Abstract

Document Sections

I. Introduction

II. Circulating Current

III. Proposed Method to Eliminate Circulating Current

IV. Simulation and Experimental Results

V. Discussion

VI. Conclusion

Abstract:

Parallel pulsewidth modulation rectifiers are a good solution for high-power ac–dc applications, which enhance quality and reliability. However, the main and inevitable shortcoming of parallel structures is a generation of circulating current. Various methods are proposed to reduce or eliminate circulating current, most of which tend to change or limit the switching pattern of parallel converters. This article presents an interfacing circuit with low rating elements, which eliminates the circulating current without any limitation for the switching pattern of parallel converters. Therefore, voltage and current waveforms are in high quality. Moreover, unlike previous methods that had complex control and high mathematical computations, the presented method has simple control. Therefore, multiple modules can be implemented in a modular fashion with a fast dynamic response. Simulation and Laboratory results are presented to validate the analysis.

INTRODUCTION

he use of parallel PWM rectifiers (PPWMR) is essential in a wide range of applications in electrical industry such as renewable energy systems and motor drives [1, 2]. High power conversion, higher reliability, enhanced power quality, improved current and voltage waveforms are among the benefits of parallel structure. The main problem with the application of such structures is the inevitable creation of circulating current, which will damage semiconductor devices, increase losses, cause distortion in current and voltage waveforms, reduce efficiency and reliability of the system [3, 4]. Circulating currents are categorized as high and low frequency components [1, 5] which are due to different switching states of parallel rectifiers and different control system of converters respectively. Also, different design components and unbalanced voltages are of concern in low frequency circulating currents.

Low frequency circulating currents are normally reduced using a droop control strategy [6] and also PI controllers which are dependent on circuit performance in different states. Among these strategies are PI controller with feed forward controller [7], deadbeat control method [8], using a PIR with Manuscript received November 12, 2020; revised April 18, 2021 and June 16, 2021; accepted July 14, 2021. H. A Porkia and J. Adabi are with the Faculty of Electrical and Computer Engineering, Babol Noshirvani University of Technology, Babol 47148- 71167, Iran (e-mail: j.adabi@nit.ac.ir). F.Zare is a Professor with School of Information Technology and Electrical Engineering, University of Queensland, Brisbane, Australia, (e-mail: f.zare@uq.edu.au). feed forward term which requires information of switching vectors in each period [9], improved D-∑ digital method [10], finite-time controller and zero-vector feed forward control method [5]. [11-14] introduces a strategy based on an average model. [15] investigated elimination of circulating current due to third harmonic order.

Main solutions for high frequency circulating current reductions are mainly classified in three main categories: Filters, PWM strategies and topology reconfiguration. Each of which has its advantages and disadvantages. Coupled inductor (CI) [16-18], common mode inductor (CMI)[19], inter-phase inductor [20] and modified LCL (MLCL) [6] are the main structures in the category of filter-based techniques. Mainly, they have issues regarding size, cost and losses. However, according to [3, 6], MLCL leads to internal common mode resonance current and external zero-sequence resonance circulating current.

1- Introduction

2- System modelling

3- Surge protective device

4- Stochastic analysis

5- Conclusion

References

Abstract

Vacuum circuit breaker operation causes transient overvoltages that may lead to severe damages to transformer insulation. Since the parameters affecting these overvoltages have stochastic nature, a statistical analysis may provide detailed insight into the overvoltages from the point of view of insulation coordination applications. In this paper, a statistical analysis of the overvoltage variations of the step-up transformer during vacuum circuit breaker operation is conducted. Some variables, including switching angle, current chopping, high-frequency current quenching capability, and wind turbine power, are assumed as random variables. Besides, some indicators representing the switching overvoltage characteristics such as the amplitude, the number of restrikes, and the rate of rise are extracted. By performing a probabilistic analysis, the destructiveness due to switching overvoltages on typical transformer insulation can be investigated. The sensitivity of different surge protective devices and their effectivities are also analyzed and statistically evaluated. The applied methodology is very useful because of the stochastic nature of the switching overvoltages. In this work, the impact of protective equipment on each of the overvoltage indicators is analyzed. It is also found that considering only the amplitudes of transient overvoltages is not enough to draw conclusions about the safety of the transformer when exposed to frequent switching surges.

