Review of Current Control Techniques for a Cascaded H-Bridge STATCOM Javier Muñoz Jaime Rohten José Espinoza Pedro Melín♠ Carlos Baier Marco Rivera
[email protected],
[email protected],
[email protected],
[email protected],
[email protected],
[email protected]
Department of Industrial Technologies, Universidad de Talca, Talca, CHILE.
Department of Electrical Engineering, Universidad de Concepcion, Concepcion, CHILE.
♠
Department of Electrical and Electronic Engineering, Universidad del Bio-Bio, Concepcion, CHILE
Abstract – This paper presents a comprehensive review of current control techniques suitable for a Cascade H-Bridge STATCOM. Particularly, four different approaches are evaluated in this work: a linear strategy using Proportional Integral controllers in the dq frame, an exact input/output linearization technique with Proportional-Resonant controllers, a multiband hysteresis modulation control, and a predictive control scheme. The main advantages and drawbacks of each scheme are depicted in terms of stationary and dynamic performance, as well as harmonic content, complexity, and computational burden. The presented results are supported with simulated waveforms that highlight the main features of each control method.
I. INTRODUCTION In power quality applications, the STATCOM has emerged as one of the most widespread compensator due its capability of power factor correction and/or voltage regulation. On the other hand, due to power rating restrictions of the semiconductor devices, multilevel STATCOM topologies have been proposed to reach higher compensation levels as required in medium voltage applications [1][2]. Among the multilevel STATCOM topologies, the Cascade H-Bridge Based (CHB) configuration has received a lot of attention from researchers; whom have addressed very important issues as current control, DC voltage balance, modulation techniques, losses, just to name a few [3]-[6]. Regarding the current control techniques, several approaches have been reported, from classical linear control strategies to elaborated nonlinear methods such as predictive control. For linear control strategies, the usual approach is to use the Park transformation in order to map the system to the Synchronous Reference Frame (SRF) and then apply classic PI controllers [7] that can be tuned with well-known tools, such as Root-Locus and/or Bode Diagrams [8]. In the side of the nonlinear schemes, the exact linearization method has gained importance in power converters applications. This technique consists in obtaining a set of equivalent linear expressions using a non-linear control law that linearizes the input-output equations, as described in [9]. Another non-linear technique suitable for the CHB STATCOM topology, is the predictive control, which has been the focus of many researches in the past years. This technique allows selecting the commutation state that
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minimizes a certain cost function that allows the current to follows its reference, as can be found in [10]. Also, the hysteresis modulation can be extended to multilevel converters, particularly for CHB STATCOMs, and therefore it can be used to track the current reference in this topology. The simplicity of this approach and its easy implementation in a digital platform has made it an attractive alternative to control power converters [11]. This paper presents a review of the four aforementioned control techniques for current reference tracking applied to a CHB multilevel STATCOM topology, giving especial emphasis to the dynamic performance, the harmonic distortion and the steady state behavior. The contribution of this work lies in the systematic comparison of several aspects of the presented control algorithms. II. THE CHB STATCOM The CHB multilevel STATCOM is presented in Fig. 1. The topology is built-up based on single phase power modules To other users
i abc pcc
i abc L
i pa Cell 1
v abc pcc
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vdc
Rp Lp RL
Cell 2 vdc Cell nc vdc Phase a Phase b
Phase c
Fig. 1 CHB Multilevel STATCOM
LL
A)
Lp abc
where, v p
d abc abc abc i p R p i abc p v p v pcc , dt
(1) abc
is the compensator injected voltage, v pcc is the abc
PCC voltage, i p is the STATCOM current and Lp and Rp are the inductance and parasitic resistance of the converter inductor, respectively. It is important to remark that transients of the source voltage and of the load power could be also included in the model; however, in order to simplify the analyses, they will be considered as disturbances henceforth. As the focus of this paper is the comparison of current control techniques and due to space limitations, the DC voltage balancing control will not be treated in this work, and therefore the DC voltages of the power modules are considered constant for modeling and control purposes. For further details on the DC voltage balance of CHB multilevel converters, please refer to [4][5]. III. CONTROL STRATEGIES A general control scheme for the CHB STATCOM is presented in Fig. 2, where three main blocks can be identified: DC voltage regulation, Reference Calculation and Current Control. The first block goal is to regulate the overall DC voltage that can be considered as the summation or average of all the individual voltages of the power modules. A dedicated control block must be included in order to ensure the voltage balancing, which will not be treated in this paper, as stated θ pcc
