N Padoy
email: padoy@cs.tum.edu

D Mateus
email: mateus@cs.tum.edu

D Weinland
email: daniel.weinland@epfl.chpadoy

M-O Berger
email: berger@loria.fr

N Navab
email: navab@cs.tum.edu

Workflow Monitoring based on 3D Motion Features

Activity recognition has primarily addressed the identification of either actions or well-defined interactions among objects in a scene. In this work, we extend the scope to the study of workflow monitoring. In a workflow, ordered groups of activities (phases) with different durations take place in a constrained environment and create temporal patterns across the workflow instances. We address the problem of recognizing phases, based on exemplary recordings. We propose to use Workflow-HMMs, a form of HMMs augmented with phase probability variables that model the complete workflow process. This model takes into account the full temporal context which improves on-line recognition of the phases, especially in case of partial labeling. Targeted applications are workflow monitoring in hospitals and factories, where common action recognition approaches are difficult to apply. To avoid interfering with the normal workflow, we capture the activity of a room with a multiple-camera system. Additionally, we propose to rely on real-time low-level features (3D motion flow) to maintain a generic approach. We demonstrate our methods on sequences from medical procedures performed in a mock-up operating room. The sequences follow a complex workflow, containing various alternatives.

Introduction

In recent years, the analysis of human activities from videos has drawn an increasing interest in the Computer Vision community. The trend is motivated, first, by the wide variety of applications (medical monitoring, surveillance, human-machine interaction, etc.) concerned with understanding and modeling human behaviors, and second, by the fact that videos provide valuable information about the environment and are easy to obtain. Previous works in the domain have addressed different problems such as recognition of human actions [START_REF] Aggarwal | Human motion analysis: A review[END_REF]; activity and anomaly detection in public environments [START_REF] Grimson | Using adaptive tracking to classify and monitor activities in a site[END_REF], modeling and identification of the primitive actions composing activities [START_REF] Moore | Recognizing multitasked activities from video using stochastic context-free grammar[END_REF]; automatic discovery of the activities [START_REF] Hamid | Structure from statistics: Unsupervised activity analysis using suffix trees[END_REF] and recognition of events in groups, such as in meetings [START_REF] Oliver | Layered representations for learning and inferring office activity from multiple sensory channels[END_REF].

A common underlying feature in the above-cited works is their ability to recognize isolated actions or activities (e.g. pick up, wave, fight, etc). In this way, they comply with most long-term applications, where relevant actions need to be detected but periods of inactivity and uninteresting actions should be discarded. Instead, we address in this paper the activity recognition problem in the context of a workflow. In this case, activities follow a well-defined structure in a long period of time and can be semantically grouped in relevant phases. The major characteristics of the phase recognition problem are the temporal dependencies between phases and their highly varying durations.

To perform real-time recognition of phases, we propose to use Workflow Hidden Markov Models (WHMMs). These are hierarchical HMMs that model the complete workflow process including its alternatives. WHMMs contain additional phase probability variables that keep track of semantic information about the phases in the model. Domain knowledge is provided in the form of a few labeled videos recorded from the workflow, indicating the interesting phases. Initialization of WHMMs is performed automatically from the labeled sequences.

Exemplary environments where workflow analysis is of interest are production lines in factories or hospital Operating Rooms (ORs). We are particularly interested in the medical application. Recent discussions about the OR of the Future [START_REF] Cleary | Or 2020: The operating room of the future[END_REF] foresee ORs will become increasingly hightech and specialized for a few kinds of surgeries. Real-time recognition of high-level phases in the OR (see Fig. 1 and Fig. 2 for an illustration of a surgical workflow) can improve synchronization between the ORs, provide a context aware support to the surgical staff and permit automatic and objective documentation.

The workflow in the OR comprises multiple, precise and complex activities usually involving the interaction of several people and objects. Furthermore, when observing the scene with a camera, colors on clothes and tissues are sim-ilar and multiple occlusions occur as the personnel principally work around a small area around the patient table. For these reasons, tracking and recognition of human actions in this specific environment are impractical and furthermore, not absolutely necessary for phase recognition. Due to specialization and sanitary conditions, high-level phases containing these activities resemble from one surgery to another and follow a regular workflow. As we will show later, a global model of the scene is sufficient for recognition since the whole activity focus is on the patient. To capture this activity coherence, we propose to use a multiple-camera system and a real-time reconstruction algorithm. This choice guarantees that the system will not interfere with the normal behavior of the medical staff in the OR and permits the usage of generic low-level features to characterize the phases.

The main contributions in this paper are as follows. We introduce and formalize the problem of recognizing phases in a workflow with alternatives. We propose WHMMs, a form of HMMs using phase probabilities to deal with semantic loss during Expectation Maximization (EM) training. Parameters of the model are initialized in a simple but effective way from annotated sequences. We show the benefits of complete workflow modeling and phase probability variables in on-line and off-line recognition results, also using partially labeled data. Finally, we propose to use 3D motion-flow for recognition in complex environments.

The remainder of the paper is organized as follows. Related work is discussed in Sec. 2. In Sec. 3, we give a formal definition of workflow and phases before stating the phaserecognition problem. In Sec. 4, we describe our proposed solution based on WHMMs and phase probabilities. Sec. 5 details the 3D-flow features. Experimental results are reported in Sec. 6. The conclusion in Sec. 7 includes some discussion on the method and future work.

Related Work

Pinhanez and Bobick [START_REF] Pinhanez | Intelligent studios modeling space and action to control tv cameras[END_REF] were among the first to analyze complex flows of actions. In their seminal work, framing in a TV studio was proposed to be done automatically, by triggering cameras based on the detection of events specified in a script. Unfortunately, their vision system was not able to detect the events and the authors were forced to generate them manually. Although progress has been done ever since [START_REF] Pinhanez | Intelligent studios modeling space and action to control tv cameras[END_REF], using vision systems for recognition in complex environments remains difficult. The problem is usually simplified by limiting the number of actors or that of actions, using a distinctive background, restricting the activity area or discriminating the actions by their spatial location.

Koile et al. [START_REF] Koile | Activity zones for context-aware computing[END_REF] introduced the concept of activity zones, regions in an environment that are linked to specific activities. Likewise, Nguyen et al. [START_REF] Nguyen | Learning and detecting activities from movement trajectories using the hierarchical HMMs[END_REF] represent the room as a collection of cells. In both cases a tracking system is used to determine the presence of a person in a zone or the occupa- tion of a cell. The goal of [START_REF] Nguyen | Learning and detecting activities from movement trajectories using the hierarchical HMMs[END_REF] is to recognize behaviors that differ in the occupied cells and in the sequence of their occupation. The behaviors/primitives hierarchy used in [START_REF] Nguyen | Learning and detecting activities from movement trajectories using the hierarchical HMMs[END_REF] can be assimilated to our definition of workflow/phases, since they both impose temporal constraints. In practice, we deal with a larger time-scale, which makes our problem more complex. Additionally, our signals contain less semantics about the underlying actions and occupation alone does not provide enough information in a crowded scenario.

The use of model constraints to recognize complex events has been suggested before in works like [START_REF] Xiang | Optimising dynamic graphical models for video content analysis[END_REF][START_REF] Moore | Recognizing multitasked activities from video using stochastic context-free grammar[END_REF][START_REF] Vu | Automatic video interpretation: A novel algorithm for temporal scenario recognition[END_REF][START_REF] Shi | Learning temporal sequence model from partially labeled data[END_REF]. Xiang et al. [START_REF] Xiang | Optimising dynamic graphical models for video content analysis[END_REF] address structure learning in HMMs to obtain temporal dependencies between a few high-level events for video segmentation. An HMM models the simultaneous output of event-classifiers to filter their wrong detections. Moore and Essa [START_REF] Moore | Recognizing multitasked activities from video using stochastic context-free grammar[END_REF] use stochastic context-free grammars to recognize separable multi-tasked activities in a card game from video. Production rules were manually defined to describe all the relations between the tracked events. Vu et al. [START_REF] Vu | Automatic video interpretation: A novel algorithm for temporal scenario recognition[END_REF] uses a symbolic approach to recognize complex activities in surveillance applications. For each activity, a formal scenario is provided by hand, including actors, objects and their spatio-temporal dependencies. Oliver et al. [START_REF] Oliver | Layered representations for learning and inferring office activity from multiple sensory channels[END_REF] propose layered HMMs for event recognition in meetings. The HMMs run in parallel at different levels of data granularity which permit event classification using multi-modal information. Each of the HMMs has to be provided with its respective data for training. Shi et al. [START_REF] Shi | Learning temporal sequence model from partially labeled data[END_REF] propose propagation networks (P-nets) to model and detect from video the primitive actions of a task performed by a Even though the aforementioned works share our initiative of imposing constraints on the flow of events to design a better model and improve recognition results, their main focus is on detecting single instances of actions. Our goal is to recognize phases containing multiple actions within a long-term, high-level workflow with alternatives. In brief, our work is different in that it considers either a higher semantical level (the phase) or an environment with more constrained temporal repetitivity.

Concerning the computation of features to observe the scene from video data, the works cited above mainly rely on detection and tracking of the persons and objects. Failure of one of these components hinders the recognition of the events. Actually, only few works address recognition directly using 3D reconstruction data. In [START_REF] Lv | Single view human action recognition using key pose matching and viterbi path searching[END_REF][START_REF] Weinland | Action recognition from arbitrary views using 3d exemplars[END_REF], actions performed by a single human, such as kicking or punching, are learned from 3D voxels. View-invariant action recognition is then performed from 2D shapes. 2D optical flow was recently used for action recognition by Efros et al. [START_REF] Efros | Recognizing action at a distance[END_REF]. To our knowledge, no previous work has used 3D flow for the analysis of complex workflows.

