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In this paper, a two-stage procedure is proposed in order to solve the centralized self-healing scheme for electrical distribution systems. The considered self-healing actions are the reconfiguration of the distribution grid and, if needed, node and zone load-shedding. Thus, the proposed procedure determines the status of the switching devices in o...
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... As the cost function of thermal power units is a quadratic function, it is often necessary to use a linearization method to approximate it as a linear function. As in the studies in the previous paragraph, most use ES-PWL interpolation, which has another general PWL formulation in [14] and [15], to linearize the cost functions. While ES-PWL interpolation provides a simple fitting method, it does not yield the best accuracy. ...
... The approximation is initiated from the last subinterval I N , where the difference value at the right terminal of the subinterval is set to zero, i.e., y N 0. Then, (14) is minimized by differentiating it with respect to y N −1 . For the neighboring subinterval I N −1 and a given y N −1 , this approach further differentiates (14) with respect to y N −2 . ...
... Then, (14) is minimized by differentiating it with respect to y N −1 . For the neighboring subinterval I N −1 and a given y N −1 , this approach further differentiates (14) with respect to y N −2 . Sequentially, the same steps are applied to the rest subintervals by with the already-computed y n from the previous subinterval calculation. ...
In the studies of unit commitment or optimal power flow, to formulate a mixed-integer linear programming model that can be efficiently solved with commercial solvers, it is necessary to approximate the quadratic cost curves of thermal units as piecewise linear (PWL) functions. The conventional approach involves evenly spaced piecewise linear (ES-PWL) interpolation, which often results in relatively large approximation errors. In order to reduce the error, this paper proposes a more accurate PWL method for approximating the quadratic cost functions of thermal units. The method employs a linear least-squares fit instead of linear interpolation within each subinterval and introduces a one-terminal-constraint approach to ensure the continuity of the piecewise function. Subsequently, a straightforward equation is derived, applicable to the widely used ES-PWL interpolation, with the potential to enhance the accuracy of the approximation. Mathematical verification attests that the proposed method substantially diminishes the squared 2-norm error, less than 37.5% of the error associated with ES-PWL interpolation. Subsequent numerical investigations are carried out on a 10-unit system, the IEEE RTS-79, and a real industrial system. The findings validate that all the approximation errors of the proposed method are within 37.5% of the errors associated with the ES-PWL interpolation, meaning that a unit commitment solution that closely approximates the outcome of the quadratic function is obtained. The computational time is also acceptable.
... Te proposed scheme was investigated for islanded systems and grid connected with loop and radial confgurations. In [39], a two-step method is used that, in the frst layer, solves a mixed-integer linear programming (MILP) problem and, in the second layer, solves a nonlinear programming (NLP) problem. In [40], a twostage stochastic program has been used, which optimizes the output power of WTs and PVs and load consumption in the frst stage and adjusts production in the second stage with suitable scenarios based on the output power of renewable sources. ...
... In the second step of a nonlinear model, the unit commitment problem is solved mathematically [41]. Te models presented in [39][40][41][42] have a very high execution time due to their nonlinearity, and it is practically impossible to use these models in large systems. On the other hand, due to intelligent algorithms, achieving the optimal solution will not be guaranteed. ...
... Te proposed model is solved using mathematical solvers. Te proposed model also uses a load-shedding tool integrated with DR schemes, while, in [39][40][41][42], DR-based methods were not used. ...
One of the essential capabilities of a smart distribution network is to improve network restoration performance using the postfault islanding method. Islanding of the faulty area can be done offline and online. Online islanding will decrease load shedding and operation cost. In this study, a novel two-step mathematical method for system restoration after the fault is presented. A new mathematical model for the optimal arrangement of the system for the faulty area in the first layer is proposed. In this layer, the main objective is to decrease the distribution system’s load shedding and operational costs. In this regard, after the fault event, the boundary of the islanded MGs is determined. Then, in the second layer, the problem of unit commitment in the smart distribution network is addressed. In addition to the load shedding, optimal planning of energy storage systems (ESSs) and nondispatchable distributed generation (DG) resource rescheduling are also determined in this layer. The important advantages of the proposed approach are low execution time and operational costs. A demand response (DR) program has also been used for optimal system restoration. Solving the problem using the multiobjective method with the epsilon-constraint method is another goal of the paper, which simultaneously minimizes the cost and the emissions of the smart distribution network. The proposed model has been tested on an IEEE 33-bus system. Better performance of the proposed model compared to the techniques in the literature has been proven.
