Voltage imbalance frequently arises in islanded inverter-based microgrids, particularly in the presence of single-phase loads. This article proposes a control scheme for grid-forming inverters that compensates for voltage imbalance at a remote sensitive node (objective 1) and ensures accurate negative-sequence current sharing (objective 2). The control scheme is derived from the synchronous consensus approach and, as in existing synchronous schemes, requires transmitting the negative-sequence voltage measured at the remote node to enable imbalance compensation. In addition, it relies on local current measurement at each controller, achieving negative-sequence current sharing without exchanging inverter current data. This key feature enables seamless control integration (property 1) and robustness to interruptions in current-signal transmission (property 2). Unlike state-of-the-art synchronous control schemes (integral, damped-integral, leader-follower, and consensus), which cannot simultaneously meet these objectives and properties, the proposed control fulfills them while preserving simplicity. Experimental validation on a laboratory microgrid demonstrates the effectiveness of the proposal in a practical scenario.

Recent publications have started to explore the application of Geometric Algebra (GA) to the modeling, analysis and control of dynamical systems and, in particular, electrical circuits. Since a crucial element there is to transform the ordinary differential equations governing the dynamical system which models the systems' behavior from the real domain to the Laplace domain, a definition of the Laplace transform in GA is needed. In the present work, we extend previous works dealing with extension to some hiper-complex algebras by introducing a definition of the Laplace transform within the framework of Geometric Algebra (GA). In particular, our definition and its properties are applicable to geometric algebras with signature lower or equal than 5.

Three-phase electrical systems (AC systems) have been traditionally represented by real-valued linear multiple-input/multiple-output (MIMO) systems or by complex-valued single-input/single-output (SISO) systems. The complex representation has the advantage to reduce the order of the model at the expenses of introducing a non-linearity when the AC system is unbalanced, which makes the analysis and control design tasks difficult. Recently, the application of geometric algebra (GA) has shown that the same AC system can be represented by a GA-valued linear SISO model. However, the simplicity (given by the order reduction and linearity) comes with a price: the lack of standard control analysis and design tools applicable to the model expressed in the GA domain. To help overcoming this difficulty, and in the context of AC systems, this chapter revisits the well-known singular value decomposition (SVD) of a linear MIMO system and derives the same decomposition for the GA-valued SISO system, namely, GA-SVD. Explicit formulas are presented for computing the singular values, the singular eigenvectors, and the three matrices that compose the GA-SVD. Additionally, its key geometrical components, namely, rotation, rescaling, and rotation, are also identified. An AC circuit example is presented to illustrate all the key findings.

Linear state-space systems expressed in complex coordinates may include the complex conjugate when they are not symmetric. Although the original real system remains linear, the conjugate operator does not allow the model to be analysed as a standard complex-valued linear system. This paper proposes a methodology for designing controllers for asymmetric complex-valued dynamical systems. The proposed technique adds an element to the control algorithm that symmetrises the open-loop dynamics. Symmetrisation allows the use of standard tools for linear complex-valued systems. Illustrative examples and an application to three-phase electrical circuits are provided.

Geometric algebra (GA) is a mathematical tool for geometric computing, providing a framework that allows a unified and compact approach to geometric relations which in other mathematical systems are typically described using different more complicated elements. This fact has led to an increasing adoption of GA in applied mathematics and engineering problems. However, the scarcity of symbolic implementations of GA and its inherent complexity, requiring a specific mathematical background, make it challenging and less intuitive for engineers to work with. This prevents wider adoption among more applied professionals. To address this challenge, this paper introduces SUGAR (Symbolic and User-friendly Geometric Algebra Routines), an open-source toolbox designed for Matlab and licensed under the MIT License. SUGAR facilitates the translation of GA concepts into Matlab and provides a collection of user-friendly functions tailored for GA computations, including support for symbolic operations. It supports both numeric and symbolic computations in high-dimensional GAs. Specifically tailored for applied mathematics and engineering applications, SUGAR has been meticulously engineered to represent geometric elements and transformations within two and three-dimensional projective and conformal geometric algebras, aligning with established computational methodologies in the literature. Furthermore, SUGAR efficiently handles functions of multivectors, such as exponential, logarithmic, sinusoidal, and cosine functions, enhancing its applicability across various engineering domains, including robotics, control systems, and power electronics. Finally, this work includes four distinct validation examples, demonstrating SUGAR's capabilities across the above-mentioned fields and its practical utility in addressing real-world applied mathematics and engineering problems.