Introduction

VCBs are commonly used in offshore wind farms due to their ability to eliminate high fault currents and their low maintenance costs. Due to wind speed variations, numerous switching actions (energization and de-energization) commonly occur in wind farms every day. VCB switching transients reach the step-up transformer through the short cable connected to the wind turbine. In case, the amplitude of a switching transient voltage rises above the BIL; it can lead to transformer winding failures. Previous statistical studies related to VCB opening were only focused on the amplitude of transient overvoltages regardless of their rise times [1–4] However, some transformer failures due to VCB operations have indicated that the leading cause of the failure was the high du/dt [5]. Recently performed detailed research showed that due to fast transients and during resonance conditions, the voltages with high amplitudes are non-linearly distributed along the windings [6], and the high du/dt accelerates failure mechanisms because of high interturn overvoltages in the transformer windings; causing coil-to-coil failures in the top or in the middle of the winding. Besides, the critical voltage of the transformer BIL remarkably decreases with the reduction of the rise time [7,8] and the amplitude [7] of the transient voltage applied. Moreover, the experimental studies confirm the effects of lightning impulses on oiled paper [9] and very fast transients on cast-resin insulation [10]. Accordingly, the rate of rise and the number of transient surges should be considered alongside their amplitude in a stochastic analysis in order to accurately assess the effects of the switching overvoltages on transformer insulation lifetime. The characteristics of the transient overvoltages occurring due to VCB operation depend on various parameters. The current chopping phenomenon in VCBs being one of the key parameters that contribute to the reignition overvoltages. Experimental tests conducted in Ref. [11] however, showed the low dependency of this parameter on the operation instant.

This paper presents a new modes switching control method based on a dual-motor centralized and distributed coupling drive system, which can achieve the centralized and distributed coupling drive and reduce the modes switching shock to improve electric vehicle dynamics performance. Initially, the influence of the switching speed on the shock is analyzed and the models of each modes switching stage are established. Furthermore, a stage-by-phase multivariable combination controller based on the control of position, velocity and force of the actuators is designed, and a load torque state observer is developed to estimate system interference. Finally, the shock suppression effect is testified by the upshift process simulation and the experiments of a centralized and distributed coupling drive electric vehicle. The research shows that the peak value of the switching process with the controller is 9 m/s3, which is lower than the recommended value of 10 m/s3. It laid the theoretical foundation for solving the mode switching problem of the centralized and distributed coupling drive electric vehicles.

Introduction

The development of pure electric vehicles is an important way to solve the problems of energy crisis and environmental pollution. The existing drive modes for pure electric vehicles are divided into distributed drive and centralized drive. The centralized drive means that only one drive system is used for the coaxial drive wheels, and the torque balance between the two-side drive wheels is accomplished by a mechanical differential. The research results show that the single-motor direct centralized drive system has the most simple structure but the worst performance; after a two gear transmission has been added, the dynamic performance is improved and the driving range is significantly increased; the main and auxiliary motors drive can further improve the above performance [1]. Although the centralized drive system has good reliability and maturity, it must rely on auxiliary devices for dynamics control [2], which makes the vehicle control system very complicated. The distributed drive means that each drive wheel has an independent drive system, which can separately adjust the output torque and speed of the drive wheel and realize dynamic control without auxiliary systems. It is currently a research hotspot in the field of vehicle dynamics [3]. However, because it is difficult to match a transmission for each drive motor, the vehicle’s driving performance depends entirely on the work of the engine and motors characteristics [4].

