The paper proposes a measurement-based method for the long-term analysis of the low-voltage (LV) distribution network. This work focuses on line power flows susceptible to cause a premature deterioration of cables and on power exchanged at the MV/LV transformer that can potentially induce adverse repercussions on its lifetime. Such estimations are indeed essential as the distribution systems are more and more frequently subject to stress conditions due to the increase of photovoltaic (PV) installations and significant loads such as electric vehicles. In this context, using a probabilistic approach is more beneficial than worst-case scenarios that yield much more restrictive conclusions. The approach is implemented in a pseudo-sequential Monte-Carlo environment and is based on quarter-hourly energy flows recorded by smart meters installed at some LV customers of the Belgian distribution network. These devices are currently located in some scarce selected areas but the penetration rate is expected to massively grow in the future. With the increase of collected measurements, this analysis tool will therefore allow Distribution System Operators (DSOs) to accurately assess important parameters for a secure and efficient operation of the network.

In this paper, an original non sequential Monte Carlo simulation tool is developed.This tool permits to compute the optimal dispatch of classical (coal, oil,…) thermal generation in order to minimize polluting gases (NO x , CO 2 ,…) emissions in presence of wind power and under constraints like the maximal generation cost or the ability of the electrical system to cover the load.In comparison with existing analytical tools based on restrictive hypotheses when it comes to wind power modelling (generally represented by a single entirely correlated global wind park), unexpected outages of conventional parks or fluctuating representation of the load, the use of Monte Carlo simulation allows to remove all those limitations.Indeed, thanks to the developed tool, the optimal dispatch of classical thermal generation can be reached under several load conditions.Well-known reliability indices can also be computed and moreover, following the wind speed sampling that is used, entirely correlated, independent or more accurate correlation level between wind parks can be considered.Finally, it is thought that the proposed solution can be a useful tool for electrical system operators in order to dispatch the polluting thermal units under cost, reliability, emissions, fluctuating wind power and unexpected outages constraints.

Corona discharge is a significant problem in the operation of high-voltage transmission and distribution systems, particularly for polymer insulators. Numerical simulation has become an effective tool for investigating the underlying physical mechanisms and optimizing the design of insulators. In this paper, we present a two-dimensional numerical simulation study on corona discharge plasma affecting the surface behavior of polymer insulators. The simulation was performed with the Comsol Multiphysic software and is based on the finite element method and the fluid plasma model, which considers ionization, recombination, and the transport of plasma species. The numerical results are analyzed to study the spatial and temporal characteristics of the corona discharge and its effect on the surface behavior of polymer insulators. The results show that the electric field is affected not only by the volume charge density but also by the surface charge density, which in turn depends on the densities of the charge carriers migrating on the insulator surface. However, the electric field drops drastically when one or two grading rings are installed. But one grading ring is not enough to limit the discharge.

A new hybrid finite element method-boundary element method (FEM-BEM) scheme is proposed for the solution of the nonlinear 2-D Laplace problem. The novelty is an original approach of the BEM where the domain integrals are eliminated at the discrete level by using the FEM approximation of the fundamental solution at every node of the related mesh in the linear regions. The implementation of this FEM-Green approach requires less computational burden than the standard BEM. The coupling with FEM is straightforward and appears to be more natural. The validity of the method is examined through numerical examples.

