Radial Distribution Grid Research Articles

Admittance matrix estimation of radial distribution grids using power and voltage magnitude measurements

Accurate knowledge of the admittance matrix of distribution grids is essential for grid operation and control as more renewable energy sources and electric vehicles are integrated into distribution grids. Due to limited observability, measurement noise, topology assumptions, and partial data availability, the exact calculation of the admittance matrix of distribution grids is challenging. In this paper, we present a method for estimating the admittance matrix of radial distribution grids. The proposed method uses low-cost measurement devices that record ten-minute-based measurements of voltage magnitudes, active power, and reactive power at a single end of the lines or transformers instead of second-based phasor measurements. The impedance of lines or transformers is then estimated using a statistical optimization subject to the distribution flow (DistFlow) model. The effectiveness of proposed method is demonstrated by simulation, laboratory testing, and field measurements taken from a distribution grid in Switzerland.

Bayesian Entropy Methodology: A Novel Approach to Setting Anti-Islanding Protections with Enhanced Stability and Sensibility

The risk of unintentional islanding creation in distributed energy systems poses a significant security concern since unintentional islanding formation could lead to a supply of energy outside of the optimal quality limits. This constitutes a risk for users, maintenance personnel, infrastructure, and devices. To mitigate this problem, anti-islanding protections are widely used to prevent the distributed generator from feeding a portion of the radial distribution grid when a protection device trips upstream. However, the effectiveness of these protections heavily relies on properly tuning protection setting thresholds (such as time delay and pickup). This work proposes a novel approach that utilizes entropy as a model and metric of the uncertainty associated with a particular protection setting. By minimizing entropy, the proposed method aims to improve stability and sensitivity, consequently improving the overall performance of anti-islanding protection. Simulation results demonstrate that the Bayesian entropy methodology (BEM) approach achieves enhanced stability in various scenarios, including frequency transients, and demonstrates a notable reduction in the size of the dataset and computational burden, ranging between 91% and 98%, when compared to related works, with an improvement of the uncertainty achieved. The findings of this study contribute to the development of more robust and reliable anti-islanding protections.

Data-driven boundary regression for equivalent identification of external parameters in steady-state models of power systems

External Network Modeling (ENM) is an important method to simplify and accelerate power system control, protection, and optimization. Traditional model-based methods obtain accurate external parameters by analyzing the physical properties of the whole system. In the case of incomplete physical information, the use of data-driven models has become an effective means to analyze the operating state of power systems. In this paper, a data-driven approach is used to propose an external equivalent parameter identification framework for steady-state models of power systems to accurately estimate the operating states of power systems of interest. Linear correction coefficients are used to deal with the challenges brought by the nonconvexities of the power flow equation to the regression. Based on the linearly mapped power flow equation, we derive the Multivariate Linear Regression (MLR) model of the external power system. The Box-Cox transformation (BCT) and ridge regression algorithm (RRA) algorithms are designed to address data normality, collinearity, and overfitting. The proposed framework is tested on a series of IEEE standard cases, which include both meshed transmission grids and radial distribution grids, with both Monte Carlo simulated data and public testing data. The results show that the proposed method can obtain a higher calculation accuracy than model-based methods can. The results also demonstrate that the proposed data-driven equivalent framework can obtain accurate regression parameter matrices under the condition of non-normal data, and accurately reflect the physical parameters of the external power system.

Investigating the performance of non‐standard characteristics‐based overcurrent relays and their optimum coordination in distributed generators connected networks

AbstractTo handle the challenges attributed to the distributed generators, the protection system of distribution networks needs to be evolved. Recent protection schemes modify the standard characteristics of overcurrent relays, called non‐standard characteristics. These non‐standard characteristics are mostly case‐dependent and have limitations in solving the variety of protection challenges attributed to distributed generators. This paper analyses the performance of six voltage‐based non‐standard characteristics on photovoltaic distributed generators (PVDG) penetrated 3‐bus, 8‐bus, and IEEE 30‐bus distribution grid, as well as the 9‐bus Canadian radial distribution grid with synchronous distributed generator, wind turbine generator, and PVDG penetrations. Besides that, the optimum coordination of these non‐standard characteristics‐based overcurrent relays is a complex problem due to the involvement of additional controlling parameters. To find the best suitable method, a comparative analysis of the genetic algorithm, differential evolution, artificial bee colony, harmony search algorithm, firefly algorithm, cuckoo search algorithm and particle swarm optimization are performed for optimum relay coordination. The outcomes of the paper are thoroughly discussed for future research on non‐standard characteristics development.

