State estimation in low-voltage distribution grids is challenging due to limited measurement availability, unbalanced operation, and computational burden. While recent neural network-based estimators report high accuracy in voltage magnitude estimation, their reliability for downstream applications remains largely unexplored. This paper presents a multi-task neural network framework for estimating phase-to-ground voltage phasors in three-phase four-wire European-type unbalanced low-voltage grids using limited measurements. The reliability of such models is investigated not only in terms of the accuracy of predicted state variables but also in terms of the impact of estimation errors on derived electrical quantities. The results show that even small voltage estimation errors can lead to significant inaccuracies in derived power. Building on this insight, the neural network outputs are leveraged within a hybrid framework to initialize a conventional estimator, significantly reducing convergence time without compromising its accuracy. The findings reveal that accurate primary outputs do not necessarily guarantee reliable derived results, underscoring the need for evaluation strategies tailored to application-level requirements and the specific needs of each DSO. The article also addresses the question of whether models based exclusively on neural networks for this type of application can be considered complete state estimators or merely tools capable of providing acceptable estimates of certain electrical variables.

Integrating renewable energy sources, especially photovoltaic, into the distribution networks supplying steelworks offers a significant opportunity to decrease reliance on fossil fuels. However, the inherent intermittency of these energy sources, combined with the lack of inertia due to the use of electronic converters, poses significant challenges to the stability of the electrical system. This study aims to analyze the impact of large loads, such as electric arc furnaces, which experience considerable fluctuations in power demand, on frequency control in networks with high photovoltaic penetration. The analysis was conducted on networks with synchronous generation systems and varying levels of photovoltaic penetration. The system response is shaped by critical parameters such as the displacement factor, shortcircuit impedance, harmonic and interharmonic injection, the rate of power demand variation, equivalent inertia, and governor gain. Effectively managing these variables is crucial for improving performance and minimizing frequency deviations. The analysis is based on measurements obtained from an operational steel plant, which served both to calibrate the simulation models and to validate selected outcomes.

Power flow analysis is a fundamental tool for the operation and planning of electrical power systems. The conventional approach relies heavily on polar coordinate representations of voltage and current, which are used to compute Jacobian matrices and solve the system of equations. However, this paper emphasizes the advantages of retaining the complex-valued representation of the equations. The complex formulation provides a more compact and efficient way to express the problem while facilitating a straightforward matrix representation for computational implementations. This compact notation enables faster and simpler derivations of solver algorithms, such as Newton-Raphson and its adaptations, like Fast Decoupled Power Flow (FDPF) and its variants for networks whose resistive part is not negligible. Furthermore, the decoupling step in FDPF can be avoided to exploit the efficiency of direct complex-domain formulations considering that decoupling is less important when Jacobian matrix is constant (as in FDPF). By implementing and comparing several algorithms with different formulations it is shown that the matrix-based complex formulations are computationally superior, offering significant reductions in execution times.

This paper investigates the reliability of neural network based state estimation in low-voltage distribution grids, focusing not only on the accuracy of direct model outputs but also on the downstream impact when these outputs are used to compute derived electrical quantities. Although these models can achieve low mean absolute errors for phase-to-ground voltages, significant discrepancies arise in derived quantities such as power injections due to error propagation. The findings reveal that accurate primary outputs do not necessarily guarantee reliable derived results, underscoring the need for evaluation strategies tailored to application-level requirements and the specific needs of each DSO. The paper also raises a critical question whether such models truly perform state estimation or merely provide approximations of specific electrical quantities.

The imperative to swiftly estimate the state of unbalanced low voltage distribution grids is paramount for effective flexibility management, where machine learning presents an efficient possibility suitable for real-time applications. This research focuses on the design and evaluation of a neural network-based state estimator tailored for unbalanced LV distribution grids. In addition, an approach to generate training datasets utilizing real-world grid profiles is proposed. The estimator’s performance undergoes thorough evaluation across various simulated scenarios conducted on a real grid located in northern Spain. These assessments showcase its resilience and precision under diverse operational conditions.