Corona discharges are due to the ionization of the gas between two electrodes when the electric field near one of them is very strong. The lack of a complete understanding of the physical processes in negative corona discharge means that interest in corona discharge is still current. In this work, we use a more realistic hydrodynamic plasma model which considers 12 charged species such electron, ions, and molecules, with 32 chemical reactions present in the plasma and coupled with Helmholtz differential model to add effect of photoionization. The model is performed by needle-to-plane 2D-axisymmetric configuration and the digital algorithm based on the finite element method is implemented using the commercial software COMSOL Multiphysics©. The aims of this work are to strengthen the understanding of negative corona discharge in air in a hydrodynamic plasma model. As well as to study the behavior of Trichel pulses when environmental parameters such as relative humidity, temperature, and pressure of the gas vary. Special attention is given when adding photoionization. The results of the numerical simulations show that the amplitude of the first Trichel pulse as well as the duration of the first pulse are strongly impacted by the variation of temperature, pressure, and relative humidity of environment gas. It is shown that the addition of photoionization has relatively impact on the results, especially with regard to the first Trichel pulse due to relative humidity which affects the ionization coefficient which in turn affects photoionization, what is needed for more realistic simulations.

A new finite element method/boundary element method (FEM/BEM) scheme is proposed for the solution of the 2D magnetic static and quasi-static problems with unbounded domains. The novelty is an original approach in the treatment of the outer region. The related domain integral is eliminated at the discrete level by using the finite element approximation of the fundamental solutions (Green’s functions) at every node of the related mesh. This “FEM-Green” approach replaces the standard boundary element method. It is simpler to implement because no integration on the boundary of the domain is required. Then, the method leads to a substantially reduced computational burden. Moreover, the coupling with finite elements is more natural since it is based on the same Galerkin approximation. Some examples with open boundary and nonlinear materials are presented and compared with the standard finite element method.

Corona discharges are due to the ionization of the gas between two electrodes when the electric field near one of them is very strong. The lack of a complete understanding of the physical processes in corona discharge in both positive and negative polarity means that interest in corona discharge is still current. In this work, we use a more realistic hydrodynamic plasma model which considers 12 charged species such electron, ions and molecules, and 32 chemical reactions present in the plasma. The digital algorithm based on the finite element method is implemented using the commercial software COMSOL Multiphysics©. A geometrical configuration of a 1D-axisymmetric wire-cylinder is considered and the set of reactions takes place in the radial direction given the symmetry of the system. The results show that the electron density in the negative corona is four orders of magnitude greater than that in the positive corona. The total number of electrons in the plasma layer of the negative corona is more than 50 times that produced in the positive corona. Under identical temperature and pressure conditions, the weakest corona current in positive polarity, which implies a lower ignition DC voltage. Temperature has an opposite effect on the distribution of the electron density present in the plasma. While the rise in temperature causes a rapid increase in the density of electrons in negative corona, the increase is slower in positive corona. In both cases, the electric field is constant on the conductor surface, however the space charge modifies the local electric field.

The aim of this study is to highlight the joint evolution of the chemical, morphological, thermal and dielectric behaviors upon the UV weathering of an industrial ethylene-propylene-diene monomer (EPDM) rubber. This latter is used as a housing of composite high voltage insulators which are installed in the Algerian desert. This material was submitted to photochemical aging by irradiating UVA rays (λ = 340 nm) at a temperature of 45 °C in order to simulate the witnessed site conditions. It was shown that the degradation process leading to the formation of oxygenated species and the depolymerization of the material are responsible of the coupling which may appear between the realized measurements. Using Kendall rank correlation analysis, joint evolution models were established. Those models introduce a novel assessment approach of the chemical and morphological status of the aged rubber using electrical and dielectric measurements.

This study addresses the voltage control problem of the medium-voltage distribution systems under uncertainty of the network model. A robust voltage control algorithm (RVCA) is developed in order to manage the voltage constraints considering uncertainties associated with the parameters of load, line, and transformer models. The RVCA determines a corrective solution that remains immunised against any realisation of uncertainty associated with the parameters of the network model. To this end, prior to formulating the voltage control problem, Monte Carlo (MC) simulations are used to characterise uncertain parameters of the network component models and load flow (LF) calculations are carried out to evaluate their impacts. The voltage constraints management under the uncertain environment is then formulated as a robust optimisation (RO) problem. The latter is constructed based on the results obtained through the MC simulations and LF calculations. Once the RO is solved, in order to check the robustness of the solution, system voltages are evaluated using the LF calculations considering the new set-points of control variables and uncertainty of network parameters. The simulation results reveal that neglecting model uncertainty in the voltage control problem can lead to infeasible solutions while the proposed RVCA, at an extra cost, determines a corrective solution which remains protected against the studied uncertainties.

