Luís Santos

Jorge Dias

Laban Movement Analysis towards Behavior Patterns

Keywords: Laban Movement Analysis, Behavior Patterns, Bayesian Networks, Movement Characterization

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Social interaction is a key issue in human life and also a relevant area in psychology and cognitive science. Social psychologists have been researching social interaction for a long time and conclude that social signals strongly determine human behavior. The majority of these signals are consciously produced, in the form of spoken language. However human interaction also involves non-verbal elements which are extensively and mainly unconsciously performed during human interaction. The nonverbal communication occurs concurrently to spoken words, through aural cues (voice quality, tone and fluency of speech) and visual cues (gestures, body language or posture, facial expression and gaze). These non-verbal signals are intuitively used by humans to understand and predict each other's behavior, mood, personality, and social relations, in a very wide range of situations. This work will focus on body's own language and movements.

By keeping track of relevant body parts (hands and head) a computational system can determine relevant features, thus providing ground for the estimation of parameters that will allow a robust analysis of performed actions and its characteristics [START_REF] Rett | Robot Human Interface Using Laban Movement Analysis Inside a Bayesian Framework[END_REF]. The acquisition method is accomplished using video sensing devices. Image processing uses mainly two algorithms: CAMshift and Haar-like features to keep track of body parts. Once Cartesian data of body part position is available, basic Low Level Features (LLF) that constitute the basis of the Bayesian Network are computed. Detailed description of this acquisition and tracking methods is out of the scope of this work, and detailed information can be found in [START_REF] Rett | Robot Human Interface Using Laban Movement Analysis Inside a Bayesian Framework[END_REF][START_REF] Rett | Laban Movement Analysis using Multi-Ocular System[END_REF][START_REF] Prado | Horopter based Dynamic Background Segmentation applied to an Interactive Mobile Robot[END_REF].

To interpret and contextualize the resulting LLF, Laban Movement Analysis (LMA) [START_REF] Zhao | Synthesis and Acquisition of Laban Movement Analysis Qualitative Parameters for Communicative Gestures[END_REF], a method for observing, describing, notating, and interpreting human movement, is used. Based on [START_REF] Rett | Robot Human Interface Using Laban Movement Analysis Inside a Bayesian Framework[END_REF] we will debate how Computational Laban Movement Analysis (C-LMA) implemented over Bayesian Networks provides a good movement classifier. Bayesian Network properties allow the independent implementation of models, one for each of the Laban Components. By merging each of the models into one global model, it is believable that it will maximize result expectation for movement identification.

It has been shown that, in many social situations, humans can correctly interpret non-verbal signals and can estimate the behavior with high accuracy. Some approaches to characterize behavior decompose it in small basic actions performed in time. These actions exhibit certain characteristics, with some of them being personal i.e. specific for each individual. However it is felt necessary to create a system with an enough abstraction degree to characterize behavior in general. This work presents LMA as a potential tool to establish the relationship of mathematical properties of acquired visual cues to higher level semantic behavior description. This work aims to provide in the future a system that will automatically analyze behavior in different situations using the developed models based on Laban Movement analysis.

Contribution to Technological Innovation

Laban Movement Analysis is a tool widely used in studies of dance and in physical and mental therapy. However its computational implementation had yet been superficial. This work presents a computational approach to LMA implementation based on Bayesian Networks. The nature of this probabilistic method provides the necessary flexibility to model each of LMA components individually. Other interesting properties relates to the ability of Bayesian Framework to deal with incomplete information, uncertainty, make predictions on future events and, most important, provides an embedded scheme for learning. This work aims to take Rett's [START_REF] Rett | Robot Human Interface Using Laban Movement Analysis Inside a Bayesian Framework[END_REF] work on movement classification using partial LMA implementation and extend the global model to a higher level: Behavior. LMA provides a set of descriptors carrying a semantic that can intuitively be seen as basic behavior characteristics. By developing LMA remaining components, hence completing the LMA global model, this work expects it will provide a good set of behavior descriptors based on LMA semantics. Behavior approaches so far, rely on pure geometric approaches, i.e. they do not carry inherent semantics which can immediately be related to behavioral aspects of human actions. Literature states that LMA provides good descriptors for the emotional content of expressive movements, thus, this work aims to take advantage of those characteristics and the flexibility given by the Bayesian approach to develop models to robustly characterize behavior.

State of the Art

Laban Movement Analysis is a descriptive language to study dancing movements. The general framework is widely applied in physical and mental therapy [START_REF] Bartenieff | Body Movement: Coping with the Environment[END_REF] as well as studies on dance. However, it is finding little application in the engineering domain. Recently, researchers from neuroscience [START_REF] Foroud | Changes in the kinematic structure and non-kinematic features of movements during skilled reaching after stroke: A Laban movement analysis in two case studies[END_REF] started to investigate LMA as a tool to describe certain effects on the movements on animals and humans. [START_REF] Rett | Robot Human Interface Using Laban Movement Analysis Inside a Bayesian Framework[END_REF] In his PhD Thesis within the Bayesian Approach to Cognitive Systems (BACS) project developed a social robot that could identify a set of movements within humanmachine interaction. His robot interface interpreted movement using Bayesian models divided in abstraction levels based on Laban Movement Analysis.

Within behavior analysis are several studies based on probabilistic approaches. Despite the flexibility of the probabilistic approach, the majority of presented methods so far, lack the psychological aspects of behavior, focusing on purely geometrical approaches. Léon and Sucar [START_REF] León | Continuous activity recognition with missing data[END_REF] developed a Bayesian model to recognize different activities, with different speed of execution for different persons. They present a very small number of movements, characterized by the global trajectory of the movement between successive images. A few years later Hongeng et al. [START_REF] Hongeng | Video-based event recognition: activity representation and probabilistic recognition methods[END_REF] presented a new method to recognize human activities. An activity is defined as being composed by events (simple or complex) executed by an individual, or through several events that model the interaction between individuals (multiple events). The event modeling, based on the body shape and trajectory of the subject is done through the hierarchical representation of activities Medioni [START_REF] Medioni | Event detection and analysis from video streams[END_REF], where events are organized in level of abstraction, allowing flexibility and modularity in activity modeling. Arsic [START_REF] Arsic | Video based online behavior detection using probabilistic multi-stream fusion[END_REF] proposed a system to automatically detect abnormal behavior from passengers in public transport vehicles monitored by a fixed video camera. Environment constrains lead the authors to observe the passengers actions performed by the upper body. Arsic and their collaborators modeled behavior using Bayesian Networks, postulating that behaviors like nervous, aggressive and others could be described through the combination of a set of simple activities, performed by different body parts, which they called low level actions. Hence small actions like face expressions and global body movement (sitting, rising, etc.) constituted basic actions used by the system to identify high level behavior.

Laban Movement Analysis

Laban Movement Analysis (LMA) is a method to observe, describe, notate and interpret human movement, developed by Rudolf Laban (1879 to 1958). Foround et al. [START_REF] Foroud | Changes in the kinematic structure and non-kinematic features of movements during skilled reaching after stroke: A Laban movement analysis in two case studies[END_REF] states that LMA places emphasis on the underlying motor patterns by notating how the body segments are moving, how they are supported or affected by other body parts, as well as whole body movement. A recent study by Rett J. [START_REF] Rett | Robot Human Interface Using Laban Movement Analysis Inside a Bayesian Framework[END_REF], explored how LMA can be used to classify human expressive movements within human-machine interaction. Rett's work also emphasizes that LMA, based in its inherent semantics, has the potential to analyze emotional content of human actions.

Laban theory consists of several major components, though the available literature does not set a standard regarding their total numbers. The work of Norman Badler's group [START_REF] Zhao | Synthesis and Acquisition of Laban Movement Analysis Qualitative Parameters for Communicative Gestures[END_REF][START_REF] Chi | The emote model for effort and shape[END_REF] mentions five major components: Body, Space, Effort, Shape and Relationship, though the latter is more abstract and deals/emerges from the other four, leading some studies to consider only the first four.

Body

The Body component deals with relative motion of body parts and the body center as well as which are moving at all. This component also deals with issues like locomotion and kinematics. More specifically, the kinematic chains try to relate the spatial Shaping and the inherent Effort qualities. Laban chose the navel as the body center. The lower part of the body is used to study the global locomotion and the upper body deals with exploring, manipulation and gesturing.

Space

The Space component presents concepts to describe the trajectory executed by the observed actor's body parts while performing a movement. These concepts are measured relative to a frame of reference determined by the body of the actor. Whilst concepts may differ in complexity of expressiveness and dimensionality, they are all reproducible in the 3-D Cartesian system and discretized in form of direction symbols [START_REF] Rett | Laban Movement Analysis using Multi-Ocular System[END_REF]. Using observed trajectories, discretized in frames I along time, Rett proposed the following Bayesian model [START_REF] Rett | Robot Human Interface Using Laban Movement Analysis Inside a Bayesian Framework[END_REF][START_REF] Rett | Laban Movement Analysis using Multi-Ocular System[END_REF] to estimate the movement M knowing 8 possible directions symbols A in a 2-D plane.

P(M | A I)

(

This approach, whilst not presenting outstanding results (presented in section 5), was a good indicator regarding future developments. Hence Effort component was implemented.

Effort

What makes the framework of LMA so special is its ability to describe an additional 'expression' that accompanies the spatial trajectory (Space component). It relates lowlevel features like velocity, acceleration and curvature to Effort qualities like Time (E.Ti), Space (E.Sp), Weight (E.We) and Flow (E.Fl). By retrieving some evidences about the emotional state or the intention of the performer, the Effort component can be seen as the key descriptor to solve the task of analyzing 'expressive movements'.

Table 1 shows the Effort qualities, the underlying cognitive process, the subject and the two extremes that characterize each quality has [START_REF] Bartenieff | Body Movement: Coping with the Environment[END_REF]. Movements are described and distinguished by those qualities close to an extreme, e.g. a Punch movement has Strong Weight, Sudden Time and Direct Space. When a person acts sudden and vigorous/strongly, socially humans interpret these signs as someone who might be angry or violent, thus estimating themselves each other's behavior. It is reasonable to state that Effort descriptors approach the semantic humans use to characterize each other's movements in terms of "`expressiveness"'. Following Rett's work, [START_REF] Santos | Human Robot Interaction Studies on Laban Human Movement Analysis and Dynamic Background Segmentation[END_REF] extends and implements the Effort model (equation 2).