The integration of renewable energy into the steel industry presents a promising alternative to reduce dependence on fossil fuels. However, due to the intermittency and grid decoupling caused by electronic converter connections, these energy sources lack inertia, posing challenges for system stability. This study aims to analyze the impact of large loads such as electric arc furnaces, which experience significant variations in power demand, on frequency control in networks with photovoltaic integration, and to outline procedures to mitigate their impact through energy storage systems. The frequency response analysis is conducted in networks with synchronous generation systems and varying levels of photovoltaic penetration. The results indicate that integrated photovoltaic generation significantly affects the overall system inertia, resulting in a decrease in the nadir and an increase in the rate of change of frequency. Furthermore, the system response is influenced by parameters such as the time constant of the regulator and the gain of the governor, emphasizing the importance of fine-tuning these control variables to achieve optimal performance and effectively mitigate frequency deviations.

This paper presents an analysis of the electric power flows in a hot rolling mill plant using a power quality analyzer and developing simulation models with Matlab-Simulink.The model inputs have been taken from process data by the process computer of the plant.A STATCOM with a control strategy based on the d-q coordinates is used as solution to improve the reactive compensation as well as to minimize the voltage fluctuations and sags effect.The overall electric model has been simulated with the STATCOM to check the improvement in the voltage stability and the consumption.

The steel industry is currently in the midst of a profound transformation aimed at decarbonization. This shift involves the electrification of various production processes that currently depend on coal or gas for power. Additionally, there are plans to integrate wind and photovoltaic generation systems into the grids supplying steelworks to align with global CO 2 emission reduction goals. The combination of these two generation systems offers notable benefits, alongside several drawbacks, primarily concerning the loss of inertia characteristic of conventional synchronous generators. In this paper, two main loads are examined because they are responsible for a significant portion of the existing electricity consumption in the steelworks: the hot rolling mill and the electric arc furnace. Concurrently, global demand forecasts are assessed, taking into account the injection of power from a wind farm and a photovoltaic plant connected to the distribution network supplying the steelworks. The analysis of the demand curve enables the projection of substantial power fluctuations capable of affecting frequency control, given the reduced equivalent inertia of the power system following the integration of renewable resources. To mitigate these power variations and enhance frequency control, the advantages of a battery-based storage system and the coordinated management of resources are scrutinized.

The use of distribution system state estimation (DSSE) can enhance the hosting capacity of an electrical distribution system (DS). DSSE allows for an accurate assessment of the DS state, to integrate a higher share of distributed energy resources. However, due to the low rate of the advanced metering infrastructure deployment in several European countries, some customers still not equipped with smart meters. In turn this limits the implementation of DSSE in the DS. Furthermore, most of distribution system operators consider the constant power load model in carrying out the power flow analysis. This leads to get biased results because of relying on an inaccurate load model. In this context, the paper proposes an efficient DSSE approach to overcome the problems addressed above. This is done by considering modelling the load as a ZIP model using the load profiles recovered by a top-down load forecasting method based on the feeder measurements and the customer information system. The ZIP model is incorporated as an equality constraint in the augmented Lagrangian based DSSE, while the recovered load profile is utilized as the nominal power at the rated voltage. A numerical analysis is conducted to highlight the significant improvement provided by the proposed approach.

A set of well-known theorems are widely used in circuit analysis with the aim of speeding up or enabling the process of solving an electrical circuit (i.e., obtaining the values of voltage and current at any location). Among these theorems, six have been selected here as the most important in view of their common use among electrical engineers and practitioners: Superposition Theorem, Thévenin's and Norton's Theorems, Millman's Theorem and Rosen's and Kenelly's Theorems.

