Loading Margin Research Articles

Fiber and interface failure characterization of glass fiber reinforced polymer for composite insulators after liquid permeation

Composite insulators are of great significance in power systems due to their excellent electrical and mechanical properties. The mechanical load of insulator is borne by the rod made of glass fiber reinforced polymer (GFRP). Despite the considerable load margin, abnormal fractures have been reported continuously during actual operation. Among them, the evolution of decay-like fracture has still not been illustrated, which is why no effective preventive measures can be proposed. Liquid permeation, especially nitric acid, is supposed to play a vital role in the fracture. Thus, in this paper, the characteristics of glass fiber, fiber-epoxy interface, and GFRP-sheath interface immersed in different liquids are investigated. Based on the results, the significant role of boron element in the stress corrosion of glass fiber is illustrated. Therefore, the application of glass fiber without B is rather necessary. Also, the failure of fiber-epoxy interface by acid is identified by broadband dielectric response, which forms the channels of current concentration. It is key for the development of decay-fracture. Moreover, the degradation of GFRP-sheath interface after immersion is recognized by the measurement of interfacial resistivity. Consequently, coupling agents with good resistance to acid should be adopted, in order to avoid further liquid permeation into the GFRP rod.

Technique for Reactive Loss Reduction and Loading Margin Enhancement Using the Curves of Losses versus Voltage Magnitude

This paper presents an alternative methodology to obtain the precise amount of shunt reactive power compensation in order to simultaneously reduce the total reactive power losses, improve the voltage profile and increase the loading margin of power systems. The amount of shunt reactive power compensation to be allocated is determined based on the curve of the total reactive power losses versus the voltage magnitude of a chosen bus. The best places for shunt reactive compensation are defined by the load bus participation factors of the critical mode provided by the static modal analysis. Simulation results employing shunt capacitors obtained with the new approach for the IEEE test systems (14, 57 and 300 buses) show that the procedure leads to a reduction in total reactive and active power losses and simultaneously improves the voltage profile and loading margin.

Optimal EV scheduling and voltage security via an online bi-layer steady-state assessment method considering uncertainties

Steady-state voltage security region (SVSR) is an important criterion that can intuitively and effectively evaluate the power system's operation security and overall safety margin. However, there is no literature on its application to electric vehicle (EV) proliferation. Since EV introduces dynamism and uncertainties to the grid, most existing indices cannot assess the grid accurately. Given this, we propose a load margin index (LMI) based on SVSR considering uncertainties. This is used to assess the impact of EV proliferation via a bi-layer optimal EV scheduling model. The upper layer of the model solves a dispatching plan for EV aggregators (EVA) by maximizing the LMI and minimizing the deviation between the upper and lower layer power schedules. The lower layer models each EV's charging/discharging strategy by minimizing the EV's operating cost, the EV user's target residual energy, and the deviation between the lower and upper layer schedules. We also employ a real-time scheduling plan to further adjust the day-ahead scheduling due to forecast errors. A case study based on the IEEE-33 node distribution network verifies the practicability and effectiveness of the proposed method.

Probabilistic load margin assessment considering forecast error of wind power generation

The increasing integration of wind power in power systems necessitates the probabilistic assessment of various uncertain factors. In operational planning, modeling short-term scale uncertainties, i.e., wind power forecast errors, plays an important role. In this paper, according to the different forecast values, the corresponding probability distributions of wind power forecast errors are developed using a data-driven manner. Then, the polynomial chaos expansion surrogate is developed to facilitate the probabilistic load margin assessment considering wind power forecast errors. The effectiveness of the forecast error model is verified using the historical data of realistic wind power plants. The results show that the probability distributions of forecast errors vary with the level of forecast values. Moreover, the performance of the polynomial chaos expansion surrogate in estimating probabilistic load margin is validated in the IEEE 30-bus system. The results demonstrate that the versatile forecast error distributions significantly impact the characteristics of load margin. Moreover, the polynomial chaos expansion surrogate can accelerate the load margin assessment compared to the Monter Carlo simulation while retaining the same accuracy.

