one station. Several scenarios are analyzed to demonstrate control flexibility and ride-through capability for grid transients. By means of analytical calculations and time simulations in PSCAD/EMTDC, the validity of the proposed MTDC system is confirmed.
Introduction In the future MTDC systems will be needed to connect the distant renewable offshore power resources to the onshore grid and also for the interconnection of different onshore grid systems. Due to the intermittent nature of wind and the increasing amount of wind energy in the electrical grids, interconnections to the grids are one of the measures that will reduce the effects of intermittency. This is not likely to be accomplished with ac transmission mainly due to the capacitive charging currents of the ac cables [1]. MTDC systems are gaining ever greater attention and different MTDC control strategies for voltage source converters are proposed [2]-[4]. The M2C topology has been presented in several papers since 2002. Due to its high efficiency, superior output voltage waveform and scalability the M2C seems to be the most promising converter topology for MTDC systems. In Figure 1 a possible MTDC layout with three M2Cs is shown. The M2C is extendable to any number of levels without adding significant complexity to its control system and voltage balancing of the sub-module capacitors. Thus M2C with an increased number of levels can be built which can be connected to high voltage networks without need for interfacing transformers and dc-link capacitors. With an increased number of levels a high quality output voltage is generated such that the need for output filters is substantially reduced [5],[9]. The system in Figure 1 is investigated in the present paper. All the M2Cs are 1000 MVA thirty six (36) sub-modules per arm modular converters with a dc-link voltage of ±320 kV. Total energy stored in the arm capacitors is 34 MJ. All the converter stations are open-loop controlled. T1, T2 and T3 are 400 kV/400 kV, 1200 MVA transformers connected to ac network with 10 GVA short-circuit capacity (SSC). DC station 1 controls the direct voltage of the system and it further controls the ac side voltage to a given reference. DC station 2 and station 3 has active power control and ac side voltage control.
EPE 2011 - Birmingham
ISBN: 9789075815153
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Open-loop Approach for Control of Multi-terminal DC systems based on Modular Multilevel Converters
HAIDER Arif
The dc cable parameters are c = 0.296 uF/km, l = 0.1056 mH/km and r = 12.1 mΩ/km. The dc cables are modeled using π-link model for each 50 km length. On Shore Grid 5000 MVA 400 kV X/R = 10 G1 SCC = 10 GVA B 1
Off Shore (Wind Farm) DC station 1
1200 MVA 400 kV / 400 kV
T1
Direct voltage control AC voltage control
DC station 2 DC B1
1000 MVA
b1
DC B2 b2
DC Link 1 300 km
M2C
b3
b4 ± 320 kV DC System
DC Link 2 200 km
DC Link 3 250 km
b5
1000 MVA
M2C
1200 MVA 400 kV / 400 kV T2
3000 MVA 400 kV X/R = 10 G2 B 2 SCC = 10 GVA
P-control AC voltage control
b6 DC B3
On Shore Grid DC station 3 1200 MVA 400 kV / 400 kV
P-control AC voltage control
1000 MVA
M2C
T3
B3
G3 SCC = 10 GVA
1000 MVA 400 kV X/R = 10
Fig 1. M2C-based 3-terminal MTDC system Figure 2 shows the M2C used for the MTDC system. The M2C comprises three phase legs with two arms each as shown in Figure 2(a). Each arm comprises a chain of series-connected sub-modules, each one containing a dc capacitor with a controlled half-bridge arrangement to insert or bypass the capacitor as shown in Figure 2(b). It is proposed in [9] that the internal voltage-sharing between the sub-module capacitors inside each converter arm is provided by a selection mechanism, which selects the individual sub-module to be bypassed/inserted, whenever the modulator asks for a switching operation to be executed. The selection criterion is based on the actual arm current direction. The bypassed sub-module with the lowest voltage is to be inserted and the inserted sub-module having the highest voltage is to be bypassed when the arm current is charging, and correspondingly the bypassed sub-module with the highest voltage is to be inserted and the inserted sub-module having the lowest voltage is to be bypassed when the arm current is discharging. This approach has shown to be quite effective in simulations and tests. Some problems related to the control of the M2C are discussed in [5]-[7]. One major problem is to stabilize the capacitor voltages in all sub-modules and simultaneously suppress second harmonic current circulating between the converter phase legs. In [8] an open-loop approach has been proposed, which utilizes the measured ac side currents to estimate the sum of all sub-module capacitor voltages (total capacitor voltage) in each arm, and to calculate insertion indices to each arm which eliminates the second harmonic currents. A string of series-connected diodes will be established between the dc bars. The potential of the ac terminal therefore can only move between the potentials defined by the dc bars.