P(M | E.sp E.ti E.fl)

(

Knowing the Effort qualities Time E.ti, Space E.sp and Flow E.fl the movement M can be estimated. Despite only Effort and Space have yet been implemented, one other component is now being studied that has special interest to the behavior concept is the Shape component. At this level of the Bayesian Network, movements are hand labeled with determined Effort characteristics, however in the lowest level, to decide which mathematical features are dominant in each of the Effort qualities, a probabilistic evaluation is made [START_REF] Rett | Robot Human Interface Using Laban Movement Analysis Inside a Bayesian Framework[END_REF].

Shape

Bartenieff and Lewis [START_REF] Bartenieff | Body Movement: Coping with the Environment[END_REF] do not define Shape a component of its own but rather a set of qualities emerging from the Body and Space components. Two Shape qualities were mentioned particularly: Shape Flow describes movements that are focused on the body itself, going towards or away from the body center and using descriptors like shrinking and growing, bulging and hollowing (also including breathing). The term Spatial Shaping is used for movements that are going towards a goal in space (e.g. reaching). It is usually described in a Euclidean frame of reference that is aligned with an initial position of the egocentric frame of reference. Due to this, movements can be described by using the vertical, horizontal and sagittal axes and relating them to bipolar descriptors like sinking and rising, enclosing and spreading, and retreating and advancing. Fig 1 . shows the descriptors (left) and some exemplary movements (right).

Fig 1.

The Shape component with its spatial qualities and some exemplary movements: 1. embracing, 2. hugging, 3. shake, 4. retreating 5.reaching and 6.ducking.

Practical Implementation

In the referred studies [START_REF] Rett | Laban Movement Analysis using Multi-Ocular System[END_REF], to test the implemented Space model, the actor performed the movements facing one vision acquisition system. The available database encompassed eight previously learned movements, yielding this model to present 32 misclassification trials out of 95, yielding a positive classification rate of 66,31%.

To study Effort model [START_REF] Santos | Human Robot Interaction Studies on Laban Human Movement Analysis and Dynamic Background Segmentation[END_REF] a database of 5 movements was designed. These movements were spatially similar, however characterized for having different combinations of Effort qualities. Table 2 summarizes the obtained results. In light of the presented results, LMA starts to present its true potential. It was demonstrated that spatial similar movements can be discretized using Effort parameters. The potential becomes clearer when the two already implemented models are fused in one global model (equation 3). Results are presented in Table 3. An improvement of the overall classification can be seen. One can argue that Effort alone provides better results than the joint global model. However, it must be taken into consideration that the studies on Effort model alone used a specific database for proof of concept. The experiments with the global model took both databases used in Effort and Space. By implementing the two remaining components we expect to strengthen the global model, leading to a good movement/body language characterization in terms of Laban descriptors. A robust tracking system has been developed to deal with actors pose changes. It is based on stereo camera system which allows the system to track body parts in 3-D space. The methodology is out of the scope of this work. Details can be found in [START_REF] Prado | Horopter based Dynamic Background Segmentation applied to an Interactive Mobile Robot[END_REF].

P(M | A I E.sp E.ti E.fl) (3)

Behavior Modeling

The previous section provided and debated LMA modeling results based on Bayesian network, demonstrating that the used probabilistic approach could potentiate a computational implementation of a this valuable tool for human movement characterization. Behavior has been studied [START_REF] Hongeng | Video-based event recognition: activity representation and probabilistic recognition methods[END_REF][START_REF] Arsic | Video based online behavior detection using probabilistic multi-stream fusion[END_REF][START_REF] León | Continuous activity recognition with missing data[END_REF] and the common fact these approaches have, is that behavior can be composed of small actions/events. With this concept in mind, this work proposed an approach based on Laban Movement Analysis, where behavior is divided in small movements and Laban parameters. Actions performed by human beings carry themselves emotion that can be expressed in form of visual cues: movements and body language. Rett [START_REF] Rett | Robot Human Interface Using Laban Movement Analysis Inside a Bayesian Framework[END_REF] demonstrated that LMA could be used to identify movements. Literature [START_REF] Zhao | Synthesis and Acquisition of Laban Movement Analysis Qualitative Parameters for Communicative Gestures[END_REF][START_REF] Bartenieff | Body Movement: Coping with the Environment[END_REF] states, that Laban semantics present a natural language to express body motion. Descriptors like sudden, strong, sinking or stretching can very well be applied when humans are trying to understand each other's behavior. Hence by knowing each of these characteristics, one can infer basic behavior actions. Using a Bayesian language, knowing movement M and Laban components Comp the behavior B can be estimated.

P(B |M Comp)

(4) Equation ( 5) presents the possible space for the variable B B {Violent, Relaxed, Quiet, (...)} [START_REF] Prado | Horopter based Dynamic Background Segmentation applied to an Interactive Mobile Robot[END_REF] Equation ( 4) is the first approach to a behavior Bayesian model, and evolution of the presented work makes it a believable and innovative solution for an expected robust behavior probabilistic characterization.

Conclusions

The implemented LMA components presented positive results. As results demonstrated, the merging of two components improved classification, which leads to the expectation of further classification improvement with the implementation of the other Laban components in future work. Also Laban parameters are found to be good behavior descriptors with an enough abstraction degree to give models the necessary flexibility. Behavior can be divided in small events, and described through Laban parameters. Future work will lead to the final LMA global implementation and behavior parameterization with the aim to provide a robust behavior characterizer to be applied in areas like rehabilitation or surveillance.

Table 1 .

 1 Effort qualities and their subjects.

	Effort	Cognitive Process Subject	Extremes
	Space	Attention	The Spatial Orientation	Direct / Indirect
	Weight Intention	The impact	Strong / Light
	Time	Decision	The urgency	Sudden / Sustained
	Flow	Progression	How to keep going	Free or Careful

Table 2 .

 2 Results for Effort qualities.

				Physical qualities
		Space		Flow	Time
		Ind	Dir	Free	Bound	Sud	Sus
	Positive Results	79.3% 90.2% 61.2%	58.7%	84.8%	97.1%

Table 3 .

 3 Results for Effort and Space combined.

			Laban Components
		Space	Effort	Space + Effort
	Classification Rate	61.3%	86,4%	79.4%


Pierre Bisiaux
email: pierre.bisiaux@centralesupelec.fr

Caroline Lelandais-Perrault
email: caroline.lelandais-perraultanthony.kolar@centralesupelec.fr

Anthony Kolar

Philippe Benabes
email: philippe.benabes@centralesupelec.fr

Filipe Vinci
email: filipe.vinci@centralesupelec.fr

Santos

A 14-b Two-step Inverter-based Σ∆ ADC for CMOS Image Sensor

Keywords: incremental, sigma-delta (Σ∆), two-step, CMOS Image Sensor, column-parallel ADC, second-order Σ∆, inverter-based amplifier

This paper presents a 14-bit Incremental Sigma Delta (IΣ∆) analog-to-digital converter (ADC) suitable for a column wise integration in a CMOS image sensor. A two-step conversion is performed to improve the conversion speed. As the same Σ∆ modulator is used for both steps, the overall complexity is reduced. Furthermore, the use of inverter-based amplifiers instead of operational transconductance amplifier (OTA) facilitates the integration within the column pitch and decreases power consumption. The proposed ADC is designed in 0.18 µm CMOS technology. The simulation shows that for a 1.8 V voltage supply, a 20 MHz clock frequency and an oversampling ratio (OSR) of 70, the power consumption is 460 µW, achieving an SNR of 83.7 dB.

Index Terms-ADC,

I. INTRODUCTION

High quality CMOS imaging sensor (CIS) arrays are reaching performance levels close to scientific CCD arrays. Frame rate and pixel pitch have increased, while read-out noise level has quickly fallen. These developments are raising considerably the requirements on the analog-to-digital (ADC) converter necessarily present in the image processing chain. Several improvements have been tried and developments in this field have arguably converged to column-parallel ADC converter arrays, because this configuration has been shown to yield the best tradeoff among pitch, conversion rate, conversion resolution and power consumption.

Fitting the ADC in the ever narrower pixel pitch has driven the converter architectures from straightforward cyclic towards successive approximation register (SAR) and single-slope (SS) converters. SS converters are widely used because of their simplicity and low power consumption. However, they are slow, and it's difficult to obtain more than 10-bits of resolution. To raise the resolution above this, the trend is to move towards hybrid converters, where two kinds of converters work in tandem.

Conceptually, the conversion is done in two steps: first the most significant bits (MSBs) are extracted generating an analog residue. In the second step, this residue is converted by the second stage and the least significant bits (LSBs) are obtained. In the Nyquist converters, the analog residue in intermediate steps is proportional to the original analog input. In oversampling converters, such as Sigma-Delta (Σ∆) ADCs, the residue at every step is proportional to the integral of an error signal. In imaging sensor applications, one uses incremental Σ∆ (IΣ∆) ADCs, where the integrators are reset before each conversion. IΣ∆ converters are able to achieve very high resolution while using simple circuits that can be easily scaled down.

For example, Seo et al. [START_REF] Seo | A low-noise high-dynamic-range 17b 1.3megapixel 30fps cmos image sensor with column-parallel two-stage foldingintegration/cyclic adc[END_REF] have developed a 17 bits IΣ∆+cyclic ADC, and Shin et al. [START_REF] Shin | Cmos x-ray detector with column-parallel 14.3bit extended-counting adcs[END_REF] introduced a 14.3-bits IΣ∆+SAR ADC, both focusing imaging systems. However, these architectures still required moderately complex circuitry due to the use of Nyquist converters in one of the steps. The work reported in Oike et al. [START_REF] Oike | Cmos image sensor with per-column σδ adc and programmable compressed[END_REF] and Chen et al. [START_REF] Chen | A micro-power two-step incremental analog-to-digital converter[END_REF] have pushed the concept further by using IΣ∆ ADCs for both steps. The overall OSR is then decreased compared to a standard IΣ∆ ADC and the implementation of the hybrid ADC takes less area and power. A further improvement of IΣ∆ ADCs was the use of inverters to implement the integrator of the Σ∆ loop, as reported by Chae et al. [START_REF] Chae | Low voltage, low power, inverter-based switchedcapacitor delta-sigma modulator[END_REF], as well as Wang et al. [START_REF] Wang | A 1.8-v 14bit inverter-based incremental σδ adc for cmos image sensor[END_REF] and Tang et al. [START_REF] Tang | 80db dynamic range 100khz bandwidth inverter-based sigmadelta adc for cmos image sensor[END_REF]. However, to obtain a high DC gain over an appreciable output voltage range is a challenging task. Still, the key advantage of inverter-based IΣ∆ ADC is the reduction in area and power consumption.