Introduction

Switching cost refers to time, monetary, and psychological cost that is incurred when consumers change their product or service (Dick and Basu, 1994). Since switching cost has important implications in analyzing competition in the market and designing marketing strategies, it has been studied in various markets with different perspectives (Park and Koo, 2016; Frank, 2015; Kenney and Pon, 2011). However, as previous studies suggest, the switching cost of consumers locked-in to a specific product or service is higher than that of those who are not (Calvo-Porral et al., 2017; Klemperer, 1995). If the market is saturated enough and market share expansion by capturing new consumers is not easy, the only choice left for a marketer is to churn in customers who are already locked-in to other products or services, and have high switching costs. Therefore, many businesses design and practice various marketing strategies to attract customers, such as quality improvement, advertisement, incentive programs, and bundling to lower locked-in customers’ switching costs (Ferguson and Brohaugh, 2008; Shin et al., 2015; Farrell and Klemperer, 2007). Among various options to lower switching costs, this study empirically analyzes the effect of the option that indirectly lowers switching costs by introducing B2B services to workplaces. A B2B transaction is a transaction between businesses. However, the ripple effect of the transaction can influence employees in the workplace and provide additional economic opportunities for the B2B service provider (Gummesson and Polese, 2009). This study tries to empirically analyze the effect of the option that indirectly lowers switching costs by using the example of a newly introduced B2B service in the Korean telecommunications market: Enterprise LTE. Enterprise LTE is a B2B service that provides businesses with faster and securer telecommunication services. However, it is also capable of providing additional services to employees who use the same mobile telecommunication service provider (TSP). If one can estimate the amount of benefits given to employees after the introduction of Enterprise LTE to their workplace, and the switching cost of employees using other TSPs, one can calculate the switching probability of employees, and measure the extent of introduction of B2B services that can affect the transaction between business and consumers (B2C market). The study also analyzes how various types of services affect the switching probability of employees, and suggests a service fee that is optimal in terms of revenue maximization of a B2B service provider. The paper is organized as follows. In Section 2, we first provide brief information about the Korean telecommunications market and Enterprise LTE services. Then, we review some related literature. In Section 3, the research framework and methodology used for the analysis are explained. Section 4 provides estimation results and the results of the simulation analysis. Finally, in Section 5, we summarize the study and provide policy implications for marketers, and conclude with a mention of the limitations and directions for future research.

High Voltage Power Supply encompass a broad application spectra such as analytical instruments for spectroscopy and electrophoresis, ion mass analyzers, smart material based actuators etc [1]–[4]. Analytical instruments like ion mass analyzer perform study and characterization of ions for space instrumentation systems. Such instruments comprise of electrostatic ion detector and deflector plates. The ion detector requires voltage in the range of 1.5 – 3 kV to scan and focus ions of specific energy level and is electrically modeled as a resistive load of 20 – 50 MΩ [2]. Analytical instrument employed in ozone generation require voltage in the range of 1 – 3 kV and is electrically modeled as resistive load (375 – 700 kΩ) [3]. Such devices are battery fed, operates with low power (typically in the range of 200 mW – 5 W) and need light weight high power density intermediate processing systems. A constant regulated output voltage with lower steady state ripple is required for effective operation of instruments modeled as resistive loads. To cater such requirements, numerous topologies each with distinct advantages and disadvantages are proposed in literature [5]. Flyback converters have been widely used because of their relative simplicity and their performance for power rating less than 100 W [6]. Some constructive features of the flyback converter include: isolation between the source and load side, requires a capacitive filter on the HV side, compact with low component count. Transfer of energy from source to load in a flyback converter occurs by energy storage in an intermediate flyback transformer. In HVLP flyback converters for the above applications feeding resistive loads, flyback transformers are designed with larger secondary turns and hence leads to higher self capacitance of transformer winding [7]–[9]. In general, the presence of parasitics impose a deviating behaviour in converter’s operation, in comparison with the ideal characteristic. In a flyback converter specific to HVLP applications, the primary requirement of achieving the desired steady state gain is itself restricted by the parasitic capacitances [10]. A significant energy exchange occurs between parasitic capacitance (Cef f ) and magnetising inductance (Lm) resulting in notable transition intervals apart from the typical intervals of an ideal flyback converter [11]. Converter’s operation is categorized as Continuous (CCM) or Discontinuous (DCM) based on the variations of the load. CCM operation is also known as incomplete energy transfer mode since a part of the energy drawn from the source is retained by the flyback transformer. CCM for flyback converters specific to HVLP applications poses semiconductors with higher voltage stress and results in an inefficient hard switching process. The presence of a high turns ratio transformer results in high effective capacitance (Cef f ) across drain to source of the primary active switch; this results in a significant amount of energy loss at the turn on instant of the active switch. Therefore the switching loss of the converter dominate the conduction loss.