... Reference [83] develops a self-healing strategy with multi-agent system in reconfiguration operations of power distribution systems to minimize switching operations. Other research papers have been published in this area including [23], [90], [100]- [111]. ...
The ever-increasing dependence on electrical power has posed more challenges to power system engineers to deliver secure, stable, and sustained energy to electricity consumers. Due to the increasing occurrence of short- and long-term power interruptions in the power system, the need for a systematic approach to mitigate the negative impacts of such events is further manifested. Self-healing and its control strategies are generally accepted as a solution for this concern. Due to the importance of self-healing subject in power distribution systems, this paper conducts a comprehensive literature review on self-healing from existing published papers. The concept of self-healing is briefly described, and the published papers in this area are categorized based on key factors such as self-healing optimization goals, available control actions, and solution methods. Some proficient techniques adopted for self-healing improvements are also classified to have a better comparison and selection of methods for new investigators. Moreover, future research directions that need to be explored to improve self-healing operations in modern power distribution systems are investigated and described at the end of this paper.
... Cavalcante et al. used two kinds of MP algorithms in [15]: one used Mixed-Integer Linear Programming (MILP) to find the optimal configuration value, and the other used nonlinear programming (NLP) to find the optimal load shedding value. [3] used MILP in 2017 to determine the minimum value of reconfiguration costs while accounting for reactive power and losses but not as an objective function. ...
... The same is true for reactive strength. (15). Constraint (16) states that if the circuit is operational, the values y i and y j must have the same value. ...
This study proposed a smart grid reconfiguration strategy that takes technical aspects into account. Convex optimization is used to answer the strategy. We find original quadratically constrained and second-order cone approximations to power flow in radial networks during the derivation of each model. Using standard commercial software, the proposed formulation guarantees global optimality with reliable and efficient outcomes. We use IEEE 33 and add DGs to model active distribution systems to evaluate the proposed method. The simulation findings show that the proposed method is capable of solving reconfiguration efficiently. Streszczenie. W badaniu tym zaproponowano strategię rekonfiguracji inteligentnej sieci, która uwzględnia aspekty techniczne. Optymalizacja wypukła służy do odpowiedzi na strategię. Znajdujemy oryginalne kwadratowe ograniczenia i przybliżenia stożka drugiego rzędu do przepływu mocy w sieciach promieniowych podczas wyprowadzania każdego modelu. Przy użyciu standardowego oprogramowania komercyjnego proponowana formuła gwarantuje globalną optymalizację z niezawodnymi i wydajnymi wynikami. Używamy IEEE 33 i dodajemy DG do modelowania aktywnych systemów dystrybucji w celu oceny proponowanej metody. Wyniki symulacji pokazują, że proponowana metoda jest w stanie skutecznie rozwiązać problem rekonfiguracji. (Model optymalizacji wypukłej dla rekonfiguracji sieci inteligentnych sieci) Introduction Power distribution reconfiguration is an essential component of modern power system engineering because it supports the efficient and effective delivery of electrical power to end users. The technique involves changing the configuration of electrical power distribution systems by selecting open or closed switch combinations that enhance specific performance criteria while maintaining a radial network topology [1], [2]. Branch exchange procedures had been employed for handling reconfiguration [1]. The main goal of power distribution reconfiguration is to increase the efficiency and reliability of the power system. Owaifeer et al. [3] divided reconfiguration optimization into three categories: heuristics algorithms, soft computing (SC), mathematical programming, and mathematical programming. Distribution network reconfiguration can be carried out using a heuristic algorithm, as demonstrated in studies conducted by [4]-[6]. In these studies, the selection of switches is used to determine the best configuration by opening all the switches, then closing the switches one by one and calculating the objective function. As a result, the best configuration is selected based on the best objective function. This method is simple and does not require complicated computations. However, extensive computational