i pd , ref
i pd i
v dc To other users
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i ap
Gating Patterns
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CHB STATCOM Modeling
The dynamic model of the system in Fig. 1 can be obtained using Kirchhoff’s circuit laws. Just for modeling purposes, let us assume that all the modules have the same capacitance and voltage in their DC side and that the AC voltage is equally shared among all the nc cells. Applying the voltage law in the AC side of the STATCOM, the following equation is obtained,
abc p
i pabc
Current Control
connected in series in order to split the total load voltage. This configuration allows a higher total equivalent switching frequency with low dv/dt waveforms, as depicted in [12]. As any other Voltage Source Converter (VSC) based topology, this configuration needs a passive filter in order to absorb the instantaneous voltage differences between the converter and the grid, and to reduce the harmonic content of the injected AC current. In this case, an inductive first order filter is used.
i pq
i
m
Fig. 2 STATCOM General Control Scheme
earlier. The second block generates the STATCOM current reference, which can be synthesized in the abc, αβ or dq frames, depending upon the specific control strategy to be used. The third block will be the object of study and comparison in this paper. This part of the control scheme must ensure current reference tracking with acceptable transient response. It is expected that the current follows its reference in few milliseconds for which several control schemes can be proposed. Particularly, this paper will review (i) a linear control scheme, (ii) an exact input/output linearization strategy, (iii) the hysteresis modulation control, and (iv) the predictive control approach.
A)
Linear Control
The easiest way to control the current in a CHB STATCOM is through linear controllers. It has been widely proved that PI controllers have satisfactory performance for power converter applications. To implement this kind of controllers, the model in the SRF must be obtained. Thus, using the Park transformation, (1) leads to, R p dq 0 ω dq 1 dq d dq dq ip ip (2) i p L v p v pcc . ω 0 dt Lp p As this equation shows, there is a clear cross coupled term in the dq currents dynamics. Then, the inclusion of a decoupling stage is mandatory for high performance of this strategy, as shown in Fig. 3. There, the decoupler coefficients and the PI parameters are selected based on the linearized model, as explained in the technical literature [13]-[14]. Although this control scheme requires an extra PLL algorithm to synchronize the Park transformation, the simplicity of the implementation of digital PI controllers makes the whole strategy very simple. More details of this approach can be found in [15].
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d p
, ref i abc p
m qp
i abc p
abc p
u abc p
m abc p
v abc pcc
abc abc u abc p R p i p v pcc
ncVdc
q , ref p
Fig. 3 Linear Control Strategy
Fig. 4 Exact Linearization Control Strategy
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Fig. 5 Hysteresis Modulation Strategy
B)
Fig. 4 shows a diagram of the Input/Output linearization technique applied to the CHB- STATCOM. As it can be seen, it uses the nonlinear model of the STATCOM to define a nonlinear control law. In fact, considering that all the nc cells inject the same fundamental voltage component and defining
Similarly than the basic 2-level hysteresis modulation control, the commutation harmonics are spread all over the spectra, which can cause harmful effects as resonances in the AC side. Further description of this strategy can be found in [12].
D)
abc
an auxiliary variable u p , the system equation is, (3)
Considering the nonlinear control law shown in Fig. 4, it is easy to demonstrate that the equivalent transfer function abc
abc
between the modulator m p and the auxiliary variable u p is a simple integrator. Then, a linear strategy can successfully control this resulting system. Actually, in the proposed scheme, a Proportional-Resonant (PR) controller is included to ensure zero steady state error for sinusoidal references. This feature avoids the use of the Park Transformation and therefore a PLL algorithm is not required. On the other hand, the main drawback of this control approach is the number of variables that must be sensed to implement the strategy. For further details of this approach, please refer to [9].
