Algorithms for network design and routing problems

In this thesis we study three combinatorial optimization problems belonging to the classes of Network Design and Vehicle Routing problems that are strongly linked in the context of the design and management of transportation networks: the Non-Bifurcated Capacitated Network Design Problem (NBP), the Period Vehicle Routing Problem (PVRP) and the Pickup and Delivery Problem with Time Windows (PDPTW). These problems are NP-hard and contain as special cases some well known difficult problems such as the Traveling Salesman Problem and the Steiner Tree Problem. Moreover, they model the core structure of many practical problems arising in logistics and telecommunications. The NBP is the problem of designing the optimum network to satisfy a given set of traffic demands. Given a set of nodes, a set of potential links and a set of point-to-point demands called commodities, the objective is to select the links to install and dimension their capacities so that all the demands can be routed between their respective endpoints, and the sum of link fixed costs and commodity routing costs is minimized. The problem is called non- bifurcated because the solution network must allow each demand to follow a single path, i.e., the flow of each demand cannot be splitted. Although this is the case in many real applications, the NBP has received significantly less attention in the literature than other capacitated network design problems that allow bifurcation. We describe an exact algorithm for the NBP that is based on solving by an integer programming solver a formulation of the problem strengthened by simple valid inequalities and four new heuristic algorithms. One of these heuristics is an adaptive memory metaheuristic, based on partial enumeration, that could be applied to a wider class of structured combinatorial optimization problems. In the PVRP a fleet of vehicles of identical capacity must be used to service a set of customers over a planning period of several days. Each customer specifies a service frequency, a set of allowable day-combinations and a quantity of product that the customer must receive every time he is visited. For example, a customer may require to be visited twice during a 5-day period imposing that these visits take place on Monday-Thursday or Monday-Friday or Tuesday-Friday. The problem consists in simultaneously assigning a day- combination to each customer and in designing the vehicle routes for each day so that each customer is visited the required number of times, the number of routes on each day does not exceed the number of vehicles available, and the total cost of the routes over the period is minimized. We also consider a tactical variant of this problem, called Tactical Planning Vehicle Routing Problem, where customers require to be visited on a specific day of the period but a penalty cost, called service cost, can be paid to postpone the visit to a later day than that required. At our knowledge all the algorithms proposed in the literature for the PVRP are heuristics. In this thesis we present for the first time an exact algorithm for the PVRP that is based on different relaxations of a set partitioning-like formulation. The effectiveness of the proposed algorithm is tested on a set of instances from the literature and on a new set of instances. Finally, the PDPTW is to service a set of transportation requests using a fleet of identical vehicles of limited capacity located at a central depot. Each request specifies a pickup location and a delivery location and requires that a given quantity of load is transported from the pickup location to the delivery location. Moreover, each location can be visited only within an associated time window. Each vehicle can perform at most one route and the problem is to satisfy all the requests using the available vehicles so that each request is serviced by a single vehicle, the load on each vehicle does not exceed the capacity, and all locations are visited according to their time window. We formulate the PDPTW as a set partitioning-like problem with additional cuts and we propose an exact algorithm based on different relaxations of the mathematical formulation and a branch-and-cut-and-price algorithm. The new algorithm is tested on two classes of problems from the literature and compared with a recent branch-and-cut-and-price algorithm from the literature.

Decomposition Methods and Network Design Problems

Decomposition based approaches are recalled from primal and dual point of view. The possibility of building partially disaggregated reduced master problems is investigated. This extends the idea of aggregated-versus-disaggregated formulation to a gradual choice of alternative level of aggregation. Partial aggregation is applied to the linear multicommodity minimum cost flow problem. The possibility of having only partially aggregated bundles opens a wide range of alternatives with different trade-offs between the number of iterations and the required computation for solving it. This trade-off is explored for several sets of instances and the results are compared with the ones obtained by directly solving the natural node-arc formulation. An iterative solution process to the route assignment problem is proposed, based on the well-known Frank Wolfe algorithm. In order to provide a first feasible solution to the Frank Wolfe algorithm, a linear multicommodity min-cost flow problem is solved to optimality by using the decomposition techniques mentioned above. Solutions of this problem are useful for network orientation and design, especially in relation with public transportation systems as the Personal Rapid Transit. A single-commodity robust network design problem is addressed. In this, an undirected graph with edge costs is given together with a discrete set of balance matrices, representing different supply/demand scenarios. The goal is to determine the minimum cost installation of capacities on the edges such that the flow exchange is feasible for every scenario. A set of new instances that are computationally hard for the natural flow formulation are solved by means of a new heuristic algorithm. Finally, an efficient decomposition-based heuristic approach for a large scale stochastic unit commitment problem is presented. The addressed real-world stochastic problem employs at its core a deterministic unit commitment planning model developed by the California Independent System Operator (ISO).