Power Loss Minimization in a Radial Distribution Network by Optimal Sizing and Placement of Energy Storage Units

It is possible to reduce distribution losses by strategically placing and sizing DG and BESS sources. Assuring low loss requires strategically placing the aforementioned devices; otherwise, the system may experience either under- or overvoltage. It is preferable to choose bus stations with less risk for loss. The proposed approach tries to pinpoint the optimal BESS size and placement to cut down on investment and operating expenses while still achieving the desired level of energy reduction. The development of optimisation algorithms for finding and scaling BESS units is the fundamental focus of this study. Two such strategies are being explored here: the Genetic Algorithm (GA) and the Ant Colony Optimization Algorithm (ACOA). The goal function, like the original issue, seeks to minimise system-wide power losses while adhering to specified levels of equality and inequality. This article explores the appropriate capacity and placement of the DGs in a 33-bus radial distribution grid to reduce power dissipations. Matlab code is used to perform a simulation, and the results are put to use gauging the method's sturdiness.

Flexibility Aggregation Perimeter for Ancillary Services in Radial Distribution Systems

The flexibility provided by prosumers is recognized as a key element for the management of the electrical grids, in particular distribution grids, in the changing scenario of electricity generation and consumption. The flexibility useful to Distribution System Operators (DSOs) is strongly local, and it is necessary to identify the busses of the grid where the flexibility can be usefully provided for a service requested by the DSO. For this purpose, the concept of flexibility perimeter is adopted; it is defined as a set of busses such that flexibility can be provided by any set of prosumers within it while the grid operation remains secure. The flexibility perimeter is a relevant concept for flexibility markets; in particular, for aggregators, since the flexibility provided by the prosumers within the perimeter can be offered as a single product to participants to electricity markets requiring grid services. The identification of flexibility aggregation perimeters for congestion-relief services in a radial grid is straightforward; for flexibility services intended to solve voltage profile problems, the identification of perimeters is not easy, even in radial grids. The paper proposes a method for the identification and evaluation of flexibility perimeters for grid services in radial distribution grids, based on the concept of Load Area; it can help decision-makers choose a compromise between technical and market efficiency of the aggregation perimeter dimension. For voltage support services, the dimension of the perimeter oppositely influences the technical soundness and the market efficiency of the aggregation; the influence is evaluated quantitatively. The results of two case studies show the features of the method.

A Distributed Algorithm for Controlling Continuous and Discrete Variables in a Radial Distribution Grid

The increased integration of distributed energy resources (DERs) in the distribution network with intermittent generation profiles will likely make voltage regulation a difficult task. However, DERs bring both challenges and opportunities, as they can provide renewable forms of local energy and act as voltage regulating components. The DERs are usually interfaced with power electronic devices, in which both their active and reactive power outputs can be regulated and treated as continuous control variables. In contrast, other voltage regulatory devices such as On-Load Tap-Changing (OLTC) transformers are often controlled by making discrete tap changes. Thus, appropriate control strategies are required to control and coordinate the DERs with other voltage regulatory devices. In this work, a distributed control strategy based on the Alternating Direction Method of Multipliers (ADMM) is developed, which controls both the continuous and the discrete variables in a distribution grid. The proposed control strategy is compared to a centralized and a local control architecture, where optimal parameters have been computed for the local controllers. Finally, a simulation study is made for the three different control architectures using a modified CIGRE medium voltage network. The results showed significant improvements in the daily voltage profiles while also reducing the power losses by over 30% when using an optimal control strategy.