C)
s abc p
Fig. 6 Predictive Control Strategy
Exact Linearization Control
d abc abc abc abc L p i abc p R p i p ncVdc m p v pcc u p . dt
R p abc T abc abc 1 Ts i abc i p k s v pcc k v p k p k 1 L L p p
Hysteresis Modulation Control
The hysteresis control of power converters has been widely used due to its simplicity of implementation and good dynamic performance. Although the implementation of a hysteresis control is quite simple for a 2-level converter, its extension for multilevel converters is not straightforward and several approaches have been reported in the literature. There are different ways to implement a multilevel hysteresis modulation, among them it is possible to find approaches with multiple bands, that can be symmetric or asymmetric and also time based schemes have been proposed [16][17]. The alternative implemented in this paper is based on a multi-band hysteresis strategy, as shown in Fig. 5, where symmetrical bands generate the gating patterns, such that the inner band is used to switch between adjacent levels, while the outer bands produce commutations of additional levels of the CHB STATCOM. Then, if the error goes further the most outside band, the higher level in the multilevel waveform must be selected in order to correct the error and bring it inside the hysteresis bands.
Predictive Control
This strategy consists in evaluating all the possible commutation states of the CHB-STATCOM and then selecting the optimal switches combination that minimizes the error between the current and its reference, as depicted in Fig. 6. To achieve this, it is essential to count with an accurate model of the system in order to predict correctly its future behavior. According with the model predictive control theory applied to power converters [10], differential equations that model the CHB-STATCOM must be firstly discretized in order to evaluate the allowable switching conditions. Considering a first-order Euler approximation, the discrete version of (1) can be expressed as, Rp abc T abc i abc i p k s v abc 1 Ts (4) p k 1 pcc k v p k , L L p p where Ts is the sampling time of the algorithm. The measured variables are used to evaluate the converter equations in the k instant and the model predicts the future behavior of the system in the next sampling time, k + 1. Once the discrete model is already obtained, a cost function must be proposed. This functional must be evaluated for all the possible switches combinations and the option that minimizes the cost function should be selected and applied in the next sampling time. A typical cost function that minimizes the current error is,
, ref g k 1 i abc k 1 i abc p p k 1 ,
(5)
that consists in the absolute value of the difference between the current reference and the predicted value of the STATCOM current, both in the next sampling time. As it can be seen, the cost function can be directly proposed in the abc frame and then no transformation is required to implement this approach, which simplifies the understanding of the strategy. The computational burden of this strategy is quite high due to the evaluation of the cost function for all the possible states in every sampling period. A detailed description of the predictive algorithm can be found in [18][19].
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TABLE I Operating Conditions and Parameters
IV. COMPARATIVE RESULTS All the aforementioned control strategies were simulated using the PSim 9.0 software, for a 7-level CHB-STATCOM. TABLE I depicts the principal parameters and Fig. 7 to Fig. 10 show the simulated results that illustrate both the static and dynamic performance of the presented control methods. Fig. 7 shows the system currents and voltage for the four control techniques. As it can be seen from the waveforms, all the strategies achieve good reference tracking, and therefore unitary power factor is obtained at the PCC. Regarding the steady state errors, it can be mathematically proved that the first two strategies ensure zero stationary error; however, from the waveforms of Fig. 7 it is possible to state that the hysteresis and predictive controllers can maintain the error within an admissible range, very close to zero. It is easily observable in Fig. 7 (c) that the hysteresis controller generates more harmonic content than the other approaches, which is due to the injected STATCOM voltage, shown in Fig. 8 and Fig. 9. There, it is possible to see that the hysteresis waveform has the higher harmonic content, which is due to the multiband approach. Some improvements can be made over the algorithm in order to reduce the harmonics amplitude; however, the hysteresis technique would lose its beauty of simplicity. As Fig. 9 (a) and (b) show, carrier based strategies (linear and exact linearization) have practically the same concentrated spectra, and thanks to multilevel modulating techniques (as PS-SPWM) their dominant harmonics can be pushed to higher frequencies. This contrasts with the spread harmonic content of hysteresis and predictive approaches,