Hybrid ground-aerial mesh networks for IoT monitoring applications: network design and software platform development

The Internet of Things (IoT) has grown rapidly in recent years, leading to an increased need for efficient and secure communication between connected devices. Wireless Sensor Networks (WSNs) are composed of small, low-power devices that are capable of sensing and exchanging data, and are often used in IoT applications. In addition, Mesh WSNs involve intermediate nodes forwarding data to ensure more robust communication. The integration of Unmanned Aerial Vehicles (UAVs) in Mesh WSNs has emerged as a promising solution for increasing the effectiveness of data collection, as UAVs can act as mobile relays, providing extended communication range and reducing energy consumption. However, the integration of UAVs and Mesh WSNs still poses new challenges, such as the design of efficient control and communication strategies. This thesis explores the networking capabilities of WSNs and investigates how the integration of UAVs can enhance their performance. The research focuses on three main objectives: (1) Ground Wireless Mesh Sensor Networks, (2) Aerial Wireless Mesh Sensor Networks, and (3) Ground/Aerial WMSN integration. For the first objective, we investigate the use of the Bluetooth Mesh standard for IoT monitoring in different environments. The second objective focuses on deploying aerial nodes to maximize data collection effectiveness and QoS of UAV-to-UAV links while maintaining the aerial mesh connectivity. The third objective investigates hybrid WMSN scenarios with air-to-ground communication links. One of the main contribution of the thesis consists in the design and implementation of a software framework called "Uhura", which enables the creation of Hybrid Wireless Mesh Sensor Networks and abstracts and handles multiple M2M communication stacks on both ground and aerial links. The operations of Uhura have been validated through simulations and small-scale testbeds involving ground and aerial devices.

Application-oriented Mixed Integer Non-Linear Programming

In the most recent years there is a renovate interest for Mixed Integer Non-Linear Programming (MINLP) problems. This can be explained for different reasons: (i) the performance of solvers handling non-linear constraints was largely improved; (ii) the awareness that most of the applications from the real-world can be modeled as an MINLP problem; (iii) the challenging nature of this very general class of problems. It is well-known that MINLP problems are NP-hard because they are the generalization of MILP problems, which are NP-hard themselves. However, MINLPs are, in general, also hard to solve in practice. We address to non-convex MINLPs, i.e. having non-convex continuous relaxations: the presence of non-convexities in the model makes these problems usually even harder to solve. The aim of this Ph.D. thesis is to give a flavor of different possible approaches that one can study to attack MINLP problems with non-convexities, with a special attention to real-world problems. In Part 1 of the thesis we introduce the problem and present three special cases of general MINLPs and the most common methods used to solve them. These techniques play a fundamental role in the resolution of general MINLP problems. Then we describe algorithms addressing general MINLPs. Parts 2 and 3 contain the main contributions of the Ph.D. thesis. In particular, in Part 2 four different methods aimed at solving different classes of MINLP problems are presented. Part 3 of the thesis is devoted to real-world applications: two different problems and approaches to MINLPs are presented, namely Scheduling and Unit Commitment for Hydro-Plants and Water Network Design problems. The results show that each of these different methods has advantages and disadvantages. Thus, typically the method to be adopted to solve a real-world problem should be tailored on the characteristics, structure and size of the problem. Part 4 of the thesis consists of a brief review on tools commonly used for general MINLP problems, constituted an integral part of the development of this Ph.D. thesis (especially the use and development of open-source software). We present the main characteristics of solvers for each special case of MINLP.

Networks, Uncertainty, Applications and a Crusade for Optimality

In this thesis we address a collection of Network Design problems which are strongly motivated by applications from Telecommunications, Logistics and Bioinformatics. In most cases we justify the need of taking into account uncertainty in some of the problem parameters, and different Robust optimization models are used to hedge against it. Mixed integer linear programming formulations along with sophisticated algorithmic frameworks are designed, implemented and rigorously assessed for the majority of the studied problems. The obtained results yield the following observations: (i) relevant real problems can be effectively represented as (discrete) optimization problems within the framework of network design; (ii) uncertainty can be appropriately incorporated into the decision process if a suitable robust optimization model is considered; (iii) optimal, or nearly optimal, solutions can be obtained for large instances if a tailored algorithm, that exploits the structure of the problem, is designed; (iv) a systematic and rigorous experimental analysis allows to understand both, the characteristics of the obtained (robust) solutions and the behavior of the proposed algorithm.