In this paper, a 14-bit two-step inverter-based IΣ∆ using second-order cascaded integrators feed-forward (CIFF) is introduced. The main contribution of our proposal is the use of a second-order modulator for both steps, in addition to the use of gain-boosted inverter-based integrators. This paper is organized as follows; In section II, the high-level IΣ∆ architecture is presented. In section III, the circuit implementation of the ADC is shown. In section IV, results from simulations are shown and compared to similar work. Section V concludes this article.

II. PROPOSED TWO-STEP ADC ARCHITECTURE

The high-level view of the proposed ADC architecture is shown in fig. 1(a). The architecture is composed of a track and hold (T/H), a Σ∆ modulator and a digital filter. The chosen modulator is a second-order CIFF architecture [START_REF] Markus | Theory and applications of incremental delta; sigma; converters[END_REF] shown in fig. 1(b). Our two-step IΣ∆ ADC first performs a coarse conversion of the pixel value stored in the T/H, giving an analog residue V 2 loaded into the T/H. Then a fine conversion is performed on this residue, using the same modulator. The residue of the coarse conversion can be expressed as follows,

V 2 [M 1] = a 1 a 2 M1-1 K=1 K-1 i=1 (X[i] -a 4 S 1 [i]) (1)
with a 1 and a 2 coefficients in the modulator, M 1 the number of samples for the first step and S 1 the bitstream of the coarse conversion. The fine conversion is then realized on this residue. The final reconstructed signal is then a linear combination of both bitstream and it can be written as,

X = K 1 M1-1 K=1 K-1 i=1 S 1 [i] + K 1 K 2 M2-1 K=1 K-1 i=1 S 2 [i] (2)
with,

K i = 2 a 1 a 2 (M i -1)(M i -2) , i = 1, 2 (3)
where M 2 is the number of samples for the second step, S 2 the bitstream of the fine conversion and K i the coefficient associated with the coarse and fine conversion. To maximize the resolution, M 1 and M 2 must be equal [START_REF] Bisiaux | A new two-step σδ architecture column-parallel adc for cmos image sensor[END_REF] with

M 1 = M 2 = 35.
In a two-step ADC the range difference between the output of the first step of the conversion (V 2 [M 1 ]) and the effective input of the second step can highly deteriorate the overall resolution. To optimize this range difference , it is well known that IΣ∆ must be analyzed in the temporal domain instead of the frequency domain. One can see from (1) that the residue depends on the modulator coefficient a 1 , a 2 and a 4 . They must be adjusted to maximize the residue range within the input range. This optimization must also guarantee a nonsaturation of the amplifier. For this design, the amplifier input range is limited to 85% of the reference scale and integrators levels do not go above 90% of the reference. The parameters a 1 , a 2 , a 3 , a 4 are set by simulation and their values are respectively 0.5, 0.5, 0.75 and 0.5. With this set of parameters, the simulation of the maximum integrator value and the residue value are respectively shown in fig. 2. In both results, values do not exceed the saturation or output limit for any input. The residue range is about 75% of the input range of the modulator. Since the saturation of the amplifier is avoided and the residue range fits the input range of this modulator, this architecture is suitable for a two-step ADC.

III. CIRCUIT IMPLEMENTATION

The T/H circuit and the switched capacitor circuit of the modulator are shown in fig. 3 and fig. 4. In both circuits, amplifiers have been designed with inverters to reduce area and power consumption. Since inverter amplifiers have very large offset variation due to the process we use an autozeroing scheme proposed in [START_REF] Chae | Low voltage, low power, inverter-based switchedcapacitor delta-sigma modulator[END_REF] for the Σ∆ modulator circuit. A similar method is applied to the T/H. Before the beginning of the coarse conversion, the pixel value is loaded into the capacitance C SH (switches S1 and S2 closed, S3 and S4 opened). Then the value of the pixel is disconnected from the amplifier (S1 and S2 being open). Then S3 is closed canceling the offset of the amplifier and storing the pixel value at the end of the operation. To load the residue V 2 [M 1 ] into the T/H at the end of the coarse conversion, the switch sequence is the same except that S4 is closed instead of S1 to select the right input. As the switched capacitor circuit is used for both steps, the CIFF architecture used requires additional reset operations to correctly perform the second step. These operations are also justified by the delayed values send to the comparator. The comparator used is a low kickback noise architecture [START_REF] Miyahara | A low-noise self-calibrating dynamic comparator for high-speed adcs[END_REF].

To perform a 14-bit resolution conversion, a minimum DC gain of 76 dB is needed [START_REF] Bisiaux | A new two-step σδ architecture column-parallel adc for cmos image sensor[END_REF]. The DC gain of an inverter is expressed as follows

A v = (g m(N ) + g m(P ) )(r o(N ) //r o(P ) ) (4)
where g m(N ) and g m(P ) represent the transconductance of NMOS and PMOS respectively, r o(N ) and r o(P ) their output 4) one can see that the gain can be increased with r o(N,P ) . Simple and cascoded inverters cannot reach a sufficiently high gain in this technology. Our solution is to add gain-boosting to the inverter [START_REF] Luo | An audio cascaded σδmodulator using gain-boost class-c inverter[END_REF]. The schematic of a gain-boosted inverter is shown in fig. 5. Thanks to the gain boosting amplifier circuit, the effective transconductance of the cascode transistor is increased, hence considerably increasing the output resistance of the inverter-based amplifier. The output linearity swing is the output range of the amplifier where a minimum DC gain of 76 dB is ensured [START_REF] Bisiaux | A new two-step σδ architecture column-parallel adc for cmos image sensor[END_REF]. A trade-off has to be found between the maximum DC gain and output linearity. To ensure good output linearity swing, low-threshold transistor are used in the gain-boosting module. With this amplifier, linear output range reaches 50% of the supply range. The settling accuracy of a transition from the voltage common mode to the extreme value is shown in fig. 6. The X-axis, the output swing, is scaled to the Σ∆ reference. From this figure, one can observe that an accuracy of 99.9% is guaranteed for an output swing of 95% of the IΣ∆ reference.

The supply voltage of the circuit is 1.8 V. The static current for a gain-boosting module is about 4 µW and 140 µW for an amplifier.

F oM = P 2 EN OB .F s (5)
with P the power dissipation of the ADC, ENOB the effective number of bits calculated from the SNR, and F s the sampling frequency of the ADC. This ADC achieves a FoM of 185 fJ/step. A comparison with similar works is shown in Table I. This work consumes lower power and is very competitive compared to previous results.

Figure 1 .

 1 Figure 1. (a) High-level view of two-steps architecture, schematic of the sample and hold and (b) the IΣ∆ second order modulator

Figure 2 .Figure 3 .

 23 Figure 2. maximum of second integrator level (top) and residue values (bottom) with both axis scaled to Σ∆ reference level

Figure 4 .Figure 5 .

 45 Figure 4. Switched capacitor circuit of the 2 nd order modulator

Figure 6 .

 6 Figure 6. Settling accuracy of an integration step

Figure 7 .

 7 Figure 7. Simulated output spectrum of IΣ∆ ADC with a 256 points FFT

  µm technology. The ADC OSR is 70 and its bandwidth is up to 200 kS/s. Output spectrum is presented in fig.7with an input signal frequency of 200 kHz and a 256 points FFT. This work achieves a SNR of 83 dB. The figure-of-merit (FoM) is written as follows,

			Table I
		PERFORMANCE COMPARISION
		[1]	[11]	[12]	[3]	This work
	Technology (µm)	0.18	0.35	0.18	0.15	0.18
	ADC architecture	Σ∆+Cyclic Σ∆+SAR Σ∆+Cyclic 2 step Σ∆ 2 step Σ∆
	Sampling rate (kS/s)	30	150	50	-	200
	Resolution	17	14.3	10.2	12	14
	Power (µW)	345	300	13	363	460
	DNL (LSB)	-0.88/1.38	-0.79/0.97	-	-0.7/1.8	-
	INL (LSB)	-26.3/35	-1.7/2.79	-	-22/20	-
	SNDR (dB)	85	-	63	-	83
	FoM (fJ/step)	790	100	220	-	185
	IV. RESULTS
	The proposed two-step inverted based ADC is simulated in
	0.18


Mariana Şerban

Livia Sângeorzan

Elena Helerea
email: helereahelerea@unitbv.ro

{mariana Şerban

On the Mineral & Vegetal Oils Used as Electroinsulation in Transformers

Keywords: Mineral oil, vegetal oil, electrical breakdown testing, statistic processing, electrode effect

Due to the relatively large availability and reduced price, the mineral transformer oils are widely used as electrical insulating liquids. However, mineral oil drastically degrades over time in service. New efforts were made to improve mineral oils characteristics, and other types of liquids like vegetal oils are proposed. This paper deals with new comparative tests on mineral and vegetal oils using as indicator the electric strength. The samples of non-additive mineral oil type TR 30 and vegetal oils of rape, sunflower and corn have been tested with increasing voltage of 60 Hz using different electrodes. The obtained data have been statistical processed. The analyze shows different average values of electrical strength for the different type of sample. New method of testing through electrical breakdown is proposed. Experimental data confirms that it is possible to use as electroinsulation organic vegetal oils in power transformers.

Introduction

Intensification of global warming, leading to environmental destruction, implicitly human health, and acute crisis of raw materials and energy have increased. In recent years new researches to find clean alternative green energy resources, replacing nonrenewable resources with new renewable and environmentally friendly resources have been developed.

The global crisis of raw material resources, including oil resources, negatively affects the energy industry [START_REF] Şerban | The Use of Vegetable Ecological Insulating Oils of High Power Transformer[END_REF]. One research direction is to improve the performance of high power electrical transformers, and in particular, of electrical insulation systems. Replacing oil as feedstock for the manufacture of transformer oil should meet the requirements imposed on electrical insulation of high voltage insulation of power transformers [START_REF] Helerea | Aspects Regarding the Monitoring and the Life Extension of Electroinsulating Oils Used in High Voltage Systems[END_REF]. One possibility is to use vegetal oils which are both clean and renewable [START_REF] Lvov | Rated Indices for Evaluating the Winding Insulation Wear of Power Transformers[END_REF]. There are different variants of oil research, seeking practical solutions to the partial or total replacement of mineral oils with other oils, such as the plant oils [4]. Condition assessment of aging and the estimation of the lifetime average insulation systems used in high power equipment, is today an important research objective for producers and users [START_REF] Forster | The Effect of the Electrode Gap on Breakdown in Liquid Dielectrics[END_REF], [START_REF] Burnet | It's a challenge for Farmers and Rape Energy Specialists[END_REF].