Nowadays, an islanded microgrid based exclusively on power electronic converters is a feasible scenario, in which one power converter is configured in grid-forming mode and the other converters in grid-feeding mode. In the event of a short circuit, the grid-forming inverter typically employs a virtual output resistor to limit the maximum current, which results in a voltage sag across the entire system. In this scenario, grid-feeding converters have the potential to follow conventional grid protocols during voltage sags. However, it remains unclear whether these protocols represent the best solution for voltage support in an islanded microgrid. This work proposes a methodology for analyzing the faulted system in the complex-valued domain, which produces a large signal linear model. Based on this analysis, a voltage support control scheme for the grid-feeding converters is then proposed. Finally, control parameters are derived to guarantee system stability. Selected experimental results demonstrate the superior performance of the proposed control scheme.

State-of-the-art techniques for modeling, analysis and control of three-phase electrical systems belong to the real-valued multi-input/multi-output (MIMO) domain, or to the complex-valued nonlinear single-input/single-output (SISO) domain. In order to complement both domains while simplifying complexity and offering new analysis and design perspectives, this paper introduces the application of geometric algebra (GA) principles to the modeling, analysis and control of three-phase electrical systems. The key contribution for the modeling part is the identification of the transformation that allows transferring real-valued linear MIMO systems into GA-valued linear SISO representations (with independence of having a balanced or unbalanced system). Closed-loop stability analysis in the new space is addressed by using intrinsic properties of GA. In addition, a recipe for designing stabilizing and decoupling GA-valued controllers is provided. Numerical examples illustrate key developments and experiments corroborate the main findings.

Microgrids (MG) are exposed to voltage quality deterioration due to the presence of voltage unbalance. To deal with this problem, existing solutions based on Distributed Generation (DG) units interfaced by power electronics offer two type of strategies for voltage unbalance compensation depending on whether the compensation is performed at one remote node or at multiple local nodes. The first type is limited to a single node, and the second type is limited to apply at the DG units output (locally). This paper presents a multi nodal control scheme where DGs can compensate for voltage unbalance at multiple remote nodes of the MG, thus overcoming both state-of-the-art strategies limitations. In particular, negative-sequence voltage is eliminated at as many remote nodes as the number of available DG's. A systematic approach for the multiple-input/multiple-output (MIMO) nature of the problem is presented covering three aspects. First, a square MIMO control strategy is established and a feasibility test is derived to assess whether the problem can be solved. Second, the cross-coupling interaction between the multiple controllers is minimized by optimally selecting which DGs will contribute to mitigate the remote unbalances. Third, stability and transient dynamics are analyzed. Laboratory experimental results corroborate the control performance.

During the last two decades, the operation of the electrical grid has undergone significant changes. This evolution is closely tied to the integration of power electronics into distributed generation systems, which led to increased utilization of renewable energy and as a consequence mitigating climate change by lowering emissions. On the other hand, artificial intelligence plays a considerable role in shaping the development and progress of various technologies, such as the electrical grid. This work presents a study for the application of Reinforcement Learning (RL) tools in distributed generation systems. The objective of using RL is to address voltage perturbations in real time. RL will be useful to maximize the resilience of the system in the event of short circuits of a short duration and minimize the risk of disconnect.

Unbalanced loads in islanded inverter-based microgrids induce voltage and current imbalances, posing significant challenges to the operation of critical equipment and sensitive loads. To address this issue, conventional circuit breakers, strategically placed between microgrids, play a key role in fault isolation during unbalanced conditions. However, they exhibit weaknesses in effectively addressing power quality issues, frequency variations, and power supply interruptions to specific loads. To solve these limitations, this paper introduces the new concept of negative-sequence virtual circuit breaker. Microgrid inverters are responsible for implementing this concept, which consists of eliminating negative-sequence voltages and currents at the point of-common-coupling between microgrids without altering positive-sequence voltages and currents. This last issue allows the entire electrical system to operate on a single frequency, guaranteeing the loads' supply. The compensators responsible for implementing the proposed concept are unilateral bandpass filters with complex coefficients. The primary advantage of these compensators over conventional integral compensators is their ability to offer plug-and-play operation. The effectiveness of the proposed concept has been verified through experimental tests in a laboratory setup.

Grid-connected ac microgrids (MG) are commonly exposed to voltage quality deterioration due to the presence of voltage imbalance. This article presents a control strategy that enables MG grid-feeding inverters (interfacing distributed generation units) to compensate for the voltage unbalance at a given remote node of the MG where for example a sensitive load is likely to be damaged. Each inverter is equipped with a new controller whose operation 1) allows to contribute in the control of the imbalance by only using a measure of the negative-sequence voltage at the remote node while 2) ensuring a fairly redistribution of the control effort among the participating inverters in terms of an inherent negative-sequence current sharing functionality. Since both control objectives are achieved without requiring the collaboration among the participating inverters, the presented solution offers an inherent robustness not found in previous state-of-the-art voltage unbalance control strategies. The new control strategy is accompanied by a controller parameter design receipt, and it is complemented by a formal analysis that permits evaluating how MG modeling errors and uncertainties affect stability and performance. Laboratory experimental results corroborate the properties of the presented control.