Small-signal modeling of dc-dc converters is a well-known topic in literature, especially considering the application of linearized state-space models to obtain transfer functions that allow closed-loop operation [1]. However, this technique depends on a considerable amount of mathematical manipulations. For example, in the classical Ćuk, SEPIC (single-ended primary inductance converter), and Zeta converters, which are fourth-order systems, the inversion of 44 matrices is necessary. Besides, the analysis becomes quite complex as more parasitic elements are taken into account [2]. Other alternative solutions dedicated to small-signal modeling have also been introduced e.g. complementarity framework, even though it presents significant complexity [3]. Fourier series decomposition can also be used to model power converters, which are based on the Fourier series analysis of the PWM (pulse width modulation) signal within the mathematical representation of the model, thus minimizing the possibility of applying different or sophisticated control laws [4]. Among several distinct solutions, circuit averaging has proven to be effective for modeling purposes [5-7]. The PWM switch model proposed by Vorpérian for the analysis of dc-dc converters operating in CCM [8] and DCM (discontinuous conduction mode) [9] consists in a simple and direct approach from the point of view of electric circuits, analogously to that used in the small-signal modeling of amplifiers using bipolar junction transistors (BJTs) [10, 11]. This technique has been widely applied to classical dc-dc converters, but it can be extended to other topologies with higher component count [12-14]. The classical nonisolated dc-dc converters i.e. buck, boost, buck-boost, Ćuk, SEPIC, and Zeta are widely employed in distinct applications [15]. However, operation at high power levels is typically not possible in practice since the load power is processed by a single semiconductor element in each operating stage. The 3SSC and a family of nonisolated dc-dc converters were proposed in [16] as an interesting alternative for this purpose, since the filter elements are designed for twice the switching frequency, with consequent reduction of overall dimension. Besides, the current stresses through the semiconductor elements are reduced and current sharing is maintained due to the autotransformer.

مقاله سال 2017

این مقاله یک روش جامع تحلیلی از طراحی فیلتر LCL  برای یکسوسازهای اصلاح ضریب قدرت دو طرفه سه فاز (PFCها) را ارائه می کند. ریپل جریان مبدل فرکانس بالا موجب می شود تا هارمونیک های مبدل فرکانس بالایی تولید شوند که نیاز است با توجه به استانداردهای شبکه تضعیف شوند. مطالعه جریان فرکانس بالا برای هر عنصر یک راه حل غیر تکرار شونده برای را طراحی فیلتر LCL ارائه می کند. در این مقاله، ریپل جریان مبدل بطور کامل آنالیز می شود تا رفتار ریپل جریان را تعمیم دهد و ریپل حداکثری جریان را برای PWM سینوسی و PWM تزریق هارمونیک سوم پیدا کند. در نتیجه، ریپل جریان استفاده می شود تا بطور دقیق ظرفیت خازنی فیلتر مورد نیاز را بر اساس بار حداکثری خازن فیلتر مشخص کند. برای انتخاب اندوکتانس جانب شبکه، دو روش بررسی می شود. روش نخست ساختار میرایی را به منظور تعریف اندوکتانس فیلتر جانب شبکه بعنوان تابعی از ریپل جریان مبدل استفاده می کند. کاهش تلفات توان در فیلتر و بهینه سازی اندوکتانس فیلتر جانب شبکه تمرکز اضلی از روش دوم است که با به کار بردن شبکه تثبیت امپدانس خطی (LISN) به دست می آید. به این ترتیب، دو فیلتر LCL برای یک PFC سه فازه مبتنی بر کاربید سیلیکون 5 کیلووات (SiC) طراحی می شود. سناریوهای تجربی مختلف به منظور بررسی عملکرد و تضعیف فیلتر انجام می شود.