This paper makes reference to the comparative analysis of traditional vegetal oils and minerals and determines some of their alternative use in high power transformers. The aim is to develop a testing methodology based on nondestructive insulating oils methods that allow comparative analysis between different types of electrical insulating oils.

Contribution to Technological Innovation

Current challenges related to implementing strategies for sustainable development of human society require the development of new technological innovations. Energy is highly relevant in this respect, to increase energy efficiency and to reduce consumption of scarce raw materials.

In the transport of electricity domain, the issue is diverse, lifetime supply systems and electricity supply being directly linked to good operating condition of high power transformers. The possibilities of replacing the transformer mineral oil, polluting, other dielectric materials such as liquid vegetable oils from plants, green, clean and renewable are under research. The characteristics of the insulation used, in particular transformer oil, establish the good function of the transformer. There are standard methods for determining the characteristics of transformer oil.

Other aspects are that, the current conditions have changed: have appeared new types of oils, namely the inclusion of categories of vegetable oils in study of transformer insulation; regulating devices firms proposed building test equipment according to specific standards, which do not meet specific conditions (which are very different from the request insulation);

insulating oil stiffness values as a parameter characteristic of electrical resistance applications depend on a number of intrinsic and extrinsic factors, which are not always specify the companies producing electrical insulating oils; data processing methods usually statistical distribution of normal type, not always applicable in the case of variable data strings.

This paper proposes an experimental analysis for different types of electrical insulating oils -mineral and vegetal -to optimize the dielectric rigidity test methodology and establish the optimal matrix properties necessary in comparative tests of insulating oils.

Challenges on Electrical Transformer Oils

The insulating oil has a dual role in the complex system of electrical insulation system of power transformers, as a cooling medium and as a medium of electrical insulation. Characteristic of the insulation, in particular of transformer oil, is to largely maintain the good functioning of the transformer.

Mineral oils are a very complex mixture, which can reach about 2900 types of molecules of paraffin, naphthen and aromatic hydrocarbons, their properties can vary greatly from one batch to another, even if they come from the same batch and even the same name.

Efforts are being made today for rapid and effective establishment of criteria for comparing electrical characteristics of the different types of oils that could run for classes of oils used in electrical insulation systems [START_REF] Helerea | Aspects Regarding the Monitoring and the Life Extension of Electroinsulating Oils Used in High Voltage Systems[END_REF].

The lifetime of transformer oil and its technical performance of operation, depend primarily on its initial quality and then on the operating conditions. As the adverse effects on the ability of insulation occur almost immediately after using the new oil refinery delivered, a special attention was paid to a set of defining characteristics of new oil and control methods of these features, before oil supply to the recipient.

The results of fast quality control methods of electrical oils, are unusually reported. The possibility of developing methods for determining the basic indicators of insulating oils -like dielectric loss angle tangent, or tangent of δ, and stiffness are continuously studied and modern models are being tried to be advantageous in terms of price and cost [START_REF] Şerban | The Use of Vegetable Ecological Insulating Oils of High Power Transformer[END_REF], [START_REF] Helerea | Aspects Regarding the Monitoring and the Life Extension of Electroinsulating Oils Used in High Voltage Systems[END_REF].

It was found that one of the main causes of decline of oil dielectrics electrical parameters (such as modification of loss angle tangent of the dielectric rigidity or other physic -chemical, organic acid, water content, etc.) is the formation of free radicals causing the formation of colloidal structures which disturb electrical insulating performance [4].

Similar concerns are found in other countries (USA, England, Belgium, etc.) the specialized technical literature noting that manufacturers use different processes transformer oil refinery to produce products similar to those already known [START_REF] Lvov | Rated Indices for Evaluating the Winding Insulation Wear of Power Transformers[END_REF]. The power transformers in the Romanian power system use only mineral insulating oil, resulting from refining crude oils selected for this purpose, in most cases being used transformer oil type TR 30 (non-additive oil) and, type TR 25 A (additive oil).

As the current conditions have changed a new approach is acquired to replace the liquid electrical insulation materials with newer more efficient ones. There are studies about the possibilities of replacing the transformer mineral oil, with other dielectric materials such as liquid vegetal oils from plants, green, clean and renewable.

There are also the standard methods for determining the characteristics of transformer oil [START_REF] Forster | The Effect of the Electrode Gap on Breakdown in Liquid Dielectrics[END_REF]. Some firms propose building test equipment according to specific standards, but not always they meet specific conditions (which are very different from the request insulation).

It notes also that the insulating oil electric strength, as a parameter characteristic of electrical insulating capacity, depends on a number of intrinsic and extrinsic factors, which are not always specified by the companies producing electrical insulating oils.

Data processing methods, usually with statistical distribution of normal type, are not always applicable in the case of variable data strings.

Experimental Data

Measurements were carried out to determine the electric breakdown voltage of different samples of mineral and vegetal oils: non-additive TR 30 oil, sunflower, corn and rapeseed oils.

The Megger AF 60/2 equipment has been used (Fig. 1). The electrodes of test vessel have different shapes: plane, sphere and semi-sphere, and could be set at different distances. A magnetic stirring could be produced by a rotating magnetic field, controlled by software. A thermometer of BK PRECISION 710 type measures the temperature of the oil and the ambient environment.

Proceeding of Data and Results

Measured data were statistically processed. Various statistic parameters have been calculated and histograms have been plotted to reveal the distribution of these measurements. Date proceeding was made using the software Statistics.

Statistical Distributions

Statistical distribution laws, which provide theoretical models as an approximation of measured values for random variables, have been analyzed.

The normal distribution function is determined by the following formula:

2 2 2 ) ( 2 1 ) ( σ π σ m x e x f - - = , (1)
where: µ is the mean, σ is the standard deviation, e is Euler's constant. The lognormal distribution is often used in simulation of variables. In general, if x is a sample with a normal distribution, then x e y = is a sample with a lognormal distribution. Thus, the lognormal distribution is defined as:

        - - ⋅ ⋅ = 2 2 2 ) ) (ln( 2 1 ) ( σ µ π σ x e x x f (2)
where: µ is the estimated population mean, σ is the estimated population standard deviation.

The Gamma distribution is defined as:

β α α β α x e x e x f - -⋅ ⋅       ⋅ Γ = 1 ) ( 1 ) ( (3)
where: Г is the Gamma function of argument alpha, α is the so-called shape parameter, and β is the so-called scale parameter. For α =1, the exponential distribution is obtained.

The Weibull distribution is commonly used in lifetime random data analysis. The Weibull distribution takes values in the range x>=0 and has one scale parameter, β, and one shape parameter, α, both of which must be positive.

Concordance Tests and Variability Coefficient

The coefficient of variation V is a synthetic indicator of random data variations and brings information on the homogeneity of the studied lot of samples.

As the percentage ratio between standard deviation and arithmetic mean, coefficient of variation V can range between 0-100 %. If the coefficient of variation tends to zero is considered a low variation, a corporate uniform and averaged a high degree of representativeness. If the coefficient of variation tends to 100 %, is considered an intense change, and a heterogeneous community with a low average of representativeness. Thus 4 thresholds of representativeness could be considered:

0<V<17%

-mean is strictly representative (has high homogeneity) 17%<V<35% -mean is moderately representative (less homogeneous) 35%<V<50% -mean is broadly representative (less homogeneous) V>50% -mean unrepresentative (lack of homogeneity). An important aspect of the description of the variables is the shape of its distribution, which shows how frequent the values are from different ranges of the variable. Typically a researcher is interested in how well the distribution can be approximated by the normal distribution. Some precise information can be obtained by performing one of the tests of normality to determine the probability that the sample came from a normal distributed population of observations. However, none of these tests can entirely substitute for a visual examination of the data using a histogram. The graph allows the evaluation of the normality of the empirical distribution because it also shows the normal curve superimposed over the histogram. It also allows the examination of various aspects of the distribution qualitatively.

The concordance tests verify if the empirical distribution differs a lot or does not differ from the proposed theoretical distribution. The Kolmogorov-Smirnov test, Shapiro-Wilks'W test, χ² test are the most used as concordance tests [START_REF] Constantinescu | Processing Experimental Data with Digital Computers[END_REF].

Results of Breakdown Voltage Tests

The empirical distribution parameters calculated for the four types of random variables data -voltage breakdown of TR 30 mineral oil, sun flower oil, corn oil, rapeseed oil -tested with sphere, plan and calotte electrodes -are given in Table 1, Table 2 and Table 3.

In the Table 1 and Table 2 are shown the values of variance coefficient V for all types of oils is between 17-38 % for the voltage breakdown tests with sphere and plane electrodes. The data illustrate that oil samples are not very homogeneous. These values highlight the fact that during the tests these types of oils change their structure.

The oils ages after the 99 breakthroughs. This shows that in this case the arithmetic mean is not representative. A test with 99 successive electric breakdowns should not be representative for the initial characterization of the insulation oils. The data of Table 3 show the variance coefficient V for mineral oil of 17.43 % for tests with calotte electrodes, which indicates a high uniformity and highlights the fact that the oil has not changed the structure.

Conclusion and Future Work

The experimental data regarding the electric breakdown of electroinsulating oils are useful in comparative analyze of new type of oils. Research conducted for the purposes of insulating mineral oil replacement potential were targeted and vegetable oils of different types and grades, which shows similarity with the characteristics of these oils as insulating mineral oil currently used. Experimental data shows that there is compatibility of vegetable oils can be used as substitutes for mineral insulating oils.

Analysis of the experimental data illustrated that there is a normal distribution of values of each type of mineral oil and vegetable. Checking the values of some key statistical parameters lead to the formulation of the following observations:

Median and module are not significantly different from that of the arithmetic mean; Frequency distribution of rapeseed oil has two maximum;

The coefficient of asymmetry is a relatively large value. Because of the obtained asymmetry and the existence of two levels in the histograms the measurement batch of 99 tests was performed again, with new oil samples. Main statistical parameters values obtained for the new values do not differ significantly from those measured earlier.

