Power Routing: A New Paradigm for Maintenance Scheduling

Currently, the necessity of efficient and reliable power systems is also increasing because of the strict requirements that standards and regulations impose, but still costs have to remain low. The monitoring and control of the components' lifetime can lead to reduce maintenance costs.However, overcoming the related challenges is not a straightforward task, as it involves knowledge of power device physics, smart management of electrical quantities, and optimal maintenance planning and scheduling. It represents a multidisciplinary issue being faced in the last decade.

C urrently, the necessity of efficient and reliable power systems is also increasing because of the strict requirements that standards and regulations impose, but still costs have to remain low. The monitoring and control of the components' lifetime can lead to reduce maintenance costs.However, overcoming the related challenges is not a straightforward task, as it involves knowledge of power device physics, smart management of electrical quantities, and optimal maintenance planning and scheduling. It represents a multidisciplinary issue being faced in the last decade. As a primary issue to be considered, it is clear that the evolution of power electronics is playing a principal role in the world in many ways including ■ the development of environmentally friendly and economically affordable clean energy sources, such as wind and solar energy [1] ■ the installation and enhancement of facilities to develop a robust, reliable, and high-quality distributed electrical grid, including the smart grid paradigm with distributed energy storage systems [2]- [5] ■ efficient and low-cost freight transportation based on electric vehicles, low-fuel-consumption cargo ships, and More Electric Aircraft [6] Power Routing

A New Paradigm for Maintenance Scheduling
©SHUTTERSTOCK.COM/IQONCEPT ■ personal transportation, such as electric motorbikes, electric cars, robust high-speed trains, efficient subways with regenerative breaking, public electric buses, and so on [7]. Power electronic applications, which include multidisciplinary research topics, such as digital signal processing, power electronics, and power systems, have actually experienced a technology disruption in the last decades [8] from 1) new power semiconductor devices with high voltage/ current ratings and very low power losses; 2) powerful microprocessor hardware platforms, including accurate sensors and high-bandwidth data-acquisition systems; and 3) effective simulation and design software tools to predict the behavior of power systems.
Power electronics reliability and, consequently, the corresponding required maintenance costs are two of the major concerns about this technology [9]. An accurate estimation of the remaining useful lifetime (RUL) of a power converter is fundamental to reduce the maintenance cost [10]. Historically, the first approaches to estimate the RUL were characterized by a fixed time. The power system operator just counted the power converter's years in operation to decide when it had to be replaced by a new unit. However, it is clear that the accuracy of this approach is low because the RUL highly depends on the operating conditions of the power system, usually called the mission profile. For instance, factors such as the ambient temperature and the actual power that is managed by the power system highly influence the possibility of failure in any power converter component [11].
A more accurate RUL estimation presents several advantages [12]. First, it allows for reduced safety margins, resulting in cheaper and, often, lighter systems. As a second advantage, it enables reduction of the cost of unscheduled maintenance. For example, in a photovoltaic system, 60% of these costs are caused by the inverter [21]. The design of an efficient maintenance schedule allows for the substitution of the system components when their failure probability reaches a maximum limit. This feature is especially beneficial in mission-critical systems, such as aircraft transportation or power distribution, where a failure is critical due to safety reasons.
In addition to the maintenance scheduling with accurate RUL estimations, the power system's availability is usually enhanced by developing power converters with inherent fault-tolerant capability [13]. It means that, even if a failure happens in the system, it can still be operational but, in most cases, with reduced nominal power. However, this feature is not easy to achieve in many instances. In Figure 1(a), a power rectifier is presented consisting of a two-level active rectifier connected to a dual active-bridge dc/dc converter (DAB). This power system does not have fault-tolerant capability because, if a component of the power converter fails, the whole system must stop its operation.
The fault-tolerant capability feature can be achieved by designing power converter topologies with high modularity [14]. In this way, a modular power converter is formed by the serial or parallel connection of basic power modules, also called power electronic building blocks (PEBBs). Modular power converters have an inherent faulttolerant capability by bypassing the damaged PEBBs after a failure. PEBBbased power converters are a very attractive solution for medium-and high-power applications, where a high voltage/current range can be achieved by the serial/parallel connection of low-voltage PEBBs [15].
