The superiority of CMI (Cascaded Multilevel Inverter) is unparalleled in high power and high voltage STATCOM (Static Synchronous Compensator). However, the parameters and operating conditions of each individual power unit composing the cascaded STATCOM differ from unit to unit, causing unit voltage disequilibrium on the DC side. This phenomenon seriously impairs the operation performance of STATCOM, and thus maintaining the DC voltage balance and stability becomes critical for cascaded STATCOM. This paper analyzes the case of voltage disequilibrium, combines the operation characteristics of the cascaded STATCOM, and proposes a new DC voltage control scheme with the advantages of good control performance and stability. This hierarchical control method uses software to achieve the total active power control and also uses chopper controllers to enable that the imbalance power can flow among the capacitors in order to keep DC capacitor voltages balance. The operating principle of the chopper controllers is analyzed and the implementation is presented. The major advantages of the proposed control strategy are that the number of PI regulators has been decreased remarkably and accordingly the blindness of system design and debugging also reduces obviously. The simulation reveals that the proposed control scheme can achieve the satisfactory control goals.
1. Introduction
Cascaded STATCOM is characterized by large voltage levels, small harmonic current, high system efficiency, small and few passive components and ease of expansion
[1

3]
, and hence leading the trend of FACTS (Flexible Alternative Current Transmission Systems) technology development
[4]
. Moreover, it’s an effective way to solve the power quality problems in high voltage and high power applications. Therefore, it has attracted widespread attention both in academic and industrial fields
[5]
.
In cascaded STATCOM, due to the 3phase unbalance compensation and the differences in component parameters and working states, different power units will receive or send different amount of active power, which results in voltages rising in the DC link of some power units and dropping in other units. This is known as the DC voltage unbalance
[6

8]
. The good performance of the device and the current control strategies are all based on the perfect consistency of the power units. Maintaining the voltage stability and balance is the basis for cascaded STATCOM to operate safely and reliably for a long time. Thus, the research on reducing the DC voltage unbalance is extremely essential
[9]
.
Currently, the DC link voltage control strategies fall into two categories
[7]
. One refers to the hardwarebased methods, such as the control method by paralleling resistors
[10]
, the balancing method by energy exchanging on AC line
[11]
, the balancing method by energy exchanging on DC line
[10

13]
, and the control strategy based on the unitypowerfactor (UPF) 4quadrant VSR
[13]
. These approaches almost employ the same hardware devices like PWM rectifiers
[5
,
13]
, diode bridges, or combination of inverters and isolated transformers
[10
,
12]
. Through these hardware circuits adopted by the hardwarebased method, the consumed energy can be compensated to maintain the balance and stability of DC capacitor voltages. The only differences among these methods lie in their topologies, sources of energy and energy flow paths.
The hardwarebased methods have some merits such as fast response, small steady state error, effective voltage control, reliable and stable operation performance, and hence find the wide practical applications
[10
,
11]
. A typical hardware method reported in
[3
,
12]
uses the combination of a multiwinding phase shifting transformer and uncontrollable rectifiers. Ref.
[14
,
15]
reported the 10kV/±75Mvar STATCOM produced by ALSTOM in 1999 and this famous project adopted the DC voltage balancing method by energy exchanging on AC line
[11]
. Ref.
[16]
reported that the 10kV/±50Mvar STATCOM installed at the 220KV Xijiao Substation in Shanghai in 2006 adopted the balancing method by energy exchanging on DC line
[10]
. The worldfamous 35kV/±200Mvar STATCOM constructed in 2011 by China Southern Power Grid Co., Ltd also adopted the balancing method by paralleling resistors controlled through PWM mode IGBTs
[17]
.
However, the hardwarebased methods require too many hardware components and have some drawbacks in weight, volume and efficiency, causing high hardware cost and inconvenience for system extension
[7]
, although these approaches are widely applied in some worldfamous projects.