Fostering restoration and power delivery efficiency by distributed generators and line switches in electricity distribution network

ABSTRACT The distribution of power is being faced with challenges during and after extreme weather events. This contingent might cause a partial or full power blackout in the distribution territory. Hence, the restoration of the service is one of the key concerns of the utilities. A strategy is adopted to felicitate the power restoration process by the deployment of distributed generators (DGs) and line switches. A fuzzy-based system model is proposed to allocate line switches considering the impact of wind-driven extreme weather and the fault frequency character of the lines. The study further recommends an arrangement of dispatchable DGs in the sections of the distribution grid. A particle swarm optimization-based model is proposed for suitable capacity and location assessment of the DGs to foster the restoration of supply avoiding voltage and frequency disturbances in the developed sections of the grid. The results are further verified with the application of the grasshopper optimization algorithm on the multipurpose composite objective function. The proposed DG allocation approach escalates the network power loss reduction by 95.10%, improvement in average voltage stability level by 6.46%, and loadability margin enhancement by 37.37% when the DGs are operated in grid-connected mode. Moreover, power supply reliability is restored with successive employment of DG units. The proposed approach has been tested on an Indian 28-bus power distribution network. The outcome of the proposed approach is compared with existing DG allocation methods. The experiment confirms the credential of the proposed approach with better value addition in multiple objectives.

Optimal Integration of Hybrid Energy Systems: A Security-Constrained Network Topology Reconfiguration

The integration of distributed energy resources, such as wind farms (WFs) and energy storage systems (ESSs), into distribution networks can lower the economic cost of power generation. However, it is essential to consider operational constraints, including loading margin, which ensures the security line contingency. This study aims to develop a comprehensive hourly distribution network reconfiguration (HDNR) model to minimize the economic cost for the power generation company. The model considers the optimal allocation of WFs and ESSs in terms of capacity and location, as well as the hourly status of the distribution network switches, based on security constraints. The proposed model is applied to an IEEE 33-bus distribution test system, and the capacities and locations of WFs and ESSs are determined. The impacts of security constraints on the optimal capacities and locations of WFs and ESSs, and the hourly configuration of the distribution network, are analyzed based on two case studies. In Case Study I, the model is solved with HDNR conditions, while Case Study II is solved without these restrictions, for comparison purposes. The results show that the optimal allocation of WFs and ESSs is affected by security constraints when HDNR is considered and highlight the crucial role of security constraints under contingency conditions, such as line outages. In the test system, three WFs and two ESSs are optimally allocated, with changes in capacity and location as the loading margin varies.

Optimal integration and coordination of distributed generation and shunt compensators using improved African vultures optimizer

This article aims to improve the performance of radial distribution systems (RDSs) by accurately solving the optimal energy management of the active powers of distributed generation units based on renewable energy and the reactive powers of shunt compensator-based flexible AC transmission system technology. An adaptive African vultures optimizer (AAVO) is proposed and applied to optimize individually and simultaneously various objective functions, including the minimization of total power loss, minimization of total voltage deviation and maximization of the loading margin. The efficacy of the proposed AAVO method is validated on three RDSs, the 33-bus, the 85-bus and the large RDS with 141-bus, under normal conditions and considering uncertainties of loads. Compared to many other techniques, the results clearly demonstrate the robustness and competitiveness of the proposed new variant in solving the power management optimization of a large-scale RDS.

Bus-bar splitting for enhancing voltage stability under contingencies

As one of the network topology optimization ways, bus-bar splitting has been applied for various purposes. In this paper, the performance of bus-bar splitting on a look-ahead (i.e., short-term, say 30 min) power system (i.e., pre-splitting base case) with contingencies is evaluated. The proposed problem aims to find an ‘optimal’ bus-bar splitting scheme that can maximize the load margin of a look-ahead base case and ensure the load margin of each contingency case with a desirable level. Due to the complexity and nonlinear nature of the proposed problem, it is very difficult to be solved with the available solvers, and a large number of contingencies (including N−1 and N−k contingencies) and bus-bar splitting schemes need to be examined. A four-stage methodology is presented for online computing efficiency. Moreover, the group properties of contingencies are explored and illustrated in this paper, which is utilized to reduce the number of nonlinear constraints from a large number of contingencies and relieve the computational burden. The other advantage of the proposed methodology is that it can derive multiple effective solutions from which the operators can choose one. The effectiveness of the proposed methodology is demonstrated on the IEEE 118-bus and 1648-bus power systems with promising results.