1. مقدمه
امروزه، مبدل های منبع ولتاژ PWM متصل به شبکه سه فازه (VSCها) در کاربردهای اصلاح ضریب قدرت (PFC) با ساختار دو طرفه یا چند طرفه بطور گسترده ای در بسیاری از کاربردها استفاده می شود [1]-[5]. با بهبود فن آوری نیمه هادی، فراوانی سوئیچینگ این مبدل ها در حال افزایش است. با توجه به سوئیچینگ مبدل، هارمونیک های جریان فرکانس بالا به شبکه تزریق می شود و لازم است آنها با برآورده کردن استانداردهای دقیق شبکه تضعیف شوند. برای تضعیف محتویات هارمونیکی در فرکانس های بالا، تکیه بر القاگر تقویتی از VSC سه-فازه منجر به القاگری عظیم با تلفات زیاد در قدرت می شود و این عملکرد دینامیکی مبدل را کاهش می دهد [7]. استفاده از فیلترهای مرتبه بالا همچون فیلتر LCL برای برآورده کردن استانداردهای شبکه بسیار جذاب است و در بسیاری از تحقیقات مطالعه می شود [7]-[22].

1. مقدمه
با الزامات موجود درباره کاهش انتشار و بهبود اقتصاد سوخت، وسایل نقلیه الکتریکی و وسایل نقلیه الکتریکی هیبریدی (HEVها) توجهات بیشتری را معطوف بخود کرده اند، که انتظار بر این است در آنها قابلیت اطمینان بالا، چگالی قدرت زیاد، و قابلیت های اضافه بار بحد کافی باشد. همچنین، موتورهای مغناطیس دائم شار سوئیچینگ (FSPM) با توجه به چگالی های قدرت و گشتاور بالا علاقمندی های قابل ملاحظه ای را برای کاربردهای درایو با عملکرد بالا جذب کرده اند [2]-[9]. علاوه بر این، از آنجا که سیم پیچ های آرمیچر و آهنرباها هر دو در استاتور واقع هستند، یک ساختار ساده و قوی از روتور موجب می شود که ماشین های FSPM برای کاربردهای سرعت بالا مناسب باشد [10].
در این مقاله، یک موتور FSPM مدولار سه فازه تولید شده همراه با جریان بالا و ولتاژ پائین استفاده شده برای HEVها با استفاده از آنالیز اجرای محدود (FEA) طراحی می شود. مدل ابتدائی FEA بصورت تدریجی با در نظر گرفتن منحنی های B-H لمینیت تحت شرایط فرکانس های مختلف الکتریکی، دمای عملیاتی، اثر پایان سه-بعدی، و همچنین ملاحظه روتور خارج از مرکز بهبود می یابد. تاثیرات مربوطه در عملکردهای الکترومغناطیسی بطور عمیق، بخصوص برای نیروی ضد محرکه فاز، و گشتاورهای الکترومغناطیسی تحت عملیات مجاز بررسی می-شود. در مقایسه با مدل اولیه FEA، یک افت کلی 40 درصدی از گشتاور الکترومغناطیسی در مدل FEA بهبود یافته دیده می شود که بطور همزمان عوامل طراحی ذکر شده را در نظر می گیرد.

ما به ارائه آزمایشگاهی یک گیت نمونه گیری تمام نوری با پیچیدگی کم و انرژی سوئیچینگ فوق اندک و خطی بودن بالا بر مبنای یک مقسم نامتقارن نوری تراهرتزی پرداختیم که با استقرار نامتقارن یک تقویت کننده نوری نیمه هادی غیر حساس به قطبش با چاه چند کوانتومی (PI-MQW-SOA) در یک آینه حلقه فیبری ساخته می شود. با استفاده از یک رشته پالس پیکو ثانیه به مانند ساعت پاندولی، ما به صورت دقیق به تجزیه و تحلیل تاثیرگذاری قدرت پالس نمونه گیری و افست PI-MQW-SOA از نقطه میانی حلقه به ترتیب بر روی شکل، عرض، و دامنه پنجره نمونه گیری پرداختیم.

علاوه بر این، انرژی سوئیچینگ و خطی بودن این گیت نمونه گیـــری تحت عرض های مختلف پنجره های نمونه گیری به طور خاص مورد بررسی قرار گرفت. نتایج نشان می دهند که گیت نمونه گیری ما دارای انرژی سوئیچینگ اندکی به اندازه fJ 25 و خطی بودن بالای بیش از 0.99 می باشد.