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ISBN: 9789075815153
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Open-loop Approach for Control of Multi-terminal DC systems based on Modular Multilevel Converters
SM
SM
SM
N Sub Modules SM
SM
SM
idc
+ iu
SM
SM
L Ua
La
Ia
Ub
Lb
Ib
Uc
Lc
N
ucu -
SM
L
HAIDER Arif
L
udc
iv
Ic L
L
SM
SM
L
SM
+ iL
SM
SM
SM
SM
SM
SM
ucl
S1
-
C0 S2
Fig 2(a). Schematic of the converter
Fig 2(b). A sub-module
Principle of open-loop control approach The arm currents can be described in terms of ac terminal output current, iv , and circulating current,
idiff , according to (1) and (2) respectively.
iU =
iv + idiff 2
(1)
iU =
iv − idiff 2
(2)
The arm voltage references contain contributions from the measured dc-side voltage, from the modulator and from the control system, as described in (3) and (4). ref uCU =
uD − eV − udiff 2
(3)
ref uCU =
uD + eV − udiff 2
(4)
The powers delivered to the arms are given in (5) and (6). Σ dWCU = iU uCU dt
(5)
dWCLΣ = −iL uCL dt
(6)
Inserting (1)-(4) in (5) and (6) yields the arm energy fluctuation, as in (7) and (8). Σ dWCU ⎛i ⎞⎛ u ⎞ = ⎜ v + idiff ⎟ ⎜ D − eV − udiff ⎟ dt ⎝2 ⎠⎝ 2 ⎠
(7)
dWCLΣ ⎛i ⎞⎛ u ⎞ = − ⎜ v − idiff ⎟ ⎜ D + eV − udiff ⎟ dt ⎝2 ⎠⎝ 2 ⎠
(8)
The voltage udiff controls the circulating current idiff according to
L
didiff dt
+ Ridiff = udiff
(9)
If the voltage udiff is constant, then also its driving circulating current idiff becomes constant as in (10) and (11).
udiff = R iˆdiff 0
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(10)
idiff = iˆdiff 0
ISBN: 9789075815153
(11)
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Open-loop Approach for Control of Multi-terminal DC systems based on Modular Multilevel Converters
HAIDER Arif
The open-loop control approach now can be derived from the assumption that the converter is operating in steady state with a circulating current that is a pure direct current. Thus we search the steady-state solution to (7) and (8) assuming (12), (13). This steady-state solution for the upper arm energy is given by (15) and the circulating current is given by (16). (12) ev ( t ) = eˆv cos ωt (13) iv ( t ) = iˆv cos (ωt + φ ) Σ Σ WCU = WCU 0 −
idiff 0 =
eˆviˆdiff 0 sin ωt
ω ˆev iˆv cos φ
⎛ uD ⎞ ⎜ − R idiff 0 ⎟ iˆv sin (ωt + φ ) eˆ iˆ sin ωt 2 ⎠ +⎝ − v diff 0 2ω 8ω
(15) (16)
u D + u D2 − 4 Reˆv iˆv cos φ
Σ In (15), WCU 0 is an integration constant which can be freely selected and used as a reference for the total arm average energy. Finally, the total capacitor voltage in the upper arm can be estimated as in (17). Σ C 2WCU (t ) ∑ (17) (18) Carm = uCU (t ) = N Carm now the insertion indices and can be calculated as
nU ( t ) =
ref uCU (t ) Σ uCU (t )
(19)
nL ( t ) =
ref uCL (t ) Σ uCL (t )
(20)
Phase estimator is used to extract the fundamental frequency component of the current. The instantaneous values of the total capacitor voltages in the arms are calculated as described above. Finally, the insertion indices for each arm can be calculated as the quotient between the desired arm voltage reference and the estimated total capacitor voltage as given by (19) and (20). The insertion indices obtained are supplied directly to the modulators. In [8] the simulations and tests have shown that the converter then very fast reaches stable steady-state operation with the average energy stored in the arms in agreement with their respective reference values. The converter using open-loop concept for inner control has shown very good dynamic performance, similar or even better than when voltage feedback has been utilized and it exhibited advantages from an implementation point of view also. An outline of this controller is shown on Figure 3.