Thus, the researches in this area have been exhausted and that they should continue to complete the final conclusions of the possibility to use organic vegetable oils as substitutes for mineral insulating oils. New research should be done relative to the type of electrodes used in ac breakdown oil testing.

Fig. 1 .

 1 Fig. 1. Equipment for oil electrical breakdown testing. Samples of oil have been subjected to increasing voltage up to breakdown of sample, with a rate of 2.5 kV/s and frequency of 61.8 Hz. A distance of 1 mm between electrodes for each type of electrodes -plane, calotte and sphere -has been fixed. The volume of oil used in each test subject to breakdown was 300 cm 3 . The temperature of oil and ambient environment was of 25-28°C. The results of breakdown voltage have been saved by a non-volatile memory.

Table 1 .

 1 Empirical parameters and estimated parameters of the distribution statistical lows obtained for the series of variables of breakdown voltage (kV) for Mineral Oil, Sun Flower Oil, Corn Oil, Rapeseed Oil, with sphere-sphere electrodes.

	Empirical Distribution		Type of Random Variables
	Parameters	Mineral Oil	Sun Flower Oil	Corn Oil	Rapeseed Oil
	(Sphere electrodes)	TR 30	SFO	CO	RO
	Sample, N	99	99	99	99
	Mean, µ, kV	17.66	16.77	20.08	18.83
	Variances, σ²	19.29	38.83	46.10	36.86
	Standard deviation	4.39	6.23	6.78	6.07
	Median, kV	17.70	16.60	19.80	19.00
	Variability coef,%	33.80	32.23	24.86	37.13
	Shapiro-Wilk	0.9874	0.9803	0.9742	0.9925
	Kolmogorov test	0,0688	0,0563	0,0353	0,0606
	Normal Distribution,	N(17,66;	N(16,7788;	N(20,0828;	N(18,8374;
	N(µ, σ²)	4.3917)	6.23)	6.79)	6.07)
	Lognormal Distribution Log (lg µ, σ²)	Log(2.8385; 0.264)	Log(2.7496; 0.4147)	Log(2.9161; 0.471)	Log(2.8685; 0.4123)
	Gamma Distribution,	G(1.1492;	G(2.5387;	G(3.2768;	G(2.4815;
	G(α, β)	15.3585)	6.6093)	6.1289)	7.591)

Table 2 .

 2 Empirical parameters and estimated parameters of the distribution statistical lows obtained for the series of variables of breakdown voltage (kV) for Mineral Oil, Sun Flower Oil, Corn Oil, Rapeseed Oil, with plan-plan electrodes.

	Empirical		Type of Random Variables
	Distribution Parameters (Plan electrodes)	Mineral Oil TR 30	Sun Flower Oil SFO	Corn Oil CO	Rapeseed Oil RO
	Sample, N	99	99	99	99
	Mean, µ, kV	14.00	24.54	19.95	23.03
	Variances, σ²	19.28	38.82	46.09	36.86
	Standard deviation	4.39	6.23	6.78	6.07
	Median, kV	14.55	23.40	11.65	25.25
	Variability coef.,%	23.70	13.57	19.61	11.70
	Shapiro-Wilk	0.9874	0.9803	0.9742	0.9925
	Kolmogorov test	0.0688	0.0563	0.0353	0.0606
	Normal Distribution,	N(17.66;	N(16.7788;	N(20.0828;	N(18.8374;
	N(µ, σ²)	4.3917)	6.23)	6.79)	6.07)
	Lognormal Distribution Log (lg µ, σ²)	Log(2,6082; 0.2617)	Log(3,1899; 0.1515)	Log(2,7213; 0.2012)	Log(3.1296; 0.1276)
	Gamma Distribution,	G(0.8744;	G(0.5144;	G(0.6045;	G(0.3483;
	G(α, β)	16.0219)	47.7115)	25.6447)	66.156)

Table 3 .

 3 Empirical parameters and estimated parameters of the distribution statistical lows obtained for the series of variables of breakdown voltage (kV) for Mineral Oil, Sun Flower Oil, Corn Oil, Rapeseed Oil, with calotte -calotte electrodes.

	Empirical Distribution		Type of Random Variables
	Parameters	Mineral Oil	Sun Flower Oil	Corn Oil	Rapeseed Oil
	(Sphere electrodes)	TR 30	SFO	CO	RO
	Sample, N	99	99	99	99
	Mean, µ, kV	16.04	20.08	18.83	17.66
	Variances, σ²	7.82	36.86	19.28	36.86
	Standard deviation	2.79	6.07	4.39	6.07
	Median, kV	16.20	15.30	15.65	14.25
	Variability coef,%	17.43	33.80	32.23	24.86
	Shapiro-Wilk	0.9239	0.9742	0.8572	0.9874
	Kolmogorov test	0.1194	0.0563	0.0353	0.0606
	Normal Distribution,
	N(µ, σ²)


Catalin Mihai
email: catalin.mihai@electricats.ro

Sorin Abagiu

Larisa Zoitanu

Elena Helerea

Interconnections between Reliability, Maintenance and Availability

Keywords: Reliability, maintenance, availability, Markov process, electric lines

The assurance of power quality depends on factors which influence the performances of the availability: the reliability and its support -the maintenance. This paper deals with the interactions between the indicators of reliability, maintenance, availability and with the methods for the calculation of the reliability indicators. For an overhead line of 110 kV the characteristics of the reliability of the system are determined by modeling and analyzing its functionality by the Markov process of continuous time. The value of the availability index and the maintenance function function contributes to ascertain for the studied case that the value of the availability coefficient has the same value with the probability of success and the probability of repairing an equipment is closely connected to the maintenance function

Introduction

The equipment used on the power systems is relatively old and increases the financial effort for their maintenance.

Therefore appear features of the electrical systems that are closely interrelated, such as: reliability, availability and maintenance, their interactions determining the qualitative and quantitative aspects of the analyzed system, its safe operation.

The reliability, as a feature of the system in fulfilling the specific functions in a certain period of time, continues to be the subject of many researches [START_REF] Nitu | Fiabilitatea in energetica[END_REF], [START_REF] Martinescu | Analiza fiabilitatii si securitatii sistemelor[END_REF], [START_REF] Mihoc | Bazele matematice ale teoriei fiabilităţii[END_REF] and [START_REF] Stillman | Power Line Maintenance with Minimal Repair and Replacement[END_REF]. There are many papers [START_REF] Mcmahon | Reliability and maintenance practices for australian and new zealand transmission lines[END_REF], [START_REF] Boşianu | Fiabilitate şi mentenanţă -îndrumar de lucrări practice[END_REF], [START_REF] Rigler | Quantitative reliability analysisof distribution systems: repair times[END_REF] and [START_REF] Fulvio | An Optimal Sparing Model for the Operational Avdability toApproach the Inherent Availability[END_REF] that have as a research subject the maintenance, their goal being to determine the optimum technical -organisational actions to maintain or to repair the system functionality. Concerning the system availability, there is analysed from this point of view: the system capacity of fulfilling its function in a certain moment within a period of time.

Taking in account the necessities for an increasing quality of the delivered electrical energy, there emerges the importance of a new approach in dealing with the aspects of reliability, availability and maintenance, in order to develop efficient methods for calculating the parameters/characteristics in relation with the operation time.

This paper analyses the connections between reliability, availability, maintenance and the "Markov chains" is the proposed method for determining the indicators of the correlation between reliability, availability maintenance and the probability of failure for an overhead line of 110 kV.

Contribution to Technological Innovation

The evaluation of repairing probability for equipment, that can be integrated rapidly in the maintenance program of studied systems, represents an innovation in technical domain based on the analysis of reliability indicators, contributing to implementation of the integrated concept reliability, maintenance and availability.

Characteristics Measures for Reliability, Maintenance and Availability

The safe operation of a technical system is defined by the totality of characteristics, Reliability, Maintenance and Availability. The function of Reliability is defined by the relation:

( ) ( ) 0 d e t z t t R t - ⋅ ∫ = , (1)
where z(t) -rate of failure is defined like the probability of uninterrupted operation until the moment of time t.

The relation [START_REF] Nitu | Fiabilitatea in energetica[END_REF] applies to any law of distribution of operation time. For the exponential repartition of operation time, the rate of failure is:

z(t) = . ) ( const t = = λ λ It results: ( ) ( ) t t R t e λ - ⋅ = (2)
Maintainability (M) represents a safety function and consists in the probability for an installation (or an equipment) to re-enter into operation after a certain time when the maintenance actions were made [START_REF] Nitu | Fiabilitatea in energetica[END_REF].

The maintenance function is defined by the relation:

t e M µ - - = 1 (3)
where: µ is the intensity of repair, representing the probability that for a device which was faulty at the moment t, to be repaired in the next very short period of time. For an exponential repartition of the repairing periods: . ) ( const t = µ

Reliability Measures

Reliability measures of repairable systems can be categorized into three groups [START_REF] Jacob | Analysis of Complex Repairable Systems[END_REF]:

o Measures based on the system's first failure, o Steady-state measures, o Time-specific measures.

As time advances progresses, the repairable system reaches a steady-state condition. This means that certain estimates of system measures do not change with time. These measures include availability, mean time between failures MTBF, mean time to failure MTTF, mean time to repair MTTR, and the expected number of failures per unit time (failure frequency). The following relations are well known:

1 ( ) ( ) ( ) 1 ( ) ( ) MTBF A MTTF A MTRF µ µ µ = ∞ ∞ = ∞ -∞ = ∞ . ( 4
)
Here A(∞)and ν(∞) are respectively the steady-state availability and failure frequency of the system. Therefore, MTTF, MTTR, and MTBF can easily be found from the steady-state availability and failure frequency.

In Fig. 1 there are shown the links between Reliability, Maintenance, Availability. Analyzing Fig. 1, it can underline that the reliability of a system is characterized by the set of measures that give information on the performance of the system functionality in a period of time.

Calculation of System Reliability Indicators. Case Study

It consider the case of a 110 kV overhead power line shown in (Fig. 2), with repair and failure intensities used in the design and provided by the Normative [9].

It aims at determining the characteristics of system analysis and adopting a model of its operation using continuous time Markov processes that can be used for operation and maintenance services of overhead power line owner. In Table 1 There are listed the average values cited in technical literature [START_REF] Nitu | Fiabilitate, disponibilitate, mentenanta in energetica[END_REF] for the following parameters: the intensity of failure, the intensity of repair for a 110 kV installation.