Softwarebased methods include such approaches as the individual voltage balancing strategy based on direct voltage error
[18]
, the balancing method based on power error regulating
[19
,
20]
, the active voltage vector superposition strategy
[21]
, and the phase angle superposition method
[22]
. By using the closedloop feedback control, the softwarebased methods measure the DC capacitor voltages of power units and regulate the output through the voltage error or the power error. The principal idea is to utilize pulse width modulation and phase angle modulation to regulate the charging and discharging time of power components. Consequently, these methods realize the regulation of DC link voltage and noticeably reduce the hardware cost. So, the softwarebased methods represent a further development trend of the DC voltage control in cascaded STATCOM.
However, for the cascaded devices with large amount of power units, these methods have to control many variables and loops. For example, the phase angle superposition method
[22]
uses (3N+7) PI regulators, where N is the number of power units in a phase. Control strategies in
[18

21]
use 3(N+1) PI regulators. However, there has been no scientific method to design the parameters of the PI regulators so far. In addition, the coupling situations for control loops increase dramatically, leading to more difficulties for controller design and system debugging
[7]
.
Furthermore, the softwarebased methods are based on the traditional error control technology such as PID control and hysteresis control, which will cause a certain time delay because these methods are not effective until the error has produced and has been measured by the sensors. In addition, finding the best parameters of the PI regulators depends on the precise mathematical model the current cascaded STATCOM lacks. Therefore, it is usually difficult to find the suitable parameters for the multitudinous PI controllers employed to regulate the active/reactive current and DC voltage to achieve a satisfactory dynamic response and good robustness, as Lehn has pointed out in
[23]
. So in practice, the trialanderror method is widely adopted, although it causes too much blindness in the process of system design and debugging.
Besides the common drawbacks aforementioned, some particular control methods still pose unique challenges. Ref.
[19]
proposed an individual voltage balancing strategy to realize independent modulation control over each power unit, in which an active component is superposed to the CMI output voltage. However, the cosine value of the current phase angle is included in the denominator
[21]
. Therefore, any system adopting this method is very sensitive to disturbance due to the zerocrossing point of the cosine value. Another balancing control method proposed in
[20]
has a disadvantage that it has poor regulation capability under small reactive current and is easily affected by the accuracy of phaselocked loop (PLL).
Generally speaking, softwarebased methods depend less on hardware, which lend them significant advantages in weight, volume and cost. However, they show slow response and large steady state error. The intrinsic problems of such schemes could not be eliminated. Therefore, the softwarebased methods are still mainly adopted by the lab researches and have not yet been applied in the high voltage and high power products for industry
[7
,
10]
. However, almost all of the worldwide famous cascaded STATCOMs use hardwarebased methods.
By considering the merits and demerits of the softwarebased and hardwarebased methods, a new method, the chopper controller based DC voltage control strategy for cascaded STATCOM, is proposed in this paper, which is expected to possess some following qualities: 1, Good steady state performance (steady state error as small as possible), meaning the stable and balanced DC voltage; 2, Good dynamic performance, i.e. the fast response and good robustness; 3, Easy to design the control parameters and the control parameters are as few as possible. Therefore, the system will be easy to debug and produce for industry; 4, The hardware is few as possible. Thus, the volume is small and the weight and the cost are low; 5, Easy to expand and enlarge the scope of use as wide as possible.
As the proposed method possesses the good control performance inherited from the hardware methods and the hierarchical control idea inherited from the software methods, it can realize the goals of stability and reliability without any noticeable increase of hardware cost. In this paper, the principles of chopper controllers and the hierarchical control for DC voltage are given and the circuit topology is described. Emphasis is given to the operating principles of balancing circuit, working modes, generation of the driving signals. Theoretical analysis and the simulation results verify the effectiveness and practicability of the control strategy.
2. Cascaded STATCOM Based on CPSSPWM
 2.1 System configuration of cascaded STATCOM
System configuration of cascaded STATCOM is shown in
Fig. 1
, where
u_{si}, i_{ci}
and
L_{i}
(
I
= a, b, c) are the grid voltages, device’s output currents and the linking inductors, respectively. The Hbridge inverter shown in
Fig. 1
is the power unit. Its DC capacitor serves as power storage while
R_{dc}
is the equivalent resistance. When
N
power units are connected in serial, the cascaded multilevel inverter is formed. The energy flowing between the STATCOM and the load is regulated through the magnitude and phase of the CMI output voltage. It is determined by the active power consumed by the device and the reactive power coming from the load
[24]
.