Fig 3. Outline of Open Loop Controller
EPE 2011 - Birmingham
ISBN: 9789075815153
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Open-loop Approach for Control of Multi-terminal DC systems based on Modular Multilevel Converters
HAIDER Arif
Power-Synchronization Control of M2Cs The concept of the power-synchronization control is that the M2C is synchronized with the ac grid through active power control instead of using a PLL. The control of active power and alternating voltage is achieved by means of the phase angle ( θ vref ) and the voltage magnitude ( V ref ) of the M2C through a multivariable controller [10]. The power-synchronization loop directly controls active power output from the M2C and alternating voltage is controlled by adjusting the magnitude of the voltage reference. The power-synchronization control principle for M2C is given as
d Δθ = k p ( P ref − Pf ) dt dV ref = ku (U ref − U f ) dt
(21) (22)
where P ref is the reference for the active power, Pf is the measured active power, k p is the controller gain, and Δθ is the output of the controller. U ref is the reference for the ac side voltage, U f is the measured voltage, ku is the controller gain, and V ref is the output. An additional PLL is obviously not necessary during normal operation. The transmitted power is increased or decreased by shifting the output voltage phasor of the M2C forwards or backwards. In Figure 4, the block diagram of the power-synchronization control loop is shown for a gridconnected M2C. It retains synchronism between the M2C and the ac system, and at the same time, it is also the active-power control. The error from power control is converted to a frequency deviation, which is then integrated to an angle increment. The d component of the three phase currents are used for damping as well. The output signal θ vref supplies the angle to transform the voltage reference from the converter dq frame to the stationary frame.
ΔU e
U ref
Uf
ia ib ic
dq abc
P ref
ku s
Aθ x + jy
id
vd
iq
vq
ΔPe
V ref Δθui
kv s
Δθ e
kp s
θ vref
θ ref Fig 4. Power-synchronization control of M2C
Direct Voltage Controller In the studied MTDC system, converter station 1 has to keep the direct voltage constant, while the other converter stations control their active power. The active power is thus automatically balanced between the stations. If the MTDC system has more than three terminals it might be of interest to implement voltage droop controllers on two or more stations for reliability and to distribute the load
EPE 2011 - Birmingham
ISBN: 9789075815153
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Open-loop Approach for Control of Multi-terminal DC systems based on Modular Multilevel Converters
HAIDER Arif
equally without over loading one of the stations. For direct voltage controller, a proportional integral (PI) controller is suggested [10] accordingly
k ⎛ P ref = − ⎜ k p + i s ⎝
⎞ ⎡ ref ⎟ ⎣⎢( ud ⎠
)
2
− ud2 ⎤⎥ ⎦
(23)
The power-synchronization loop acts as an inner loop for the direct voltage controller. The output of the direct voltage controller provides the power reference P ref to the power-synchronization loop. Figure 5 shows the control block diagram for the direct voltage controller.
U ref
P
+
ΔU e
-
ΔPe
ref
+
Uf Power Synchronization Controller
-
PM 2C1
PM 2C 2
M2C
Pf
( udc )
PI Controller
+
2
-
(u ) ref dc
2
Fig 5. Control block diagram of direct voltage controller
Simulation Results In the MTDC system in Figure 1, DC station 1 controls the dc link voltage while DC station 2 and station 3 are assigned to control active power. All the converter stations are equipped with powersynchronization controllers while only converter station 1 is equipped with a direct voltage regulator. In order to show the effectiveness of the of the MTDC system in active power management, station 2 is set to inject 600 MW, station 3 is set to take 700 MW power from the system while station 1 regulates the active power sharing between stations 1 and station 2 and injects the required power in the system. At t = 0.5 s the active power command is given to station 2 to ramp down the power from 600 MW to 400 MW within 500 ms. The power of Station 3 is maintained at 700 MW. It can be noticed that station 1 starts to increase its active power injection in the system to compensate for the power cutoff while maintaining the direct voltage at 640 kV. At t = 2.0 s another command is given to station 2 to ramp up the active power to 600 MW again within 500 ms. The system gets stable after each interval of changing the power for the converter stations. P
800
Q
300
P
800
Q
200 100 0 -100 0
0.5
1
1.5
2 2.5 time (s)
3
3.5
4
P(MW) & Q(MVAR)
600 P(MW) & Q(MVAR)
P(MW) & Q(MVAR)
400
400 200 0 -200 0
0.5
1
1.5
2 2.5 time (s)
3
3.5
4
600
P
Q
400 200 0 -200 0
0.5
1
1.5
2 2.5 time (s)
3
3.5
4
(a) (b) (c) Fig 6. Active and Reactive power at ac systems of station 1 (a), station 2 (b) and station 3 (c).