Mathematical Optimization Applied to Thermal and Electrical Energy Systems

This Thesis aims at building and discussing mathematical models applications focused on Energy problems, both on the thermal and electrical side. The objective is to show how mathematical programming techniques developed within Operational Research can give useful answers in the Energy Sector, how they can provide tools to support decision making processes of Companies operating in the Energy production and distribution and how they can be successfully used to make simulations and sensitivity analyses to better understand the state of the art and convenience of a particular technology by comparing it with the available alternatives. The first part discusses the fundamental mathematical background followed by a comprehensive literature review about mathematical modelling in the Energy Sector. The second part presents mathematical models for the District Heating strategic network design and incremental network design. The objective is the selection of an optimal set of new users to be connected to an existing thermal network, maximizing revenues, minimizing infrastructure and operational costs and taking into account the main technical requirements of the real world application. Results on real and randomly generated benchmark networks are discussed with particular attention to instances characterized by big networks dimensions. The third part is devoted to the development of linear programming models for optimal battery operation in off-grid solar power schemes, with consideration of battery degradation. The key contribution of this work is the inclusion of battery degradation costs in the optimisation models. As available data on relating degradation costs to the nature of charge/discharge cycles are limited, we concentrate on investigating the sensitivity of operational patterns to the degradation cost structure. The objective is to investigate the combination of battery costs and performance at which such systems become economic. We also investigate how the system design should change when battery degradation is taken into account.

Many-core Algorithms for Combinatorial Optimization

Combinatorial Optimization is becoming ever more crucial, in these days. From natural sciences to economics, passing through urban centers administration and personnel management, methodologies and algorithms with a strong theoretical background and a consolidated real-word effectiveness is more and more requested, in order to find, quickly, good solutions to complex strategical problems. Resource optimization is, nowadays, a fundamental ground for building the basements of successful projects. From the theoretical point of view, Combinatorial Optimization rests on stable and strong foundations, that allow researchers to face ever more challenging problems. However, from the application point of view, it seems that the rate of theoretical developments cannot cope with that enjoyed by modern hardware technologies, especially with reference to the one of processors industry. In this work we propose new parallel algorithms, designed for exploiting the new parallel architectures available on the market. We found that, exposing the inherent parallelism of some resolution techniques (like Dynamic Programming), the computational benefits are remarkable, lowering the execution times by more than an order of magnitude, and allowing to address instances with dimensions not possible before. We approached four Combinatorial Optimization’s notable problems: Packing Problem, Vehicle Routing Problem, Single Source Shortest Path Problem and a Network Design problem. For each of these problems we propose a collection of effective parallel solution algorithms, either for solving the full problem (Guillotine Cuts and SSSPP) or for enhancing a fundamental part of the solution method (VRP and ND). We endorse our claim by presenting computational results for all problems, either on standard benchmarks from the literature or, when possible, on data from real-world applications, where speed-ups of one order of magnitude are usually attained, not uncommonly scaling up to 40 X factors.

Development and characterization of a distributed measurement system for the evaluation of voltage quality in electric power networks