Cascaded multilevel STATCOM
System control strategy
 2.2 System control strategy of cascaded STATCOM
Cascaded STATCOM uses the feed forward decouple control strategy
[21]
, as shown in
Fig. 2
, where
i_{li}
(
i
=a, b, c) are the load currents. The modulation of the CMIs utilizes the CPSSPWM (Carrier Phase Shifted Sinusoidal Pulse Width Modulation) technology
[13]
, which could improve the equivalent switching frequency, reduce the harmonics, and minimize the size of passive filter components. The basic principle of the modulation technique is that all the power units of a CMI share the same sinusoid modulation signal while each unit uses carrier waves with 1800/N degree apart according to the sequence of power units. In a power unit, the carrier waveforms for the two bridge arms are reversed. Thus the CMI in each phase could generate a maximum of 2N+1 voltage levels.
3. Chopper Controller Based Control Strategy
Chopper controller based voltage control strategy proposed in this paper consists of two layers. The upper layer is to control the total active power based on software design while the lower layer control is to balance the DC voltage of power units through chopper controllers.
 3.1 Total active power control
Due to the loss (e.g. switching loss), the DC voltage of STATCOM will gradually decrease. The decrease rate is determined by the active power consumption rate. In other words, the reduction of DC voltage reflects the active power consumption by the device. Therefore, the total DC voltage drop of power units has a positive correlation with the total active power demanded by the system. With regard to the negative feedback control principle, the control algorithm of total active power (the fundamental positive sequence active power) can be derived, as shown in
Fig. 3
, where ur is the voltage reference of DC capacitors and
u_{dc_ai}
,
u_{dc_bi}
,
u_{dc_ci}
are the DC voltages of the Power Unit
i
in Phase A, B and C, respectively.
Using this method to inject the power units with the active power could compensate the power loss, which leads to the DC voltage drop. When the syst achieves equilibrium, the following equation holds:
Where
u_{d}
is the equivalent DC CMI voltage.
Meanwhile, since the component parameters and the operating conditions of different power units are different, the DC voltages of power units are also not consistent. Therefore, after maintaining the DC CMI voltage at the designated value stably, we still have to rationally distribute the active power to make sure that the individual DC capacitor voltages of power units are equal to each other. Similarly, the power units in different phases also demand different active currents, and the active power control should include the total active power control and the equilibrium control among phases. However, this effect is slight and generally negligible. In this paper, the focus is on the voltage consistency among power units. Therefore, let us assume the parameters in each phase are consistent and thus the balance control among phases is not considered.
Total active power control
 3.2 Voltage balance control for power units
The hardware employed in this paper is depicted in
Fig. 4
, where diode
D
_{1}
and switch
T
_{1}
construct the path for positive power flow while
D
_{2}
and
T
_{2}
compose the path of negative power flow. Thus, the chopper circuit can realize the bidirectional power flow. The fully controlled switch could be IGBT or MOSFET which is characterized by high frequency and low voltage rating.
The connection between chopper circuits and power units is shown in
Fig. 5
. The DC capacitor
C
_{1}
and
C
_{2}
are connected via two chopper controllers. The chopper circuits allow the unbalanced power to flow between power units and distribute the active power to achieve voltage equilibrium, which is shown by the shadow region in
Fig. 5
. Actually, an extra resistor
R_{extra}
is added to the voltage balancing loop in series to limit the balancing current in a reasonable range.
Topology of chopper controller
Topology of units shunting by chopper controllers
Obviously, the employed auxiliary circuit cannot interfere with the normal operation of CMIs. In
Fig. 5
, switches
S
_{1}
and
S
_{2}
could operate in 4 different combination modes: 00,01,10,11. If the DC voltage of a power unit is defined as
U_{dc}
, the corresponding output voltage is 0, 
U_{dc}
,
U_{dc}
, 0. Likewise, two units connected by the chopper controllers have 16 operation modes, as shown in
Fig. 6
.