Calculating multiple loadability points in the power flow solution space

Calculating loadability margins is indispensable for maintaining secure and stable operations of electric power grids. Loadability margins closely resemble boundedness placed by the Power-Flow (PF) equations solution space. Estimating these limits is a computationally demanding task linked to the non-convex structure of the PF solution space, technological constraints, and intricate grid topology. Furthermore, multiple loadability points exist within the PF solutions space due to the non-convex topology, representing either a structural change in the number of equilibria or the disappearance of all system equilibria. To address the problem of accurately estimating loadability margins, we present a computationally robust two-stage algorithmic framework that guarantees to identify all isolated loadability points within the PF solution space for a given set of parameters. Numerical results from different test cases validate the proposed algorithmic framework computational performance and also illustrate the convoluted structure of the PF solution space with disjoint sections.

A Joint Optimization Model for Transmission Capacity and Wind Power Investment Considering System Security

Due to continuous growth in electric demand and increasing connection of renewable energy, the power systems are being operated with smaller stability margins. Therefore, a sufficient loading margin is essential to maintain the system secure and ensure voltage stability. To this end, this paper studies the joint optimization of transmission capacity and wind power investment problem, the unique feature of which is incorporating voltage stability margin (VSM) in the planning model. A bi-level model has been formulated whose upper level minimizes the total investment and operation cost minus the weighted VSM. The lower level evaluates the VSM given the optimal expansion plan from the upper level. In addition, the stochastic nature of wind power and load can impact voltage stability. Thus, uncertainties related to intermittent wind generation and demand must be modeled. We use an approximated linear representation to model the AC power system at both levels of the problem. The duality theory (primal-dual formulation) is utilized to transform bi-level programming into single-level mathematical programming. The validity of the constructed methodology is demonstrated on the IEEE 24-bus RTS, which indicates the efficacy and feasibility of the presented model.

On the accuracy of power flow and load margin calculation caused by incorrect logical PV/PQ switching: Analytics and improved methods

Power Flow (PF) and Continuation Power Flow (CPF) are key tools for power system static calculation and analysis. This paper shows that the widely used logical PV/PQ switching method can lead to calculating non-physical power flow solutions and incorrect load margin calculations. From a computational viewpoint, several small and large numerical examples are presented to show the non-physical power flow solution and inaccurate load margin calculation made by the outer loop PF method. The existence of a non-physical power flow solution caused by logical PV/PQ switching and its impact on incorrect load margin calculation will be demonstrated. To address these issues, two smooth functions to approximate the generator Q-V curve and an active-set scheme will be presented. The Type-I smooth model is suitable for calculating physically feasible power flow solution, in addition it will be shown to contribute to faster convergence than the logical PV/PQ switching methods. The type-II smooth model is suitable for continuation power flow calculation for accurate load margin and speed improvement. A smooth-model-based active-set-assisted power flow method is then developed and its effectiveness in converging to the feasible (physical) power flow solution and the correct calculation of load margins will be shown. Numerical studies on several test systems were conducted to demonstrate the effectiveness of the proposed method in computing physical power flow solutions and achieving faster speed. For example, the proposed method for 70,000-bus PF computation is 1.7 times faster than that of the inner loop-based method and for the 25,000-bus CPF computation is about 3 times faster than that of the outer loop-based method.