Problem Statement

We begin by defining the usage of certain terms in order to formally state the problem. An action is the fundamental element in the semantic interpretation of a scene; it consists e.g. in picking up, handing, waving, etc. When several of these actions are considered together, they form activities or behaviors [START_REF] Bobick | Movement, activity, and action: The role of knowledge in the perception of motion[END_REF]. With increasing complexity and timescale, we define a phase as a semantically meaningful group of activities occurring somewhere inside a temporal sequence of actions, i.e. a "step" in a process. Phases occur repetitively across different sequences; the order in which they appear matters. Phases can have huge differences in durations, even across recordings. Notice that the semantic relevance which leads to considering a group of activities as a phase, is determined on the basis of domain knowledge. Finally, a set of phases along with their temporal relations are named a workflow.

The Phase Recognition Problem

The goal of phase recognition is to determine which phases occur and when, while observing an instance of a given workflow described by a temporal sequence of T observations {O 1:T } ⊂ O. If we give to each phase a label p from a set of labels L, the problem reduces to finding a label assignment P for each time-step: P : {1, . . . , T } → L.

The challenge is to construct a model that explains the workflow sufficiently well to allow the estimation of P from the observations. In the next section, we explain how to build such a model from the a-priori knowledge contained in a few labeled exemplary sequences of the workflow.

Once the model is built, we address two forms of the recognition problem: off-line when the complete observations O 1:T is available; or on-line on the basis of partial observations O 1:t up to time t ≤ T .

Proposed Method for Workflow Modeling

As mentioned previously, given an observation sequence our aim is to recognize (on-line or off-line) at each time step the current phase of the workflow. We therefore learn a statistical model of all phases and their dependencies. The model, which we call Workflow-HMM (WHMM), represents a hierarchical HMM that we augment with additional phase-probability variables. Effectively, the model has a two-layer hierarchy: nodes on the top layer represent dependencies between distinct phases, while nodes on the bottom layer represent dependencies within individual phases. The additional phase variables link those latent nodes to semantic meaningful phase labels, and hence allow us to infer the phase at each time step. As we will detail in section 4.2, those variables are in particular necessary to keep track of a semantic shift [START_REF] Shi | Learning temporal sequence model from partially labeled data[END_REF] that can occur between latent states and observations during a global EM training.

The detailed structure of our WHMM is illustrated using the convenient graphical description of Dynamic Bayesian Networks [START_REF] Murphy | Dynamic Bayesian Networks: Representation, Inference and Learning[END_REF] in Fig. 3. In this formalism, the random variables Hierar, Event and Trigger enforce the two-level hierarchy, which models the phases and their dependencies. Mixture and Obs represent the observation distributions occurring within the process. Finally, Phase models the probabilities of being in a phase knowing the current Event. Note that different architectures could also be plugged into our framework. Our main objective is to show the general usefulness of phase probabilities for workflow monitoring with a widely-used kind of HMM.

We construct the WHMM using labeled and unlabeled observation sequences of the workflow. The construction involves the generation of the top-level topology, the initialization of the parameters in the lower hierarchy (Sec. 4.1), and the overall training using EM (Sec. 4.2) to refine all probabilities. For initialization, we only use labeled data, and hence do not require structural learning. This is in particular of advantage when we only have a small set of training sequences available. Moreover, by using the labeling we can directly derive a meaningful high level topology. Consequently, learning of the model can be simplified by using a conventional HMM with a single state variable x, which encodes all possible combinations of the Markov states of the original model. The topology shown in Fig. 3 is nevertheless preserved by enforcing its structure on the transition matrix of x, i.e. by setting non-possible transitions to zero.

Formally, the resulting HMM is a sextuplet λ = (N, A, O, B, π, φ) where N is the number of states {x i :

1 ≤ i ≤ N } in

Initialization of Model Parameters

The initialization consists in two steps: 1) generating the top-level topology by enforcing the temporal constraints between the phases using a set of labeled sequences {O l }.

2) initializing the bottom level from the labeled information.

As each labeled sequence provides the temporal relationships between its labels, a directed graph can be deterministically derived from the data, modeling the temporal relationships between the phases, i.e. the workflow (as illustrated in Fig. 4). For the sake of recognition, interphases, namely the chunks of observations between two consecutive labels, are also used to build nodes of the graph. Inter-phases model background and intermediary activities, which are also repetitive across instances of the workflow.

Fig. 4 also shows that the resulting initialization is obtained by replacing each node of this graph with a sub-HMM modeling the corresponding group of events. Each sub-HMM is first initialized using the sub-sequences of data corresponding to its label. The number of states is defined based on the average-length of the sub-sequences and the transition probabilities are set so that the expected duration corresponds to the duration of the phase. We use a left-right skip-one-ahead transition model with mixtures of gaussians to model the observations. The mixtures are initialized using k-means from temporal splits of the training sub-sequences. Each sub-HMM is finally trained independently with EM on the sub-sequences.

Model Refinement and Phase Probability Variables

After learning the individual sub-HMMs (white nodes Fig. 4), we apply a global EM training to the complete model using all available training sequences (labeled and non-labeled), to refine the dependencies between different phases and their overall structure. At this point, the additional phase probabilities φ x (p) = P (p | x) come to importance, as they allow to keep track of a possible shift that can occur between state variables and the associated labels. Initially, after training individual sub-HMMs, each hidden state clusters only observations of a single phase, and consequently phase probability variables φ x are simply a binary indicator of the respective phase. When applying global EM, however, observations can shift to neighboring states, and consequently hidden states might no longer exclusively represent single phases. Phase probabilities are hence used to track this shift.

Different proposals have been made to deal with such a shift in the semantic meaning of the hidden states. For instance Shi et al. [START_REF] Shi | Learning temporal sequence model from partially labeled data[END_REF] proposed for learning of their propagation networks the use of a labeled anchor sequence during EM to prevent alteration of semantic information. In that work, sub-actions are represented only through single nodes and the model topology is provided manually. When the topology is derived from the data and the modeling involves longer and more complex sub-phases represented by several nodes, constraining the EM algorithm is less natural. Instead, we propose a general approach that keeps track of the phases precisely by using the phase probability variables. This provides moreover a convenient formulation during on-line recognition in the WHMM (see Sec. 4.3) and is potentially more powerful by permitting the addition of new labels without performing another EM training.

We compute φ x a-posteriori using a set of labeled sequences {O l }, in a way similar to a single update of model parameters during EM [START_REF] Rabiner | A tutorial on hidden markov models and selected applications in speech recognition[END_REF]. Using γ l t (x) = P (X t = x|O l ), indicating the probability to be in state x at time t while knowing the sequence O l , we count the number of visits that a label makes to each state:

φ l x (p) = {t,phase(O l t )=p} γ l t (x) t γ l t (x)
.

(1)

Finally, φ x is obtained by taking all available sequences into account.

Recognition

According to the available observation data at the moment where the recognition is performed, the computation of P can be done off-line or on-line, as follows:

Off-line: The Viterbi algorithm [START_REF] Rabiner | A tutorial on hidden markov models and selected applications in speech recognition[END_REF] is used to find the most likely path through the topology of the WHMM, i.e. path : {1, . . . , T } → {(x i ) 1≤i≤N }. Using path, the sequence is labeled by:

P(t) = argmax p φ path(t) (p) . (2)
On-line: In the WHMM model, the forward probabilities [START_REF] Rabiner | A tutorial on hidden markov models and selected applications in speech recognition[END_REF] permit to compute:

P(t) = argmax p P (phase = p | O 1:t ) (3) = argmax p xi φ xi (p)P (X t = x i | O 1:t ) . (4)

Observations

The multi-camera system provides sequences of 3D occupation grids. For phase recognition, we compute features which coarsely describe the spatial distribution of motion in the OR over time, without linking these to specific instances of persons and objects. We thereby rely on the fact that the different phases are discriminative with respect to different motion patterns appearing at key-locations in the OR. For instance, the patient entering (Ph. 1 in Fig. 1) can be identified by a strong motion close to the entrance of the OR, while the surgery phases are characterized through distinct motion patterns appearing in the neighborhood of the operation table. We experimented as well with occupancy based features for phase discrimination. Unfortunately, it revealed to provide poorly discriminative information, even in combination with motion features. Below, we only present the computation of the flow features.

3D Motion Flow Features

For feature computation we split the reconstruction volume into a set of Q × R × S evenly spaced cells c. For each cell, we compute a histogram of 3D motion orientations (cf Fig. 5). To avoid quantization effects at the boundaries of the cells and to introduce invariance to small variations, we use a smooth voting scheme for histogram computation based on radial basis functions. In detail, from the occupation grid sequences we compute 3D optical-flow sequences:

{f 1:T }, f (v) : Ω → R 3 , Ω ⊂ R 3 , (5)
using the Lucas-Kanade method applied in 3D [START_REF] Simon Baker | Lucas-kanade 20 years on: Part 5[END_REF]. The flow vectors f (v) for all voxels v are then quantized into n orientation bins h1 (v), . . . , hn (v) using a soft voting scheme, and accumulated into histograms {H 1:Q•R•S,1:n }, one for each of the Q × R × S evenly spaced cells c i :

H ij = v∈Ω hj (v) exp -(v -ci ) 2 /2σ 2 i , (6)
where ci is the centroid of cell c i , and σ i controls the radius at which flow vectors contribute to a certain cells.

To quantize the 3D flow vectors we adapt a recently proposed approach [START_REF] Kläser | A spatio-temporal descriptor based on 3d-gradients[END_REF], which uses regular polyhedrons to define the histogram bins. This quantization scheme avoids well-known problems of standard spherical quantizations. Given a regular n-sided polyhedron with facet normals {p 1:n }, a flow vector f (v) votes into each bin as follows:

h i (v) = max f (v) T • p i f (v) 2 -q, 0 . (7)
q is chosen such that a flow vector lined up with one of the bin's normals will only vote into this bin, i.e. q = p j p k , with p j , p k being direct neighbors. Otherwise, it votes into several neighboring bins, in proportion to its closeness to the corresponding bin. The final contribution of flow vector f (v) into histogram bin h(v) i is computed by normalizing the values of h i (v) to the unit and weighting them by the flow vectors magnitude:

h(v) i = f (v) 2 • h i (v) i h i (v) . (8)
In practice, we use a dodecahedron with 12 bins for the quantization. The volume is split into a grid of 3×3×2 cells and we set σ i = r i * 0.6, where r i is the average spacing between cell c i and its neighbors. The vectors of size 12 × 3 × 3 × 2 obtained by vectorization of the histograms are passed as observations O 1:T to the recognition system after dimensionality reduction using PCA.