The research activity carried out during the PhD course in Electrical Engineering belongs to the branch of electric and electronic measurements. The main subject of the present thesis is a distributed measurement system to be installed in Medium Voltage power networks, as well as the method developed to analyze data acquired by the measurement system itself and to monitor power quality. In chapter 2 the increasing interest towards power quality in electrical systems is illustrated, by reporting the international research activity inherent to the problem and the relevant standards and guidelines emitted. The aspect of the quality of voltage provided by utilities and influenced by customers in the various points of a network came out only in recent years, in particular as a consequence of the energy market liberalization. Usually, the concept of quality of the delivered energy has been associated mostly to its continuity. Hence the reliability was the main characteristic to be ensured for power systems. Nowadays, the number and duration of interruptions are the “quality indicators” commonly perceived by most customers; for this reason, a short section is dedicated also to network reliability and its regulation. In this contest it should be noted that although the measurement system developed during the research activity belongs to the field of power quality evaluation systems, the information registered in real time by its remote stations can be used to improve the system reliability too. Given the vast scenario of power quality degrading phenomena that usually can occur in distribution networks, the study has been focused on electromagnetic transients affecting line voltages. The outcome of such a study has been the design and realization of a distributed measurement system which continuously monitor the phase signals in different points of a network, detect the occurrence of transients superposed to the fundamental steady state component and register the time of occurrence of such events. The data set is finally used to locate the source of the transient disturbance propagating along the network lines. Most of the oscillatory transients affecting line voltages are due to faults occurring in any point of the distribution system and have to be seen before protection equipment intervention. An important conclusion is that the method can improve the monitored network reliability, since the knowledge of the location of a fault allows the energy manager to reduce as much as possible both the area of the network to be disconnected for protection purposes and the time spent by technical staff to recover the abnormal condition and/or the damage. The part of the thesis presenting the results of such a study and activity is structured as follows: chapter 3 deals with the propagation of electromagnetic transients in power systems by defining characteristics and causes of the phenomena and briefly reporting the theory and approaches used to study transients propagation. Then the state of the art concerning methods to detect and locate faults in distribution networks is presented. Finally the attention is paid on the particular technique adopted for the same purpose during the thesis, and the methods developed on the basis of such approach. Chapter 4 reports the configuration of the distribution networks on which the fault location method has been applied by means of simulations as well as the results obtained case by case. In this way the performance featured by the location procedure firstly in ideal then in realistic operating conditions are tested. In chapter 5 the measurement system designed to implement the transients detection and fault location method is presented. The hardware belonging to the measurement chain of every acquisition channel in remote stations is described. Then, the global measurement system is characterized by considering the non ideal aspects of each device that can concur to the final combined uncertainty on the estimated position of the fault in the network under test. Finally, such parameter is computed according to the Guide to the Expression of Uncertainty in Measurements, by means of a numeric procedure. In the last chapter a device is described that has been designed and realized during the PhD activity aiming at substituting the commercial capacitive voltage divider belonging to the conditioning block of the measurement chain. Such a study has been carried out aiming at providing an alternative to the used transducer that could feature equivalent performance and lower cost. In this way, the economical impact of the investment associated to the whole measurement system would be significantly reduced, making the method application much more feasible.

Design and Performance Evaluation of Network-on-Chip Communication Protocols and Architectures

The scale down of transistor technology allows microelectronics manufacturers such as Intel and IBM to build always more sophisticated systems on a single microchip. The classical interconnection solutions based on shared buses or direct connections between the modules of the chip are becoming obsolete as they struggle to sustain the increasing tight bandwidth and latency constraints that these systems demand. The most promising solution for the future chip interconnects are the Networks on Chip (NoC). NoCs are network composed by routers and channels used to inter- connect the different components installed on the single microchip. Examples of advanced processors based on NoC interconnects are the IBM Cell processor, composed by eight CPUs that is installed on the Sony Playstation III and the Intel Teraflops pro ject composed by 80 independent (simple) microprocessors. On chip integration is becoming popular not only in the Chip Multi Processor (CMP) research area but also in the wider and more heterogeneous world of Systems on Chip (SoC). SoC comprehend all the electronic devices that surround us such as cell-phones, smart-phones, house embedded systems, automotive systems, set-top boxes etc... SoC manufacturers such as ST Microelectronics , Samsung, Philips and also Universities such as Bologna University, M.I.T., Berkeley and more are all proposing proprietary frameworks based on NoC interconnects. These frameworks help engineers in the switch of design methodology and speed up the development of new NoC-based systems on chip. In this Thesis we propose an introduction of CMP and SoC interconnection networks. Then focusing on SoC systems we propose: • a detailed analysis based on simulation of the Spidergon NoC, a ST Microelectronics solution for SoC interconnects. The Spidergon NoC differs from many classical solutions inherited from the parallel computing world. Here we propose a detailed analysis of this NoC topology and routing algorithms. Furthermore we propose aEqualized a new routing algorithm designed to optimize the use of the resources of the network while also increasing its performance; • a methodology flow based on modified publicly available tools that combined can be used to design, model and analyze any kind of System on Chip; • a detailed analysis of a ST Microelectronics-proprietary transport-level protocol that the author of this Thesis helped developing; • a simulation-based comprehensive comparison of different network interface designs proposed by the author and the researchers at AST lab, in order to integrate shared-memory and message-passing based components on a single System on Chip; • a powerful and flexible solution to address the time closure exception issue in the design of synchronous Networks on Chip. Our solution is based on relay stations repeaters and allows to reduce the power and area demands of NoC interconnects while also reducing its buffer needs; • a solution to simplify the design of the NoC by also increasing their performance and reducing their power and area consumption. We propose to replace complex and slow virtual channel-based routers with multiple and flexible small Multi Plane ones. This solution allows us to reduce the area and power dissipation of any NoC while also increasing its performance especially when the resources are reduced. This Thesis has been written in collaboration with the Advanced System Technology laboratory in Grenoble France, and the Computer Science Department at Columbia University in the city of New York.