In islanded microgrids, when a short circuit or a sudden overload occurs, it provokes an abrupt increment in the currents supplied by the generation nodes, which feed the load collaboratively. This is particularly challenging for inverter-based nodes, due to its reduced power capacity. This work takes advantage of the droop-method basic configuration to propose an additional closed-loop control, which ensures maximum current injection during any kind of short circuit maintaining the underlying droop control. Ensuring that any node injects its maximum rated current during the short circuit, it emulates the most common low-voltage ride-through protocols for grid-feeding sources oriented to support the grid and, in this way, the voltage unbalance is reduced. To develop the control proposal, a model of the faulted system is presented in order to evaluate the stability of the closed-loop system. A general modelling methodology is introduced in order to derive the control for any microgrid configuration. Finally, selected experimental results are reported in order to validate the effectiveness of the proposed control.

Existing research has shown the effectiveness of genetic strategies in generating Petrin-Net (PN)-based controllers, but limitations exist in the ease of controller generation due to the designer’s ability and the system’s complexity. In the case of automated controller generators based on genetic programming (GP), limitations arise from the static nature of their chromosome over the evolution process. In this short paper we introduce a first discrete PN-based controller designer that can accept systems modeled either continuously or discretely, making it more flexible in handling a wide range of systems. By utilizing genetic algorithms and PNs, the program can generate controllers tailored to the specific requirements of a given system, including the optimal size of the controller. This novel approach has the potential for far-reaching applications in various fields.

Machine learning algorithms and the increasing availability of data have radically changed the way how decisions are made in today’s Industry. A wide range of algorithms are being used to monitor industrial processes and predict process variables that are difficult to be measured. Maintenance operations are mandatory to tackle in all industrial equipment. It is well known that a huge amount of money is invested in operational and maintenance actions in industrial gas turbines (IGTs). In this paper, two variations of autoencoders were used to analyse the performance of an IGT after major maintenance. The data used to analyse IGT conditions were ambient factors, and measurements were performed using several sensors located along the compressor. The condition assessment of the industrial gas turbine compressor revealed significant changes in its operation point after major maintenance; thus, this indicates the need to update the internal operating models to suit the new operational mode as well as the effectiveness of autoencoder-based models in feature extraction. Even though the processing performance was not compromised, the results showed how this autoencoder approach can help to define an indicator of the compressor behaviour in long-term performance.

This paper introduces the application of a genetic programming (GP)-based method for the automated design and tuning of process controllers, representing a noteworthy advancement in artificial intelligence (AI) within the realm of control engineering. In contrast to already existing work, our GP-based approach operates exclusively in the time domain, incorporating differential operations such as derivatives and integrals without necessitating intermediate inverse Laplace transformations. This unique feature not only simplifies the design process but also ensures the practical implementability of the generated controllers within physical systems. Notably, the GP’s functional set extends beyond basic arithmetic operators to include a rich repertoire of mathematical operations, encompassing trigonometric, exponential, and logarithmic functions. This broad set of operations enhances the flexibility and adaptability of the GP-based approach in controller design. To rigorously assess the efficacy of our GP-based approach, we conducted an extensive series of tests to determine its limits and capabilities. In summary, our research establishes the GP-based approach as a promising solution for automating the controller design process, offering a transformative tool to address a spectrum of control problems across various engineering applications.

The presence of unbalanced loads in power systems creates voltage imbalances that perturb the operation of sensitive equipment like induction motors, power electronics converters, and adjustable speed drives. To address this issue, this article presents a novel control scheme to perform remote negative-sequence voltage fair compensation at any node of a grid-forming inverter-based islanded ac microgrid. The fair compensation reduces the voltage imbalance of the remote node by adjusting the negative-sequence output voltage of the inverters according to a predefined objective. For example, the goal could be to equalize the inverters’ negative-sequence output voltage. Alternatively, the aim could be to reduce this voltage at some inverters to perturb less the local loads at the expense of increasing it in other inverters. Therefore, the proposed controller achieves two control objectives: negative-sequence voltage reduction at a remote node and fair compensation through the inverters running this service. The controller also features inherent plug-and-play and parallel operation. Unlike state-of-the-art controllers on negative-sequence voltage compensation, the control scheme operation is accomplished by only broadcasting the remote node voltage measurement, thus significantly reducing the communication control data. The article presents the large-signal control design and stability analysis, and the performance in a laboratory microgrid with selected experimental results.