processing is still necessary because the load flow needs to be calculated at every switching step. Soft computing techniques are widely used in power systems, with meta-heuristic optimization methods being particularly popular for network optimization [7]-[13]. One advantage of meta-heuristic optimization is that it can provide a global optimum multi-objective solution while searching for the best local solution in each iteration. However, when applied to power systems with numerous constraints that must be met, achieving global optimality is not always possible, and extensive computational time may be required. Mathematical Programming (MP) was rarely used to handle reconfiguration problems prior to the development of sophisticated solvers and high-speed processors. This is due to the fact that finishing reconfiguration optimization with MP takes more computational time than heuristic and soft computing methods. Nonetheless, MP has a substantial
... Traditionally, an SHS is deployed using a centralized architecture. In this case, a central server supervises and controls all the electricity assets that participate in the restoration process (i.e., remote-controlled switches, distributed generation (DG) units, flexible loads, among others) [3]. A centralized SHS is easy to install and maintain, but more vulnerable to singlepoint failures and cyber-attacks. ...
... service and commitment of the power supply department (Wang & Wang, 2015). At the same time, as the global energy supply is shifting toward cleanness, low carbon, high efficiency, and electrification, great advances have been made in distributed generation that involve more eco-friendly technologies, and the wide applications of these technologies have made the distribution network, originally radiated by single power sources, increasingly huge and complex (Cavalcante et al., 2015). Adapting to the development of the future network on the basis of the existing network and making the feeder of the distribution network locate quickly after tripping are pressing issues for power supply enterprises and power practitioners (Srivastava et al., 2012;Zidan & El-Saadany, 2012;Cavalcante et al., 2015;Leite & Mantovani, 2016). ...
... At the same time, as the global energy supply is shifting toward cleanness, low carbon, high efficiency, and electrification, great advances have been made in distributed generation that involve more eco-friendly technologies, and the wide applications of these technologies have made the distribution network, originally radiated by single power sources, increasingly huge and complex (Cavalcante et al., 2015). Adapting to the development of the future network on the basis of the existing network and making the feeder of the distribution network locate quickly after tripping are pressing issues for power supply enterprises and power practitioners (Srivastava et al., 2012;Zidan & El-Saadany, 2012;Cavalcante et al., 2015;Leite & Mantovani, 2016). Therefore, power supply enterprises continuously enhance the reliability of grid structure construction and power supply, and they also strive to improve the automation and intelligence level of distribution networks. ...
At present, the distribution network fault self-healing method based on deep learning in smart grid work often has problems such as low accuracy and insufficient feature extraction ability. To overcome this, the authors propose a method of fault self-healing in a distribution network based on robot patrol and deep learning in a cloud edge architecture. Firstly, the data collected by the robot fault collection system is preprocessed by using one-hot coding and normalization methods to prevent data flooding. Secondly, they propose an improved bi-directional short-term memory (BiLSTM) fault location method which combines the advantages of both BiLSTM and attention mechanism, adjusts attention weight, filters, or weakens redundant information. Finally, the I-BiLSTM network and the U-BiLSTM network are trained, respectively, and the fault section can be accurately located based on the data of each node of the robot fault collection system topology. Experimental results show that this method has achieved accuracy scores of 0.928, 0.933, 0.948, and 0.942, respectively, in four fault types, namely single-phase grounding, two-phase grounding, phase-to-phase short circuit, and three-phase short circuit, which outperform those in previous literature. The proposed method is well suited for applications in smart grid work because of its desirable fault self-healing ability.
... In [108], a two-stage technique to restore power in electrical distribution network was proposed. In the first stage, the original problem is expressed as a mixed integer linear programming problem using linearization. ...