Collaborative Change: Environmental Jolt, Network (Re)Design and Firm Performance

Motivated by the need to understand which are the underlying forces that trigger network evolution, we develop a multilevel theoretical and empirically testable model to examine the relationship between changes in the external environment and network change. We refer to network change as the dissolution or replacement of an interorganizational tie, adding also the case of the formation of new ties with new or preexisting partners. Previous research has paid scant attention to the organizational consequences of quantum change enveloping entire industries in favor of an emphasis on continuous change. To highlight radical change we introduce the concept of environmental jolt. The September 11 terrorist attacks provide us with a natural experiment to test our hypotheses on the antecedents and the consequences of network change. Since network change can be explained at multiple levels, we incorporate firm-level variables as moderators. The empirical setting is the global airline industry, which can be regarded as a constantly changing network of alliances. The study reveals that firms react to environmental jolts by forming homophilous ties and transitive triads as opposed to the non jolt periods. Moreover, we find that, all else being equal, firms that adopt a brokerage posture will have positive returns. However, we find that in the face of an environmental jolt brokerage relates negatively to firm performance. Furthermore, we find that the negative relationship between brokerage and performance during an environmental jolt is more significant for larger firms. Our findings suggest that jolts are an important predictor of network change, that they significantly affect operational returns and should be thus incorporated in studies of network dynamics.

Analysis and design of high performance multiphase electric drives for vehicle and aircraft applications

The first part of this thesis has focused on the construction of a twelve-phase asynchronous machine for More Electric Aircraft (MEA) applications. In fact, the aerospace world has found in electrification the way to improve the efficiency, reliability and maintainability of an aircraft. This idea leads to the aircraft a new management and distribution of electrical services. In this way is possible to remove or to reduce the hydraulic, mechanical and pneumatic systems inside the aircraft. The second part of this dissertation is dedicated on the enhancement of the control range of matrix converters (MCs) operating with non-unity input power factor and, at the same time, on the reduction of the switching power losses. The analysis leads to the determination in closed form of a modulation strategy that features a control range, in terms of output voltage and input power factor, that is greater than that of the traditional strategies under the same operating conditions, and a reduction in the switching power losses.

Design and Development of Network Monitoring Strategies in P4-enabled Programmable Switches

Network monitoring is of paramount importance for effective network management: it allows to constantly observe the network’s behavior to ensure it is working as intended and can trigger both automated and manual remediation procedures in case of failures and anomalies. The concept of SDN decouples the control logic from legacy network infrastructure to perform centralized control on multiple switches in the network, and in this context, the responsibility of switches is only to forward packets according to the flow control instructions provided by controller. However, as current SDN switches only expose simple per-port and per-flow counters, the controller has to do almost all the processing to determine the network state, which causes significant communication overhead and excessive latency for monitoring purposes. The absence of programmability in the data plane of SDN prompted the advent of programmable switches, which allow developers to customize the data-plane pipeline and implement novel programs operating directly in the switches. This means that we can offload certain monitoring tasks to programmable data planes, to perform fine-grained monitoring even at very high packet processing speeds. Given the central importance of network monitoring exploiting programmable data planes, the goal of this thesis is to enable a wide range of monitoring tasks in programmable switches, with a specific focus on the ones equipped with programmable ASICs. Indeed, most network monitoring solutions available in literature do not take computational and memory constraints of programmable switches into due account, preventing, de facto, their successful implementation in commodity switches. This claims that network monitoring tasks can be executed in programmable switches. Our evaluations show that the contributions in this thesis could be used by network administrators as well as network security engineers, to better understand the network status depending on different monitoring metrics, and thus prevent network infrastructure and service outages.