Experimental Validation

To validate our method, we recorded in a mock-up OR different instances of the surgery workflow described in ... Fig. 1, performed by actors familiar with the OR. The scene contained simultaneously up to three persons, three tables and a ceiling OR light. The room where the activities take place is observed by a multi-camera system consisting of 9 synchronized and calibrated cameras fixed to the ceiling of the room. The acquisition, as well as the computation of the background subtraction and the 3D reconstruction are distributed over a small computer network (1 server, 3 clients), to achieve the required real-time execution. The resulting data-set is composed of a series of 22 videos (illustrated in Fig. 2) of 3D volumetric reconstructions of resolution 128x128x128. All videos are acquired with 15 frames/s.

We conducted several experiments to evaluate the phase recognition results on-line and off-line, as well as with and without final computation of the phase probabilities after global EM. The utility of the phase probabilities to track semantic shift appears in particular in experiments conducted with sub-sets of annotated sequences and sub-sets of the labeled phases to be recognized. We also compare WHMM with two methods that do not use the temporal constraints of the workflow. In the first method used for comparison, named MAP-HMMs, all phases are modeled independently by different HMMs trained on sub-windows of the data. Maximum likelihood classification is performed at each time-step using a sliding-window. In the second method, sub-HMMs for all phases are arranged in parallel and connected via a sub-HMM modeling background activity. We use this form of connections instead of fully inter-connected HMMs, having a single or multiple HMMs modeling the background activities, since it showed better results. We call this approach CO-HMMs. For evaluation, we perform a full cross-validation. The presented results are the mean over all tests performed with the leave-one-out method.

Error Measures

We use 5 types of error measures to present the recognition results on a sequence. All these errors apply for both on-line and off-line recognition. Accuracy indicates the percentage of correct detections compared to the ground truth in the complete sequence. To account for variations in length between the phases, we also define the following errors computed per phase: Recall (or correct positives) is the number of true positives divided by the total number of positives in the ground truth. Correct negatives is the number of true negatives divided by the total number of negatives in the ground truth. Precision is the number of true positives divided by the number of true and false positives. Overall success is the number of true positives and true negatives divided by the length of the sequence. Correct positives, correct negatives and overall success are inspired from the error measures used in [START_REF] Shi | Learning temporal sequence model from partially labeled data[END_REF].

Phase Recognition Results

Summarizing results are displayed in table 1. As expected, on-line results are slightly worse than off-line results since less information is available. WHMM outperforms both CO-HMMs and MAP-HMMs approaches, showing the importance of using all information provided by the annotation. A difficulty when performing on-line recognition with MAP-HMMs on phases with highly varying lengths, is the choice of the window size. We performed experiments with different sizes but could not match the results of the two other approaches. CO-HMMs perform worse than WHMM as they are less constrained and do not take advantage of all temporal relationships, even after EM training. An additional disadvantage of CO-HMMs are the numerous short and incorrect transitions that occur both offline and on-line. This effect also occurs on-line for WH-MMs, but in a much smaller scale, as shown in figure Fig. 6. This figure shows the number of transitions occurring between all pairs of phases during a complete cross-validation test. Self-transitions on the diagonal were removed for better visualization and the background phase is not taken into account. CO-HMMs perform 4 times more short incorrect transitions than WHMMs.

The influence of EM training and of phase probabilities is shown in Fig. 7. We see that performing the phase probability computation after EM training improves the results. Additionally, this figure shows how the overall results vary depending on the percentage of labeled sequences available in the training set. For this experiment, results were computed from a single random split of the sequences into training and test data for each number of labeled sequences and cross-validation test. Results are expected to get smoother if they are averaged on all the possible subsets.

Results using only a subset of the labels are shown in table 2 . In this experiment, only four labels are available in the training sequences, corresponding to phases 3,6,7 and 8. WHMMs clearly outperform in this case CO-HMMs. Phase probabilities also improve significantly the results, as a semantic shift during EM can easily occur in the long background phases.

On-line results for each phase are given for WHMMs in table 3. This table shows reliable detection using 3Dflow, except for phase 5. Interestingly, this corresponds to an emergency, which is actually an anomaly. Indeed, it consists of an accelerated performance of the first preparation phases and only occurs 4 times in our dataset. When wrongly detected, it is recognized as these similar phases.

Conclusion

In this paper, we addressed the problem of monitoring environments constrained by an overall and repetitive workflow containing alternatives, such as operating rooms and production lines. We proposed to capture the activity in such complex environments with 3D-motion flow, obtained in real-time using videos from a multi-camera system. To perform reliable on-line recognition of the phases, we introduced WHMMs, a form of HMMs augmented with phase-probabilities which models the complete workflow. 1. Summarized results in percent, comparing WHMMs (W), CO-HMMs (CO) and MAP-HMMs (MA), on-line (ON) and off-line (OFF), using EM and computation of phase probabilities. Off-line and on-line results, as well as comparison to other approaches have shown the advantages of WHMM over simpler methods that do not fully use the information provided by the labeled sequences. The proposed approach was demonstrated on sequences from a medical application. Given the generality of the features, it could also be applied to other workflow processes.

In future work, we plan to learn a more efficient model, by allowing the phases to share parts of their structure. This can prove especially useful in cases where the labeled sequences contain partial and complementary information. We will also focus on recognizing additionnal semantic information, such as the number of persons and their role, using high-level domain descriptions such as ontologies

Figure 1 .

 1 Figure 1. Scenario describing the operating room workflow with the phase labels in parentheses.

1 ) 1 )Figure 2 .

 112 Figure 2. Two instances of the workflow. Images from one view and associated 3-D real-time reconstruction. Rows a,b) : a minimallyinvasive surgery. Rows c,d) : an open-surgery. tracked person. P-nets explicitly model parallel streams of events and are used for classification. The detailed topology is handcrafted and trained from partially annotated data.Even though the aforementioned works share our initiative of imposing constraints on the flow of events to design a better model and improve recognition results, their main focus is on detecting single instances of actions. Our goal is to recognize phases containing multiple actions within a long-term, high-level workflow with alternatives. In brief, our work is different in that it considers either a higher semantical level (the phase) or an environment with more constrained temporal repetitivity.Concerning the computation of features to observe the scene from video data, the works cited above mainly rely on detection and tracking of the persons and objects. Failure of one of these components hinders the recognition of the events. Actually, only few works address recognition directly using 3D reconstruction data. In[START_REF] Lv | Single view human action recognition using key pose matching and viterbi path searching[END_REF][START_REF] Weinland | Action recognition from arbitrary views using 3d exemplars[END_REF], actions performed by a single human, such as kicking or punching, are learned from 3D voxels. View-invariant action recognition is then performed from 2D shapes. 2D optical flow was recently used for action recognition by Efros et al.[START_REF] Efros | Recognizing action at a distance[END_REF]. To our knowledge, no previous work has used 3D flow for the analysis of complex workflows.

Figure 3 .

 3 Figure 3. Dynamic Bayesian Network (DBN) representation of the WHMMs: two-levels hierarchy with a phase variable.

  the model, A the transition probability matrix between the states, modeling the topology, and O the space of observations. B is the observation model, indicating for any observation o ∈ O and state x the probability B x (o) = P (o | x) that o can be observed by x. π is a probability distribution over the initial states. φ denotes the phase probability variables, indicating the probability φ x (p) = P (p | x) of each state x to belong to a phase p ∈ L. Relating this definition to Fig. 3, A models the dependencies of random variables Hierar, Event and Trigger; O of Mixture and Obs; φ of Phase and Event.

Figure 4 .

 4 Figure 4. Graph representing the temporal relationships between the phases of workflow in Fig. 1, as extracted from annotated sequences. Colored nodes stand for labeled phases and gray nodes for inter-phases. Bottom levels of gray nodes are not displayed in this figure.

Figure 5 .

 5 Figure 5. Computation of 3D flow histograms within the reconstructed volume, using regular polyhedron quantization.

Table 3 .

 3 On-line results in percent presented for all phases using WHMMs. Column Phase indicates the phase label, as in Fig.1. B stands for the phase modeling background activity. Column # shows the number of occurrences of each phase within the dataset.

Figure 6 .

 6 Figure 6. Occurring phase transitions, on-line, for WHMMs and CO-HMMs. White color means absence of transition.

Figure 7 .

 7 Figure 7. Precision and Recall of WHMMs as a function of the percentage of annotated sequences in the training set. On-line results before global EM (none), after global EM (EM) and after global EM and computation of phase variables (EM+PV).

  .4 70.5 92.2 80.7 63.6 89.9 72.8 53.5 99.3 97.4 96.3 98.5 95.6 96.6 ON 89.2 78.2 70.5 87.8 79.5 63.6 85.3 62.3 53.5 98.8 97.3 96.3 97.5 95.4 96.6

		Accuracy			Recall			Precision			CorrNeg			OveSuc
	W	CO	MA	W	CO	MA	W	CO	MA	W	CO	MA	W	CO	MA
	OFF 92.5 79Table

Acknowledgments:

This research was partially funded by Siemens Healthcare, the german excellence cluster CoTeSys and the european project PHAROS. The authors thank A. Ladikos, A. Ahmadi and J. Deville for helping with the data acquisitions.