Fast contingency screening for voltage stability analysis considering both SNBs and SIBs

Polynomial extrapolation usually leads to crude approximations of the so-called nose curves due to the nonlinear nature of power system operational limits. In particular, these polynomial approximations fail to obtain estimates of the voltage stability margin when the system is subject to structure-induced bifurcations. This paper proposes smoothing out power flow equations to deal with structure-induced bifurcations and verifies the validity of a quadratic approximation of a smooth nose curve in estimating load margin for contingency screening and ranking in voltage stability analysis. Tests of the proposed method in large power systems revealed that an appropriate smooth power flow model can indeed result in better estimates of the exact contingency ranking as compared to the estimates obtained with the original power flow equations. • A smooth formulation of the power flow equations can improve the estimation of VSM. • Both accuracy and speed can be controlled by means of a scalar parameter. • Smoother equations are faster to solve and produce a better contingency ranking.

Enhancement of Voltage Stability by Optimal Placement of Shunt Compensation using Bus Voltage Stability Indices and Reactive Power Margin

Voltage stability problem has caused several blackouts in many countries in recent years. Impending voltage instability has been a significant threat to modern power system's security and reliability. Moreover, the operation and planning of large interconnected power systems is becoming increasingly complex as power demand rises, posing a security risk to the grid. Appropriate efforts to improve power system security and increase voltage stability margin should be planned to keep the system secure. This work investigates the voltage stability of a power system with and without a shunt capacitor. The bus voltage stability index, L index, is used to measure the distance of the power system to its stability limit in order to assign the shunt capacitor. The L-index for a particular load state is computed for all load buses, and the greatest L-index indicates the system's approach to voltage collapse. The system's load ability margin is being traced utilizing a static voltage stability evaluation approach, i.e., PV and QV curve analysis. The minimal power loss approach is used to calculate the optimal capacitor size. The effect of shunt compensation was simulated, and the results with and without compensation were compared. The IEEE-9 bus system was employed in this work, and the system was simulated using MATLAB and Power World Simulator. The result demonstrates that the shunt capacitor enhances voltage stability by injecting the appropriate reactive power.

Artificial Neural Networks: Multilayer Perceptron and Radial Basis to Obtain Post-Contingency Loading Margin in Electrical Power Systems

This paper presents the ANN (Artificial Neural Networks) approach to obtaining complete P-V curves of electrical power systems subjected to contingency. Two networks were presented: the MLP (multilayer perceptron) and the RBF (radial basis function) networks. The differential of our methodology consisted in the speed of obtaining all the P-V curves of the system. The great advantage of using ANN models is that they can capture the nonlinear characteristics of the studied system to avoid iterative procedures. The applicability and effectiveness of the proposed methodology have been investigated on IEEE test systems (14 buses) and compared with the continuation power flow, which obtains the post-contingency loading margin starting from the base case solution. From the results, the ANN performed well, with a mean squared error (MSE) in training below the specified value. The network was able to estimate 98.4% of the voltage magnitude values within the established range, with residues around 10−4 and a percentage of success between the desired and obtained output of approximately 98%, with better result for the RBF (radial basis function) network compared to MLP (multilayer perceptron).

Scenario-based line switching for enhancing static voltage stability with uncertainty of renewables and loads

The fast-growing renewables, such as wind power and photovoltaic, introduce a large number of uncertainties into the power grid. The uncertainty of renewables, coupled with that of load, increases the complexity of the analysis of static voltage stability of power systems. In this paper, the nonlinear impact of the uncertainties from both renewables and loads on static voltage stability (limited by two types of typical bifurcations, i.e., saddle-node bifurcation and structure-induced bifurcation) is investigated and illustrated. To model the uncertainties, a scenario-based scenario construction method is presented to obtain the representative scenarios tailored for the static voltage stability problem which can avoid the mis-elimination of the extreme scenarios. Then, a stochastic line switching problem is formulated to maximize the load margin to the static voltage stability of the look-ahead power system. To fast identify the line solutions, a three-stage methodology, including a scenario construction stage, the identification stage, and the evaluation stage, is proposed to balance the speed and accuracy. Finally, the computational results based on the IEEE 118-bus power system, 1648-bus power system, and 3120-bus power system demonstrate the efficiency of the proposed methodology.