In
Fig. 6(a)
,
S
_{1}
S
_{2}
S
_{3}
S
_{4}
work at the combination mode 1010, making the output voltages of these two units be
U_{dc}
. At this time
S
_{2}
,
T
_{2,}
S
_{3}
and
C
_{1}
compose a short circuit
,
T
_{3,}
S
_{3}
and
C
_{2}
form another short circuit path which is paralleled with the previous one. These two short circuit paths will cause large current discharge of
C
_{1}
and
C
_{2}
, and hence the CMI cannot operate normally. Thus, the chopper controller switch
T
_{2}
T
_{3}
must be turned off, known as the combination mode 00. As the operation states of
T
_{1}
T
_{4}
will not affect the main circuit, their combination modes could be any one of 00, 01, 10 or 11. In order to simplify the logic expression and minimize the operation errors, their combination mode is assigned to be 00. Therefore,
T
_{1}
T
_{2}
T
_{3}
T
_{4}
becomes 0000. Likewise, when
S
_{1}
S
_{2}
S
_{3}
S
_{4}
operate at the combination modes 1010, 1010, 1100, 1101, 0010, 0011, 0100 or 0101, there will be two paralleled short circuit circulation paths, shown as the regions inside the dashed lines in
Fig. 6(
a, b, g, hj, o, p), respectively. At this time,
T
_{1}
T
_{2}
T
_{3}
T
_{4}
should work in the combination mode 0000 to avoid the short circuit.
In
Fig. 6(c)
,
S
_{1}
S
_{2}
S
_{3}
S
_{4}
work in the mode 1000. There is no circulation path and turning on or off the chopper controller will not affect the operation of CMI at this time. Therefore, the chopper controllers should work in the voltage balancing state. The DC voltages of power units could be balanced through the power flow as
T
_{1}
T
_{2}
T
_{3}
T
_{4}
work in the combination mode 1111. Likewise, when
S
_{1}
S
_{2}
S
_{3}
S
_{4}
work in the modes 1000,1001,1110,1111, 0000,0001,0110 and 0111, there will be no short circuit circulation path and the chopper controllers work in the voltage balancing state, as shown in
Fig. 6
(cf, k, ln), respectively. At this time,
T
_{1}
T
_{2}
T
_{3}
T
_{4}
work in the mode 1111
Based on the previous analysis, the working principles can be summarized as follows: 1. Switches in a pair of chopper controllers operate in the synchronous state, meaning they are on or off at the same time. 2. Chopper switch’s working state is related to the switches of its adjacent power units, but not affected by the magnitude and the direction of the output current in CMIs. The switching frequency of chopper switches is two times than that of power units. 3. If there is a short circuit circulation path, the chopper controllers cannot work in the voltage balancing mode. 4. If the right arm of upper power unit has the opposite logical working condition with the left arm of the downward power unit, the short circuit circulation paths exist. 5. If a short circuit circulation path is formed, there must be another one, and these two paths are paralleled.
Operation principle of chopper controllers
 3.3 Extension to the NUnitSeriesConnected CMI
In order to verify that the method could be extended to any amount of power units, the power unit is simplified firstly, as shown in
Fig. 7(a)
.
A
and
B
are the midpoints of the left arm and the right arm, respectively. The points
P
and
N
represent the positive and negative poles of DC capacitor. When A connects to
P
and
B
connects to
N
, the output voltage of power unit is +
U_{dc}
. The voltage becomes −
U_{dc}
if
A, N
and
B, P
are connected. If
A
and
B
connects simultaneously to
P
or
N
, the output voltage will be 0. Likewise,
Fig. 5
could be simplified as
Fig. 7(b)
, where the midpoint of the second power unit’s left arm is connected with the midpoint of the first power unit’s right arm, which is all signed by
B.
According to the simplification, the short circuit circulation path in
Fig. 6
could be depicted as
Fig. 8.