Sabrié Antoine

Battiston Alexandre

Jean-Yves Gauthier

Lin-Shi Xuefang

Three-Phase Bidirectional Active Split Source Inverter for Automotive Traction Applications

Keywords: DC -AC converter, Voltage source inverter (VSI), single-stage inverter, Z-source inverter (ZSI), Split Source inverter

The Split Source Inverter (SSI) is an attractive single-stage boost DC-AC converter topology. It requires fewer components than the Z-source inverter to achieve the boost function and also maintains a continuous input current. However, a significant drawback of this topology is its limited DC-bus voltage utilization. This paper introduces a new inverter topology derived from the SSI, aimed at addressing the DC voltage utilization issue and assessing its viability for traction applications. The new three-phase single-stage boost DC-AC inverter topology is named B-ASSI, and a potential modulation scheme is proposed to accompany it. To verify their functionality, the proposed converter and modulation scheme are simulated using Matlab/Simulink. Furthermore, a Proof of Concept (POC) is executed to experimentally validate the performance of the proposed inverter topology

Introduction

In automotive applications, a common approach involves a two-stage configuration comprising a DC-DC Boost converter followed by a DC-AC two-level voltage source inverter (VSI) conversion stage. The purpose of the DC/DC Boost stage is to maintain a constant and higher voltage on the DC-bus. However, the introduction of an extra conversion stage in this configuration leads to a reduction in the overall efficiency of the powertrain. Over the last decade, there have been advancements in single-stage topologies that offer a promising solution. These single-stage topologies can achieve the boosting function of the DC-DC stage without significantly compromising the overall efficiency of the system. The Z-source inverter [START_REF] Peng | Z-source inverter[END_REF] and the quasi-Z-source inverter [START_REF] Anderson | Four quasi-z-source inverters[END_REF] are both examples of single-stage boosting topologies. A comprehensive review of impedance source inverter topologies, their modulation techniques, and their application in traction systems can be found in references [START_REF] Siwakoti | Impedance-source networks for electric power conversion part i: A topological review[END_REF][START_REF] Siwakoti | Impedance-source networks for electric power conversion part ii: Review of control and modulation techniques[END_REF][START_REF] Mande | Comprehensive review on main topologies of impedance source inverter used in electric vehicle applications[END_REF]. The main drawback of these topologies is the need for bulky and voluminous passive components. While space is limited in an embedded environment, some research has explored the integration of these topologies in electrical automotive traction applications and compared them with the traditional DC-DC Boost + VSI configuration [START_REF] Battiston | Comparison criteria for electric traction system using z-source/quasi z-source inverter and conventional architectures[END_REF]. However, the high cost and control complexity associated with these impedance source inverters are still preventing their widespread adoption in automotive applications. The Split source inverter (SSI) was initially introduced as a single-phase topology for grid-connected photovoltaic application in [START_REF] Abdelhakim | Split-source inverter[END_REF]. Later, a three-phase version of this topology was proposed in [START_REF] Abdelhakim | Three-phase split-source inverter (ssi): Analysis and modulation[END_REF] and illustrated in Fig. 1, making it a promising candidate for renewable energy applications [START_REF] Cocco | Modeling and control of hydro-pv hybrid power system with three-phase three-leg split-source inverter[END_REF]. The SSI has emerged as a competitive alternative, offering distinct advantages over other topologies. Unlike the traditional Z-source inverter, the SSI achieves the elevation of the DC-bus voltage using just one inductor and three input diodes. In contrast, the Z-source inverter (ZSI) requires 2 inductors and 2 capacitors for the same purpose. The main advantages of the SSI, as highlighted in [START_REF] Abdelhakim | Three-phase split-source inverter (ssi): Analysis and modulation[END_REF], can be summarized as follows :

1. A continuous input current. 2. Lower voltage stresses for higher boosting factors. 3. A lesser component count compared to the ZSI. [START_REF] Siwakoti | Impedance-source networks for electric power conversion part ii: Review of control and modulation techniques[END_REF]. Same switching states as the Voltage Source Inverter (VSI).

And the main drawbacks are :

1. Dead-times are still required. 2. Higher current stress is imposed on the switches for higher boosting factors. 3. Unequal distribution of current stress among the switches.

+ - V in L SSI Di a Di c Di b C h c C l c C h a C l a C h b C l b ν an ν bn ν cn C DC i DC i L V DC
Figure 1: Three-phase Split source inverter. From [START_REF] Abdelhakim | Three-phase split-source inverter (ssi): Analysis and modulation[END_REF].

Many studies have been conducted to improve the SSI topology. In [START_REF] Abdelhakim | Performance evaluation of the single-phase split-source inverter using an alternative dc-ac configuration[END_REF], the authors propose an alternative connection of the source to the positive side of the DC-bus using common-cathode diodes to reduce the converter's size. Another approach is presented in [START_REF] Lee | Improved single-phase split-source inverter with hybrid quasi-sinusoidal and constant pwm[END_REF], where the diodes are replaced with switches operating in synchronous rectification mode. This modification enables bidirectional power flow in the topology. In [START_REF] Lee | Single-phase simplified split-source inverter (s 3 i) for boost dc-ac power conversion[END_REF] and [START_REF] Lee | Single-phase simplified split-source inverter (s3i) for boost dc-ac power conversion[END_REF], an alternative configuration for the SSI is proposed. The idea is to add a switch to an inverter leg to achieve the same effect and effectively reduce the component count of the SSI. However, this modification results in an unequal current distribution among the switches and introduces limiting factors when extending this topology to a three-phase version. Furthermore, other variations of the Split Source Inverter 2 have been proposed for three-level topologies [START_REF] Abdelhakim | Analysis of the three-level diode-clamped split-source inverter[END_REF][START_REF] Abdelhakim | Three-phase three-level flying capacitors split-source inverters: Analysis and modulation[END_REF] by using the diode-clamped or flying capacitor configuration. Another multilevel operation of the SSI has also been proposed in [START_REF] Montazeri | A new modeling and control scheme for cascaded split-source converter cells[END_REF] or in [START_REF] Montazeri | Multidimensional pulsewidth modulation for cascaded splitsource inverter[END_REF] with a cascaded operation of SSI. However, the adoption of multilevel topologies for automotive applications is still limited due to the higher volume requirements of passive elements. The authors in [START_REF] Hassan | Parallel operation of split-source inverters for pv systems: Analysis and modulation for circulating current and emi noise reduction[END_REF][START_REF] Hassan | Three-phase split-source inverter-fed pv systems: Analysis and mitigation of common-mode voltage[END_REF] investigate the common mode voltage generated in the SSI and propose a new modulation scheme to address this issue. One of the key aspect of the SSI is that the obtained boost factor depends on the modulation. In [START_REF] Abdelhakim | Decoupled control scheme of grid-connected split-source inverters[END_REF], a modulation scheme has then been adopted as a way of decoupling the boost factor of the DC side from the AC side and controlling each independently. All of the proposed topologies suffer from a low DC bus voltage utilization ratio. Researchers have thus proposed alternative configurations of the DC side with additional coupled inductors or other high gain boost cells to increase the boost factor [START_REF] Chen | Magnetically coupled high-voltage-boost split y -source inverter without leakageinduced voltage spikes[END_REF][START_REF] Abramovitz | High-gain single-stage boosting inverter for photovoltaic applications[END_REF][START_REF] Akbar | A family of single-stage high-gain dual-buck split-source inverters[END_REF][START_REF] Chen | Magnetically coupled high-voltage-boost split y-source inverter without leakageinduced voltage spikes[END_REF][START_REF] Dabour | Modeling and control of single-stage quadratic-boost split source inverters[END_REF]. However, increasing the boost factors exacerbates the DC bus utilization ratio problem and results in higher cost due to higher voltage stresses on the switches. The authors in [START_REF] Yin | Single-stage active split-source inverter with high dc-link voltage utilization[END_REF] propose a comprehensive analysis of this inherent limitation and present a topology called the Active Split Source inverter to solve the problem. Nevertheless, this topology has only been proposed for single-phase photovoltaic applications. More recently, alternative configurations have emerged, such as Multi-outputs Split source inverters [START_REF] Dabour | Analysis and control of simplified dual-output single-phase split-source boost inverters[END_REF] or multi-inputs [START_REF] Cocco | Multi-input split-source inverter (missi)[END_REF], which are good candidates for interfacing multiple voltage sources. Very few studies have been conducted on the adoption of the SSI for Electric Vehicles (EV) traction applications. The authors in [START_REF] Dabour | An optimal pwm technique for dual-output nine-switch boost inverters with minimum passive component count[END_REF][START_REF] Pinjala | Improving the dc-link utilization of nine-switch boost inverter suitable for six-phase induction motor[END_REF] proposed the adoption of the SSI with a nine-switch inverter for 6 phase induction motors. The multiphase version of the SSI studied in [START_REF] Dabour | Performance analysis and evaluation of multiphase split-source inverters[END_REF] could be interesting due to the numerous advantages that multiphase machines provide for traction applications. However, in both studies, the modulation index is kept constant. In electric automotive traction applications, the modulation index depends on the electrical motor's operating conditions (Torque and Speed). Furthermore, the topologies in the literature often propose to keep the usage of the input diodes of the classical SSI, which renders the architectures unidirectional in power flow. That is not applicable in traction application where regenerative breaking is needed. This paper proposes a novel three-phase inverter based on the Active Split Source inverter (ASSI) presented in Fig. 2 to solve the low DC bus voltage utilization ratio. The proposed converter has bidirectional capabilities and will be called Bidirectional Active Split Source Inverter (B-ASSI). A possible modulation scheme for the proposed converter is also presented, ensuring compatibility with electric automotive applications. This paper is structured as follows : In Section 2, the limitatiosn of the SSI for automotive applications will be presented. Section 3 introduces the proposed converter and its operation, along with a possible modulation scheme. Finally, Section 4 and 5 present the simulation and experimental results, respectively.