Table 1.

Intensities of repair and failure in installations of 110 kV. Being a serial system components, to study some elements of the scheme is considered a system of 7 elements characterized by indicators of reliability λi and µi. In such a scheme, failure of any of the items that goes into them has the effect of removing all successful schemes in the state. The schema elements can be considered dependent or independent, the states which may take different elements of the scheme. If the items are functionally dependent, the number of states is equal to (n +1).

Elements of overhead power line

Intensity of failure

-in state 0 -all elements are in operation, -in state 1 -element 1 is defective, -in state n -element 2 is defective.

There is no possibility of transition from states with a defective component in states with two defective elements or states with two defective elements in states with three defective elements, since at the failure of one element, the scheme is decommissioned, therefore there is assumed that the other elements can not be damaged.

States denomination:

-successful state (all elements in service): 0 -failure state: 1, 2, 3,...,7. Transition graph for a system with elements in series is shown in Figure 4.

Calculation and Analysis of Reliability Measures

Based on the analysis of state transitions [START_REF] Kececioglu | Reliability Engineering Handbook[END_REF] has made the transition intensities matrix. Transition intensities matrix, column matrix of absolute probability and matrix equation of state of absolute possibility tending to constant values independent of time.

If the system with n elements series, matrices are given below:

λ µ µ λ µ λ µ   -            -  =               -   ∑ K K K K K K K K 0 1 1 1 1 1 0 0 0 n n i n n n P P P (5)
Calculation of success and failure probabilities is carried out by solving the relation [START_REF] Martinescu | Analiza fiabilitatii si securitatii sistemelor[END_REF], where P0 is the probability for the system to be in working order, P1-P7 corresponding to 7 states of transition. In this case:

λ µ = = + ∑ 0 1 0,998 1 i i P ; λ µ - - - - - -   ⋅   ⋅     ⋅     = ⋅ = ⋅     ⋅     ⋅   ⋅    
For an operation time planned for the Tp = 8200 h/year the following measures are calculated:

Probability of success: = = S 0 0,998 P P [START_REF] Mihoc | Bazele matematice ale teoriei fiabilităţii[END_REF] Probability of rejection:

= = ∑ 7 1 0,002 R i P P (8)
Mean total success time:

α λ µ = = = ⋅ = + ∑ 7 1 1 [ ( ) 0,
( ) λ ν λ λ λ µ - = = = + + = + = ⋅ ⋅ ⋅ = ∑ ∑ ∑ ∑ ∑ 0 0 0 0 2 [ ( )] ... 1
0,998 14 10 0,936 0,13

p i p i j p j p i n p i i T M T P q T P q T P T (11)
Mean duration of a successful state:

α β λ - = = = ⋅ ∑ 2 [ ( )] 1 1 [( )] [ ( )] 14 10 p f p i M T M T year M T ( 12
)
Mean duration of continuous operation (a state of failure):

λ β µ λ = = = = ∑ ∑ [ ( )] [( )] 0,0087 [ ( )] i p i d p i M T M T MTBF year M v T (13)
Since the system is studied with a series structure is inferred that the failure of any component of the system generates damage of the entire line. Therefore, it is of tantamount importance to have a system with intensity of repair and an intensity of failure, such as:

λ λ λ µ λ µ - - = = = = = = ∑ ∑ ∑ 1 1 1 0,14 [ ] 1 114,75 [ ] e i p i e i d i year M T year M T (14)

Determination of availability and maintenance functions

To write the coefficient of availability and maintenance function will be used for repair and failure, the intensities equivalent to the system analyzed. Maintainability function is:

µ - = - 1 e t M e (16)
After analysis, we have the following cases presented in Table 2. It is noted that for the time to repair the overhead line of 110 kV, for t = 1 h, the probability for that line to be repaired is 1.6%, and the acceptable probability (96.32%) repair for overhead line studied, leads to a minimum for 8 days.

Conclusions

The method used for determining the characteristics of reliability is easy to apply and almost draw up and provided maintenance plans and procedures and likewise and maintenance programs related equipment or systems studied.

The case study was performed with the parameters of professional norms, which is useful for design calculations.

For operating systems is useful to introduce the value of operating parameters that may substantiate more rigorous maintenance plans.

Calculated data were compared with data mining from SC Electrica SA (Electricity Distribution Company from Romania) and they are the values around which confirms the validity of the calculation.

Fig. 1 .

 1 Fig. 1. Connections between reliability, maintenance and availability.

Fig. 2 .

 2 Fig. 2. The scheme of supply of a consumer to 20 kV through 110 kV overhead line.

Fig. 3 .

 3 Fig. 3. Equivalent scheme for calculating the reliability indicators of 7 elements connected in series.

Fig. 4 .

 4 Fig. 4. Graphical representation of transitions for the series schedule.

Table 2 .

 2 Probability of repair of overhead line.

	Time required for repair [h]	Probability to be repaired [%]
	t = 1	1.6%
	t = 24	32.73 %
	t = 48	54.75 %
	t = 200	96.32 %


Eunice Ribeiro
email: eribeiro@co.it.pt

António Cardoso
email: ajmcardoso@ieee.org

Chiara Boccaletti
email: chiara.boccaletti@uniroma1.it

Fuel Cell Systems for Telecommunications

Keywords: Telecommunications power system, fuel cell, dc-dc converter

Standalone power systems for telecommunications are becoming an emergent need, due to environmental problems and their current tendency to be localized in remote places. Along with photovoltaic and wind generators, fuel cells are one of the most mature technologies to be employed in this kind of systems. As they are expensive and complex systems, it is important to simulate their behaviour to study different operating modes. This paper intends to propose a simulation of a fuel cell system with a voltage-fed full-bridge converter in the Matlab-Simulink © environment fulfilling the strict telecommunications equipment requirements.

Introduction

Due to the attention to environmental concerns that has been increasing at a worldwide level and the proliferation of telecommunications equipment in remote places, one of the best choices for the future of the telecommunications power supply systems is based on renewable energies applied to stand-alone power systems. This kind of power systems combines a set of different renewable energies to guarantee an autonomous and sustainable operation with a reduced need of maintenance, suitable for supplying remote telecommunications equipment. The majority of standalone power systems are based on wind and photovoltaic generators. These kinds of generators are intermittent and, consequently, it is necessary to include energy storage systems to balance the energy production during periods of low solar radiation or wind speed.

In combination with solar or wind generators, fuel cells associated to electrolyzers and hydrogen tanks are a good solution to store energy, as an alternative to the most standard batteries, because they increase the system availability while reducing its maintenance costs. This paper intends to present the simulation of a fuel cell system operation, where the included DC-DC converter plays a very important role to fulfill the telecommunications equipment requirements. The simulation has been performed as closely as possible to actual conditions, using dynamic models of fuel cells. Different operating modes are studied and compared to the telecommunications requirements verifying the excellent performance of the fuel cell to supply this kind of equipments.

Contribution to Technological Innovation

Since telecommunications equipments are being organized in dispersed networks, reliable remote power solutions are emerging as a critical need, where a backup system like a fuel cell combined with an electrolyzer and a hydrogen tank has a vital role. The proposed simulation permits to improve the application of fuel cells as a backup in these kinds of systems, since the power electronics interface simulation is included and different modes of operation can be designed and studied in advance.

The DC-DC converter employed in this simulation is different from the usual ones, which are simple topologies without galvanic isolation [START_REF] Yalcinoz | Improved dynamic performance of hybrid PEM fuel cells and ultracapacitors for portable applications[END_REF][START_REF] El-Sharkh | A dynamic model for a stand-alone PEM fuel cell power plant for residential applications[END_REF][START_REF] Uzunoglu | Dynamic modeling, design, and simulation of a combined PEM fuel cell and ultracapacitor system for stand-alone residential applications[END_REF][START_REF] Uzunoglu | Dynamic modeling, design and simulation of a PEM fuel cell/ultra-capacitor hybrid system for vehicular applications[END_REF][START_REF] Onar | Dynamic modeling, design and simulation of a wind/fuel cell/ultra-capacitor-based hybrid power generation system[END_REF][START_REF] Uzunoglu | Modeling, control and simulation of a PV/FC/UC based hybrid power generation system for stand-alone applications[END_REF]. Indeed, in order to fulfill the telecommunications equipment requirements, galvanic isolation is required. At low power levels, simple, non-isolated topologies are commonly used, such as buck, boost and buck-boost [START_REF] Kirubakaran | A review on fuel cell technologies and power electronic interface[END_REF]. Their topologies include an electronic switch, an inductor to store energy, and a flywheel diode [START_REF] Mohan | Power Electronics Converters, Applications and Design[END_REF]. The electronic switch commutation is controlled in order to maintain the required load voltage. The flywheel diode carries the current during that part of switching cycle when the electronic switch is off.

Higher levels of power (above 1 kW) require isolated topologies, e. g. flyback, forward, push-pull, half-bridge and full-bridge. These are more complex topologies, but, once again, the load voltage depends on the switching control of the electronic switches [START_REF] Mohan | Power Electronics Converters, Applications and Design[END_REF]. Fuel cells brought other challenges to power electronics like the need for low input current ripple, in order to reduce the ripple of the stack voltage and this is why current-fed converters are usually specified as a good power electronics interface for them [START_REF] Kirubakaran | A review on fuel cell technologies and power electronic interface[END_REF]. The study of these kinds of converters as power electronics interfaces between the fuel cell and the load is usually performed through analytical calculations to describe their operating behaviour [START_REF] Averberg | Analysis of a voltage-fed full bridge DC-DC converter in fuel cell systems[END_REF] or simulations with usual DC voltage sources instead of fuel cell system models as this paper proposes [START_REF] Kovacevic | Advanced DC-DC converter for power conditioning in hydrogen fuel cell systems[END_REF]. The advantages of such a study are obvious. Fuel cell systems are expensive and complex and, therefore, they need to be carefully designed and studied before their implementation, especially for high power applications or critical applications where uninterruptible power is required.

The converter chosen for this system was the voltage-fed full-bridge converter. According to [START_REF] Krykunov | Comparison of the DC-DC converters for fuel cell applications[END_REF], where a mathematical analysis is presented as a criterion to choose the most efficient and appropriated DC-DC converter for fuel cells applications, the voltage-fed full-bridge converter is the most efficient DC-DC converter with galvanic isolation and it needs the least core cross section of the transformer. The input current ripple is low [START_REF] Kirubakaran | A review on fuel cell technologies and power electronic interface[END_REF].