The fourth operating principle mentioned above indicates that the existence of short circuit circulation paths should be determined by the right arm of the first power unit and the left arm of the second power unit.
If
B
is connected to
N
_{2}
and
P_{1}
in chorus, which means
P_{1}
connects to
N_{2}, S_{2}
and
S_{3}
must be
S_{2}S_{3}
=01. Therefore the first Short Circuit Circulating Mode (SCCM) also exists when
S_{1}S_{2}S_{3}S_{4}
are X01X, where X means either 0 or 1, corresponding to the Mode 7, 8, 15, 16 in
Fig. 6
. At this time, the switches of chopper controllers are off and the short circuits are thus avoided. If
B
is connected to
N_{1}
and
P_{2}
in chorus, respectively, which means
P_{2}
connects to
N_{1}
,
S_{2}
and
S_{3}
must be
S_{2}S_{3}
=10. Therefore the second SCCM also exists when
S_{1}S_{2}S_{3}S_{4}
are X10X, where X means either 0 or 1, corresponding to the Mode 1, 2, 9, 10 in
Fig. 6
. At this time, the switches of chopper controllers are off and the short circuits are thus avoided.
Simplified power unit and Fig. 5
Simplified short circuit circulation paths
Both the first and second SCCM cannot exist between any two different power units when the SCCM of the two adjacent capacitors is avoided, which can be demonstrated as follows. In the CMI, composed by
N
power units, it is supposed that
T (1
power units are chosen randomly and continuously, as shown simply in
Fig. 9
.
Case 1:
the first SCCM.
Assuming
P_{1}
and
N_{T}
are shortcircuited at a certain time, which is determined by the operation state of the CMI, we can demonstrate that there is no equivalent path
through which the capacitor
C
_{1}
can be shorted. Otherwise, the following equation should be true.
Firstly,
means the path from point
N_{i}
to
N_{i1}
. The existence of this path depends on the state of the chopper controller between points
N_{i}
to
N_{i1}
. Based on the fourth principle as stated above, the state of the chopper controllers can be obtained.
Secondly,
means the path from
P_{1}
to
N_{T}
. Obviously, there are multiple routes
changed by the switches of these
T
power units. But as points
P_{1}
and
N_{T}
have the equal potential (they are shorted as mentioned previously and this short circuit case may appear at a certain time for the CMI), so there are only two choices for the CMI to form Path

1. One is the route that will not pass the capacitorsCi(1≤i≤T).

2. The other one is the route which will go through the capacitors and its positive passing (fromPtoN) times equal to the negative passing (fromNtoP) times. If not, pointsP1andNTcannot have the same potential.
.
Therefore, there must be
k
paths working in the first SCCM and
k1
paths working in the second SCCM to build the route from the positive pole
P_{1}
to the negative pole
N
_{T}
. In all, at least
2k1
chopper controllers work in the SCCM isolated condition. Thus, no equivalent path
works in the first SCCM and can short capacitor
C_{1}. k
is subject to the range as follows:
The simplified first SCCM among power units
As
Fig. 9
shows, a specific example is given. In this example, the path
forms by the route as follows
There is 1 path
working in the first SCCM and 0 paths working in the second SCCM. As a result, the path
is blocked to avoid this SCCM, which is determined by the fourth principle aforementioned. So the path
working in the first SCCM cannot be formed between any two power units.
Case 2:
the second SCCM.
For the same reason, if it is assumed that points
P_{T}
and
N_{1}
are shortcircuited at a certain time, there must be
k1
paths in the first SCCM and k paths in the second SCCM within the route
, which means at least
2k1
chopper controllers work in the SCCM isolated condition. In this case, the path
working in the second SCCM is determined by the following expression.
Also a specific example is given to explain, as
Fig. 10
shown. In this example, the path
forms by the route as follows.
There are 2 paths
and
working in the second SCCM and 1 path
working in the first SCCM. The path
goes through the capacitors twice and its positive passing (from
P_{T}
to
N_{T}
) times equals to the negative passing (from
N_{T1}
to
P_{T1})
times. As a result, these paths
,
and
are blocked to avoid the SCCM, which is determined by the fourth principle aforementioned. So, the path
working in the second SCCM cannot be formed between any two power units.