+ - V in L SSI C a1 C b1 C h b C l b C h a C l a ν a ν b C DC i DC i L V DC

SSI analysis and its limitation

SSI analysis and modulation

The SSI (Fig. 1) shares the same states as the two-level inverter, namely six active states and two zero-sequence states, as enumerated in Tab. 1. During any of the active states, as well as during the zero-sequence state V 000 , one of the diodes will be conducting and connects the inductor to the negative pole of the DC bus. Thus, the inductor will be charging. On the other hand, during the zero-sequence state vector V 111 , the inductor will only discharge (and charge the DC bus capacitor) for the duration T 111 . The Split Source inverter can be described as a boost converter with an equivalent duty cycle that represents the time during which the inductor is in the charging state. This duty cycle M DC is expressed by [START_REF] Peng | Z-source inverter[END_REF] :

M DC = 1 - T 111 T PW M (1)
Where T PW M is the duration of one PWM cycle, and T 111 is the duration of the zero-sequence state V 111 . This duration T 111 is mirrored by the lower envelope of the three-phase duty cycles of the inverter legs.

The static characteristics of the classical SSI can be obtained from the charge and discharge states of the inductor. With i L as the input current and V DC as the DC bus voltage being the state-space variables, the SSI can be modeled by equation (2) during T 111 . This corresponds to the state of inductor discharge where the diodesare conducting and the DC bus is connected to the input voltage.

For 0

≤ t ≤ (1 -M DC )T PW M              di L dt = V in -V DC -r L i L L S S I dV DC dt = i L C (2)
Where V DC is the voltage across the DC bus capacitor, V in is the input voltage from the source. The current i L représents the current circulating through L S S I as depicted in Fig. 1. The duty cycle M DC is defined by the level of the lower envelope relative to 1 (see Fig. 3). Then, for all other states where at least one diode is conducing, this corresponds to the state of inductor charging. Thus, for (1 -M DC )T PW M ≤ t ≤ T PW M , the model can be described by equation [START_REF] Siwakoti | Impedance-source networks for electric power conversion part i: A topological review[END_REF].

             di L dt = V in -r L i L L S S I dV DC dt = -i load C (3)
Where i load is the current absorbed by the motor. It is defined in equation ( 4), which is the same as the one in a two-level inverter.

i load = C h a • i a + C h b • i b + C h c • i c (4)
It can be noticed in (3) that during the state V 111 , the current i load = 0 and is removed from the term dV DC /dt. The following equation ( 5) describes the averaged state-space model of the SSI.

            di L dt dV DC dt             = -r L L S S I -1-M DC L S S I 1-M DC C 0 i L V DC + 1 L S S I 0 0 -M DC C V in i load (5)
Thus, the SSI is mathematically described as a Boost converter. The static gain or elevation ratio can be defined by ( 6) :

V DC V in = 1 1 -M DC ( 6
)
M DC is linked with the duration of the zero-sequence state vector V 111 , corresponding to the lower envelope of the duty cycles of the inverter legs in the case of classic PWM schemes based on the same triangle carrier. By using a Space Vector Pulse Width Modulation (SVPWM), the lower envelope is not constant. This will induce low-frequency ripple on the boost factor as well as on the inductor current and DC bus capacitor voltage, leading to increased requeirements in their sizing. To maintain stable DC bus voltage, a modulation scheme called a Modified Sinusoidal Pulse Width Modulation (MSPWM) has been proposed for SSI [START_REF] Abdelhakim | Decoupled control scheme of grid-connected split-source inverters[END_REF]. This modulation scheme modifies the timing of the zero-sequence states and ensures a constant duration T 111 . If the duration T 111 is constant, the obtained elevation ratio from ( 6) is also constant. The resulting duty cycles are presented in Fig. 3. The inductor discharging time can then be controlled by adjusting the duty cycle biases. Thus, the authors in [START_REF] Abdelhakim | Decoupled control scheme of grid-connected split-source inverters[END_REF] proposed a control scheme to decouple the boost factor M DC from the modulation index M ac defined by [START_REF] Abdelhakim | Split-source inverter[END_REF].

M ac = V ac V DC √ 3 (7)
V ac being the output phase voltage of the inverter.

Limitation of the SSI for traction applications

The SSI and the associated MSPWM present numerous advantages. However, there is an inherent limitation that prevents the use of the SSI in automotive applications. This limitation is indicated by the implicit condition in the MSPWM, as stated in [START_REF] Abdelhakim | Three-phase split-source inverter (ssi): Analysis and modulation[END_REF] and illustrated in Fig. 3.

M ac ≤ M DC (8)
It can be observed in Fig. 3 that if the modulation index is increased to a level above M DC , the duty cycles will be saturated. In this scenario, the load cannot be controlled anymore. This constraint also affects the maximum AC output that can be obtained in steady-state, which can be expressed from ( 6),( 7) and ( 8) :

V ac ≤ V DC -V in (9)
As indicated by [START_REF] Cocco | Modeling and control of hydro-pv hybrid power system with three-phase three-leg split-source inverter[END_REF], with the use of a classical SSI, even with the implementation of MSPWM, the maximum output phase voltage V ac remains bounded by the difference between the elevated V DC and the input voltage V in . In [START_REF] Yin | Single-stage active split-source inverter with high dc-link voltage utilization[END_REF], the authors state that to solve the DC link utilization ratio, increasing the boost factor or modifying the modulation alone cannot resolve this limitation. Consequently, a topological modification is required. Indeed, since the states of the passive diodes are imposed by M ac , the system does not present the Degree of Freedom (DoF) to control the elevation ratio. One solution was to add switches to gain a new DoF, which is the case with the single-phase Active Split Source Inverter presented in Fig. 2.

The following sections present an inverter topology and its modulation to overcome this limitation in the three-phase inverter case and to drive the motor for its entire range of load operating conditions without losing control over the regulated DC link voltage. The proposed B-ASSI is described in Fig. 4. This inverter uses two clamping switches connecting the input voltage source to each inverter leg middle point. The command of the first switches S a1 , S b1 and S c1 allows the control of the inductor current charging or discharging state during the actives states without influencing the voltage applied to the load. The second set of switches S a2 , S b2 and S c2 replaces the diodes in the ASSI to allow bidirectional power flow. Thus, there is a new degree of freedom in the control of inductor current charging or discharging time during the active state of the two-level inverter. This way, without impacting the load in any way, complete control over the inductor current as well as the DC bus voltage is achieved. All the states of the inverter topology used with the proposed modulation are depicted in Tab. 2. Where C h a , C h b , C h c are the command signals of the inverter leg switches S h a , S h b , S h c and C a1 , C b1 , C c1 are the command of the first set of clamping switches S a1 , S b1 , S c1 . Fig. 5 illustrates the degree of freedom in the choice of the inductor current state when an active state V 100 is used on the inverter side. The original inductor charging state forced for classical SSI topologies depicted in Fig. 5 (top) can be changed to an alternative inductor discharging state in Fig. 5 (bottom) for the proposed topology.

B-ASSI : Analysis and modulation

Operation and model of the proposed topology

+ - V in L SSI C a1 C a2 C b1 C b2 C c1 C c2 C h c C l c C h a C l a C h b C l b ν an ν bn ν cn C DC i DC i L V DC
+ - Vin LSSI Ca1 Ca2 Cb1 Cb2 Cc1 Cc2 C h c C l c C h a C l a C h b C l b νan νbn νcn VDC V 100 Inductor Charging + - Vin LSSI Ca1 Ca2 Cb1 Cb2 Cc1 Cc2 C h c C l c C h a C l a C h b C l b νan νbn νcn VDC iDC iL
V 100 Inductor Discharging The converter can operate in two different modes. The first mode is called the non-saturated mode, in which the discharge of the inductor operates only during the zero state V 111 . This means that, no discharge happens during any active state. The modulation used is the MSPWM described in Fig. 3. Now the second mode is accessible and is called the Saturated conduction mode. The Discharge of the inductor can happen in any active state, and the duration is chosen by the desired DC bus voltage level. Thus, the model of the B-ASSI in the non-saturated mode is the same as the model of the classical SSI and is described by [START_REF] Mande | Comprehensive review on main topologies of impedance source inverter used in electric vehicle applications[END_REF].

The model in saturated mode for the discharge and charge of the inductor is described by ( 10) and ( 11) respectively.

For 0

≤ t ≤ (1 -M DC )T PW M              di L dt = V in -V DC -r L i L L S S I dV DC dt = i L -i load C (10)
For (1

-M DC )T PW M ≤ t ≤ T PW M              di L dt = V in -r L i L L S S I dV DC dt = -i load C (11)
Finally, the averaged state-space model of the B-ASSI in saturated mode is described in the following equation ( 12) :

            di L dt dV DC dt             = -r L L S S I -1-M DC L S S I 1-M DC C 0 i L V DC + 1 L S S I 0 0 -1 C V in i load (12)
For both mode, with Volt-Second balance, it can be found :

V in M DC T L S S I + (V in -V DC )(1 -M DC )T L S S I = 0 (13)
The static characteristic or boost ratio can then be derived from [START_REF] Lee | Single-phase simplified split-source inverter (s3i) for boost dc-ac power conversion[END_REF] and is expressed by equation ( 14) :

V DC V in = 1 1 -M DC (14)

Proposed Modulation

With the simple SSI and an MSPWM, it is possible to decouple and control both the AC load and the DC bus voltage. But this is true only if the modulation index satisfies [START_REF] Abdelhakim | Three-phase split-source inverter (ssi): Analysis and modulation[END_REF]. To solve this limitation, the principle of a possible modulation scheme of the proposed converter is presented in Fig. 6. With this modulation, the duration of the state V 111 is adjusted according to the load operating condition. The command signals C a1 , C b1 , and C c1 of the clamping switches, then adjust discharging time of the inductor current during the active state according to the desired boost factor. This can be seen as the duty cycle for S a1 is set to the same 1 -M DC independently of the M ac . The DC bus voltage boost factor 1/(1 -M DC ) and the modulation index M AC are truly decoupled for the entire speed range of the drive.