Static Voltage Stability Assessment Using a Random UnderSampling Bagging BP Method

The increase in demand and generator reaching reactive power limits may operate the power system in stressed conditions leading to voltage instability. Thus, the voltage stability assessment is essential for estimating the loadability margin of the power system. The grid operators urgently need a voltage stability assessment (VSA) method with high accuracy, fast response speed, and good scalability. The static VSA problem is defined as a regression problem. Moreover, an artificial neural network is constructed for online assessment of the regression problem. Firstly, the training sample set is obtained through scene simulation, power flow calculation, and local voltage stability index calculation; then, the class imbalance problem of the training samples is solved by the random under-sampling bagging (RUSBagging) method. Then, the mapping relationship between each feature and voltage stability is obtained by an artificial neural network. Finally, taking the modified IEEE39 node system as an example, by setting up four groups of methods for comparison, it is verified that the proposed method has a relatively ideal modeling speed and high accuracy, and can meet the requirements of power system voltage stability assessment.

Impact of Electric Vehicles on Energy Efficiency with Energy Boosters in Coordination for Sustainable Energy in Smart Cities

The use of electric vehicles (EVs) has recently increased in a smart city environment. With this, the optimal location of the charging station is a great challenge and, hence, the energy efficiency performance (EEP) of an electrical system is important. Ideally, the EEP is realized through passive energy boosters (PEBs) and active energy boosters (AEBs). PEBs require no external resources, and EEP is achieved through altering the network topology and loading patterns, whereas, in AEBs, integrating external energy resources is a must. The EEP has also become dynamic with the integration of an energy storage system (ESS) in a deregulated environment. Customer energy requirement varies daily, weekly, and seasonally. In this scenario, the frequent change in network topology requires modifying the size and location of AEBs. It alters the customers’ voltage profile, loadability margin, and supply reliability when the EV works differently as a load or source. Therefore, a comprehensive EEP analysis with different probabilistic loading patterns, including ESS, must be performed at the planning stage. This work uses a harmony search algorithm to evaluate EEP for AEBs and PEBs, in coordination, when ESS works as a load or source, at four locations, for customers’ and utilities’ benefits.

Optimal WTGUs Placement for Performance Improvement in Electrical Distribution System Using Improved TLBO

The optimal location and size for Distributed Generation (DG) to get maximum advantages and improve the performance of electrical distribution systems (EDS) is a difficult challenge to solve. With EDS performance indices, this research offers a constrained generalized multi-objective performance index (MOPI) objective function. Improved Teaching Learning Based Optimization (ITLBO) is used to solve the proposed objective function by removing the convergence issue of basic Teaching Learning Based Optimization (TLBO). By optimizing the MOPI, the Wind Turbine Generation Unit (WTGU) is examined for single and multiple DG placement and sizing in EDS performance improvement. The ideal approach reduces the burden of EDS consumer loss allocation by minimizing power losses, improving the consumer voltage profile and voltage stability, increasing the line loadability margin (LLM), and increasing the line loadability margin (LLM). The performance test was carried out on a 33-node EDS and used MATLAB software to demonstrate the efficacy of optimal solution.

Pareto optimality for FACTS devices placement considering demand variations

The placement of flexible AC transmission system (FACTS) devices in modern power systems requires analytical tools that enable the detailed modelling of demand. In this regard, the different methods found in the literature that have been proposed for demand modelling do not consider demand patterns. In this paper, a methodology for FACTS device placement considering demand variations is proposed. The mean relative improvement of different performance indices is used to evaluate the candidate solutions considering several demand scenarios. Pareto optimality is used for decision making. A one-year test, comprising 8760 demand scenarios, was carried out. The results concur with those in the published literature, and the methodology is shown to be successful in accounting for demand variations. Additionally, two tests were used to evaluate the worst case scenario approach by analysing the peak demand and least loading margin scenarios. It was found that, when demand scenarios with variable load share are used, the peak demand scenario may not coincide with the least loading margin scenario. The results show significant discrepancies between the mean annual and the worst case scenario approach, whether this is the peak demand or the least loading margin scenario.

Investigation on the stability and anti-eccentric load margin of a novel structure bearing lubricated by low viscosity medium

Investigation on the stability and anti-eccentric load margin of a novel structure bearing lubricated by low viscosity medium