Consequently, there is also no path working in the second SCCM. In other words, there is no equivalent path
which works in the first or second SCCM and can short
C_{1}
. Obviously,
C_{1}
can be any one of the
N
power units.
The simplified second SCCM among power units
According to the analysis above, the conclusion can be safely drawn as follows: If a pair of neighboring power units does not have a short circuit path, there will be no such path in any pair of power units or among random power units. Therefore, the algorithm proposed by this paper could be extended to any amount of power units even if it is derived by two power units. This algorithm is demonstrated to avoid coupling and allow for easy expansion.
 3.4 Implementation
Based on the analysis above, a conclusion can be drawn that the logic variables
T_{1}T_{2}T_{3}T_{4}
are determined by the logic states
S_{1}S_{2}S_{3}S_{4}
. Truth table in
Table 1
expresses their relationship.
According to the truth table, Eq. (7) can be derived,
Switch logic of units and chopper controllers
Switch logic of units and chopper controllers
Generation method of driving signals
Similarly, based on the operational rules, the general switch logic of the chopper controllers can be deduced,
Based on this equation and the CPSSPWM rule
[21]
, it is easy to get the generation method of the driving signals of the power units and its shunting chopper controllers, as illustrated in
Fig. 11
.
4. Performance Analysis
It’s very important to evaluate the hardware investment and research on the chopper controller circuit’s performance, which will affect the performance of the new strategy proposed by this paper.
The equivalent circuit of the voltage balancing loop between the two capacitors is illustrated in
Fig. 12
.
R_{esr}
and
C_{e}
are the equivalent series resistance and the equivalent capacitance of the voltage balancing loop, respectively.
ΔU
is the initial voltage difference.
u_{e}
(
t
) and
i_{b}
(
t
) are the voltage difference and the balancing current, respectively.
It is clear that the small steady error means small voltage difference, small balancing current and low hardware cost.
From (12), the energy loss
caused by the voltage balancing between the capacitors
C_{1}
and
C_{2}
is given by
Based on (13), the total energy loss
ΔE
can be calculated as
Equivalent circuit of the voltage balancing loop
Obviously, the energy loss is independent of the impedance
R_{e}
in the balancing circuit. In other words, the additional hardware for the voltage balancing control will not affect the system efficiency, only increasing the hardware cost slightly. Therefore, the value of the additional resistor
R_{extra}
is determined by the expected steady error and the affordable voltage/current rate of the chopper controllers. Ref.
[7]
gives a concrete design method which has comprehensively considered the hardware cost, the affordable voltage/current rate and the balancing control performance.
From (14), we know that all the DC voltage control methods will cause energy loss invariably, which is determined by the essential characteristics of DC capacitor voltages’ disequilibrium. Nevertheless, Expression (14) is not convenient to predict and evaluate the total energy loss. Hence, this paper analyzes this issue from another perspective.
Assuming that the DC capacitor voltage offset of power unit
i
is
ε_{i}
, and its voltage ui can be described by
Therefore, the DC CMI voltage
u_{d}
is deduced.
From (1) and (10), the fact that the sum of the individual voltage offset is zero can be found easily.
Based on the CapacitorEnergy Formula and from (17), the energy loss
ΔE
can be deduced by
Where
σ
^{2}
represents the voltage variance, which reflects the degree of the DC capacitor voltage unbalance.
When the system is in the steady state, every power unit can keep its voltage stable and balanced with the chopper controller based DC voltage control strategy. Therefore,
ε_{i}
can be approximated as zero, as well as the energy loss Δ
E
. Based on the previous discussion, we know that the energy loss can be designed to be arbitrarily small on condition that the system parameters are reasonable and the DC voltage control strategy can ensure good performance.
