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Monitoring power system to assure its performance is of the highest priority. However, installment of measuring instruments at every single bus of the system is not cost-efficient. Therefore, this paper presents a method to determine the optimal location and the number of monitoring buses to study voltage sags by considering possible variables affecting the voltage sag depth. In this method, first considering the probability density functions of the variables that affect the depth of voltage sag, including type of fault, fault impedance, and so forth, a comprehensive database is formed by Monte Carlo method. A 4000-year simulation has been performed to attain a trustworthy database. Then, using this data, a probabilistic monitor reach area matrix (PMRA) is formed to consider the reliability of the effect of voltage sag on monitoring buses. Employing Pearson coefficient, the correlations between buses are determined. Finally, to determine the optimal number and location of monitoring buses, two conditions of the pre-defined probability of observability and pre-defined correlation rate between buses data must be considered. The proposed method is examined and verified on two test systems, the IEEE-14-bus system, and the 57-bus system. The simulation results are brought and discussed to validate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Parallel restoration following blackouts can reduce economic and social losses. This paper aims to develop a parallel restoration method coordinating the partitioning scheme of the blackout system and restoration strategies of subsystems. The susceptible-infected-recovered model, i.e., a virus propagation model of complex networks, is used to decide the parallel restoration strategies online. Firstly, various types of viruses are used to represent different subsystems. The probability vector of virus infection is obtained according to the importance level of each bus. Secondly, an immunization strategy is developed based on the faulted buses in the blackout situation. According to the infection rate and the immunization strategy, the virus propagation direction will be changed based on real-time system conditions. The startup characteristics of units and the charging reactive power of restoration paths are considered as constraints to embed in the virus propagation process. Finally, the partitioning scheme and the restorative actions for subsystems are determined based on the infected results of viruses. The effectiveness of the proposed method is validated by case studies on the IEEE 39-bus and the IEEE 118-bus test systems. [ABSTRACT FROM AUTHOR]

Robust look-ahead dispatch (RLAD) is essential to manage uncertainties in power systems. As its key step, the worst-case scenario identification (WCSI) problem is cast to a max-min program. This computationally intensive procedure has to be performed repeatedly, impairing the computational efficiency of RLAD. To address this issue, an efficient RLAD scheme incorporating critical region preparation in gap time is proposed. The computation burden is mostly transferred from the online decision stage to the gap time via a customized technique based on multi-parametric programming. The accuracy of computing the critical regions is validated by the test in a six-bus system, and the proposed method is shown to cut down 21% of total iterations and save computational time dramatically by the test in a practical-scale system in Northeastern China. [ABSTRACT FROM AUTHOR]

The transformation of passive distribution systems to more active ones thanks to the increased penetration of distributed energy resources, such as dispersed generators, flexible demand, distributed storage, and electric vehicles, creates the necessity of an enhanced test system for distribution systems planning and operation studies. The value of the proposed test system, is that it provides an appropriate and comprehensive benchmark for future researches concerning distribution systems. The proposed test system is developed by modifying and updating the well-known 33 bus distribution system from Baran & Wu. It comprises both forms of balanced and unbalanced three-phase power systems, including new details on the integration of distributed and renewable generation units, reactive power compensation assets, reconfiguration infrastructures and appropriate datasets of load and renewable generation profiles for different case studies. [ABSTRACT FROM AUTHOR]

The emerging multimodal active energy resource units make it necessary to introduce constant voltage amplitude buses (PV bus) in the operation of modern distribution systems. To enable the analysis of PV bus using linear power flow models, this letter proposes a relaxed PV bus model for solving power flow related problems using an indirect modeling approach. The developed PV bus model can be applied to linear power flow models in both rectangular and polar coordinates. Besides, the approximation error of the relaxed PV bus model can also be controlled and quantified. Lastly, the proposed relaxed PV bus model is validated using different test systems. According to the numerical studies, the maximum error on the PV bus approximation in all case studies is only 0.61%, and the maximum error of the supporting power at the PV buses is 6.5%. [ABSTRACT FROM AUTHOR]