The steel industry is undergoing a deep transformation for decarbonization purposes. This transformation involves the electrification of many production processes currently powered by coal or gas. Therefore, electricity consumption in an already electro-intensive industry is to increase in the coming years. The incorporation of wind and photovoltaic generation systems into the grids supplying a steelworks is planned to meet global CO 2 emission targets. The hybridization of these systems has significant advantages, as well as various drawbacks mainly regarding the loss of the inertia that is characteristic of conventional synchronous generators. The use of a storage system consisting of lithium batteries is proposed to compensate for the loss of inertia. The coordinated management of the charging and discharging processes of the storage system enables the control of the frequency and the load level in the transmission grid supplying a steelworks. The proposal also reviews the main foreseen demand and generation curves and provides results that are representative of the storage system role.

The low coupling between phases in European-type low-voltage grids makes the estimation of phase-angles in this context a challenging task for distribution system state estimators. A poor estimation of these state variables can make the calculation of quality indices, such as the voltage unbalance factor, singularly unreliable. This contribution offers a comparison between different solutions recently proposed in the literature to overcome the difficulties faced by standard implementations. The advantages and drawbacks of these solutions are analyzed and discussed in this work. While the use of synthetic measurements achieves the best results in terms of accuracy, the use of a virtual reference can provide a good trade-off between accuracy and cost. A real low-voltage grid in northern Spain, which is fed from a terminal transformer and endowed with advanced metering infrastructure, is taken as test bed to provide a significant set of case studies

This paper proposes an online grid impedance estimation method for AC Grids under the presence of grid-tied converters. A novel modelling approach in the $\alpha,\beta,0$ reference frame is proposed, including the relationship with the instantaneous power theory. The proposed modelling framework considers both balanced and unbalanced conditions and operation in the four quadrants. For the impedance identification, a Pulsed Signal Injection (PSI) approach together with a Recursive Least Square (RLS) algorithm is used. The proposed modelling and identification method is thoroughly evaluated by simulation and experimental results. The work presents a contribution for the optimization of the distribution grid operation with high-dynamic impedance changes due to the integration of distributed resources.

The pervasive use of communication technologies in industrial facilities puts them in an excellent position to pioneer the active management of distribution grids. In this context, only a decentralized online state estimator can allow for a proper flexibility management, and thus, for an adequate use of distributed generation and energy storage systems. Due to the lack of current solutions tailored for 4-wire unbalanced LV grids, i.e., European type, this proposal presents the implementation of an edge computing device, aimed at the terminal transformer level, which can perform distribution state estimation at a low cost. The state estimator which is designed to be run in a compute module with a compact form factor for deeply embedded applications, solves the state estimation problem by minimizing an objective function formulated using the modified augmented weighted least squares method. Additionally, this contribution presents a testbed for the evaluation of the proposed solution: (1) an external device is used to carry out an online emulation of the distribution grid and to generate the corresponding field measurements including Gaussian noise, and (2), the embedded device obtains the measurements via Modbus TCP/IP and performs the state estimation making these results available for higher-layer applications. To confirm the effectiveness of this implementation, a comprehensive set of tests are conducted using the model and data of a real LV grid in Spain. The results show good accuracy and an acceptable execution time for a cost-effective embedded solution.

This article analyzes the dynamic behavior of the voltage control loop based on proportional-integral regulators, commonly used for grid-forming converters in 3-phase AC and DC Microgrids and applications that involve a DC-link voltage control. The article proposes a simple and accurate generalized analysis useful both for the system characterization and design. Two different control schemes, based on linear (Direct Voltage Control, DVC) and quadratic voltage feedback (Quadratic Voltage Control, QVC), are analytically studied, simulated and experimentally tested, demonstrating a superior performance of the QVC under the presence of constant power loads. The operation limits, the system stability and the disturbance rejection capability are analyzed considering the effect of control and plant parameters and the effect of the different types of disturbances and the operating point, taking into account the non-linearities of the system. The analysis is mainly focused on the effect of constant power loads given their negative impact on the system performance. The study provides a generic procedure for the analysis and design of proportional-integral voltage controllers, including the selection of the system capacitance for meeting specific dynamic specifications while considering system characteristics as the load level, the stability margins and the maximum voltage deviation under disturbances.