The boundary element method (BEM) is typically used for solving potential problems and has several advantages over the traditional finite element method (FEM).However, the normal derivative of the potential appears explicitly as an unknown, with some inherent ambiguity at the corner nodes.Moreover, the BEM requires time consuming numerical integration (Gaussian quadrature) along the boundary of the domain.In this paper, we propose a new approach of BEM by introducing the weak nodal "cap" flux approach defined in the context of the finite element method.The domain integrals are eliminated at the discrete level by introducing the FEM approximation of the fundamental solutions at every node of the related mesh as basic functions in the Galerkin formulation of the BVP under study.The implementation of this new technique appears to be simpler as no numerical integration on the boundary of the domain is required so that the method leads to a substantially reduced computational burden.Our method is compared to the classical BEM for the numerical solution of the two-dimensional Laplace equation.It is observed that the normal flux presents a better behaviour at corners.A loss of accuracy may occur but it is compensated by a smaller execution time, allowing a finer mesh.

The Ethylene-Propylene-Diene Monomer (EPDM) is a material used for the housing of the high voltage composite insulators. The stress conditions related to that outdoor exposure causes alteration of the material's properties. Several characterization techniques were used in this study for the evaluation of the thermal aging of the EPDM. The FTIR technique was used to evaluate the molecular behaviors of the material. The Carbonyl Index measurement was used to assess the oxidation rate of the material along the aging by means of FTIR spectroscopy. The crosslink density was measured using the solvent swell method. For the macroscopic characterization, the surface roughness of the aged samples was measured. This study showed that both crosslinking and oxidation were observed within the studied samples with a linear variation along the aging time. The correlation between the molecular and morphological properties was investigated. This study showed that for each structural scale a phenomenon of degradation is observed during the aging. The erosion of the material observed by the use of the surface roughness measurement has an impact on the oxidation of the material which was monitored by the use of the FTIR spectroscopy. Both of these measured parameters increase along the aging time. This increase is more important when the aging temperature became higher.

-In this paper, a novel voltage sensitivity analysis method is proposed. It presents a complementary formulation of the direct sensitivity analysis approach which has been previously developed based on the topological structure of the network. The proposed method named improved direct sensitivity analysis (IDSA) incorporates variations of power losses in the system branches due to the nodal power changes and their eventual impacts on the node voltages. Effectiveness of the IDSA in voltage estimation is investigated and compared with the voltage results obtained by the direct, Jacobian-based, as well as the perturb-and-observe sensitivity analysis methods. To this end, firstly, the introduced sensitivity analysis methods are tested when active or reactive power is changed at the selected nodes of the studied test systems. Accuracy of voltage responses obtained by each of the considered sensitivity analysis methods is evaluated with respect to the exact voltage value obtained from the load flow study. Moreover, performance of the introduced sensitivity analysis methods is examined when they are separately embedded in a multi-step voltage control algorithm which manages active and reactive powers of distributed generation units in order to keep the system voltages within the permitted voltage limits. Simulation results confirm that when the power losses impact is considerable, the IDSA outperforms the direct, perturb-and-observe, and Jacobian-based sensitivity analysis methods in terms of accuracy of the voltage estimation.

During the lifetime of a High Voltage composite insulator, the housing of that latter is exposed to stress conditions. Those exposures alter the insulating behavior of the insulator in term of Electrical field (E-field) distribution and, consequently, the leakage current flow. The assessment of that evolution is an important parameter to be considered during the design of the insulator in order to prevent additional stresses such as dry band arcing which is caused by the leakage current increase. In this paper, an attempt has been made to build a model based on the Finite Element Method (FEM) for the calculation of the E-field distribution around a composite insulator. This model was used to assess the impact of the aging of the housing material. A program was developed in order to minimize the effect of the aging of the housing. That optimization was done by modifying the construction parameters of the insulator.