In addition, modular power converters generate high-quality-output waveforms, reducing the required filtering stage, and also present advantages from the point of view of the mass production of PEBBs [16]. However, the component count is higher, which could still be seen in industry as a possible cause of more failures if old approaches to reliability prediction based on part count are considered. In any case, the system availability will be higher [17]. The knowledge of the RUL is particularly beneficial to maximize the reliability and to preserve the highest availability, which a modular system could guarantee [18].
An example of a modular system is shown in Figure 1(b), consisting of a cascaded H-bridge converter (CHB) connected to multiple dc/dc quadruple active-bridge converters. In this modular system, even if a failure happens in some PEBB, the system can continue operation. For instance, in the case of the CHB, a bypass switch can be added to the H-bridge-based PEBB to overcome the failure in the corresponding PEBBs [19]. Fault-diagnosis methods are applied to find the damaged PEBBs, carrying out the bypass and adapting the power converter control to achieve optimal operation [20]. A summary of the advantages and drawbacks of modular converters is also included in Figure 1.
From a cost reduction point of view, it is clear that it would be beneficial if the RULs of converter devices could be adjusted according to the maintenance requirements. If this feature were achieved, the PEBBs could adapt their operation to fit with the scheduled maintenance, making the planned maintenance tasks more cost efficient.
This article describes how the basic idea of managing the operation of the single PEBBs in a modular power converter provides the capability to manage the thermal stress of the components. This solution, aided by advanced condition monitoring and carried out by proper control strategies, maintains the advantages of the modular converters with the added capability of managing the RUL according to external constraints, i.e., Power electronics reliability and, consequently, the corresponding required maintenance costs are two of the major concerns about this technology. the maintenance schedule. This article provides an overview of a series of techniques that make the operation of modular converters smarter, with reliable operation included as a design parameter. These techniques could be the foundation of a new paradigm in the power converter field that has been emerging in recent years.

Power Converter Reliability Issues
In the field of power electronics reliability, a paradigm shift has taken place due to the extremely high reliability requirements present in many applications, such as automotive or aerospace: use of the physics-of-failure methodologies developed in the last 50 years in the design and control of power electronics [21]. Failure mechanisms must be understood and need to be taken into account in the design of the system along with the lifetime target. Knowledge of power component failures and the expected real operating conditions of the device are being taken into account during the design process [22]. These estimated real conditions are included in an expected mission profile that includes relevant stressor like temperature, vibration, humidity, and others.
In power converters, the most sensitive components in the system are reported to be the power semiconductors and the capacitors. These components are usually the source of more than 50% of unscheduled maintenance cost [23]- [25]. The wide range of nominal power of the converters focuses attention on the different power devices to extend their expected lifetimes. Power converters for lowvoltage/high-current applications may see their lifetimes reduced by output capacitors, while, for grid interface converters at higher voltages, the power modules are usually regarded as more critical [25]. For power semiconductors, thermal stress by means of thermal cycles (heating-cooling or vice versa) and the presence of high temperatures have been identified as the main causes of device aging and final failure. The most important failure mechanisms of power semiconductors are bond-wire liftoff, chip solder fatigue, and base-plate solder fatigue, all caused by thermal stress [26]. In the case of power capacitors, the capacitor type has an impact on the relevant failure mechanisms, but a   common stressor is also the high temperature. A reduction of the hotspot temperature of the capacitor increases the lifetime of the device [27].
Detailed knowledge of the failure mechanism in power electronics components, such as power modules and capacitors, also allows the introduction of predictive maintenance, which has already been adopted for several other types of power system equipment, into the field of power electronics [47]. On the basis of aging indicators and estimation, the RUL maintenance can be accurately scheduled, minimizing the already highlighted costs of unscheduled maintenance.
Condition monitoring of power semiconductors focuses on aging indicators, such as the collector-emitter saturation voltage, gate-emitter threshold voltage, short circuit current, gate current, turn-on and -off times, power device thermal resistance, and current change rate [28]. Various online and offline condition-monitoring techniques have been established to monitor these parameters to define the health status of the power device [29]. Apart from these aging indicators, lifetime models are also employed to predict failures when the converter is working under different operating conditions. However, the parameter sensitivity to degradation of the devices, measurement complexity, and degree of uncertainty in the state of health estimation (SoH) remain challenges.