Present energy and environmental scenarios promote the incorporation of generation systems based on renewable sources into the distribution grids of electro-intensive industries, the benefits of which transcend the local generation of energy with minimal greenhouse gas emissions. In this regard, coordinated management of reactive power in a joint installation of a hot rolling mill plant and a wind farm can improve the immunity of both facilities against voltage sags. In this paper, the various factors influencing the response of the joint installation against voltage sags are analyzed. In this regard, special attention is paid to the wind farm location and, consequently, to the topology of the joint installation distribution network. The closer the wind farm and the rolling mill, the more relevant the shared impedances and the more significant the effect of the reactive power supplied by the wind farm. The main variables of interest are analyzed under actual rolling conditions both in normal operation and in the face of voltage sags to determine the most indicated distribution network topology.

The analysis of electrical circuits is based on the application of two essential laws of physics originally proposed by the German physicist Gustav Kirchhoff in 1845. These laws, which can be applied in both the time and frequency domains, may be considered as particular cases of Maxwell equations (which would be proposed 20 years later). Both laws are described in the following considering only their formulation in the time domain (nevertheless, they can be applied in the same form to phasor analysis at any given frequency). Beforehand, some basic definitions related with circuit topology are introduced.

This paper addressesthe problem of real-time state estimation in European-type four-wire low-voltage distribution networks with advanced metering infrastructure based on power line communication (PLC). The main drawback of this type of infrastructure is its high latency and a sequential data sampling process. Both factors make it difficult to obtain instantaneous values from the smart meters in a timely and adequate manner to estimate the real-time state of the system. This problem may be solved in the future with the deployment of metering systems based on other technologies such as 5G. However, PLC technology prevails in many countries, and is not likely to be replaced in the medium term. In the meantime, a solution is needed to provide acceptable real-time state estimates in low voltage networks, not to hinder the active management of these assets in the context of smart grids. In this work, a solution is proposed that allows estimating the state of the low voltage network with a reasonable accuracy considering the low quality of the measurements provided by the deployed infrastructure. The system is validated using a portion of a real pilot network located in the north of Spain fed by a transformer station with seven feeders.

This article proposes a coordinated management of electrical energy in a steelworks and a wind farm that are connected to the same distribution network. The suggested solution seeks to improve the efficiency of the hot rolling mill, to reduce greenhouse gas emissions, to minimize the cost of the electrical energy utilized in the manufacture of steel coils, to increase the power system chargeability, and to guarantee power quality. The proposal consists of constituting a virtual plant (comprising the wind farm and the rolling mill) to be managed by a single operator. The approach is mainly focused on the management of the virtual plant reactive power. The algorithm proposed to optimize this reactive power is based on the so-called particle swarm optimization. Three optimization strategies are analyzed: minimization of losses in the distribution network, minimization of the voltage deviation at two of its nodes, and maximization of the displacement factor in both the rolling mill and the wind farm. Energy losses are reduced by up to 20% when adopting the first strategy in comparison to the least efficient case. Voltage variations are kept at less than 1% at both nodes when using the second strategy, whereas deviations between 1% and 5% are obtained when implementing the other two strategies. The study is based on actual measurements and simulation tests.

The traditional model used to represent the electrical behavior of supercapacitors (SCs) operating at constant power leads to a well-known differential equation which allows to obtain the charge/discharge time of the device as a function of its internal voltage. However, the opposite is not true, i.e. it is necessary to resort to numerical methods to derive the internal voltage of the SC at any specific time. In this paper, new explicit expressions for the evolution of the electrical variables involved in the charge/discharge process of a SC bank operated at constant power are derived. The proposed formulation, which is based on the use of the Lambert W function, does not only allow a straightforward calculation of all the electrical variables as a function of time, but also sheds light on the direct relations between those variables. In the assumption of validity of the classic model, the results derived in this work can be considered exact, as no further approximations are made. The accuracy of the proposal is demonstrated by comparing the results derived from the new formulation with those yielded from the classical iterative resolution of the differential equations using numerical methods. The new closed-form expressions presented in this paper have the potential to simplify the sizing, regulation and control of power applications with embedded SC banks operated at constant power.