Optimal Reactive Power Compensation in Distribution Networks with Radial and Meshed Structures Using D-STATCOMs: A Mixed-Integer Convex Approach.

This paper deals with the problem regarding the optimal siting and sizing of distribution static compensators (D-STATCOMs) in electrical distribution networks to minimize the expected total annual operating costs. These costs are associated with the investments made in D-STATCOMs and expected energy losses costs. To represent the electrical behavior of the distribution networks, a power flow formulation is used which includes voltages, currents, and power as variables via incidence matrix representation. This formulation generates a mixed-integer nonlinear programming (MINLP) model that accurately represents the studied problem. However, in light of the complexities involved in solving this MINLP model efficiently, this research proposes a mixed-integer convex reformulation. Numerical results regarding the final annual operating costs of the network demonstrate that the proposed mixed-integer convex model is efficient for selecting and locating D-STATCOMs in distribution networks, with the main advantage that it is applicable to radial and meshed distribution grid configurations. A comparative analysis with respect to metaheuristic optimizers and convex approximations confirms the robustness of the proposed formulation. All numerical validations were conducted in the MATLAB programming environment with our own scripts (in the case of metaheuristics) and the CVX convex disciplined tool via the Gurobi solver. In addition, the exact MINLP model is solved using the GAMS software.

Superposition Principle-based Method for Power Loss Allocation in Power Systems

The paper presents a novel method for power loss allocation of power systems to demands. This loss allocation technique is based on the contribution of individual demands to the branch power loss of power grids. Results of power flow analysis, precise power system modelling and superposition theorem are deployed in this proposed method. The advantage of the method described in the paper is that it is accurate and ensures fairness among network users. In addition, this allocation method is simple and can be effectively exploited to both meshed and radial electrical networks. A six-node meshed transmission system and an IEEE 33-bus radial distribution grid are utilized to implement power loss allocation based on the proposed method. The influence of demands’ power factor on the power loss allocated is also taken into account using the six-node meshed transmission network.

Optimal Placement of Capacitors in Radial Distribution Grids via Enhanced Modified Particle Swarm Optimization

This paper presents the integration of shunt capacitors in the radial distribution grids (RDG) with constant and time-varying load consideration for the reduction of power losses and total annual cost, which turns to enhance the voltage profile and annual net savings. To gather the stated goals, three objective functions are formulated with system constraints. To solve this identified problem, a novel optimization technique based on the modification of particle swarm optimization is proposed. The solution methodology is divided into two phases. In phase one, potential candidate buses are nominated using the loss sensitivity factor method and in phase two the proposed technique first selects the optimal buses for the capacitor placement among the potential buses then it decides the optimal sizing of the capacitors as well. To demonstrate the performance in terms of efficiency and strength, the proposed technique is tested on IEEE 15, 33, and 69 bus system for the optimal placement and sizing of capacitors (OPSC) problem. The results are achieved in terms of annual net savings for 15 bus (47.66%case−1, 32.76%case−2, 26.46%case−3), 33 bus (33.09% case−1, 27.06%case−2, 24.15%case−3), and 69 bus (34.51% case−1, 29.43%case−2, 25.83%case−3) which are comparable to other state of the art methods, and it also indicates the success of the proposed technique.

An iterative linear DistFLow for dynamic optimization in distributed generation planning studies