For capacitors, the main RUL indicators are the equivalent series resistance (ESR), capacitance, ripple voltage, volume, and temperature [30]. One common methodology is to sense the capacitor ripple current to obtain the ESR or capacitance either with or without signal injection. To avoid additional current sensors, model-based methods estimate the capacitance from the converter model. More advanced data-driven methods are also proposed to estimate the capacitance using available signals, such as input/ output voltages and current, dc-link voltage, and so on [31]. In summary, it can be affirmed that the capacitor hotspot temperature and semiconductor junction temperature are critical parameters to achieve an accurate estimation of their RULs. These parameters can be obtained by ■ model-based sensors from the converter operating parameters ■ a combination of model-based and additional sensors (for example, to estimate the capacitor's ESR) ■ embedded sensors in the capacitors and extra voltage sensors to measure the thermosensitive electrical parameters of the power switches, such as the on-state collector-emitter Vce voltage.

Maintenance-Scheduling Management in Modular Converters
Maintenance tasks related to power systems usually require trained personnel with expertise, and, according to the level of failure, the system downtime may vary. Unscheduled maintenance can result in revenue loss and unavailability of the systems, and these facts become crucial with increasing operational demands and lack of financial resources. Therefore, prognostic maintenance has become an essential requirement for systems requiring high reliability and availability. A definition of prognostics is the ability to provide early detection of the incipient faults of a component and to predict the progression of such a fault to a result of component failure [32]. With prognostics, the system RUL can be predicted with an acceptable degree of confidence, and, when such information is used to schedule the maintenance, it is termed prognostic maintenance [33].
As challenges for modular power conversion systems, replacement of building blocks, device-to-device parameter mismatching, and different impacts of the cooling system result in a significant difference in the PEBB RULs in the system. The first step to determine the RULs of all sensitive components in a power conversion system is to use a condition-monitoring system that is applied to determine the average time when each component will fail, represented with orange bars in Figure 2.
The estimation of the components' RULs in each PEBB can be taken into account to apply an RUL management method for the PEBB. For power semiconductors, the active thermal control (ATC) method has been proposed, which targets regulation of thermalmechanical stress. ATC methods are able to manage the rate of change of the power semiconductors' degradation by preventing overtemperatures and reducing the power cycling, obtaining a reduction in thermal stress [34], [35]. For the capacitors, the voltage ripple reduction (VRR) method has been proposed to reduce their hotspot temperature. VRR can be achieved in several ways: 1) at the design phase, by adding more capacitors in parallel, with the disadvantage of increasing the cost; b) by reducing the current of that capacitor, for example, by affecting the power transfer of the cells connected to that capacitor; and c) by employing active methods implemented by advanced control and modulation methods [36]- [38].
The combination of ATC and VRR takes into account the most relevant failure mechanisms of the most sensitive components. The application of these methods makes possible the smart management the RUL of the PEBBs. This is shown in Figure 2 with blue and purple bars, where the ATC and VRR methods, at the PEBB level, use the information provided by the condition monitoring to extend, as much as possible, each PEBB RUL. It is expected that, with the improvement of the RUL estimation method, Unscheduled maintenance can result in revenue loss and unavailability of the systems, and these facts become crucial with increasing operational demands and lack of financial resources. the efficacy of these techniques will improve. However, even with an estimation that is affected by inaccuracies, putting reliability at the center of the power electronics design and control still allows for a reduction in the spread of the failures, with benefits in terms of maintenance scheduling.
Several researchers have focused their efforts on optimizing the maintenance schedule based on the monitored data, considering operational constraints using the previously introduced monitoring of the power device condition [39], [40]. However, the literature discussing how to actively influence the RUL, and thereby optimize the maintenance scheduling, is scarce. In fact, maintenance optimization can have multiple conflicting objectives, such as reducing the amount of maintenance, maximizing the utilization of the RUL of the components, scheduling the maintenance according to the availability of personnel and material, and so on. In the conventional method, prognostic maintenance with condition-monitoring schedules the maintenance operations when the probability of failure reaches a threshold value, and the PEBBs that are close to failing before the next possible maintenance are replaced. This results in a loss of RUL of the PEBBs, which could potentially operate for a longer time.