The generated command signals C x1 are plotted in Fig. 7. Those command signals are generated from a duty cycle called D x1 (x = a, b, c) described in Fig. 6 and defined by the following equation [START_REF] Abdelhakim | Three-phase three-level flying capacitors split-source inverters: Analysis and modulation[END_REF] :

D x1 = (1 -M DC ) when (1 -M DC ) ≥ D x 0 otherwise (15)
The resulting duty cycles of the inverter legs D x (x = a, b, c) and of the clamping switches D x1 are then compared to the same triangle carrier wave. Since only one or at most two duty cycles D x are equal to the lower envelope, at least one duty cycle D x1 is set to one. This ensures that at any moment, all three clamping switches are not set OFF at the same time. The command signals of the switches S a2 , S b2 and S c2 are generated from the other command signals for the switches S x and S x1 , and are plotted in Fig. 7. If the inductor is charging, the switches imitate

Vector C h a C h b C h c C a1 C b1 C c1 C a2 C b2 C c2 Inductor State V 000 0 0 0 1 1 1 1 1 1 Charge V 100 1 0 0 0 0 0 - - - - V 100 1 0 0 x x x 0 1 1 Charge V 100 1 0 0 1 0 0 1 1 1 Discharge V 110 1 1 0 0 0 0 - - - - V 110 1 1 0 x x x 0 0 1 Charge V 110 1 1 0 1 1 0 1 1 1 Discharge V 010 0 1 0 0 0 0 - - - - V 010 0 1 0 x x x 1 0 1 Charge V 010 0 1 0 0 1 0 1 1 1 Discharge V 011 0 1 1 0 0 0 - - - - V 011 0 1 1 x x x 1 0 0 Charge V 011 0 1 1 0 1 1 1 1 1 Discharge V 001 0 0 1 0 0 0 - - - - V 001 0 0 1 x x x 1 1 0 Charge V 001 0 0 1 0 0 1 1 1 1 Discharge V 101 1 0 1 0 0 0 - - - - V 101 1 0 1 x x x 0 1 0 Charge V 101 1 0 1 1 0 1 1 1 1 Discharge V 111 1 1 1 1 1 1 1 1 1 Discharge - Forbidden State x
Any other state the diode function. It is set to one if the lower switch of the considered leg is ON or when there is a state V 111 . If the inductor discharge is requested during an active state, then the switch must be ON when the high side switch of the considered inverter leg is ON. Finally, the lower envelope is dependent on the load operating conditions and can be freely increased or decreased. Two cases can be differentiated and are stated in [START_REF] Montazeri | A new modeling and control scheme for cascaded split-source converter cells[END_REF]. If M ac ≤ (1 -M DC ), the classical MSPWM Fig. 5 can be used and if M ac > M DC , the proposed modulation Fig. 6 is used. The block schematic of the proposed modulation is represented in Fig. 12.

(

-M DC ) when M ac ≤ (1 -M DC ) (1 -M ac ) when M ac > (1 -M DC ) 1
In order to ensure that all the states are well respected, the duty cycles D x1 must be saturated by a maximal value expressed by [START_REF] Montazeri | Multidimensional pulsewidth modulation for cascaded splitsource inverter[END_REF] :

M DC ≥ (1 - √ 3/2) • M ac (17)
The minimal elevation ratio function of the modulation index is stated by equation ( 18) :

V DC V in ≥ 1 1 -(1 - √ 3
2 )

• M ac = 2 √ 3 • M ac (18) 1 -𝑀 𝐷𝐶

Generation of the command signals taking Dead-Time into account

As stated in [START_REF] Yin | Single-stage active split-source inverter with high dc-link voltage utilization[END_REF], the use of a single switch in reverse conduction mode is not sufficient to overcome the inherent SSI limitation. In the ASSI, the use of diodes in series with the clamping switch was sufficient, as the diode passively open to prevent the DC bus from the shoot-through phenomenon. However, in an automotive application, the use of reverse blocking devices will not enable bidirectional power flow, which is needed for regenerative braking. Therefore, the additional second clamping switches S a2 , S b2 and S c2 are required, and their commands C a2 , C b2 , and C c2 must avoid the same shoot-trough states and allow bidirectional power flow. The generations of the command signals must be controlled precisely to enable adequate performance and avoid creating any undesired state. This subsection focuses on how to generate the appropriate command signals for the additional switches to ensure bidirectionality under any load operating conditions, taking into account the practical constraints of the converters.

There are three conditions to respect when selectring the states :

1. The two switches of the inverter leg should not be turned on simultaneously. Dead-times are still mandatory. 2. The three clamping switches S a1 , S b1 and S c1 should not be turned off simultaneously.

The inductor current shall not be discontinuous. 3. The clamping switches S a1 , S b1 and S c1 as well as S a2 , S b2 and S c2 must not create a state where the DC bus would be experiencing a shoot-through phenomenon.

With the proposed modulation, bidirectional power flow is achieved by generating the command signals C a2 , C b2 and C c2 with simple logic from existing PWM signals (C x and C x1 , x = a, b, c). This means that no additional PWM driver is needed for the switch S x2 . The function is implemented in programmable logic and is given by [START_REF] Hassan | Three-phase split-source inverter-fed pv systems: Analysis and mitigation of common-mode voltage[END_REF] and [START_REF] Abdelhakim | Decoupled control scheme of grid-connected split-source inverters[END_REF].

C x2 = ((C l a • C l b • C l c ) + C l x ) • Discharge + Discharge (19)
Discharge = C a1 + C b1 + C c1 (20)
This function is generated by considering all the conduction cases. For demonstration, three cases are presented in Fig. 8, Fig. 9 and Fig. 10. Since the proposed B-ASSI can operate in two modes, it may or may not require an inductive discharge during an active state. When an inductive discharge is not necessary, the switches S x1 are always ON, and the diode mimic the conduction states from the SSI described in Tab. 1. In the other mode, the inductive discharge can take place during the first or the second active state of the switching period. The difference lies in whether one or two clamping switches S x1 need to be turned OFF. In Fig. 8, the latter case is depicted. On the left-hand side, the chronogram of the modulation for the given switching period is given. The sub-figures from Fig. 8b to Fig. 8e describe the circuit from the initial states until the inductive discharge is achieved. This case represents the most complicated scenario that can be encountered under normal conditions. The discharge function is thus created to detect the exact states where the discharge is needed. The appropriate states of the switches C x2 are given to prevent any shoot-trough phenomenon during the entire switching cycle. Furthermore, the inductor current can be negative during the entire operation, thus achieving bidirectional power-flow. Since dead-times are still required for the topology, it is necessary to consider the proper operation of the switches S x2 in any state that could occur. Fig. 9 shows the importance of considering dead-times, as well as the significance of referencing the logic function [START_REF] Hassan | Three-phase split-source inverter-fed pv systems: Analysis and mitigation of common-mode voltage[END_REF] to the signals with applied dead-times (C l x ). The scenario depicted in Fig. 9 shows the operation of the B-ASSI in non-saturated mode, meaning there is no need to discharge the inductor during an active state. In these figures, the commands signals C x2 are not the ones that are implemented, but a version that does not take into account dead-times. In this mode, when C x1 = 1, the function Discharge = 0, and finally, the logic function is set to

C x2 = C h a •C h b •C h c +C l
x . This case considers 12 a particular moment where the dead-times of two different phases (B and C) overlap each other.

As depicted in Fig. 9f, the operation of the B-ASSI under this altered modulation results in a state where all three switches S a2 , S b2 and S c2 are OFF. If the inductor current is positive, this does not pose a problem for the topology and a discharge of the inductor will take place through the diodes. But if the inductor current is negative during this instant, it will create a discontinuity in the inductor current accompanied by an over-voltage across the switches, which can lead to their destruction. Since in this work the topology has to work in both motor and generator modes, the proposed logic function is created considering all the states where a discontinuity of the inductor current or a shoot-through of the DC-bus voltage may occur. In order to demonstrate the robustness of the proposed modulation, Fig. 10 illustrates a case where the discharge requested by the control can take place during the dead-time of any phase. Fig. 10 depicts the same case as in Fig. 8 but when the inductive discharge begins during the dead-time. To prevent any undesired phenomena, the logic function references the signals C l x with dead-time applied. This enables the circuit to perform under these specials occurrences without being damaged or without impacting the load.

Voltage and current stresses and comparison with other single-stage topologies

This subsection aims to illustrate the degree of freedom gained by the proposed topology compared to other classical single-stage boosting topologies. This is done by considering the maximum attainable AC phase voltage at a given DC bus voltage for different topologies. It is equivalent to considering the voltage stresses across the switches. Two ratios are thus being considered : the boost ratio given by V DC /V in and the peak phase voltage V ϕ normalized by the input voltage V in . The calculated ratios for the studied topologies are summarized in Tab. 3.