In this paper, a novel framework is proposed in order to evaluate impacts of the uncertain models of the system components on the voltage regulation problem of the medium-voltage distribution systems. The investigation focuses on the model uncertainty associated with voltage dependency of loads, power factor of loads, thermal dependency of lines, shunt admittances of lines and internal resistance of substation transformer. To this end, firstly, voltage constraints are managed using a centralised voltage control algorithm (VCA) by relying on the simplified models of the system components. The system loads and lines as well as the substation transformer are then modelled with the uncertain variables which are bounded in the predefined ranges. Monte Carlo (MC) simulations are used to create wide series of scenarios that cover the possible values that the parameters of the system components can take due to their uncertain nature. The model uncertainty impacts on the voltage regulation problem are finally evaluated by the load flow calculations considering the scenarios created by the MC simulations and the set-point obtained by the VCA. The proposed investigation brings useful information regarding the possible deviations that the node voltages can have due to the uncertain models of the studied components.

The electric distribution systems are generally modelled in an inaccurate way since the exact model of their components is not practically available. The model inaccuracy creates errors in the calculations and can mislead the analyses into the wrong directions. In this regard, this paper studies impact of the model inaccuracy on the voltage control problem of the Medium Voltage (MV) distribution systems. Firstly, a Voltage Control Algorithm (VCA) is proposed which is subject to the inaccuracies associated with the load and line models. Then, Monte Carlo (MC) simulation are used to create a wide range of scenarios that covers the possible values that parameters of the model under study can take. These scenarios represent the uncertain nature of the model under study. Finally, the load flow calculations are performed considering the set-point obtained by the VCA and for each of the scenarios created by the MC tool. By evaluating all scenarios, impact of the model inaccuracy on the voltage control problem is obtained. If the system voltages are found to be within the permitted voltage range, it is concluded that the inaccuracy in the studied model will not create a voltage violation problem for the VCA.

In LV systems, Probabilistic Load Flow techniques have been developed in order to accurately assess the uncertainty associated to fluctuating PV generation and are based on the use of pseudo-sequential Monte Carlo simulations. Those probabilistic tools are practically developed on the direct basis of the data provided by smart meters or on irradiance measurements. Based on this information, the statistical behavior of each PV generation unit (prosumer) is defined for each quarter of an hour of a “typical day” (per month or, even, per year) and a sampling on the exchanged power with the grid is made for each simulated quarter of an hour. Currently, when sampling PV generation in the Monte Carlo framework, no particular attention is paid on the correlation existing between PV units. Practically, this correlation could change with time and will influence the behavior of the LV network. In that way, in this contribution, a fast incremental algorithm is implemented and repeated for each quarter of an hour of each defined “typical day”. Thanks to this non-iterative approach, clusters of PV generation are defined for each quarter of an hour and are based on a pre-defined geographical correlation threshold. It is shown that the correlation between PV units connected to the same LV system stays high for each useful 15min interval of the day and that, practically, all PV generation units can be grouped in a single cluster and considered as entirely correlated. The same process is conducted for the load and the correlation between load and PV generation for each customer is also taken into account. Finally, in order to demonstrate the interest of the proposed study, a new sampling process based on the defined PV/load clusters is implemented and the collected indices (probability of overvoltage…) are compared with the ones computed when only considering complete independency between all the connected LV customers.