Moreover, almost all the softwarebased methods must use the information of every DC capacitor voltage’s changing trend. Thus, all the DC voltages of the power units must be detected simultaneously. But the new control strategy needs only one physical quantity that is the DC CMI voltage used by the upper layer control. Considering that the new strategy can ensure that the individual DC voltage is stable and balanced, we can deduce that the DC CMI voltage can be calculated based on (1) and only one DC capacitor voltage should be detected. Consequently, the hardware cost and microprocessor resource, which are spent by the high DC voltage sensors and signals processing (e.g. signals’ acquisition, analysis and calculating), can be cut down significantly. Based on the previous discussion, that the new strategy provides a cost advantage compared to the existing technologies is gotten.
It’s necessary to explain that this new scheme has two defects. One is that the added chopper controllers will reduce the system reliability. But with the development of design capability and manufacturing engineering, the reliability of the semiconductor switching device is high enough. So the effect caused by the first defect is negligible. Another defect is that the SCCM may cause the CMI fail to operate properly and efficiently. When the chopper controller operates from the voltage balancing state to the SCCM isolating state and if the chopper controller is not turned off in time, the aforementioned issue will occur. This problem can be solved by setting dead time which is chosen to be just a few microseconds for the fast switching devices, as is often the case with avoiding the crossconduction current through a halfbridge inverter leg.
5. Simulation Verification
In this section, a cascaded STATCOM comprised in each phase by a 5unitseriesconnected CMI has been built by using Matlab/Simulink to verify the effectiveness of the proposed scheme. Wiring between chopper controllers and its adjacent power units is shown in
Fig. 5
. In order to simulate the active power loss absorbed by the operating power units, a resistor is shunted to the DC capacitor. Obviously, the resistances of these resistors are different to each other for the different parameters and distinct operation modes of the power units. A list of the system parameters considered in this simulation is included in
Table 2
.
Parameters of the simulation model
Parameters of the simulation model
Obviously, cascaded STATCOMs without the DC voltage control cannot work normally and the capacitor voltages of each power unit will fall quickly. At this time, the cascaded STATCOM acts as a harmonic generator for the system.
 5.1 Operation with the total active power control
Fig. 13
shows the simulation results when only the total active power control is implemented. In
Fig. 13(a)
, the DC CMI output voltage keeps stable and maintains at 12.5kV with small steadystate error, about 0.23V.
Fig. 13(b)
shows that the DC capacitor voltages’ imbalance aggravates with time elapsing, though the total voltage of DC side is maintained. The maximum voltage difference reaches 250V within 3 minutes. This difference attributed to the variation of active energy loss results in a lot of serious influence. First, the DC voltage imbalance leads CMI output voltage/current waveforms to distort, and the levels of the AC CMI voltage have aggravating ripples. Second, the distorting CMI output waveforms make source current distorted and the distortion is positively correlated with the voltage imbalance. Third, the CMI operates as a harmonic generator at this moment. The fact that some capacitors are overcharging and others are undercharging reveals that the active power isn’t allocated reasonably and the active power allocating strategy should be employed.
 5.2 Operation with the proposed control strategy
Fig. 14
displays the simulation results when the new control strategy is employed. The DC CMI output voltage remains stable and maintains at 12.5kV, which is the same with the
Fig. 13(a)
.
Fig. 14(a)
reveals that the system is able to hold the voltage of the five capacitors within a tiny range across 2.5kV which is the designated voltage, costing only little time for dynamic adjustment. The largest voltage deviation is about 0.8V out of 2.5kV and that of the cascaded STATCOM with the softwarebased methods may be several tens of volts, indicating that this strategy accomplishes the targets of stability and balance of the DC voltages. Therefore, the CMI output voltage/current waveforms and the modulation waveform are regular and smooth, and the THD of the AC CMI voltage is only 17.21%, as shown in
Fig. 14(b)
. Best stabilization and balance of the DC voltage ensure that the STATCOM operates in the stable and highefficiency state.
Fig. 14(c)
shows the compensated source voltage and current whose waveforms without any distortion and phase difference, indicating the STATCOM has a good performance with the new control strategy.
Operation with the total active power control
Operation with the chopper controller based DC voltage control strategy
Fig. 15(a)
reveals the fact that the chopper controllers’ switch frequency is twice that of the power units also agrees with the theoretical result.