Architectures V DC /V in V ϕ /V in 2L -VSI 1 M ac √ 3 ZSI -constant Boost [32] 1 √ 3M ac -1 M ac 2( √ 3M ac -1) SSI -SPWM [8] 4π 2π-3 √ 3M ac 2πM ac 2π-3 √ 3M ac SSI -MSPWM [8] 1 1-M ac M ac √ 3(1-M ac ) Proposed B-ASSI 1 1-M DC M ac √ 3(1-M DC )
The characteristics of the two-level inverter is also derived for comparison purposes, where the DC bus voltage cannot be increased and is fixed. The peak phase voltage can take values from 0 to the maximum modulation ratio in SVPWM M ac = 1/ √ 3 = 0.57. The Z-source inverter can achieve the same peak phase voltage as the two-level inverter when the shoot-through time is set to zero. It can elevate the DC bus voltage with one of the proposed modulation (for instance, the constant Boost modulation [START_REF] Shen | Constant boost control of the z-source inverter to minimize current ripple and voltage stress[END_REF]). The classical SSI with SPWM has an inherent boost ratio that is linked to the modulation index. The static gain can be derived from the average value of the lower envelope of the reference wave of the duty cycle. The use of MSPWM with the classical SSI can decoupled the boost ratio and the modulation index at a certain point. However, the condition stated in equation ( 8) must be respected. To minimize the voltage stress, the minimal DC bus voltage needed to achieve the desired peak voltage is used. Thus, the static characteristic of the SSI with MSPWM, originally given by 1/(1 -M DC ), is transformed to 1/(1 -M ac ) to respect equation ( 8) and minimize voltage stresses. Finally, for the proposed topology, the modulation index and the boost ratio are truly decoupled, [START_REF] Abdelhakim | Three-phase split-source inverter (ssi): Analysis and modulation[END_REF] does not need to be respected. As a result, the required DC bus voltage for a given peak voltage can be much lower. The new limit of the converter resides in the DC bus voltage needed when no elevation is required, as stated earlier in equation [START_REF] Hassan | Parallel operation of split-source inverters for pv systems: Analysis and modulation for circulating current and emi noise reduction[END_REF]. Fig. 11 presents the static gain and the attainable peak voltages for the different discussed topologies. As stated, it can be observed that the lower the curves, the less voltage stress is applied to the switches. This means that the proposed topology offers significantly more achievable operating points than previous SSI topologies and lesser voltage stress compared to any SSI-derived topology. The advantages in terms of voltage stresses becomes even more significant when compared to the first version of the ZSI proposed in [START_REF] Peng | Z-source inverter[END_REF]. With the topology, there is no needed for over-elevation of the DC bus voltage, unlike other single-stage boosting topologies. The current stresses, symbolized by the maximal current I max seen by the switches of the proposed B-ASSI, summarized in Tab. 4 where I ϕ is the peak phase current, i L is the mean input current flowing through L S S I , and ∆i L is the current ripple. The current stresses are identical to those of the classical SSI. Lastly, Tab. 5 summarizes the added degree of freedom as well as the cost of the topology to put things into perspective. The proposed B-ASSI includes more active switches,resulting in an increase in losses and cost. All SSI topologies have the same boosting ratio, but the degree of freedom to control it entirely is only accessible to the ASSI and the B-ASSI. Thus, the proposed B-ASSI offers access to operating points that are not attainable with classical SSI topologies, which is needed for automotive applications. The B-ASSI also presents reduced voltage stress with the same current stress as the classical SSI. Furthermore, the very fast switching of the input diodes are necessary and becomes a problem for classical SSI. This problem is resolved with the use of active switches components such as Wide band Gap semiconductors like GaN or SiC. Entire modulation ratio range in boosting mode ZSI in [START_REF] Peng | Z-source inverter[END_REF] 2L -2C 0 1 three no no QZSI in [START_REF] Anderson | Four quasi-z-source inverters[END_REF] 2L -2C 0 1 three no no SSI in [START_REF] Abdelhakim | Three-phase split-source inverter (ssi): Analysis and modulation[END_REF] 1L 1C 0 3 three no no ISSI in [START_REF] Lee | Improved single-phase split-source inverter with hybrid quasi-sinusoidal and constant pwm[END_REF] 1L -1C 2 0 single yes no ASSI in [START_REF] Yin | Single-stage active split-source inverter with high dc-link voltage utilization[END_REF] 1L -1C 2 2 single no yes Proposed B-ASSI topology 1L -1C 6 0 three yes yes

Simulation Results

The sizing of the proposed converter can be done in the same manner as the SSI, considering the current ripple of the inductor and the voltage ripple of the DC bus voltage. For comparison purposes, the sizing process of the SSI with a classical SVPWM will be recalled. In the case of the SVPWM, the boosting ratio of a classical SSI will exhibit varations at six times the fundamental freqeuncy, mirroring the lower enveloppe of the duty cycle.

L ssi ≈ KV DC 6ω 1 ∆i L + V in M max DC f sw ∆i L C ≈ Ki L 6ω 1 ∆V DC + i L (1 -M min DC ) f sw ∆V DC (21)
For the SSI operated with a MSPWM, as well as for the proposed B-ASSI, the boosting factor will be constant. The sizing of the component does not need to take into account the low-frequency ripple. The difference is that for the B-ASSI, the boosting factor is completely decoupled from the load operating condition and will not be as limited as for the SSI. The choice of values for L S S I and C can be expressed in this case as follows :

L ssi ≈ V in M DC f sw ∆i L C ≈ i L (1 -M DC ) f sw ∆V DC (22)
It is important to note that a particular effort has been made to enable bidirectionnal power flow. The inductor current of the proposed B-ASSI with the modualtion can be negative. In fact, it is also reversible at near-zero currents, meaning that the proposed B-ASSI would always operate in Continuous Conduction Mode (CCM), which is not possible with the SSI. For this reason it has been chosen to undersize the inductor selection to effectively reduce the volume of the converter. The ripple of the inductor current will be significantly increased, but it will not affect the good operation of the converter since it operates in CCM in both motor and generator modes. The B-ASSI achieves a trade-off by reducing the size of passive elements in exchange for the increaed current ripple.

In this section, a simulation of the proposed converter is carried out with a Permanent Magnet Synchronous Machine (PMSM) in Matlab/Simulink and SimScape, and SimPowerSystems toolboxes. The motor is speed-controlled using classical Field Oriented Control (FOC), and the different parameters used for the simulation are reported in Tab. 6.

The dynamic models of the SSI and B-ASSI can both be derived from their state-space models using small-signals modelling. As a reminder the state-space models of the SSI and B-ASSI are derive in ( 5) and [START_REF] Lee | Single-phase simplified split-source inverter (s 3 i) for boost dc-ac power conversion[END_REF], respectively. In order to linearize the model, let us replace each state variable with its mean value plus a small perturbation signal. Those newly formulated state variables are presented in (23) :

v DC (t) = V DC + ṽDC (t) i L (t) = I L + ĩ L (t) m DC (t) = M DC + m DC (t) (23)
Then the following linearized model for the B-ASSI in saturated Mode can be decribed as follow in [START_REF] Chen | Magnetically coupled high-voltage-boost split y-source inverter without leakageinduced voltage spikes[END_REF] :

ĩ L = - (1 -M DC ) L • s + r L ṽDC - V DC L • s + r L m DC ṽDC = - (1 -M DC ) C • s + r L ĩ L - I load C • s m DC (24)
Where I load and V in are supposed constant. The transfert function of the DC side of the B-ASSI in saturated mode can be calculated from the given linearized model. Their expression are given in

ĩ L m DC = I load -C p V DC L S S I C (1-Mdc) 2 s 2 + rl C (1-Mdc) 2 s + 1 (25)
and

ṽDC m DC = V DC (1 -Mdc) + I L (rl + L p) L S S I C (1-Mdc) 2 s 2 + rl C (1-Mdc) 2 s + 1 (26)
with the natural frequency of the system and its damping factor that are given in [START_REF] Dabour | Analysis and control of simplified dual-output single-phase split-source boost inverters[END_REF] and derived from the caracteristic equation of the system.

ω n = (1 -M DC ) L S S I C ξ = C L S S I r L 2(1 -M DC ) (27)
In this paper, a simple solution to control the DC link voltage and inductor current is proposed using cascaded PI controllers, as described in Fig. 12. The design considerations for the two PI controllers should take into account the output current regulations, which will define the constant value I load for a given operating point. Both controllers should present a bandwidth at least a decade apart from each other. The same is done for the input current and DC bus voltage PI controllers.

In Fig. 13 and Fig. 14, two main tests are carried out. A constant DC bus voltage reference is set to 60V, and the motor reference speed is gradually increased to increase the modulation index. In Fig. 13a, the MSPWM is used. It can be seen that, as long as the load operating conditions impose a modulation respecting the condition (8) the DC bus voltage can be controlled. Since V * DC is set to two times the input voltage, M DC is set to 0.5. It can be seen that when the modulation index is increased above 0.5, the duty cycle becomes saturated, and the load cannot be controlled anymore. The results for the same conditions with the proposed modulation are plotted in Fig. 13b. Two cases can be distinguished. If the load operating conditions impose a modulation index that satisfies [START_REF] Abdelhakim | Three-phase split-source inverter (ssi): Analysis and modulation[END_REF], then the lower envelope of the reference wave is chosen by the DC bus voltage controller. The clamping switches S a1 , S b1 and S c1 can remain ON. This is the same operation as a simple SSI with a MSPWM. When the modulation index is increased and when [START_REF] Abdelhakim | Three-phase split-source inverter (ssi): Analysis and modulation[END_REF] is not satiffied, the lower envelope is set by the modulation index. This way, the controllability of the load is ensured. The clamping switches are then driven accordingly to achieve the required DC bus voltage. Simulation results show that the load can be driven up to its base speed of ω BaseS peed = 8450rpm with a modulation index up to one, while maintaining the DC link voltage at a constant level. This base speed corresponds to a two-level VSI with a 60V battery. In contrast, for the proposed converter, the 60V motor can be driven from a battery delivering only 30V, as chosen for the simulation parameters. Thus, this converter can actually adapt the DC bus voltage from a wide variety of input DC voltage sources. Two more tests are carried out by simulations. Firstly, in Fig. 14a the DC bus voltage can be increased above 60V to drive the motor to a speed higher than the base speed of the vehicle, meaning that the entrance into the flux weakening region can be postponed. Lastly, Fig. 14b shows the obtained waveform for a step load change from Γ ch = +2.7N.m to Γ ch = -2.7N.m. This validates the performance of the converter in generator mode, demonstrating the bidirectional power flow capability of the proposed converter. In this last section, a first experimental verification of the proposed three-phase Active Split Source Inverter is carried out. A prototype of a few kW of the converter is proposed and presented, and the setup on the test bench shown on Fig. 15. The values of the parameters of the motor, as well as the sizing for the passive components of the B-ASSI, are presented in Tab. 7. The converter is first tested in open-loop control operation to validate the good operation on a hardware point of view.

Experimental Results

Open-loop operation validation

Three experiments are conducted. The first operating mode, called "non-saturate" mode, involves closing three switches S h a ,S h b and S h c . In this mode, the duty cycles of the AC-DC conversion stage D a ,D b and D c are not saturated. Within this region, two tests are conducted. Firstly, the second set of switches S a2 ,S b2 and S c2 are forced open to simulate the behavior of diodes used in a classical SSI. The results obtained from this test are presented in Fig. 16. This test illustrates the limitations of a classical SSI for automotive applications, as it can only achieve discontinuous conduction mode. Then, the second switches S a2 ,S b2 and S c2 are controlled using the logical function derived from the command signals C h a , C h b and C h c . This test thus verifies also the bidirectional power flow capability of the proposed converter in the non-saturated mode. The results of this test are plotted in Fig. 17. In this test, a constant elevation ratio of D dc = 0.65 is applied, implying that the theoretical bus voltage V DC = 29.5V should be achieved without considering any losses. It is thus in agreement with the experimental voltage. These tests successfully confirm that the proposed control of the switches S a2 ,S b2 and S c2 indeed enables bidirectional power flow, even in close to zero operation region . Furthermore, the Boost operation with a constant elevation ratio using the MSPWM is verified.