مقاله سال 2016

As noted in the previous research conducted by Farrell and Klemperer (2007) and Klemperer (1995), switching cost sets a higher price for locked-in consumers by making the market less competitive. The lock-in effect due to switching cost may also restrict consumer’s choices, decrease utility, and cause less innovative firm behavior (Cline, 2012). Switching costs have received much attention both theoretically and empirically because switching costs play an important role in analyzing market competition, firms’ price strategies, and consumer welfare. Like other products, a smartphone also has important issues with the relationship between its switching cost and market competitiveness. Frank (2015) argues that consumers’ switching costs should be critically considered because they affect market entry barriers or a dominant firm’s discriminating behavior. Kenney and Pon (2011) note that several layers can arise due to the lock-in effect from Google with search engines, email, maps, and YouTube; Apple with their App store; Microsoft with MS office; and others. They also note that switching cost would be increased due to subsidies for smartphone devices from telecommunication companies inducing a one- or two-year contract and due to incompatibility between CDMA and GSM technologies.

Cullen and Shcherbakov (2010) and Nakamura (2010) estimated switching costs in mobile in the wireless industry. Nakamura (2010) evaluated lock-in effects of Subscriber Identity Module (SIM) cards in Japan and showed SIM unlock policies reduce consumer switching costs. Cullen and Shcherbakov (2010) concluded that switching costs for changing mobile service providers ranged from $225.7 to $236.3. They noted that there are additional hassle costs because early termination fees in the U.S. range from $175 to $200. Lee, Kim, Lee, and Park (2006) and Maicas, Polo, and Javier Sese (2009) investigated the effect of mobile number portability on switching costs. The adoption of mobile number portability significantly reduced switching costs in both studies. Although there have been a few studies that empirically analyze switching costs in the mobile telecommunications market, studies considering the characteristics of smartphones are hardly found. Although, up to now, contracts, mileage, and mobile number portability have been considered as major factors in mobile handset change, we should consider additional factors related to smartphone characteristics because market situations have changed. Smartphone users face new switching factors such as operating systems and the applications market.

One of the important characteristics of a smartphone is that it is possible to install various applications on it. However, the applications are not compatible among different operating systems (OS). This means a customer cannot use his/her own purchased applications after switching to a smartphone with a different operation system. In addition, there is a learning cost for using other smartphones. That is, a consumer accustomed to a current smartphone needs time and effort to be familiar with other smartphones with different operation systems or user interfaces. In this study, we will discuss some implications of making a competitive mobile market, based on the empirical evidence on smartphone switching cost. The rest of this study is structured as follows: Section 2 briefly explores the switching costs of smartphones. Section 3 provides data and an econometric model for measuring switching costs. Estimation results are presented in Section 4 and Section 5 discusses the main findings.

مقاله سال 2016

In recent years, large fluctuations in crude oil prices have caused grave concern among both market participants and regulators. One of the reasons for this concern is that the oil price uncertainty has a significant impact on the economy (Elder & Serletis, 2010). Theories of both investment under uncertainty and real options predict that an uncertainty about oil prices can depress current investment (Bernanke, 1983; Brennan & Schwartz, 1985; Henry, 1974; Majd & Pindyck, 1987). In addition, the volatility is a key input in pricing options and a major determinant of the value at risk (VaR). Therefore, the modeling and forecasting of the crude oil return volatility are of considerable interest among academics.