: This study examines the conceptual features of Fault Detection, Isolation, and Restoration (FDIR) following an outage in an electric distribution system.This paper starts with a discussion of the premise for distribution automation, including its features and the different challenges associated with its implementation in a smart grid paradigm. Then, this article explores various concepts, control schemes, and approaches related to FDIR. Service restoration is one of the main strategies for such distribution automation, through which the healthy section of the power distribution network is re-energized by changing the topology of the network. In a smart grid paradigm, the presence of intelligent electronic devices can facilitate the automatic implementation of the service restoration scheme. The concepts of service restoration and various approaches are thoroughly presented in this article. A comparison is made among various significant approaches reported for distribution automation. The outcome of our literature survey and scope for future research concludes this review.
... A procedure to improve resilience includes optimizing the topological reconfiguration and solving an optimal power flow (OPF) to provide a safe and economical operation. Self-healing is the first step of resilience [2], [3], [4] and restoration is the next step [5]. Combining both instances results in a nonlinear, non-convex optimization problem containing continuous and integer variables. ...
... On the other hand, a matheuristic approach corresponds to the use of heuristic algorithms along with classical mathematical techniques [6], [17]. Matheuristics can combine "the best of both worlds" [2], [7], i.e., the computational performance of metaheuristic algorithms and the robustness and mathematical soundness of classical mathematical programming methods. Matheuristics have been explored recently to solve the OPF problem, as in [6], and the reconfiguration problem in distribution systems [7], [17]. ...
... The major optimization objectives of this problem include the minimization of load outage loss [9] and the number of switching operations required for restoration [10]. The restoration schemes are usually optimized based on mathematical programming [11], heuristic methods [12], or meta-heuristic methods [13]. ...
Aiming at the high-dimensional uncertainties of restoration process, an optimization model for distribution system restoration control is proposed considering expected restoration benefits, expected restoration costs, and security risks of the overall restoration scheme. In the proposed model, the effect of security control on restoration process is actively analyzed considering the security control costs of preventive, emergency, and correction controls. A two-layer decision support framework for distribution system restoration decision support system (DRDSS) is also designed. The upper layer of the proposed framework generates the pre-adjustment schemes of operation mode for energized power grid by load transfer and selects the optimal pre-adjustment scheme and the corresponding partitioning scheme based on the partition adjustment results of each pre-adjustment scheme. In addition, it optimizes the spatial-temporal decision-making of the inter-partition connectivity. For each partition, the lower layer of the proposed framework pre-selects the units and loads to be restored according to the pre-evaluated restoration income, generates the table of alternative restoration scheme for coping with uncertain events through simulation and deduction, and evaluates the risk and benefit of each scheme. For the uncertain events in the actual restoration process, the current restoration scheme can be adaptively switched to a sub-optimal scheme or re-optimized if necessary. Meanwhile, the proposed framework provides an information interaction interface for collaborative restoration with the related transmission system. A 123-node test system is built to evaluate the effectiveness and adaptability of the proposed model and framework.
... [IEEE] at https://doi.org/10.1109/TSG.2015.2454436], reference number [27]. ...
The distribution system's economic operation is significantly impacted by the management of distributed generation (DG) resources, energy storage (ES), and controllable loads. The paper employs a smart distribution system that incorporates dispatchable and non‐dispatchable DG resources, as well as battery storage, in addition to the demand response (DR) scheme. New modelling was performed in hourly steps to achieve the optimal unit commitment. In smart homes, appliances are prioritized and classified into four types: adjustable, interruptible, shiftable, and uncontrollable loads. Load reduction in smart homes is also considered based on load prioritization and customer participation in the DR scheme to achieve the proposed scheme's objectives. The proposed method considers costs associated with microturbines (MTs), including manufacturing, start‐up, shutdown, and pollution. Additionally, planning is conducted to purchase or sell electricity to the upstream network. The simulation is run on an IEEE 33‐bus system to demonstrate the proposed method's effectiveness. The system is assumed to be capable of operation in both island and grid‐connected modes. The results demonstrate the proposed approach's efficacy in load reduction, operation cost, and execution time.