In islanded ac microgrids, when multiple voltage source inverters (VSIs) operate in parallel, it is challenging to simultaneously obtain both accurate complex (active and reactive) power sharing and voltage regulation (in terms of frequency and amplitude). State-of-the-art strategies that target these two objectives often rely on hierarchical primary droop plus communication-based secondary controls and adaptive virtual impedance methods. However, control dynamics and/or accuracy are still affected by inverters line impedances mismatches. To overcome these limitations, this article presents for balanced ac microgrids a distributed control strategy that simultaneously guarantees both voltage regulation and accurate power sharing. The distributed strategy is based on having at each VSI a single controller that merges two control loops that can be designed in isolation, thus decoupling the design of the power sharing control from the design of the voltage control. The cooperative operation of all VSI controllers, which requires exchanging control data over a communication network, ensures meeting both control objectives with the independence of the line impedance mismatches or the connection and disconnection of inverters and loads. And these properties are achieved without changing the controller structure and (easy-to-tune) parameters nor increasing the control effort. Experimental results corroborate the control proposal.

The opportunities now afforded by increasingly available, dense, aerial urban LiDAR point clouds (greater than100 pts/m2) are arguably stymied by their sheer size, which precludes the effective use of many tools designed for point cloud data mining and classification. This paper introduces the point cloud voxel classification (PCVC) method, an automated, two-step solution for classifying terabytes of data without overwhelming the computational infrastructure. First, the point cloud is voxelized to reduce the number of points needed to be processed sequentially. Next, descriptive voxel attributes are assigned to aid in further classification. These attributes describe the point distribution within each voxel and the voxel’s geo-location. These include 5 point-descriptors (density, standard deviation, clustered points, fitted plane, and plane’s angle) and 2 voxel position attributes (elevation and neighbors). A random forest algorithm is then used for final classification of the object within each voxel using four categories: ground, roof, wall, and vegetation. The proposed approach was evaluated using a 297,126,417 point dataset from a 1 km2 area in Dublin, Ireland and 50% denser dataset of New York City of 13,912,692 points (150 m2). PCVC’s main advantage is scalability achieved through a 99 % reduction in the number of points that needed to be sequentially categorized. Additionally, PCVC demonstrated strong classification results (precision of 0.92, recall of 0.91, and F1-score of 0.92) compared to previous work on the same data set (precision of 0.82-0.91, recall 0.86-0.89, and F1-score of 0.85-0.90).

This article presents a control scheme that simultane-ously solves the problems of negative-sequence voltage compensation and negative-sequence current sharing in grid-connected microgrids using grid-feeding inverters. State-of-the-art schemes have previously solved these problems with low-performance control solutions or, alternatively, with high-performance solutions but paying the cost of high control-data traffic in the communication network. The proposed control scheme improves the performance of previous schemes for grid-feeding inverters with the following characteristics: 1) negative-sequence voltage compensation at any point of the microgrid, 2) accurate negative-sequence current sharing, and 3) low control-data traffic. In terms of implementation, two key points of the proposed control scheme are: the voltage compensation is based on a band-pass filter with complex coefficients and the current sharing is reached only with local current measurements. In the theoretical analysis, the system model is based on transfer functions with complex coefficients. This fact facilitates the control design due to 1) the system model is linear in this complex domain and 2) the multiple-input single-output model can be represented as a single-input single-output model for voltage compensation. The characteristics of the proposed control are validated by means of experimental results measured in a laboratory microgrid.

This paper presents a distributed complex power sharing approach that solves the problem of active and reactive power sharing in inverter-based islanded microgrids. Previous state-of-the-art strategies based on droop controls with possibly virtual impedance methods and supplemented with hierarchical schemes may provide poor power sharing due to the R/X ratio and mismatched line impedances, even compromising microgrids stability if droop control parameters are not properly set. The novel control approach, that uses a communication network to exchange data among all inverters to fairly inject power, provides a set of appealing properties. First, it achieves accurate active and reactive power sharing for both resistive and inductive power lines with no additional control cost (avoiding unnecessary power injections), and regardless of load changes and connections and disconnections of inverters. Moreover, it ensures an exponential convergence rate, and the tuning of the control parameters can not compromise microgrid stability. The theoretical development relies on a change of variables that linearizes the complex power dynamics, thus easing the control law design task and providing the means for computing the appropriate amplitude and phase for each inverter output voltage. Selected experimental results on a laboratory microgrid certify the applicability and performance of the proposed control scheme.