Fig. 15(b)
indicates that the chopper controller currents are satisfactorily low, because the largest peak value is below 1A and the mean values are of approximately 0A in this model. Tiny currents and voltages mean little dissipation, high efficiency and low hardware cost.
Balancing currents and driving signals waveforms
Operation with load transient
 5.3 Operation with load transient
Fig. 16
displays the simulation results when the load has been changed to 50Ω and 80mH suddenly. The load current value increases from 75A to 150A suddenly at 0.45s. The steadystate value of DC CMI voltage still holds at 12.5kV and the fluctuation range increases from 42V to 81V within 0.01s. In
Fig. 16(a)
, individual capacitor voltage keeps 2.5kV with tiny steady error and the fluctuation range increases from 9.8V to 16.3V within 0.01s. The CMI output current and the source current have the same changing trend as well as the physical quantities described above, increasing from 40A to 75A and from 82A to 150A without any oscillation, also within 0.01s, showing in
Fig. 16(b)
.
Fig. 16
indicates that the cascaded STATCOM with the new control strategy has good dynamic performance and steadystate performance.
6. Conclusion
Keeping the DC voltages of cascaded STATCOM stable and balanced is significant for its reliability and safety. Due to the different parameters and working modes of power units, DC capacitor voltages cannot maintain the reference value and are different from each other. The existing strategies can be categorized as hardwarebased and softwarebased methods. The former can reach good performance but cost too much. The latter does not need so many facilities but it is impractical in highpower devices. Neither of them can achieve the best performance with the lowest cost simultaneously. This paper proposes a new control method with a combination of the chopper controllers and the hierarchical control to fulfill the control targets. Both theoretical analysis and simulation results verify that the strategy can be extended for STATCOM composed by Nunitseriesconnected CMI. The major advantages of the proposed control strategy are that the number of PI regulators can be reduced remarkably and accordingly the blindness of system design and debugging also decreases obviously. For its excellent performance, good robustness, easy expansion, few control parameters and low hardware cost, it is practical in high power and high voltage equipment. The simulation results reveal that the proposed control scheme could achieve the desired control goals.
Acknowledgements
This work was supported by the National High Technology Research and Development Program (863 Program), P.R. China, No.2012AA050206 and the Natural Science Foundation of China (NSFC), P.R. China, No. 51177130.
BIO
LianSong Xiong He was born in Sichuan Province, China, in 1986. He received the B.S. and M.S. degrees from Xi’an Jiaotong University, Xi’an, China, in 2009 and 2011, respectively. Since 2012, he has been pursuing the Ph.D. degree in the Department of Electrical Engineering, Xi’an Jiaotong University. His research interests are power electronics and power quality improvement.
Fang Zhuo He was born in Shanghai, China, on May, 1962. He received his B.S. degree in Automatic Control from Xi’an Jiaotong University in 1984, and then he joined Xi’an Jiaotong University. In 1989 and 2001, he received the M.S. and Ph.D. degree respectively in Automation and Electrical Engineering in Xi’an Jiaotong University. In 2004, he worked as a visiting scholar in Nanyang Technological University. He was an Associate Professor with Xi’an Jiaotong University in 1996, and a Full Professor in power electronics and drives in 2004. Then he was employed as a supervisor of PhD student. He is also the associate Dean of the Faculty of Industry Automation.
Dr. Zhuo’s research interests are power electronics, power quality, active power filter, reactive power compensation, inverters for distributed power generation, etc. He is the author or coauthor of more than 160 publications, more than 30 papers was indexed by SCI, EI and ISTP, in his research fields, and he is also the coauthor of two handbooks. He is the key finisher of four projects sponsored by National Natural Science Foundation of China, and more than 40 projects cooperated with companies from industry. He is the owner of four provincial and ministerial level science and technology advancement award. And four patents are applying or owned by him. Professor Zhuo is a member of IEEE, China Electro technical Society, Automation Society and Power Supply Society. Also he is the Power Quality professional chairman of Power Supply Society in China.
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