Crow search optimizer is considered as the latest meta-heuristic algorithm that is influenced by crow's behavior. The proposed oppositional crow search optimizer (OCSO) is intended here, for solving the intentional islanding problem. This paper has proposed a novel two-step method by considering the most significant factors such as the constraints of line capacity, bus voltage, load priority, load controllability, problem occurred due to spacing of solutions as well as the capability of integrating the islands to produce higher intentional islands. Initially, the tree knapsack problem is considered as an intentional islanding issue and therefore the OCSO algorithm is employed in solving such shortcomings. In OCSO approach, the opposition-based generation jumping and population initialization concept are used in crow search optimizer for improving the convergence profile and computational speed. In next process, island feasibility is verified by means of conducting power flow computation and providing significant modifications. Six distributed generations containing IEEE 69-bus test system are employed in validating experimentally the efficiency of the proposed approach, and comparison was done for the obtained results with the other existing approaches. The comparative analysis is evaluated to enhance the level of reliability, particularly critical load. [ABSTRACT FROM AUTHOR]

This paper discusses an energy management system–based demand response scheduling strategy in distribution system. The proposed strategy includes customer payment minimization and network loss minimization as responsive load scheduling objectives through centralized approach. Two types of optimization strategies each based on payment minimization and network loss sensitivity are discussed in this paper. Thus, the proposed scheduling strategy can effectively resolve the optimality issue between different objectives of the distribution system scheduling under demand response penetration. The demand response scheduling strategies are simulated using standard IEEE 37 bus distribution test system through different cases of scheduling and optimization scenarios. The simulation results are presented, discussed, and compared with the base test cases without demand response penetration and without optimization strategies under demand response penetration to demonstrate the effectiveness of network loss, sensitivity consideration and optimization strategies in carrying out distribution system scheduling. In addition, sensitivity analysis is performed. The variation of distribution network performance is analyzed for various test cases and scenarios at different penetration levels. [ABSTRACT FROM AUTHOR]

In recent days, the optimal allocation of distributed generators (DGs) problem in the distribution system caught several reader's attention to improve the system efficiency, to meet the future load growth. In this article, a multiobjective approach is proposed to determine the optimal locations for DGs, optimal DGs sizes, optimal power factors of DGs in the presence of optimal network reconfiguration to maximize the maximum loadability (λmax), minimize the active power loss and maximize the loading margin factor (λv) of the system. Butterfly Optimization (BO) algorithm is implemented to optimize the desired objectives. The Ɛ‐constraint method is used for multiobjective optimization, spanning tree technique is used for checking the radiality of the system and modified repetitive power flow using radial load flow algorithm is developed for finding theλmax, λv.The proposed approach is tested on 33 bus and 69 bus radial distribution test systems. Four scenarios are considered to achieve the desired objectives and each scenario consists of two cases: optimal allocation of DGs in the initial configured network, optimal allocation of DGs in the optimal reconfigured network. Results suggest that optimal allocation of DGs in scenario 4 gives a better improvement in maximum system loadability, loading margin factor, and active power loss reduction of the system. Obtained results compared with the suitable methods and algorithms that are available in the literature. [ABSTRACT FROM AUTHOR]

Transmission system expansion leads to excessive short-circuit currents that exceed the capacity of circuit breakers. To avoid over short-circuit current; transmission system operators make various alterations in the transmission system by changing the topology of the system. The feeders can be distributed to different buses in substations through disconnecting coupling circuit breaker between buses. Having been interchanged, the transmission system may face up a lot of problems even in single outage. Therefore, the optimal positions of feeders in substations are important in order to maintain system security. However, this optimization problem has non-convex properties due to AC load flow equations and it has a multi-objective structure to provide the limitation of short-circuit current and security of N-1 contingency. The constraints are the short-circuit current, voltage and transmission line limits in the single contingency. In this paper, the Genetic Algorithm and Binary Particle Swarm Optimization methods were utilized to find a near-optimal bus layout. Algorithms coding was made with Python programming language and PSS/E program was used to obtain power flow and short-circuit data. The results of applying the methods to the IEEE 14-bus test system demonstrated the effectiveness of the methods to take overloads away and restrict short-circuit current and hold voltage in its limit. [ABSTRACT FROM AUTHOR]