This paper implements an iterative linear DistFlow for the modelling of radial distribution grids. The method is intended for dynamic optimizations under gird constraints, and in the presence of distributed generation including storage units with time coupled constraints. It is demonstrated that traditional piecewise linearization for the losses estimation in conventional linear DistFlow can lead to significant errors. This is due in particular to the setting of static upper bounds for the active and reactive branch flows in the linearization process, which may differ greatly from the actual power. The proposed iterative approach addresses this shortcoming with successive runs of linear DistFlow and updates for the flows upper bounds, dynamically along the simulated horizon. The method is compared to conventional linear DistFlow as well as other relaxed formulations such as Second Order Conic Programming and Quadratic Programming. All the methods are discriminated with regard to a reference AC power flow, in terms of error for the voltages and losses profiles on different test systems. The proposed iterative procedure displays the lowest error for the line losses with five to forty times more accuracy than conventional linearized formulations. It also outperforms the Second Order Conic relaxation in terms of scalability with one month dynamic simulation (at 1 h time step) run in 7 min with 30 distributed units on a 69-bus system. The approach is further validated with typical uses cases for the operation, the sizing, and the siting of distributed assets consisting of solar generators and storage units. Especially, the procedure is coupled with a genetic algorithm in order to test different system configurations on a 90-bus system. The solutions are discriminated in terms of number of assets, installed capacities, connection bus(es), installation costs, system losses and system self-sufficiency.

Distributed State Estimation for Multi-Feeder Distribution Grids

The real-time monitoring of electric distribution grids via state estimation is a fundamental requirement to deploy smart automation and control in the distribution system. Due to the large size of distribution networks and the poor coverage of measurement instrumentation on the field, designing fast state estimation algorithms and achieving accurate results are two major challenges associated to distribution system state estimation. In this paper, an efficient and accurate solution for performing state estimation in multi-feeder radial distribution grids is presented. The proposed algorithm is based on a two-step approach. In the first step, state estimation is performed in parallel on the different feeders suitably processing the available measurements and pseudo-measurements and taking into account their uncertainty characteristics. In the second step, the results on each feeder are post-processed to refine the estimations and to improve the accuracy performance. To this purpose, the second step considers how measurement uncertainties propagate towards the final estimates and how measurements shared among the feeders could adversely affect the final estimation. Performed tests show that the conceived design leads to accuracy performance very close to those achievable by running state estimation on the full grid. At the same time, the parallelization of the estimation process on the different feeders allows decentralizing the state estimation problem, with the associated benefits in terms of computation time and distribution of the communication and storage requirements.

Short-Circuit Analysis of DER-Based Microgrids in Connected and Islanded Modes of Operation

Since microgrids should be able to smoothly operate in two distinct modes—grid-connected and islanded, their fault currents can widely fluctuate depending on the operational mode. When the microgrid is connected to the grid, the highest fault current, by far, is supplied by the utility grid. In this mode, the fault current contribution from distributed energy resources (DERs) is less than 20%. However, when the microgrid switches to the islanded mode, the fault current contribution from the utility grid is lost and DERs are the sole fault current sources. Thus, the overall fault current in the islanded mode is multiple times lower when compared to the grid connected mode. Moreover, most of the DERs are inverter-based, with limited fault currents, which further reduces the overall fault current in the islanded mode. With the rapid rise of the microgrid penetration around the globe, this phenomenon can adversely influence the relay protection, and thus the microgrid fault current needs to be precisely analyzed. Therefore, the main purpose of this paper is to thoroughly analyze the fault current differences in two distinct operation modes of a microgrid, and to consequently derive conclusions regarding the required improvements in fault calculations and relay protection analysis in emerging microgrids. A representative microgrid test bed is developed and modelled using the in-house developed software as well as in a state-of-the-art hardware-in-the-loop environment. Several different short-circuit faults were simulated and analyzed in both grid-connected and islanded modes. The results show that the fault currents significantly differ depending on the operating mode, and thus highly influence the protection system. Moreover, test results show that the fault calculation algorithms aimed at radial distribution grids, mostly used for microgrid fault calculations in the available literature, need to be further improved to provide precise and time-efficient results when the emerging microgrids are considered. These results provide a valuable insight into the current state of the microgrids’ fault calculation and protection and reveal several important directions for future research.