ATC methods through power routing and VRR methods have the capability to manipulate the RUL of the system to achieve these conflicting goals more efficiently [41], [42]. The main novel concept of power routing is that equal power sharing across the cells in a modular converter is not always the optimal solution. In the case of having power cells with unequal aging, the application of an unbalanced power sharing between the cells by applying a power-routing method achieves important maintenance goals. The application of power-routing control allows optimization, at system level, of the maintenance schedule, minimizing the cost and leading to maximum operation profit.
As commented previously, the power-routing method is based on a flexible power sharing between the PEBBs of the power converter, taking into account the actual estimated values of the RUL of each PEBB. In this way, power routing must take into account not only instantaneous electric measurements but, also, the knowledge of the previous operational conditions of the power system. For instance, in data centers, the powerrouting implementation is done based on energy consumption (kilowatthour and instantaneous current) [43].
Remarkably, power routing can be implemented in parallel building blocks as well as in series-connected building blocks [41], [45]. This concept is shown in Figure 2, where the power routing is applied to achieve an RUL equalization between the PEBBs. This method considers that, looking for the optimization of the maintenance schedule, it is interesting to equalize all of the PEBB RULs at the exact maintenance time [36]. With active RUL control via power routing that considers the maintenance schedule, the maintenance can be planned without wasting significant RULs of certain components. This idea is represented in Figure 2, where the expected time of failure of each PEBB, represented with red bars, is modified by the powerrouting method to merge them into only one instant, represented with a green bar.  It is important to notice that system parameters, such as the collector-emitter voltage ( ) Vce and turn-on/ turn-off energies of the devices, are subjected to device-to-device parameter mismatch. In addition, the thermal coupling creates temperature differences in the components, and, also, nonuniform cooling systems provoke temperature differences among the components. As an example, the datasheet of power devices indicates a variation of up to 20% from the mean value for Vce [46].
To evaluate the performance of the power-routing method incorporating the parameter mismatch, a Monte Carlo analysis [42] can be done with and without the power-routing control. This analysis considers the unavoidable parameter mismatch with suitable probabilistic distributions, such as the Gaussian distribution. The impact on a modular converter RUL is studied with electrothermal models generating the estimated power device junction temperatures for the selected long-term mission profile. Finally, the RUL estimations are based on state-of-the-art lifetime models using rainflow counting [47], [48].
As an example, a modular DAB system with four input-parallel, output-parallel converters for a More Electric Aircraft application is considered in the Monte Carlo analysis. In Figure 3(a), the results obtained from this study are summarized by a histogram that delineates the number of times that the converter failed at some specific instant.
The analysis of the obtained results is derived from the determination of the factor , Bx which represents the time when the system has a probability of x% of failure. Remarkably, this methodology assigns a probability of failure, which is dependent on the previous operation and, thereby, differs from the constant failure rate assumption. In Figure 3 Figure 3(b). Depending on the application and the corresponding availability requirement, the probability of failure at which to consider the replacement of PEBBs is defined. For instance, in aerospace applications, where safety is a critical issue, factors such as B . 0 1 and B1 can be considered eligible to be used for maintenance scheduling purposes.
In addition to the lifetime extension achieved by the power-routing method, another important feature can be also highlighted. In the case of modular systems with many converter PEBBs, a single maintenance to replace all of the cells appears to be impractical, especially if the components' RULs are spread out. From the results in Figure 3(a), approximating the histogram envelope with a Gaussian waveform, it can be observed that the average time to failure (μ) is very similar when applying and not applying the power-routing method (approximately 25.65 years). However, it can be seen that power-routing control is able to achieve a 44% reduction in the standard deviation of failures ( ) v compared to that of normal operation.
This feature is clearly observed in Figure 3(b), where it is can be seen that, by applying power-routing control, 98% of failures are reduced from 7.7 down to 4.3 years. This represents an advantage from a maintenance scheduling point of view in that it The unreliability or cumulative probability distribution over time [42]. reduces the spread of the PEBB failure probability. This fact increases the possibility of minimizing the maintenance tasks by replacing all of the PEBBs at the same time.