EPE 2011 - Birmingham
ISBN: 9789075815153
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Open-loop Approach for Control of Multi-terminal DC systems based on Modular Multilevel Converters
HAIDER Arif
646
646
644
644
644
642
642
642
640 638 636
U dc (k V )
646
U dc (k V )
Udc (k V )
The active and reactive powers at the ac sides of the converters are shown in Figure 6. Due to alternating voltage control reactive power delivered to the system increases when the active power increases. It can be noticed that the power-synchronization controller works well in this scenario and controls the active and reactive power of the converter stations. The dc bus voltage shows very little transients during ramping up and down of the active power as depicted in Figure 7.
640 638
0.5
1
1.5
2 2.5 time (s)
3
3.5
634 0
4
638 636
636
634 0
640
0.5
1
1.5
2 2.5 time (s)
3
3.5
634 0
4
0.5
1
1.5
2 2.5 time (s)
3
3.5
4
(a) (b) (c) Fig 7. DC bus voltages of station 1 (a), station 2 (b) and station 3 (c). The active power through the dc links shows that the power flow from station 1 to station 3 through dc link 2 and the power from station 2 to station 3 flows directly through dc link 3 and also via dc link 1 and 2. It is obvious from the simulation results that an efficient active power flow control in the MTDC transmission system can be achieved. 320
480
-30
300
460
280
440
P (M W )
P (M W )
-50 -70 -90 -110
260
0.5
1
1.5
2 2.5 time (s)
3
3.5
4
220 0
420 400
240
-130 -150 0
P (M W )
0 -10
0.5
1
1.5
2 2.5 time (s)
3
3.5
4
380 0
0.5
1
1.5
(a) (b) Fig 8. Power flow in dc link 1 (a), dc link 2 (b) and dc link 3 (c).
2 2.5 time (s)
3
3.5
4
(c)
P
500 300 100 -100 -300
800
Q
P
0
0.25
0.5
0.75 time (s)
1
1.25
1.5
600 400 200 0 -200
800
Q P (M W ) & Q (M V A R )
1300 1100 900 700
P (M W ) & Q (M V A R )
P (M W ) & Q (M V A R )
To evaluate the transient performance of the MTDC system shown in Figure 1, the system is subjected to a shutdown of converter station 2. The MTDC system is setup such that the station 2 injects 600 MW in the system and station 3 takes out 700 MW from the system. Station 1 is responsible for the power balance in the system. At t = 0.5 s the station 2 is shutdown as a permanent fault and the power at station 2 changes to 0 MW through the rest of the simulation. Figure 9 shows that the active power delivered by station 1. 600
0.25
0.5
0.75 time (s)
1
1.25
1.5
Q
200 0 -200
0
P
400
0
0.25
0.5
0.75 time (s)
1
1.25
1.5
(a) (b) (c) Fig 9. Active and Reactive power at ac systems of station 1 (a), station 2 (b) and station 3 (c).
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ISBN: 9789075815153
P.7
Open-loop Approach for Control of Multi-terminal DC systems based on Modular Multilevel Converters
HAIDER Arif
650
650
640
640
640
630 620 610
U d c (k V )
650
U d c (k V )
U d c (k V )
The power delivered increases immediately to compensate for the demand of the power in the MTDC system while the power delivered to station 3 remains at 700 MW with a negligible transient. The peak in the power observed in Figure 9(a) can easily be reduced if a current limitation is introduced. This would, however, cause an associated drop in the dc side voltage. The power-synchronization controller responds quite fast to deliver the required power to the system and bring back the system to stability. The dc bus voltages of the converter stations show some transients during the shutdown of station 2 as shown in Figure 10. The voltage drop during the transient are lower than 5% and the voltage controller at station 1 works well to stabilize the direct voltage to 640 kV and prevent the system to get unstable.