In order to solve the placement problem of three kinds of feeder terminal units (FTU) in the distribution network, this paper proposes a novel mathematical model. The model considers economic cost and electricity supply reliability from the perspective of life cycle cost. The reliability algorithm in this model is established for the distribution network configured with centralized feeder automation. Different evaluation indices of reliability and the importance of several kinds of customers are also considered in this model. Aiming at the reliability evaluation in this model, this paper puts forward the reliability analysis method for the distribution network with three kinds of FTUs. In view of the difficulty to express the reliability of distribution network in a formula with decision variables, and the non-deterministic polynomial hard (NP-hard) nature of this model, a variety of intelligent algorithms are applied to solve the model. The feasibility and effectiveness of the model and methods for FTUs placement optimization problem are verified by a case study of the Roy Billinton test system (RBTS) Bus 5 system. [ABSTRACT FROM AUTHOR]

While contiguous power systems are often operated by several regional system operators, optimization models have traditionally been designed to generate optimal system-wide scheduling decisions. This paper presents an approach to reflect the existence of multiple system operators making scheduling decisions within an interconnected power system. This approach is explicitly designed to reflect each operator's limited knowledge about other regions when making scheduling decisions. Detailed analysis using a modified IEEE Reliability Test System reveals that the approach mimics real system operations by providing imperfect information to each operator about external operations and external constraints. This approach scales to a 78 000-bus model of the Eastern Interconnection, where a regression analysis provides quantitative insight into which constraints cause inefficiencies when improperly managed in a multi-operator simulation. Because the approach generates distinct regional scheduling problems, unit commitment, and economic dispatch simulations can be applied to individual regions and solved in parallel, enabling production cost simulations at a previously intractable scale. [ABSTRACT FROM AUTHOR]

In this paper is proposed a reconfiguration methodology with the presence of Distributed Generation (DG), aimed at achieving the minimum power loss, minimum number of switching operation and minimum deviation of bus voltage while satisfying all constraints using improved shuffled frog leaping algorithm (ISFLA).The performance of the proposed method is examined on 33 and 69 bus IEEE test distribution systems. The ISFLA performance is evaluated with the well-known algorithm including of harmony search algorithm (HSA), refined genetic algorithm (GRA), particle swarm optimization (PSO), differential evolutionary (DE) and conventional SFLA. Simulation results showed that the total power loss and voltage bus minimum in primary distribution network can be reduced significantly. Also the results in different scenarios are showed that the simultaneous reconfiguration and DG placement method is better in less losses and also in more minimum voltage. Moreover, the ISFLA superiority is proved in comparison with the HAS, GRA, PSO, DE, and SFLA in view of more convergence speed and accuracy and also converges in less number iteration. Also, the performance of the proposed method is favorable compared to previous studies. [ABSTRACT FROM AUTHOR]

Currently, the distribution system has been adapted to include a variety of Distributed Energy Resources (DERs). Maximum benefits can be extracted from the distribution system with high penetration of DERs by transforming it into a sustainable, isolated microgrid. The key aspects to be addressed for this transformation are the determination of the slack bus and assurance of reliable supply to the prioritized loads even during contingency. This paper explores the possibilities of transforming the existing distribution system into a sustainable isolated network by determining the slack bus and the optimal locations and capacity of Distributed Generators (DGs) in the isolated network, taking into account the contingencies due to faults in the network. A combined sensitivity index is formulated to determine the most sensitive buses for DG placement. Further, the reliability based on the loss of load in the isolated system when a fault occurs is evaluated, and the modifications required in for reliability improvement are discussed. The supremacy of the transformed isolated network with distributed generators is comprehended by comparing the results from conventional IEEE 33-bus grid connected test system and modified IEEE 33-bus isolated test system having no interconnection with the main grid. [ABSTRACT FROM AUTHOR]