In the literature on the forecasting of volatility, the family of generalized autoregressive conditional heteroscedasticity (GARCH) models (Bollerslev, 1986) has been usedwidely for capturing the dynamics of oil return volatility (see for example Alizadeh, Nomikos, & Pouliasis, 2008; Giot & Laurent, 2003; Kang, Kang, & Yoon, 2009; Mohammadi & Su, 2010; Narayan & Narayan, 2007; Nomikos & Pouliasis, 2011; Sadorsky, 2006; Wang & Wu, 2012; Wei, Wang, & Huang, 2010). However, several shortcomings of GARCHclass models have been observed. First, most GARCHclass models can only capture the characteristic of short memory, rather than long-range dependence, even though long-range dependence in volatility has been documented commonly in the literature. The fractional integrated GARCH (FIGARCH) of Baillie, Bollerslev, and Mikkelsen (1996) and its extensions seem to capture the long memory in volatility well. However, the unanimous finding of hyperbolic decay of the autocorrelation function of absolute returns or squared returns is more likely to be a fiction due to unaccounted structural breaks, rather than the ‘‘genuine’’ one revealed by FIGARCH. Lamoureux and Lastrapes (1990) argue that the persistence implied by GARCH models becomes much weaker following the incorporation of structural breaks. Specifically, Lee, Hu, and Chiou (2010) show empirically that some sudden events (e.g., the Iraqi invasion of Kuwait and the Gulf Wars) result in anincrease in the permanent component of the conditional variance, which is evidence of structural breaks. The simple regime switching process can capture structural shifts in the volatility well, but can also lead to the spurious finding of fractional integration (Granger & Terasvirta, 1999) and exponential rather than hyperbolic decay of the autocorrelation function (Ryden, Terasvirta, & Asbrink, 1998). Baillie and Morana (2009) claim that the proposed adaptive FIGARCH (AFIGARCH) incorporates both long memory and structural breaks by allowing the intercept of FIGARCH to follow a slowly varying function specified by Gallant’s (1984) flexible functional form. As was pointed out by Wang, Bauwens, and Hsiao (2013), this parametric model is less efficient if there are no structural breaks in the sample period. In addition, the AFIGARCH model has the problem of needing to determine the order of the trigonometric terms in the Gallant flexible functional form, in addition to the order of the specification of the stationary components in the conditional variance equation. For larger values of the order of the trigonometric terms, the AFIGARCH model has more parameters that need to be estimated, and hence is more likely to result in over-fitting, where a model includes irrelevant explanatory variables that may improve the in-sample fitting but cause a poorer out-of-sample performance.

Second, GARCH-class models cannot accommodate the property of multiscaling (or multifractality) (Lux & Kaizoji, 2007), which is a well-known stylized fact in economic data (Cont, 2001). The scaling property, which is a concept borrowed from statistical physics, defines the behaviors of some forms of volatility measures (e.g., the squared or absolute returns) as a function of the time interval on which the returns are computed.1 The scaling behavior is characterized by the so-called Hurst exponent and its related index. If q-order moments of the distributions of price increments display different scaling behaviors for different values of q, a multiscaling behavior is revealed. The investigation of scaling behaviors in economic and financial data has expanded considerably since the work of Mandelbrot (1963) (see for example Mandelbrot, 1997, 2001; Mantegna & Stanley, 1995; Muller et al., 1990; Stanley & Plerou, 2001). Multiscaling in crude oil markets, which is what we are interested in, is also found in a few studies (AlvarezRamirez, Alvarez, & Rodriguez, 2008; Wang & Liu, 2010; Wang & Wu, 2013). Traditional GARCH-class models are always related to the dynamics of squared returns rather than to another order of moments, and therefore, they do not take into account multiscaling behavior in price movements. The recent empirical study by Wang, Wei, and Wu (2011) also shows the lack of ability of GARCH-class models to capture multiscaling volatility in crude oil markets. In this paper, we use the Markov switching multifractal (MSM) model of Calvet and Fisher (2001) to forecast the crude oil market volatility. This model is motivated by the stylized fact of multiscaling behavior or multifractality in financial data. The MSM model assumes a hierarchical and multiplicative structure of heterogeneous volatility components, which differs fundamentally from conventional volatility models (such as GARCH-class ones) (Lux & Kaizoji, 2007). The advantage of a MSM model over the conventional regime-switching model is that, while the number of parameters grows quadratically as the number of states increases in a regime-switching model, the MSM model is more parsimonious in parameterization, even after allowing for hundreds of states in order to capture possible structural changes. The MSM model is known to generate outliers and long memory in the volatility and to decompose the volatility into components with heterogeneous decay rates (Calvet & Fisher, 2004). Therefore, it can address the aforementioned problems of traditional volatility models well.