630 620
0
0.25
0.5
0.75 time (s)
1
1.25
610
1.5
630 620 610
0
0.25
0.5
0.75 time (s)
1
1.25
1.5
0
0.5
1
1.5
time (s)
(a) (b) (c) Fig 10. DC bus voltages of station 1 (a), station 2 (b) and station 3 (c).
800
-600
800
600
-650
600
400
-700
400 200 0
P (M W )
1000
P (M W )
P (M W )
The power flow at dc Bus 1 increases to 700 MW and the power flow at dc Bus 3 stabilize after a transient of 100 MW. The power at dc Bus 2 becomes 0 MW as shown in Figure 11.
200 0
0
0.25
0.5
0.75 time (s)
1
1.25
-200
1.5
-750 -800
0
0.25
0.5
0.75 time (s)
1
1.25
-850
1.5
0
0.25
0.5
(a) (b) Fig 11. Power at dc Bus 1 (a), dc Bus 2 (b) and dc Bus 3 (c).
0.75 time (s)
1
1.25
1.5
(c)
Figure 12 shows the power flow in the dc links. The direction of power flow in dc link 1 reverses after shutdown of station 2. Now, most of the power delivered to station 3 flows through dc link 2 and rest of the power flow through dc link 3 via dc link 1. It can be noticed in the results that the system is able to recover from the transient and return to a stable operation without significant difficulty. 500
600
400 300
500 100 0
400
300
300
-100 -200
P (M W )
400 P (M W )
P (M W )
200
0
0.25
0.5
0.75 time (s)
1
1.25
1.5
200
0
0.25
0.5
0.75 time (s)
1
1.25
1.5
200
0
0.25
0.5
0.75 time (s)
1
1.25
1.5
(a) (b) (c) Fig 12. Power flow in dc link 1 (a), dc link 2 (b) and dc link 3 (c).
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ISBN: 9789075815153
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Open-loop Approach for Control of Multi-terminal DC systems based on Modular Multilevel Converters
HAIDER Arif
Conclusion An MTDC system based on M2Cs using open-loop control has been simulated. The M2Cs are synchronized to their ac grid connections using power-synchronization control. Both power steps and total drop-outs of power have been studied, and the results confirm that a very good stability can be achieved.
References [1] Ackermann T., Ed.: Wind power in power systems, NJ Wiley, 2005. [2] Adam G. P., Finney S. J., Williams B. W., Bell K., Burt G.: Control of Multi-Terminal DC Transmission System Based on Voltage Source Converters, IET ACDC 2010, London, UK, 19-22 October 2010. [3] Adam G. P., Lara O. A., Burt G.: Multi-terminal dc transmission system based on modular multilevel converter, Universities Power Engineering Conference (UPEC) 2009 , Glasgow, UK, 1-4 September 2009 [4] Gnanarathna U. N., Chaudhary S. K., Gole A. M., Teodorescu R.: Modular multilevel converter based hvdc system for grid connection of offshore wind power, IET ACDC 2010, London, UK, 19-22 October 2010. [5] Allebrod S., Hamerski R., Marquardt R.: New transformerless, scalable modular multilevel converters for hvdc transmission, IEEE Power Electronics Specialists Conference (PESC), Rhodes, Greece, June 15-19, 2008. [6] Antonopoulos A., Ängquist L., Nee H.-P.: On dynamics and voltage control of the modular multilevel converter, European Power Electronics Conference (EPE), Barcelona, Spain, Septemeber 8-10, 2009. [7] Hagiwara M., Akagi H.: Control and experiment of pulse-width-modulated modular multilevel converters, European Power Electronics Conference (EPE), Barcelona, Spain, Septemeber 8-10, 2009. [8] Ängquist L., Antonopoulos A., Siemaszko D., Ilves K., Vasiladiotis M., Nee H.-P.: Inner control of modular multilevel converters – an approach using open-loop estimation of stored energy, The 2010 Power Electronic Conference (ECCE Asia) IPEC-Sapporo 2010, Sapporo, Japan, June 21-24, 2010. [9] Glinka M., Marquardt R.: A New AC/AC Multilevel Converter Family, IEEE Transactions on Industrial Electronics, vol. 52, no. 3, June 2005. [10] Zhang L., Harnefors L., Nee H.-P.: Interconnection of Two Very Weak AC Systems by VSC-HVDC Links Using Power-Synchronization Control, IEEE Transactions on Power Systems, vol. 26, no. 1, February 2011.
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