This article introduces a new method for optimizing the placement of a multiple of D‐Statcoms for voltage sag mitigation in distribution systems. The D‐Statcom's placement is optimally selected not only for improving system voltage sag caused by a single fault event but also for all possible fault events in the system of interest. Therefore, D‐Statcom's placement is optimized in a problem of optimization where the objective function is to minimize the system voltage sag index—SARFIx. D‐Statcom's effectiveness for voltage sag mitigation is modeled based on the method of Thevenin's superimposition for the problem of short‐circuit calculation in distribution systems. This article considers the case of using a multiple of D‐Statcoms with a proposed voltage compensating principle that can be practical for large‐size distribution systems. This article uses the IEEE 33‐buses distribution feeder as the test system for voltage sag simulation and influential parameters to the outcomes of the problem of optimization are considered and discussed. © 2019 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [ABSTRACT FROM AUTHOR]

• A two-stage, efficient solution methodology for AC TNEP is proposed. • N-1 security constrained static and dynamic AC TNEP problems are solved. • Network voltage stability constraints in the form of L-index is considered. • Above 85% reduction in computational burden is obtained. • Can be an attractive alternative to conventional methods of solving AC TNEP. Modern transmission network expansion planning (TNEP) is carried out with AC network model, which is able to handle voltage and voltage stability constraints. However, such a model requires optimization with iterative AC power flow model, which is computationally so demanding that most of the researchers have ignored the vital (N-1) security constraints. Therefore, the objective of this research work is to develop an efficient, two-stage optimization methodology for security constrained AC TNEP. As single-stage, rigorous methods cannot be considered for solving this problem for even a moderately sized system due to extreme computational burden involved, the proposed two-stage methodology provides an attractive alternative. By this methodology, in the first stage, a DC expansion planning problem is solved which provides an initial guess as well as some very intelligent strategies to reduce the number of power flow solutions required for the second stage of AC transmission and reactive expansion planning. A modified artificial bee colony (MABC) algorithm is used to solve the resulting optimization problem. Static AC TNEP results for Garver 6 bus, IEEE 24 bus, IEEE 118 bus and IEEE 300 bus test systems have been obtained with the proposed approach. Wherever possible, the results are compared with that obtained by the rigorous method and with similar results reported in literature, to demonstrate the substantial benefits of the proposed method. Also, multi-stage dynamic AC TNEP for the Garver 6 bus system is solved to show the applicability of the methodology to such problems. [ABSTRACT FROM AUTHOR]

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This paper presents a day-ahead (DA) multi-objective based joint energy and reactive power dispatch in the deregulated electricity markets. The traditional social welfare in the centralized electricity markets comprises of customers benefit function and the cost function of active power generation. In this paper, the traditional social welfare is modified to incorporate the cost of both active and reactive power generation. Here, the voltage dependent load modeling is used. This paper brings out the unsuitability of traditional single objective functions, e.g., social welfare maximization (SWM), loss minimization (LM) due to the reduction of amount of load served. Therefore, a multi-objective based optimization is required. This paper proposes four objectives, i.e., SWM, load served maximization (LSM), LM and voltage stability enhancement index (VSEI); and these objectives can be combined as per the operating condition. The simulation studies are performed on IEEE 30 bus test system by considering the both traditional constant load modeling and the proposed voltage dependent load modeling. [ABSTRACT FROM AUTHOR]

• An innovative three-stage hybrid framework is developed for RODNP problem. • Multi-objective resource allocation is done to boost normal and emergency conditions. • The most conservative scenario is used to assess the potential hurricane's impact. • A risk-averse hardening re-plan is done in the third stage to improve system's resilience. • Different planning and operational measures are adopted for resilience enhancement. This article tackles the resilience-oriented distribution network planning (RODNP) problem utilizing a novel three-stage hybrid framework. The decision-making on the line hardening and DG placement is carried out in the first stage. In the second stage, emergency and normal operation optimization are conducted. The worst-case scenario is considered for evaluating the effect of a potential hurricane in post-event emergency operation conditions. In addition, a scenario-based stochastic approach is used to assess normal operation conditions. Finally, a risk-averse hardening re-plan is implemented in the third stage using the information gap decision theory (IGDT) notion as an effective non-deterministic optimization strategy under severe uncertainty. At this stage, distribution system planner (DSP) tries to develop a more resilient distribution network scheme against the most powerful hurricane possible while taking into account a predetermined parameter known as the resilience budget. The efficacy of the proposed approach is validated by conducting several case studies on the IEEE-33 bus test system. The results reveal that the proposed strategy may dramatically reduce the cost of both normal and emergency operations simultaneously. [ABSTRACT FROM AUTHOR]