Normal Operation
As another example to show this advantage, the control strategy focused on scheduling the maintenance while maximizing the utilization of the RULs of individual converter PEBBs for a smart transformer (ST) application has been analyzed [49]. Considering the fact that even the lifetime models are developed by curve fitting of the power-cycling test results, the variability in the lifetime model motivates the representation of the RUL or time to failure as a probability density function. The probability of failure, incorporating the variability in the lifetime model, is obtained through Monte Carlo simulations, considering the curve-fitting parameters in the lifetime model as Gaussian distributions. The probability of failure of a modular converter with 10 unequally aged PEBBs working as an ST without applying power routing is illustrated in Figure 4(a). In this experiment, it is assumed that the individual PEBBs are replaced when they reach a probability of failure equal to 10%. The probability of failure of the overall modular converter shows that there is a high chance of failure in the system spread over years, which can significantly affect the availability of the ST.
On the other hand, Figure 4(b) shows the probability of failure of the modular converter with power-routing control by setting the same individual PEBB replacement criterion. To minimize the maintenance cost, the objective of the power-routing control method is to force the substitution of multiple PEBBs at the same time. This can be done by managing the RULs of the PEBBs that are close to reaching the probability-of-failure threshold within the next maintenance interval. Compared to the failure probability with normal operation, applying the power-routing method with management of maintenance scheduling causes a concentrated probability of failure around only three maintenance instants, obtaining a reduction in the maintenance cost.
It is true that the maintenance schedule depends on many issues, and, usually, it is periodically scheduled since it covers not only electrical issues but also ambient and mechanical conditions. In any case, the powerrouting method is also useful when a programmed maintenance is going to be carried out. In this situation, the power-routing technique can take this information into account, managing the PEBB RULs to squeeze the remaining lifetime out of those PEBBs that are close to reaching the replacement threshold. This strategy actually saves some lifetime of the remaining PEBBs, improving the overall lifetime of the power system.

The Implementation of Power Routing in Modular Converters
As described previously, the powerrouting technique can be applied to modular dc/dc or dc/ac converters to manage the power devices' temperatures and, consequently, their RULs. In dc/dc converters working with an output parallel connection, when the power-routing concept is applied, the power managed by each PEBB is different, generating different output currents in the PEBBs. Since the power devices' losses are mainly dependent on the current, the power routing in the paralleled dc/dc converters facilitates the management of the power devices' RULs. On the other hand, in modular dc/ac converters, such as the CHB, each phase voltage is determined by the addition of the PEBB voltages because they are connected in series. When the power-routing technique is applied to the CHB, the voltage generated by each PEBB is different, while the same phase current is flowing through all PEBBs. Therefore, both modular-series and parallel-connected PEBB-based converters are dual. When the power-routing technique is applied, the voltage or the current is determined by the sum of the unbalanced voltages or currents.
The power routing forces a nonbalanced power among the PEBBs, while the total power of the system usually remains constant. In the case of modular dc/dc converters, a possibility for applying the power-routing method is  to implement a closed-loop controller that takes into account the SoH of the power cells to optimize the maintenance cost. An example of this type of strategy is shown in Figure 5 [50].
The SoH uses knowledge about the previous operation of the power system and the instantaneous electrical measurements to determine the aging of each cell. This information is taken into account by the maintenance cost optimizer, which determines the most proper power sharing between the modules ( ). kn The total power of the overall converter P is shared among the power cells (with input and output dc voltages denoted by Vd and , Vo respectively, and In indicating the inductor current), considering the information provided by the maintenance optimizer, and the power to be managed by each cell Pn is, finally, obtained by a conventional dedicated controller in the cell. The application of this method in a modular dc/dc converter permits management of the temperature of the cells, extending the overall converter lifetime [51].
On the other hand, to implement power routing in modular-series converters, the approach based on applying modified modulation strategies is the most promising, since they enable the power losses and, consequently, the thermal stress of each PEBB to be individually manipulated. The usual way to operate modularseries or parallel converters is the phase-shifted pulsewidth modulation (PS-PWM) technique [52], [53]. In fact, the well-known interleaved operation of parallel dc/dc converters is a particular case of the PS-PWM method. As examples of including the powerrouting techniques in the modulation strategy based on the PS-PWM technique, several modulation methods applied to the CHB can be addressed (see Figure 6): 1) the modulation technique based on pure sinusoidal references, 2) the multifrequency modulation method, and 3) the discontinuous modulation technique.