Determining maximum hosting capacity for PV systems in distribution grids

Power systems face increasing challenges on reliable operations due to the widespread distributed generators (DGs), e.g., rooftop PV systems in distribution grids. Characterizing the hosting capacity (HC) is vital for utilities to assess the total amount of distributed generations that a grid can deploy efficiently before upgrading. Some methods conduct extensive simulations for analyzing HC, which lack theoretical guarantees and can be time-consuming. Therefore, there are also methods employing optimization over all necessary operation constraints. However, the complexity and inherent non-convexity lead to non-optimal solutions. To solve the problems, this paper provides a constructive model for HC determination. Based on geometrical understanding, HC solutions are constructed sequentially according to realistic constraints so that the optimal solution can be reserved even with a non-convex model. For practical adaption, the three-phase unbalance condition is considered, and parallel computation is developed for speed-up. The method is validated by extensive numerical results on IEEE standard systems, such as 8-bus and 123-bus radial distribution grids. In comparison, the proposed approach obtains analytical hosting capacity solutions of larger values and uses less computation time. The results of HC verify that the proposed method reserves optimality and thus has good performance in complex scenarios, including more operational constraints, different PV deployment, and larger system size.

Single‐pole fault line selection method for MVDC distribution grid based on 0‐mode power

At present, the MVDC distribution grid is developing rapidly and relay protection is the key technology to ensure stable operation. Therefore, this paper focuses on the fault line selection method. Firstly, the fault characteristics are analysed when a fault occurs in the line, and a novel single-pole fault line selection method is proposed based on 0-mode power. The polarity of current fault component measured at the terminal of each line is used to identify the internal and external faults. And the 0-mode power is used to select the faulty line. Finally, to verify the correctness of the proposed method, a radial MVDC distribution grid is built in PSCAD to output fault data in different fault conditions, and the fault line selection algorithm is implemented in MATLAB. The simulation results show that the proposed method is fast, effective, reliable and it has a certain degree of tolerance to transition resistance with a strong anti-data delay and anti-interference ability. Moreover, the fault line selection method proposed in this paper can still correctly select the fault line in the case of serious faults such as multiple line faults, sudden removal of lines, and sudden changes in photovoltaic output power.

The Equivalence between Successive Approximations and Matricial Load Flow Formulations

This paper shows the equivalence of the matricial form of the classical backward/forward load flow formulation for distribution networks with the recently developed successive approximations (SA) load flow approach. Both formulations allow solving the load flow problem in meshed and radial distribution grids even if these are operated with alternating current (AC) or direct current (DC) technologies. Both load flow methods are completely described in this research to make a fair comparison between them and demonstrate their equivalence. Numerical comparisons in the 33- and 69-bus test feeder with radial topology show that both methods have the same number of iterations to find the solution with a convergence error defined as 1×10−10.

Learning With End-Users in Distribution Grids: Topology and Parameter Estimation

Efficient operation of distribution grids in the smart-grid era is hindered by the limited presence of real-time nodal and line meters. In particular, this prevents the easy estimation of grid topology and associated line parameters that are necessary for control and optimization efforts in the grid. This article studies the problems of topology and parameter estimation in radial balanced distribution grids where measurements are restricted to only the leaf nodes and all intermediate nodes are unobserved/hidden. To this end, we propose two exact learning algorithms that use balanced voltage and injection measured only at the end users. The first algorithm requires time-stamped voltage samples, statistics of nodal power injections, and permissible line impedances to recover the true topology. The second and improved algorithm requires only time-stamped voltage and complex power samples to recover both the true topology and impedances without any additional input (e.g., number of grid nodes, statistics of injections at hidden nodes, and permissible line impedances). We prove the correctness of both learning algorithms for grids where unobserved buses/nodes have a degree greater than three and discuss extensions to regimes where that assumption doesn't hold. Further, we present computational and, more important, the sample complexity of our proposed algorithm for joint topology and impedance estimation. We illustrate the performance of the designed algorithms through numerical experiments on the IEEE and custom power distribution models.