• A weak bus identification index is derived to identify the critical bus when power flow is unsolvable. • An extended system considering new bus type is proposed to improve power flow solvability. • A weak bus identification and bus type switching based framework is established to provide adjustment measures efficiently and automatically. • The method could provide a suitable solution automatically for unsolvable power flow in a variety of scenarios, retains stable convergence and has potential in large-scale power grids. The power flow solvability is greatly challenged by the growing pressure on power grid induced by the rapid development of economy. The approaches of restoring power flow solvability should be profoundly studied. Most of adopted power flow adjustment methods are based on manual interference which require extensive human resources with inefficiency. Thus, a power flow adjustment strategy based on a weak bus identification and a new bus type conversion is proposed. A weak bus identification index is defined and expressed when power flow has no solution. We propose a novel bus type and a concept of the power shortage to restore power flow solvability. The generator action set is determined by calculating the left eigenvector of the Jacobian matrix. At last, we establish a linear programming model to determine the generator output adjustment. Numerical results are obtained in 3 test systems and an actual system in China. Compared with other methods, the proposed method is verified to have a higher success rate of restoring power flow solvability and has robustness in various scenarios. [ABSTRACT FROM AUTHOR]

• The model requires only pre-fault steady state information and the impact data at the fault occurrence period. • The method can provide multivariate STVS indices of each bus, and identify the instability patterns. • The heterogeneous graph attention network HGAT combine the zoning characteristics with the influence of bus type. • The improved multi-tasking learning (MTL) algorithm is proposed. • Excellent accuracy and robustness to topological changes. Compared with time-domain simulation (TDS), data-driven models show great advantage in time consumption of the power system security analysis. This paper proposes a novel graph neural network (GNN) based model for the short-term voltage stability (STVS) assessment. Based on mainly the steady-state information as the inputs, the model can provide multivariate stability indices for each bus and adapt to minor topological changes. Both the fast voltage collapses (FVC) and fault-induced delayed voltage recovery (FIDVR) events can be identified. A modified multi-task learning (MTL) process improves the multi-index evaluation performance of the model. As the kernel of the model, a heterogeneous graph attention deep network (HGAT) with various types of nodes works to aggregate the local information and generate new features. Then several micro-detectors scan over the network to provide the STVS indices of each bus with only the feature vector of one node as input for the prediction. Comparisons on the test system show that the proposed method can provide fine-grained STVS evaluation and show good robustness in the scenarios of different dynamic load distribution and network topology changes. [ABSTRACT FROM AUTHOR]

• Bus splitting is a powerful tool in relieving transmission network congestion. • Line switching and bus splitting are employed to minimize the operation cost. • AC feasibility and compliance with N-1 contingency requirements are considered. • A pre-screening step is proposed to select candidate substations for reconfiguration. Optimal transmission line switching and/or bus splitting is shown to contribute in relieving congestion and reducing the operation cost by rerouting power flows throughout the network. Although bus splitting may be as powerful as line switching in congestion mitigation and is typically considered a smaller disturbance compared with line switching, it has received less attention in the literature in part due to the more complicated node-breaker modeling requirement. In this paper, an optimal transmission line switching and bus splitting heuristic is presented to minimize the operation cost while respecting AC and N-1 contingency constraints. We present a two-level solution method where switching decisions are made in the upper level problem formulated as a mixed integer second order cone programming master problem, while the resulting network topology is checked against AC and N-1 contingency constraints in lower level subproblems. Line switching and bus splitting are modeled as switching actions assuming double-bus double-breaker substation arrangements where all elements at a substation, including generators, loads, lines and shunt elements, are given switches to connect to either of the busbars if the respective substation is split. We also introduce additional constraints to model a breaker-and-a-half substation scheme. Furthermore, a pre-screening step is presented to limit the search space of the problem, thus accelerating the solution process. We demonstrate the application of the proposed method on IEEE standard test systems. [ABSTRACT FROM AUTHOR]