Optimizing AI at the Edge: from network topology design to MCU deployment

The first topic analyzed in the thesis will be Neural Architecture Search (NAS). I will focus on two different tools that I developed, one to optimize the architecture of Temporal Convolutional Networks (TCNs), a convolutional model for time-series processing that has recently emerged, and one to optimize the data precision of tensors inside CNNs. The first NAS proposed explicitly targets the optimization of the most peculiar architectural parameters of TCNs, namely dilation, receptive field, and the number of features in each layer. Note that this is the first NAS that explicitly targets these networks. The second NAS proposed instead focuses on finding the most efficient data format for a target CNN, with the granularity of the layer filter. Note that applying these two NASes in sequence allows an "application designer" to minimize the structure of the neural network employed, minimizing the number of operations or the memory usage of the network. After that, the second topic described is the optimization of neural network deployment on edge devices. Importantly, exploiting edge platforms' scarce resources is critical for NN efficient execution on MCUs. To do so, I will introduce DORY (Deployment Oriented to memoRY) -- an automatic tool to deploy CNNs on low-cost MCUs. DORY, in different steps, can manage different levels of memory inside the MCU automatically, offload the computation workload (i.e., the different layers of a neural network) to dedicated hardware accelerators, and automatically generates ANSI C code that orchestrates off- and on-chip transfers with the computation phases. On top of this, I will introduce two optimized computation libraries that DORY can exploit to deploy TCNs and Transformers on edge efficiently. I conclude the thesis with two different applications on bio-signal analysis, i.e., heart rate tracking and sEMG-based gesture recognition.

Design of mobility infrastructures to promote sustainability and accessibility of urban areas

This doctoral dissertation represents a cluster of research activities carried out at the DICAM Department of the University of Bologna during a three-year Ph.D. course. The goal of this research is to show how the development of an interconnected infrastructure network, aimed at promoting accessibility and sustainability of places, is fundamental in a framework of deep urban regeneration. Sustainable urban mobility plays an important role in improving the quality of life of citizens. From an environmental point of view, a sustainable mobility system means reducing fuel discharges and energy waste and, in general, aims to promote low carbon emissions. At the same time, a socially and economically sustainable mobility system should be accessible to everybody and create more job opportunities through better connectivity and mobility. Environmentally friendly means of transport such as non-motorized transport, electric vehicles, and hybrid vehicles play an important role in achieving sustainability but require a planned approach at the local policy level. The aim of this study is to demonstrate that, through a targeted reconnection of road and cycle-pedestrian routes, the quality of life of an urban area subject to degradation can be significantly improved just by increasing its accessibility and sustainability. Starting from a detailed study of the European policies and from the comparison with real similar cases, the case study of the Canal Port of Rimini (Italy) has been analysed within the European project FRAMESPORT. The analysis allowed the elaboration of a multicriterial methodology to get to the definition of a project proposal and of a priority scale of interventions. The applied methodology is a valuable tool that may be used in the future in similar urban contexts. Finally, the whole project was represented by using virtual reality to visually show the difference between the before and after the regeneration intervention.

Analysis and improvements of four-wire power converters for electric vehicle chargers

A robust and well-distributed backbone charging network is the priority to ensure widespread electrification of road transport, providing a driving experience similar to that of internal combustion engine vehicles. International standards set multiple technical targets for on-board and off-board electric vehicle chargers; output voltage levels, harmonic emissions, and isolation requirements strongly influence the design of power converters. Additionally, smart-grid services such as vehicle-to-grid and vehicle-to-vehicle require the implementation of bi-directional stages that inevitably increase system complexity and component count. To face these design challenges, the present thesis provides a rigorous analysis of four-leg and split-capacitor three-phase four-wire active front-end topologies focusing on the harmonic description under different modulation techniques and conditions. The resulting analytical formulation paves the way for converter performance improvements while maintaining regulatory constraints and technical requirements under control. Specifically, split-capacitor inverter current ripple was characterized as providing closed-form formulations valid for every sub-case ranging from synchronous to interleaved PWM. Outcomes are the base for a novel variable switching PWM technique capable of mediating harmonic content limitation and switching loss reduction. A similar analysis is proposed for four-leg inverters with a broad range of continuous and discontinuous PWM modulations. The general superiority of discontinuous PWM modulation in reducing switching losses and limiting harmonic emission was demonstrated. Developments are realized through a parametric description of the neutral wire inductor. Finally, a novel class of integrated isolated converter topologies is proposed aiming at the neutral wire delivery without employing extra switching components rather than the one already available in typical three-phase inverter and dual-active-bridge back-to-back configurations. The fourth leg was integrated inside the dual-active-bridge input bridge providing relevant component count savings. A novel modified single-phase-shift modulation technique was developed to ensure a seamless transition between working conditions like voltage level and power factor. Several simulations and experiments validate the outcomes.