Parameter Load Nominal Line-to-line Voltage
Value 380 Vrms
Load Nominal Power Load Power Factor System Nominal Frequency STATCOM AC Inductance Filter STATCOM DC Capacitor
5 kVA 0.8 50 Hz 3mH 4500µF
which could be quite critical because this feature can cause undesired and harmful resonances. Two dynamic tests were performed to evaluate the presented control strategies: reference step change and load impact. In fact, Fig. 10 illustrates a reference change from 50% up to 100% of reactive power compensation in 40 ms. Then, at 80 ms a 100% load impact is produced. As stated earlier, in steady state the four control techniques achieve good reference tracking, but also the results in Fig. 10 demonstrate that the control strategies are well suited for disturbance rejection. Furthermore, the dynamic response of all the schemes is quite satisfactory, as they reach the new operating condition very quickly. Fig. 10 (a) shows that the linear controller has an oscillatory response for the reference step change. This is due to the operating point dependency of this strategy. When the operating point changes, the linear controller degrades its performance. This does not occur in the other strategies, as all of them are based on non-linear approaches. On the other hand, all the presented strategies – including the linear controller – have a satisfactory dynamic response for the load impact.
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(c) (d) Fig. 7 Key Static Waveforms (a) Linear Control, (b) Exact Linearization Control, (c) Hysteresis Modulation Control, (d) Predictive Control.
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TABLE II Comparative Comparison Summary Control Strategy
PLL
THD
Spectra
S.S. Error
Computational Burden
Tuning
Complexity
Operating Point
Linear
Yes
Low
Concentrated
Zero
Low
Medium
Simple
Dependent
Exact Linearization
No
Low
Concentrated
Zero
Medium
Difficult
Complex
Independent
Hysteresis Modulation
No
High
Spread
Low
Low
Simple
Simple
Independent
Predictive
No
Medium
Spread
Low
High
Simple
Complex
Independent
TABLE II shows a summary of the main features of the presented control techniques for the CHB STATCOM discussed in this paper. As it can be observed, each strategy has advantages and disadvantages, depending on the point of view. For instance, linear and hysteresis controller highlight due to the simplicity of their algorithms and therefore the low computational burden of their digital implementation. The predictive controller has the advantage of easily include restrictions and nonlinearities; however, the computational burden and the spread spectra rise as the main drawbacks. Finally, the exact linearization method achieves satisfactory results in almost every aspect; nevertheless as a negative implementation aspect, it is very sensitive to the tuning parameters of the PR controllers.
V. CONCLUSIONS Four representative control techniques for the CHB STATCOM were presented in this paper. Static and dynamic simulations allowed highlighting the main advantages and drawbacks of each scheme. In carrier based strategies, the switching harmonics are well known, which is especially useful for the filter design. On the other hand, hysteresis and predictive control produce unpredictable harmonics, which can cause unexpected resonances that could be harmful. However, they are easily implementable in a digital control system. In summary, each presented approach has positive and negative aspects that must be weighted in order to select the proper scheme for a particular case. 100
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(d) Fig. 8 Injected STATCOM Voltage Waveforms (a) Linear Control, (b) Exact Linearization Control, (c) Hysteresis Modulation Control, (d) Predictive Control.
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(d) Fig. 9 Injected STATCOM Voltage Spectra (a) Linear Control, (b) Exact Linearization Control, (c) Hysteresis Modulation Control, (d) Predictive Control.
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(c) (d) Fig. 10 Key Dynamic Waveforms (a) Linear Control, (b) Exact Linearization Control, (c) Hysteresis Modulation Control, (d) Predictive Control.
ACKNOWLEDGMENT
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The authors wish to thank the financial support provided by the Chilean Government through project CONICYT/ FONDECYT/ 11121261. REFERENCES [1]
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