• End-users' investments in DERs is introduced to the distribution network planning. • A planning model is presented that considers neighborhood energy trading schemes. • The model helps to reduce the network stress by optimum design of network charge. The widespread adoption of small-scale distributed energy resources (DERs) amongst energy users has drastically changed the operation of distribution networks. To date, there has not been a consolidated model to incorporate the investment decisions of the end-users in the distribution network planning. The contribution of this paper is a distribution network planning model for the utility which considers the neighborhood energy trading (NET) as a platform for end-users to directly exchange energy between them. The proposed mixed-integer second-order cone programming (MISOCP) problem provides the optimal decisions for line and transformer upgrades, as well as for photovoltaic (PV) and battery in end-users' premises. Moreover, it indicates a fair allocation of network charges among the participants to NET schemes. The simulation results on the IEEE-33 bus test system confirm the effectiveness of the proposed model in lowering the total cost of the planning and the operation. This platform can be used by government-owned utilities as a guide to avoid sunk investments while motivating the increased installation of renewable distributed generation and storage units by end-users. [ABSTRACT FROM AUTHOR]

In this paper, the idea of solving algebraic equations (AEs) through the fixed-point iterative method (FPIM) is generalized for the differential algebraic equations (DAEs) of power systems in order to analyze transient stability problems, which are particularly relevant when the number of DAEs in high-order models increase. In the loop form, reducing the number of variables by explicitly solving AEs is no longer required. It also allows for adding or removing the equations in order to easily analyze the effect of equations in the system's response. Furthermore, through the loop solving (LS) mechanism, the simplification assumption about power consumption in the PQ buses to fixed impedances is not necessary and the loads can be assumed with each arbitrary model. The LS mechanism is the first innovation provided hereby which facilitates the programming of high-order models and increases the accuracy of the system's response. On the other hand, because consistent and redundant variables are in place, solving DAEs in the loop form requires an iterative method with strong a convergence property that provides a convergent solution to the load flow (LF) AEs, and then a convergence solution for the DEs of the machines. This can be developed by extending the FPIM to the traditional Gauss-Siedel (GS) method, called modified GS (MGS), which is the second innovation herein. It can converge the solution of LF equations to the equilibrium point despite the numerical anomalies. Moreover, in order for the same performance as that of the MGS to be achieved, the Newton-Raphson (NR) method is first developed by a new formulation to full complex form, called complex based NR (CNR), which is the third innovation addressed hereby, and then applied with the same technique as that of the MGS to modified NR (MNR). The CNR increases the speed and simplicity of the LF computations and does not require decomposition of AE for both real and imaginary components; therefore, it simplifies the simulation training problems and reduces the computational time for large system dimensions. The proposed method is implemented in Simulink/MATLAB, tested and validated for the Western System Coordinated Council (WSCC) IEEE 9-bus system and compared with the results obtained by power system simulators, such as PowerWorld (PW) and SymPowerSystems (SPSs), and previous works published in the literature. Then, the experience gained from the first test is also applied to the IEEE 57-bus test system as a large scale system. The simulation results show the ability of the proposed method to represent the system's response for severe transient conditions, with better results than those achieved by previous methods. The new results are obtained from the effect of the network's transient on mechanical response of some synchronous machines. Also, the importance of removing damping coils in the system's transient response and the transition of response divergence during the severe fault with the method proposed hereby can be observed. [ABSTRACT FROM AUTHOR]