Fuel Cell System Simulation

The aim of the proposed simulation is to study the dynamic performance of a fuel cell system composed only by a fuel cell carefully dimensioned and a power electronics interface capable of maintaining the required telecommunications equipment voltage. As it was already explained, telecommunications power systems must obey to strict power requirements and, due to this, power converters play a very important role in this kind of systems. The importance of the power converters simulation increases when a not yet consolidated technology to produce electrical power, such as fuel cells, is used.

The fuel cell model and its parameters were taken from [START_REF] Yalcinoz | Improved dynamic performance of hybrid PEM fuel cells and ultracapacitors for portable applications[END_REF][START_REF] El-Sharkh | A dynamic model for a stand-alone PEM fuel cell power plant for residential applications[END_REF][START_REF] Uzunoglu | Dynamic modeling, design, and simulation of a combined PEM fuel cell and ultracapacitor system for stand-alone residential applications[END_REF][START_REF] Uzunoglu | Dynamic modeling, design and simulation of a PEM fuel cell/ultra-capacitor hybrid system for vehicular applications[END_REF][START_REF] Onar | Dynamic modeling, design and simulation of a wind/fuel cell/ultra-capacitor-based hybrid power generation system[END_REF][START_REF] Uzunoglu | Modeling, control and simulation of a PV/FC/UC based hybrid power generation system for stand-alone applications[END_REF] and they have been used to simulate innumerous standalone applications like portable equipments (laptops, for example) [START_REF] Yalcinoz | Improved dynamic performance of hybrid PEM fuel cells and ultracapacitors for portable applications[END_REF], residential houses [START_REF] El-Sharkh | A dynamic model for a stand-alone PEM fuel cell power plant for residential applications[END_REF][START_REF] Uzunoglu | Dynamic modeling, design, and simulation of a combined PEM fuel cell and ultracapacitor system for stand-alone residential applications[END_REF], vehicles [START_REF] Uzunoglu | Dynamic modeling, design and simulation of a PEM fuel cell/ultra-capacitor hybrid system for vehicular applications[END_REF], and hybrid power generation plants [START_REF] Onar | Dynamic modeling, design and simulation of a wind/fuel cell/ultra-capacitor-based hybrid power generation system[END_REF][START_REF] Uzunoglu | Modeling, control and simulation of a PV/FC/UC based hybrid power generation system for stand-alone applications[END_REF]. The model has been implemented in the Matlab-Simulink © environment, as shown in Fig. 1. q [kmol (s) -1 ] that is consumed by the fuel cell is related to the stack current I (A) by [1-6]:

2 2 o H N I q F = (1)
where o N is the number of cells in series in the stack and F is the Faraday's constant. This value allows calculating the partial pressure of hydrogen (

H O o o H O p p RT E N E F p         = +         (2)
where o E is the no-load voltage [V], R is the universal gas constant and T is the

stack temperature [K].
The stack output voltage V is ( )

ln V E B C I R I = - × -× (3)
where B and C are constants to simulate the activation overvoltage in the fuel cell system [1-6] and R is the internal resistance of the fuel cell stack [Ω]. The whole simulation system is presented in Fig. 2. The modeled telecommunication equipment is a Radio Base Station (RBS). The model includes resistances and switches aiming to simulate load variations, as shown in Fig. 3. A typical RBS load has a nominal power of 3 kW and an overload (until 4 kW) is imposed to study the transient behaviour of the system in case of load variations. Its nominal operating voltage range is 48 V and the operating voltage ranges from 42.75 V to 56.7 V [START_REF] Reeve | DC Power System Design for Telecommunications[END_REF].

Simulation Results

The dynamic performance of the fuel cell is tested under a load variation of 33%, applied between 0.3 and 0.6 seconds, which is shown in Fig. 4.

In Fig. 5, the output stack voltage is shown and a voltage ripple of 1.5 V is visible. During the increase of power, the voltage ripple also increases to 2 V. As it can be seen in Fig. 6, the voltage is always kept under the required levels for telecommunications equipment with a reduced ripple of 0.4 V, even in presence of the transients caused by the turn-on of the system or the power variations. A LC filter was used, with a capacitor of 200 µF and an inductance of 2 mH. When the load power increases, the voltage reduces to 37.6 V during the 15 ms transient as it can be seen in detail in Fig. 7. At 0.6 seconds, an overvoltage of 60.7 V is caused by the load power decreasing again to the nominal value (Fig. 8). Also this transient takes 15 ms.

Conclusion

Telecommunications equipments are strictly exigent on their requirements, such as establishing dc nominal voltage, keeping voltage at its operating level and assuring a reduced ripple and noise in voltage and current waveforms. The presented results of the simulation show how effective the chosen fuel cell system is in fulfilling the load requirements. The present work permits to improve the application of fuel cells as a backup device, since the power electronics interface simulation is included and different modes of operation can be designed and studied in advance.

Directions for future work, include the implementation of a complete standalone power system model of which the fuel cell system will be a part. Mathematical models of the different system components (photovoltaic and wind generators) will be interconnected and a supervisory control system will be developed to define the interaction among them. The most important objective of this control system is to supply the load at its full demand while monitoring the pressure in the hydrogen storage tank. To design such a control system is a challenging task that requires the definition of monitoring key system parameters to be compared one with another to transmit the precise commands, allowing the accomplishment of the load requirements. The conceived fuel cell system model already takes these parameters into account. Further work will be done to achieve a more complex and reliable system. For example, a supercapacitor could be added to the fuel cell system in order to improve its dynamic response.

Fig. 1 .

 1 Fig. 1. Fuel cell system Simulink © model.

Fig. 2 .

 2 Fig. 2. Fuel cell system Simulink © model with power electronics interface and telecommunication equipment.

Fig. 3 .

 3 Fig. 3. Simulink © load model.

Fig. 4 .Fig. 5 .Fig. 6 .Fig. 7 .Fig. 8 .

 45678 Fig. 4. Simulink © load model: Load Power.

Acknowledgments.

This work was partly supported by Fundação para a Ciência e a Tecnologia (FCT) under Project No. SFRH/BD/47741/2008 and Project No. SFRH/BSAB/950/2009.


David Inácio

João Martins

Mário Ventim Neves

Alfredo Álvarez

Amadeu Leão Rodrigues

Disc Motor: Conventional and Superconductor Simulated Results Analysis

Keywords: Axial disc motor, Superconductivity, HTS, YBCO, Finite elements program

Taking into consideration the development and integration of electrical machines with lower dimensions and higher performance, this paper presents the design and development of a three-phase axial flux disc motor, with 50 Hz frequency supply. It is made with two conventional semi-stators and a rotor, which can be implemented with a conventional aluminum disc or a high temperature-superconducting disc. The analysis of the motor characteristics is done with a 2D commercial finite elements package, being the modeling performed as a linear motor. The obtained results allow concluding that the superconductor motor provides a higher force than the conventional one. The conventional disc motor presents an asynchronous behavior, like a conventional induction motor, while the superconductor motor presents both synchronous and asynchronous behaviors.

Introduction

The development and research of lower size electrical machines with higher performance has become a fundamental issue in the electrical machines community. With applications in many systems, the development and improvement of traction electrical motors presents one of the nowadays biggest challenges. Being the automobile the principal means of transport used in the world, they have deserved higher attention. Some countries, such as Portugal, promote and ensure financial advantages to users that acquire electrical vehicles. The integration of electrical motors in the active production of movement in a vehicle, instead of fuel motors, is the main challenge face to the various automobile's constructors, forcing them to establish lines of ecological vehicles, hybrids and fully electric, essential for environmental preservation. The electrical motors development is also "forced" by the increasing fuel prices and by the CO 2 limited emissions, imposed by the European Commission. These actions and incentives were the starting point for a all new ecological journey, where the simultaneous use of combustion and electrical motors makes possible the simultaneous reduction of CO 2 emissions and fuel consumption, desired in the actual economical crisis. On the other hand the production of fully electric cars has also become an important objective integrating, for the example, the use of hydrogen based power supplies [START_REF] Barclay | Fuel Cells, Engines and Hydrogen[END_REF] [START_REF] Thomas | Fuel options for fuel cells vehicle: hydrogen, methanol or gasoline?[END_REF] or renewable energies, such as photovoltaic [START_REF]Solar electrical vehicles information[END_REF].

The discovery of high temperature superconductor -HTS -materials along with their characteristics [START_REF]Superconductivity information[END_REF], has improved the development and integration of superconducting electric motors and superconductivity in various systems replacing conventional motors. Those superconducting motors are applied in different systems: measurement instruments (Superconducting Quantum Interference Devices [START_REF] Casas | Performance of a double SQUID Magnometer[END_REF]), electronics [START_REF] Van Duzer | Superconductor Electronic Device Applications[END_REF], train motors and technology [START_REF]MAGLEB Official Website information[END_REF], ships [START_REF] Snitchler | The performance of a 5 MW high temperature superconductor ship propulsion motor[END_REF], vehicles [9] and small airplanes [START_REF]Electromechanical Systems Applied Superconductivity information[END_REF]. The use of HTS materials provides the achievement of smaller and lighter electrical vehicles. Fuel cells and hydrogen technology can also be integrated, where the low temperature of liquid hydrogen can cool down the HTS elements of the traction motor, making them superconductors. This integration can rise some security aspects that must be overcome with the correct development and improvement of such systems, in order to ensure the safety of users of these vehicles [START_REF] Thomas | [END_REF].

Contributions to Technological Innovation

This paper compares the performance of two disc motors: a conventional one and a HTS one. From the obtained results, one can observe that the superconductor motor develops a higher force than its equivalent aluminum motor. Furthermore, a technological important feature, the HTS motor present synchronous behavior while the conventional present asynchronous behavior.

Superconductivity

The high temperature superconductor -HTS -materials present zero resistance only in stationary conditions. In alternate field applications HTS material presents losses. The HTS materials are subject to penetration of quantized flux within the superconductor sample through the cores of current vortices [START_REF] Abrikosov | [END_REF]. These vortices consist of a magnetic flux cylindrical core aligned with the applied magnetic field, with a distance equal to the coherence length ξ. This core is surrounded by a cylinder of supercurrents that flow in a vortex ring with a thickness equal to the London penetration depth λ. The vortices are distributed in a cantered hexagonal geometry, as presented in Fig. 1, which appears in the superconductor from the edges to the centre. The vortices are subject to the Lorentz force that tends to move them. Accordingly to Maxwell Law, an electric field (1) is induced due to the magnetic field variation inside the vortices within the superconductor.