The modulation method based on sinusoidal voltage reference waveforms is very simple. This modulation method modifies the modulation index of each PEBB, as shown in Figure 6(a). However, the power-routing capability, that is, the possibility of forcing a power imbalance between the PEBBs, is highly limited by the overmodulation in the PEBBs. To tackle this problem, other strategies, such as the multifrequency modulation technique [ Figure 6(b)] [54] or the discontinuous modulation method [ Figure 6(c)], have been proposed [45], [55].
In the multifrequency modulation strategy, the third-harmonic injection concept is applied to the PEBB duty cycles, allowing to the power-routing capability of the system to be extended by means of the extended linear modulation region. Remarkably, two variants of the modulation signal are utilized to make this technique feasible to be applied to single-phase inverters. However, this method offers limited capability to handle the thermal stress of PEBBs connected in series. This is because the phase current flowing through them is not affected (only the current of parallel PEBBs is changed) by the power routing, causing the limited variation of thermal stress of series PEBBs.
Discontinuous modulation uses two variants of the modulation signal: a clamped signal to force an additional loading power in a PEBB and a nonclamped signal to relax the PEBB loading power. The basic principle used to perform the power routing with this modulation strategy is based on determining the clamping angle .
z The most interesting feature of this method is the ability to efficiently manage the thermal stress of series PEBBs, since their losses are varied by the clamped signal, achieving the power routing as well.
The major characteristics of three modulation techniques are summarized

Mitigating the Collateral Negative Effects of the Modulation Approaches
The implementation of the power routing with the modulation methods introduced in the previous section achieves the objective of the power routing improving the maintenance scheduling. However, the appli cation of these methods presents collateral negative effects in the converter operation. The PS-PWM method is a highperformance solution for operating modular converters, but only if all PEBBs manage the same power. When the power-routing concept is applied, the conventional PS-PWM method loses, partially, its high performance. This phenomenon can be observed in Figure 7, where a three-cell CHB and a three-module interleaved dc/dc converter are tested.
In the case of the CHB results, the CHB is formed by three power cells with dc voltage equal to 150 V and a modulation index equal to 0.8. A balanced operation is forced during the first 40 ms, generating the highperformance output voltage shown in Figure 7(a), with the superior harmonic performance represented in Figure 7(b). From t 40 ms, = a power-routing method achieved by implementing a discontinuous modulation method is applied, as shown in Figure 6(c). The application of this power-routing method permits modification of the average temperature of the cells, permitting the lifetime of the clamped cell to be saved, thereby extending the lifetime of the overall converter [56]. However, as can be clearly observed in Figure 7(b), the harmonic performance is degraded by the appearance of carrier-frequency-order harmonic distortion.
A similar conclusion can be obtained from the results considering the modular dc/dc boost converter. In this case, initially, the power managed by each boost converter is 1.6 kW, and the interleaved operation presents a superior harmonic performance of the current through the output capacitor, as shown in Figure 7(d). However, from t 1 ms, = the power is    [51]. However, the power imbalance forced by the powerrouting method provokes the degradation of the harmonic performance of the interleaved converter, as can also be found in Figure 7(d).
In summary, it can be observed that, due to the unbalanced operation of the modular converters, a harmonic distortion appears at the switching frequency fc (for the dc/dc converters operated with bipolar PWM in each PEBB) or at f 2 c (for the CHB operated with unipolar PWM in each PEBB). On one hand, this phenomenon in serialconnected modular converters, such as the CHB, generates distorted output voltages, and, consequently, the output filter has to be redesigned to the requirements on the output waveforms' quality. On the other hand, in parallelconnected modular converters, such as the interleaved dc/dc boost topology, the low-frequency harmonic distortion in the output current created by the unbalanced operation creates an increase in the output capacitor temperature, provoking a reduction in its expected RUL.