• A new dynamic-adaptive load shedding technique is proposed. • Load buses are ranked and feeders are dynamically selected for load shedding. • Effectiveness of the proposed methodology is demonstrated via simulations. Frequency stability is one of the major concerns for secured operation of a power system. A severe disturbance causes rapid frequency decline, which may instigate power system blackout in an extreme case. In emergency situations, load shedding is applied to arrest frequency excursion. Therefore, a load shedding scheme needs to be sufficiently adaptive to tackle sudden generation loss. Note that conventional load shedding schemes may fail to provide satisfactory frequency response in certain cases. To address this challenge, a new dynamic-adaptive load shedding mechanism is proposed in this paper. The proposed methodology considers the actual contingency size, frequency sensitivity due to load damping, frequency response and ranking of load buses according to voltage stability index. The method ensures that the actual load cut is sufficiently close to the required load shedding to keep system frequency within the given acceptable limit. To do so, it ranks the load buses within a zone and dynamically selects appropriate feeders for load shedding. It also proportionally applies higher amount of load shedding to relatively weaker buses for taking care of the voltage stability. To examine the performance of the proposed scheme, it is applied to the IEEE 39 bus test system that is divided into six zones. It is found from simulations that for 600 MW, 700 MW and 900 MW generation loss events in zone-3, the required amounts of load shedding are 430 MW, 531 MW and 730 MW respectively to keep system frequency above 49.1 Hz. However, these quantities increase to 450 MW, 550 MW and 749 MW respectively to retain system frequency above 49.2 Hz. Furthermore, the impact of 400 MW generation loss in zone-1 is explored. It is found that after shedding additional loads in zone-1 and zone-2, the risk of tie line overloading is mitigated that eventually assures tie line security. In addition, performances of the proposed algorithm are compared to that of an adaptive technique and a semi-adaptive technique. It is noticed that the proposed methodology provides better results than the existing methods. Therefore, it can be articulated that the developed scheme ensures the correct amount of load shedding to maintain satisfactory frequency response and voltage stability. [ABSTRACT FROM AUTHOR]

• Method is independent of initial guess of allowable transaction for ATC calculation. • Accurate computation of ATC, even under stressed system condition. • Fast computation of ATC in comparison with NRPF based method. • Proposed method is tested and validated on IEEE 30, 118 and 300-bus test system. • Tested for bilateral and multilateral transactions at different operating points. Available Transfer Capability (ATC) is the additional power that can be securely and reliably transacted over and above the already committed transactions in a power network. In the electricity market, where every player (power producer and consumer) tries to earn higher profit, quick and accurate assessment of ATC of the power network is a prime concern. Holomorphic Embedding (HE) is a novel and non-iterative way of solving the Power Flow (PF) equations, which guarantees to find the operational High Voltage (HV) solution, in case it exists. Analytic continuation extends the domain of convergence of non-analytic functions to have voltage solutions. This paper, thus, proposes an extremely efficient and accurate approach for evaluation of ATC using the Holomorphic Embedded PF (HEPF) considering the intact system condition and N - 1 contingency situations. This approach is successfully tested on IEEE 30 bus, IEEE 118 bus, and IEEE 300 bus systems for various bilateral and multilateral transactions. The results, thus, obtained prove the efficacy of the proposed approach in comparison with those obtained from the repeated Newton-Raphson PF (NRPF), Fast Decoupled PF (FDPF) and Continuation PF (CPF) based methods. [ABSTRACT FROM AUTHOR]

• We propose a new method to model the effect of series impedance changes on the bus impedance matrix. • We verify the method by showing its relationship with Sherman–Morisson identity and numerical simulations to verify accuracy. • Tests with systems of different sizes show that our method is accurate and faster than others making it more suitable for online applications. This paper derives new expressions for updating Bus Impedance Matrix ( Z bus) elements to account for the modification of the series impedance of a line connected between two existing buses. Such kind of modification is not accounted for in Brown's method and requires building Z bus all over again which is time-consuming, and redundant. Afterwards, we show that a modified form of Sherman–Morisson identity is the generalization of our work. We test our modeling approach with seven systems of different sizes. Results show very minor errors between the predictions of our techniques and Brown's method. Further, speed comparison shows that our method substantially improves calculation speed from a few minutes with Brown and Bus Admittance Matrix ( Y bus) inversion methods to seconds (1.35 s and 2.9 s for 2383 and 3120 bus systems, respectively) making it more suitable for online applications. [ABSTRACT FROM AUTHOR]