E B v = × ur ur r (1)
In ( 1), B ur denotes the magnetic field and v r the vortices displacement speed. Current densities J are induced in HTS material and there are resistive losses, proportional to the product of the induced current density by the electric field created. According to Barnes [25], these losses are proportional to torque by a factor of 2π. For pure superconductor materials the variation of applied magnetic field in a superconductor makes the vortices traveling freely by the sample. When the superconducting materials present impurities or defects, the vortices are subject to the pinning flux, the vortices stay trapped in impurities or imperfections (pinning centers) and the magnetic behavior of the sample depends on its magnetic history, independent of time. For higher pinning is need higher current density to Lorentz force win the pinning force, causing more losses and torque.

Electric Disc Motors

The first developed electrical machine was the primitive axial flux machine, built by Faraday. Since then, the constant development of radial flow electric machines has made it to prevail on axial flow, and around 1900 was already used in large scale. At that time, the study and development of electric machines was influenced by the materials and manufacturing processes available. Even before 1980 the axial flux machinery begun to have great applicability in low speed applications. The expensive production of axial flux induction motors was a factor that limited the use of such motors, such as the fact that the faulty construction of the rotor limited the speed of the machine [START_REF]Axial flux technology information[END_REF].

Today is possible to build axial flux motors with relatively low weight, low volume and with excellent mechanical and dynamic performance, which makes the axial flux induction machine a solution in several applications. Disc motors using HTS materials have been used mainly in two topologies: disc motors where the rotor elements of superconducting materials act as magnets [14] or motors where the rotor is a single superconductor disc presenting hysteresis behaviour composed, for example, by YBCO [START_REF] Álvarez | Disk-shaped superconducting rotor for an axial flux induction motor[END_REF] or BSCCO [START_REF] Nakamura | Synchronization of an axial-type Bi-2223 bulk motor operated in liquid nitrogen[END_REF].

With the first topology the motor presents behaviour similar to a synchronous motor, while with the second one presents a more complex behaviour. Experimental results for a rotoric ring (cylinder) [START_REF] Tsuboi | Torque characteristics of a motor using bulk superconductors in the rotor in the transient phase[END_REF] or for a disc [START_REF] Álvarez | Disk-shaped Superconducting Rotor under a Rotating Magnetic Field: Speed Dependence[END_REF] in the HTS hysteresis motors show this dual behaviour. This does not happen when one has a rotoric ring with low electrical conductivity, as in ferromagnetic materials, due to the characteristics of pinning that HTS materials present and due to the dynamics of vortices in this type of material [START_REF] Álvarez | Superconducting armature for induction motor of axial flux based on YBCO bulks[END_REF]. The stators of the disc motor can be conventional ones, composed by copper windings and steel, or superconductor ones, when high current densities are required [START_REF] Álvarez | Superconducting armature for induction motor of axial flux based on YBCO bulks[END_REF].

The disc motors have been elected to be used in electric vehicles that use fuel-cell technology [START_REF] Rahman | Application of Direct Drive Wheel Motor for Fuel Cell Electric and Hybrid Electric Vehicle Propulsion System[END_REF]. The liquid hydrogen used as fuel cells, could also be used [START_REF] Thomas | [END_REF] to cool the HTS materials in the rotor disc of the motor installed on the electric vehicle.

Currently there are essentially three categories of machines optimized with superconductor materials: hysteresis, reluctance and trapped field motors [START_REF] Match | Electromagnetic an Electromechanical Machines[END_REF], [START_REF] Mcculloch | Brushless Ac machines with high temperatures superconducting rotors[END_REF], [START_REF] Barnes | Applications and Modelling of Bulk HTS in Brushless AC Machines[END_REF]. Theoretically, the torque produced from an HTS machine is three to five times higher than the torque obtained for the same conventional machine, made by conventional materials [START_REF] Bondrea | Torque comparison of an eight-pole permanent magnet excited and a high temperature superconductor disc motor[END_REF].

Developed Motor

Topology

The built disc motor is composed by two semi-stators with 24 slots and 24 conventional cooper windings each one, a steel shaft, a rotor consisting of an aluminum disc or a YBCO disc, two support bearings and fixing screws. Fig. 2 shows the built motor.

Complete motor.

Conventional rotor with shaft. Superconductor rotor.

Fig. 2. Built disc motor.

The spacing between the semi-stators and rotor should be as small as possible to assure lower dispersion in the flux produced by the coils of semi-stators, ensuring a higher torque. In the mechanical connection between the semi-stator paramagnetic material (mica) high magnetic reluctance screws were used, in order to cancel the magnetic connection between semi-stators. A system that ensures the adjustment nuts of airgap was also integrated.

Characteristics

This motor, when the rotor is composed of aluminum, has an asynchronous behavior, functioning as a conventional induction motor.

The operation of this motor is quite similar to the drum induction motor, where the flux, coming from one semi-stator, penetrates the rotor disc perpendicularly and closes itself onto the other semi-stator. The disc motor in study has the electrical circuit on the side of the stator, with 24 independent coils, and the rotor consists of an aluminum disc. The stator coils create a magnetic rotating field making the aluminum rotor "feel" a variable inductive magnetic field. Thus, electromotive forces will be induced on the disc giving origin to currents in the rotor disc. The induced currents produce an electromagnetic torque, T elect , which places the rotor to rotate.

When the rotor is composed of HTS materials it presents a complex behavior, showing both synchronous and asynchronous behaviors [START_REF] Barnes | Computational modelling for type-II superconductivity and the investigation of high temperature superconducting electrical machines[END_REF]. At startup, the stator rotating field magnetizes the rotor HTS materials and, in this rotor magnetization process, vortices are induced in the HTS material. These vortices traveling in the HTS disc and can be subject to pinning centers, that pinning them, magnetizing the rotor and creating a field in the rotor that, in steady state, presents a constant phase relatively to the rotating field created by the stator. The interaction between these two fields origins a motor torque that presents an amplitude equal to the product of the amplitudes of two fields with the phase between them (2).

(

)

max max B H = × × sin ^. T B H α α (2)

Simulations

The motor described above was simulated with a commercial finite elements software package, FLUX2D®. In this package, the non-HTS material parameterization was made with same materials already included, like copper, aluminum and steel. In this program, the material parameterization was made with same materials that were parameterized, like the copper, the aluminum and the steel. For the HTS materials, namely YBCO, the parameterization was based using the E-J power law (

,

n B n B c n B c E E B E J B ρ ρ - = + (3)
J c denotes the critical current density, E c the critical electric field, n the exponent and ρ 0 the resistivity. The following parameter values, available from the used software package, were used for the HTS material (YBCO): E c = 10 -4 V/m (Critical Electric Field); J c0 = 4,4x10 6 A/mm -2 (Critical Current Density); B 0 =10 6 T (Magnetic Induction Field); n 0 =15 (Exponent); ρ 0 = 10 -13 Ωm (Additional resistivity).

The analysis of the motor characteristics is done with FLUX2D®, being the modeling performed as a linear motor. The obtained results are presented below. The flux lines resulting from the supply of the coils in the stator are shown in Fig. 3. It can be seen that, for a linear stator with identical dimensions to the cylindrical motor designed, two magnetic poles are created magnetizing the rotor. The current density distribution analysis over the airgap shows, as expected, a sinusoidal distribution with two poles, as presented in Fig. 4. The results presented in Fig. 5 and Fig. 6 allows concluding that the motors present the expected behavior. Fig. 5 shows the force, for both motors in a no-load condition. The motor with the aluminum rotor presents an asynchronous behavior. In Fig. 6 is possible to observe that the aluminum rotor motor, in steady state, does not achieve synchronous linear speed (approximately 25 m/s for an effective length stator of 0,495 m, a frequency of 50 Hz and 2 poles). The HTS rotor motor behaves like a synchronous motor. In steady state, as shown in Fig. 6, it can be seen that it does achieve synchronous speed, behaving as an asynchronous motor when not in steady state. Two important characteristics of the HTS motor can be observed in above figures. The HTS linear motor presents a higher force than the conventional aluminum motor and also presents dual synchronous and asynchronous behavior. Running this motor from start up to steady state, it behaves like an asynchronous motor, working with slip until it reaches the steady state. After reaching the steady state condition the rotor rotates with synchronous speed, acting like a permanent magnet motor.

Conclusions & Future Work

From the obtained results it is possible conclude that the conventional disc motor behaves like an induction motor, with asynchronous behavior while the HTS disc motor presents asynchronous and synchronous behaviors. During asynchronous regime, the magnetization of the superconductor, by the rotating field created in the stator, induces currents in superconducting materials, which establish a magnetic flux that, reacting with the stator flux give rise to an electromagnetic torque, proportional to the losses. In steady state operation, the motor torque is null due the synchronism between the field created by the stator and the field resulting in the rotor. Both fluxes are synchronous thus no flux variation exists and no losses are created.

From the Flux2D® obtained results it can be seen that the HTS motor presents a higher force than the equivalent aluminum motor. However, the obtained force in the simulated HTS disc motor has not been as superior as in the aluminum disc motor. Possible causes may be the simplified simulation problem, a godless accurate parameterization of the materials in the finite element package and the use of a simulated linear motor instead a rotary motor.

Future work considers improving the material parameters in the finite elements program, and develops a more realistic simulation of this linear motor in order to obtain an approach of the electromagnetic characteristic of disc motor. Another approach is the study of this motor considering the load and/or speed variation.

Fig. 1 .

 1 Fig. 1. Vortices dynamics in a superconductor sample.

Fig. 3 .

 3 Fig. 3. Flux lines produced by the semi-stators supply.

Fig. 4 .

 4 Fig. 4. Simulated current density distribution over the airgap.

Fig. 5 .

 5 Fig. 5. Comparison of longitudinal force time evolution between the simulated obtained characteristics for motors without load.

Fig. 6 .

 6 Fig. 6. Comparison of longitudinal force time evolution between the simulated obtained characteristics for motors without load.

Acknowledgements. Authors would like to thank CTS (Centre for Technology and Systems) of UNINOVA (Institute of New Technologies) for financial supporting this work.