Maximizing the share of renewable resources in the electric energy supply is a major challenge in the design of smart cities. Concerning the smart city power distribution, the main focus is on the Low Voltage (LV) level in which distributed Photovoltaic (PV) units are the mostly met renewable energy systems. This paper demonstrates the usefulness of smart metering (SM) data in determining the maximum photovoltaic (PV) hosting capacity of an LV distribution feeder. Basically, the paper introduces a probabilistic tool that estimates PV hosting capacity by using user-specific energy flow data, recorded by SM devices. The probabilistic evaluation and the use of historical SM data yield a reliable estimation that considers the volatile character of distributed generation and loads as well as technical constraints of the network (voltage magnitude, phase unbalance, congestion risk, line losses). As a case study, an existing LV feeder in Belgium is analysed. The feeder is located in an area with high PV penetration and large deployment of SM devices. The estimated PV hosting capacity is proved to be much higher than the one obtained with a deterministic worst case approach, considering voltage margin (magnitude and unbalance).

In three-phase Low Voltage (LV) networks, distributed photovoltaic (PV) units can contribute to voltage unbalance mitigation in case they are connected with the use of three-phase inverters integrating unbalance mitigation control schemes. This paper presents a probabilistic framework that simulates the time-varying action of voltage magnitude and unbalance mitigation schemes, locally implemented by PV inverters in LV feeders. The scope includes evaluating the effect of such strategies, in the context of a long-term techno-economic planning of the LV network, and characterizing LV network operation for increasing the observability of state estimation techniques applied in the Medium Voltage level. The presented framework evaluates the action of four distributed control schemes in an extensive range of possible network states assembled with the use of feeder-specific smart metering (SM) data. The simulation of a real LV feeder with distributed PV generation and historic SM measurements is presented. A control strategy that acts resistively towards the negative- and zero-sequence voltage components, without modifying the total nodal injected power (three-phase damping control strategy), results to be more effective compared with traditionally applied voltage control schemes.

This chapter presents two probabilistic planning tools developed for the long-term analysis of distribution networks. The first one focuses on the low-voltage (LV) level and the second one addresses the issues occurring in the medium-voltage (MV) grid. Both tools use Monte Carlo algorithms in order to simulate the distribution network, taking into account the stochastic nature of the loading parameters at its nodes. Section 1 introduces the probabilistic framework that focuses on the analysis of LV feeders with distributed photovoltaic (PV) generation using quarter-hourly smart metering data of load and generation at each node of a feeder. This probabilistic framework is evaluated by simulating a real LV feeder in Belgium considering its actual loading parameters and components. In order to demonstrate the interest of the presented framework for the distribution system operators (DSOs), the same feeder is then simulated considering future scenarios of higher PV integration as well as the application of mitigation solutions (reactive power control, P/V droop control thanks to a local management of PV inverters, etc.) to actual LV network operational issues arising from the integration of distributed PV generation. Section 2 introduces the second planning tool designed to help the DSO, making the best investment for alleviating the MV-network stressed conditions. Practically, this tool aims at finding the optimal positioning and sizing of the devices designed to improve the operation of the distribution grid. Then a centralized control of these facilities is implemented in order to assess the effectiveness of the proposed approach. The simulation is carried out under various load and generation profiles, while the evaluation criteria of the methodology are the probabilities of voltage violation, the presence of congestions and the total line losses.

Lately distribution utilities worldwide have been incentivized to reduce operating expenses that have severely increased with the integration of distributed generation. Enabling demand flexibility in the low voltage network seems a promising means at this direction. Given the current (low) electricity prices and the stochasticity of distributed generation and loads, this paper explores whether a capacity-based distribution tariff that rewards low power withdrawal during peak hours could incentivize small end-users to participate in demand side management. The assessment deploys a pseudo-sequential Monte Carlo simulation that uses quarter-hourly energy measurements and accounts for network constraint management. The presented case study highlights that a coordinated technical implementation is required, both during peak and non-peak periods, for not stressing LV network operation with the integration of flexibility. The potentially generated revenue for end-users, thanks to their response to the considered distribution tariff, results sufficiently motivating for engaging them in flexibility actions.