Application of Machine Learning for Fault Classification and Location in a Radial Distribution Grid

Fault location with the highest possible accuracy has a significant role in expediting the restoration process, after being exposed to any kind of fault in power distribution grids. This paper provides fault detection, classification, and location methods using machine learning tools and advanced signal processing for a radial distribution grid. The three-phase current signals, one cycle before and one cycle after the inception of the fault are measured at the sending end of the grid. A discrete wavelet transform (DWT) is employed to extract useful features from the three-phase current signal. Standard statistical techniques are then applied onto DWT coefficients to extract the useful features. Among many features, mean, standard deviation (SD), energy, skewness, kurtosis, and entropy are evaluated and fed into the artificial neural network (ANN), Multilayer perceptron (MLP), and extreme learning machine (ELM), to identify the fault type and its location. During the training process, all types of faults with variations in the loading and fault resistance are considered. The performance of the proposed fault locating methods is evaluated in terms of root mean absolute percentage error (MAPE), root mean squared error (RMSE), Willmott’s index of agreement (WIA), coefficient of determination ( R 2 ), and Nash-Sutcliffe model efficiency coefficient (NSEC). The time it takes for training and testing are also considered. The proposed method that discrete wavelet transforms with machine learning is a very accurate and reliable method for fault classifying and locating in both a balanced and unbalanced radial system. 100% fault detection accuracy is achieved for all types of faults. Except for the slight confusion of three line to ground (3LG) and three line (3L) faults, 100% classification accuracy is also achieved. The performance measures show that both MLP and ELM are very accurate and comparative in locating faults. The method can be further applied for meshed networks with multiple distributed generators. Renewable generations in the form of distributed generation units can also be studied.

Location and Sizing of Micro-Grids to Improve Continuity of Supply in Radial Distribution Networks

The steady decline in the prices of distributed energy resources (DERs), such as distributed renewable generation and storage systems, together with more sophisticated monitoring and control strategies allow power distribution companies to enhance the performance of the distribution network, for instance improving voltage control, congestion management, or reliability. The latter will be the subject of this paper. This paper addresses the improvement of continuity of supply in radial distribution grids in rural areas, where traditional reinforcements cannot be carried out because they are located in secluded areas or in naturally protected zones, where the permits to build new lines are difficult to obtain. When a contingency occurs in such a feeder, protection systems isolate it, and all downstream users suffer an interruption until the service is restored. This paper proposes a novel methodology to determine the optimal location and size of micro-grid systems (MGs) used to reduce non-served energy, considering reliability and investment costs. The proposed model additionally determines the most suitable combination of DER technologies. The resulting set of MGs would be used to supply consumers located in the isolated area while the upstream fault is being repaired. The proposed methodology is validated through its application to a case study of an actual rural feeder which suffers from reliability issues due to the difficulties in obtaining the necessary permissions to undertake conventional grid reinforcements.

A Study on the V2G Technology Incorporation in a DC Nanogrid and on the Provision of Voltage Regulation to the Power Grid

Currently, environmental and climate change issues raise a lot of concerns related to conventional vehicles and renewable energy generation methods. Thus, more and more researchers around the world focus on the development and deployment of Renewable Energy Sources (RES). Additionally, due to the technological advancements in power electronics and electrical batteries, Electrical Vehicles (EVs) are becoming more and more popular. In addition, according to the Vehicle-to-Grid (V2G) operation, the EV batteries can provide electrical energy to the power grid. In this way, many ancillary services can be provided. A Direct Current (DC) nanogrid can be composed by combining the aforementioned technologies. Nanogrids present high efficiency and provide a simple interaction with renewable energy sources and energy storage devices. Firstly, the present study describes the design considerations of a DC nanogrid as well as the control strategies that have to be applied in order to make the V2G operation feasible. Furthermore, the provision of voltage regulation toward the power grid is investigated though the bidirectional transfer of active and reactive power between the DC nanogrid and the power grid. Afterwards, the voltage regulation techniques are applied in an Alternating Current (AC) radial distribution grid are investigated. The proposed system is simulated in Matlab/Simulink software and though the simulation scenarios the impact of the voltage regulation provided by the DC nanogrid is investigated.