The effects provoked by the unbalanced operation forced by the power routing in modular converters (series or parallel connected) can be partially mitigated by applying advanced modulation methods, which apply the PS-PWM method but with nonfixed carrier-phase-shift angles. These methods, called variable-angle PS-PWM techniques, consider that the converter output waveforms (voltages and currents) are periodic signals and, therefore, can be described by a Fourier series determining its Fourier coefficients. This harmonic description can be based on the fundamental frequency or switching frequency, as shown in Figure 8, where the output voltage waveform of a full-bridge PEBB belonging to a CHB is represented.
Variable-angle PS-PWM methods are focused on eliminating or reducing the harmonic distortion below N times , fc mitigating the negative effects of the unbalanced operation of the converter forced by the power-routing technique to manage the power device's RUL. The mathematical description of the output waveforms is the base to achieving this goal by helping to determine the carrierphase-shift angles i i that minimize the low-frequency distortion.
The angle solution set to eliminate or mitigate some particular harmonic content can be easily obtained through an analytic approach for modular converters composed by three PEBBs [56]- [58]. However, as the number of PEBBs grows, the analytical solution to mitigate the negative effects of power routing can be hard to obtain or even does not exist because these solutions are highly dependent on the number of PEBBs [59].
In this sense, it is necessary to find and define new techniques to obtain a particular angle solution set that fulfills the requirements. Considering the mathematical harmonic description for these systems, the distortion provoked by power routing can be eliminated, minimized, or even reshaped, formulating the mathematical problem as a flexible, multiobjective, multivariable cost function. The computing capability of controller systems has experienced huge growth in the last decade. In this way, personal computers; server-based solutions; multicore, low-cost microcontrollers; field-programmable gate arrays; systems on chip; and cloud-based solutions currently overcome the computational requirements, and they are available in the manufacturer's portfolio at a very competitive price. This fact means that numerical computation approaches, advanced metaheuristic searching algorithms, or artificial intelligent can be used to face out this kind of multiobjective and multivariable mathematical problem in real time [60], [61].
The application of the variable-angle PS-PWM has been tested in both modular converters: series connected, such as the CHB, or parallel connected, such as the interleaved dc/dc converters. In Figure 9, the obtained results for both series and parallel modular converters are shown. In the figure, the power converters' output waveforms and the corresponding   30 40 The computing capability of controller systems has experienced huge growth in the last decade.
harmonic spectra are represented. It can be seen that the application of the variable-angle PS-PWM methods improves the output waveform quality, reducing the output filter stage in the CHB [56], [57] and decreasing the output capacitor average hotspot temperature in the interleaved dc/dc boost converter, giving rise to achieving an extension of its lifetime [44].

Conclusion
This article advocates for increased intelligence of the power electronics of modular systems. The goal is to include the end-of-life or the maintenance schedule in the actual operations of the converter. To accomplish this goal, there are several conditions to fulfill. ■ Condition monitoring for the components is implemented in all PEBBs to determine the RUL. ■ It is possible to control the power processed by the PEBBs in the modular structure (power routing). ■ The performance of the system shall not be degraded because of this modified operation. ■ The overall cost of the system should not be impacted by the additional functionalities.
The two main methods that make possible this intelligent operation mode are the thermally compensated modulation and ATC methods. ATC allows the electrical quantities of the power converter to be changed to modify the component stress. In particular, the power-routing technique shifts the power among the PEBBs composing the modular converter to affect their individual lifetimes. In this way, the probability of failure can be modified to locate the failure at a specific instant in time, allowing simplification of maintenance scheduling and reducing the corresponding cost.
To avoid the performance degradation in terms of power quality when the power routing is applied, advanced modulation techniques based on the adaptive phase shifting of the PWM carriers of the PEBBs can be implemented. Despite asymmetric operations, the harmonic spectrum still retains very low total harmonic distortion.
To conclude, the power routing in conjunction with adaptive carrier PS-PWM constitute a technology combination that has the impact of improving the reliability of power electronics systems without performance deterioration with a minimum additional initial cost. Future research on the topic at all levels is envisaged to further enhance the scope of the proposal: ■ component level: including more components, i.e., gate drivers and printed circuit boards, in the condition monitoring ■ topology level: evaluating the best topologies to take full advantage of the power-routing concept ■ system level: optimizing the maintenance scheduling by considering actual variabilities in the real word and applying new approaches such as artificial intelligence and the Internet of Things; big data; neural networks; and so on.