Finally, the proposed converter in the saturated mode operation is illustrated in Fig. 18a, using the proposed modulation scheme and the experimentally applied duty cycles depicted in Fig. 18b. The input voltage is set to V in = 12V, maintained a constant elevation ratio D DC = 0.8 , and an effective modulation index of m = 0.24 is used. These results successfully validate the open-loop operation of the converter, demonstrating that the modulation index can increase above the limit initially imposed by the elevation ratio. As a result of this test, D dc = 0.8 is achieved, and the experimental DC-bus voltage of 15V is verified.

Closed-loop operation validation

The converter is tested in a closed-Loop control operation on the test-bench as depicted in Fig. 15. The test bench includes PMSM machines designed for very high-speed operations. To achieve four-quadrant testing capabilities, two machines are connected in a back-to-back configuration. One of the motor is connected to a classical two-level inverter and is controlled independently. This motor will impose the speed of the shared mechanical shaft between the two machines at a mechanical speed of Ω = 30000rpm. The other motor is driven by the proposed B-ASSI. Both inverters are suplied with the same fixed input voltage V in = 20V. The AC load is operating in a closed-loop operation. In this second test, the DC bus voltage operated in an openloop operation and is set to the minimum value required to achieve the necessary peak voltages. The amplitude of the peak currents is regulated at I ϕ = ±20A, enabling precise control of the torque, and allowinf the machine to operate in motor or generator modes. Fig. 19 illustrates the simulation of the operating point that was tested experimentally. In this simulation, the converter can operate in both motor and generator modes. This can be observed from the sign of the mean input DC current in the inductor of the SSI. The currents waveforms are plotted for comparison with the experiment in Fig. 20. This figure validates and demonstrates the bidirectionality of the proposed converter. The waveforms show good agreement with the simulation, although there is some low-frequency ripple, which can be explained by the very low modulation index of the operating point M ac ≈ 0.15. This can be further explained by that the dead-times are set to a value quite higher than necessary. It is also possible that the dead-time distortions induce more harmonics on the output compared to the two-level counterpart due to the complexity of the structure. However, the waveforms still show good agreement with the simulation and can be well explained. The proposed converter can thus operate a three-phase machine throughtout its entire operation range, making it bidirectional. Additionnaly, it offers a boost function of the DC bus voltage with a ratio identical to that of the classical DC/DC Boost converter.

Conclusion

In this paper, a novel single-stage two-level bidirectional boost inverter compatible with traction applications is presented. The topology is based on the SSI and its derivative, the Active split source inverter. These topologies have previously shown a low DC link voltage utilization ratio. This issue has been effectively resolved in this paper. By using a single inductor and six switches, the inverter functions as a single-stage boost inverter with the capability to independently adjust its DC bus voltage regardless of the load operating conditions. This can effectively offer an EV inverter, reducing constraints on the input sources and provinding robustness to voltage variations. Moreover, the controllable DC link voltage can provide a solution to postpone field weakening operation by increasing the DC link voltage once the initial base speed is reached. Furthermore, only the first set of switches requires additional PWM drivers, as the command for the second set of power switches is generated using simple logic gates based on the command signals of the other switches. Compared to its single-stage counterpart, the proposed B-ASSI presents lower voltage stresses, while maintaining consistent current stresses with the classical SSI. The validity of the proposed converter has been experimentally confirmed through a Proof of Concept prototype.

Figure 2 :

 2 Figure 2: Existing single-phase Active Split source inverter (ASSI) presented in [26].

1 ! M DC ) > 1 Figure 3 :

 113 Figure 3: Duty cycles for a MSPWM and limits when M ac > M DC .

Figure 4 :

 4 Figure 4: Proposed B-ASSI topology : Three-phase single-stage bidirectional Active Split Source Inverter.

Figure 5 :

 5 Figure 5: One possible active state for both Inductor Charging and Discharging state (impossible state for a classical SSI).

Figure 6 :

 6 Figure 6: Definition of the proposed Modulation for phase A, in blue the duty cycle D a for S h a , in orange the duty cycle D a1 for S a1 .

Figure 7 :

 7 Figure 7: Obtained command signals for each clamping switch S x , and S x2 .

Figure 8 :

 8 Figure 8: Operation of the B-ASSI with the proposed modulation under normal conditions, (a)-Chronogram, (b)-tϵ[0; t 0 ], (c)-tϵ[t 0 ; t 1 ], (d)-tϵ[t 1 ; t 2 ], (e)-tϵ[t 2 ; t 3 ], (f)-tϵ[t 3 ; t 4 ].

Figure 9 :

 9 Figure 9: Fault appearance of the B-ASSI in non-saturated mode without the proposed command signals C x2 , (a) -Chronogram, (b)-tϵ[0; t 0 ], (c)-tϵ[t 0 ; t 1 ], (d)-tϵ[t 1 ; t 2 ], (e)-tϵ[t 2 ; t ] : discontinuity of the inductor current.

Figure 10 :

 10 Figure 10: Operation of the B-ASSI with the proposed modulation under the worst-case scenario , (a)-Chronogram, (b)-tϵ[0; t 0 ], (c)-tϵ[t 0 ; t 1 ], (d)-tϵ[t 1 ; t 2 ], (e)-tϵ[t 2 ; t 3 ], (f)-tϵ[t 3 ; t 4 ], (g)-tϵ[t 4 ; t 5 ].

Figure 12 :

 12 Figure 12: Schematic of the classical FOC implemented for the simulated inverter-fed PMSM.

Figure 13 :Figure 14 :

 1314 Figure 13: Simulation results : (a)-Illustration of the limitation of the classical MSPWM used in SSI, (b) for the proposed modulation

Figure 15 :

 15 Figure 15: Experimental validation : (a) -Proposed converter prototype, (b) -experimental setup

Figure 16 :

 16 Figure 16: Experimental Results in Open Loop : Proposed converter operating in non-saturated mode with C a1 = C b1 = C c1 = 1 and C a2 = C b2 = C c2 = 0.

Figure 17 :

 17 Figure 17: Experimental Results in Open Loop : Proposed converter operating in non-saturated mode for bidirectional power flow verification with only C a1 = C b1 = C c1 = 1.

Figure 18 :

 18 Figure 18: Experimental validation in open-loop of the proposed bidirectional Active Split source inverter in saturated mode (a)-Experimental waveforms, (b)-measured experimental duty cycles applied to the converter.

Figure 19 :

 19 Figure 19: Simulated waveforms in closed-loop operation for the same experimental operating point : (a) -Phase currents in motor mode, (b) -Phase current in generator Mode, (c) -Mean input current i L in motor mode, (d) -Mean input current i L in motor mode

Table 1 :

 1 States of the Split Source Inverter.

		Switches States	Diodes States
	Vector	S h a	S h b	S h c	D ia	D ib	D ic	Inductor State
	V 000	OFF OFF OFF ON	ON	ON	Charge
	V 100	ON OFF OFF OFF ON	ON	Charge
	V 110	ON	ON OFF OFF OFF ON	Charge
	V 010	OFF ON OFF ON OFF ON	Charge
	V 011	OFF ON	ON	ON OFF OFF	Charge
	V 001	OFF OFF ON	ON	ON OFF	Charge
	V 111	ON	ON	ON	ON	ON	ON	Discharge

Table 2 :

 2 All working states of the proposed modulation for the inverter.

Table 3 :

 3 Input/Output relationship of classical two-level inverter and different considered single-stage topologies

Table 4 :

 4 Current stresses of the proposed topologyFigure 11: Voltage stresses : boost ratio V DC /V in versus normalized peak voltage V ϕ /V in

		B-ASSI
	Upper Switch	I max = I ϕ
	Upper freewheeling Diode Lower Switch	I max = i L +∆i L 3 I max = i L + ∆i L + I ϕ
	Lower freewheeling Diode	I max = I ϕ
	DC side additional Switches	I max = i L + ∆i L

Table 5 :

 5 Comparison of the offered functionality by the proposed converter compared to other single stage topologies

	Architectures	Passive elements required	Additional Active Switches required	Additional Passive Diodes required	single or three-phase	Bidirectional capability

Table 6 :

 6 Simulated Motor and converter parameters.

	Parameter	Symbol	Value
	Battery Voltage	V in	30V
	Split source Inductor	L S S I	16µH
	DC bus Capacitor	C	200µF
	Motor Nominal Voltage	V	60V
	Switching frequency	f sw	50kHz
	Number of pole pairs	p	4
	Motor Inductance	L s	10µH
	Motor Resistance	R s	5mΩ
	Flux linkage	ϕ f	9.5.10 -3 Wb
	Motor inertia	J	2.8.10 -6 kg.m 2
	Friction coefficient	f	5.2.10 -6 N.m.s/rad
	Speed reference	ω *	[0-15000 rpm]
	Maximal load Torque	Γ ch	15 Nm

Table 7 :

 7 Experimental Motor and converter parameter.

	Parameter	Symbol	Value
	Battery Voltage	V in	20V
	Split source Inductor	L S S I	6µH
	DC bus Capacitor	C	460µF
	Motor Nominal Voltage	V	48V
	Switching frequency	f sw	30kHz
	Number of pole pairs	p	1
	Motor Inductance	L s	5µH
	Motor Resistance	R s	3mΩ
	Flux linkage	ϕ f	0.9mWb
	Speed reference	Ω *	[0-30 000 rpm]
	Maximal load Torque	Γ ch	3 Nm