Load Flow Research Articles

High-performance computing for static security assessment of large power systems

Contingency analysis (CA) is one of the essential tools for the optimal design and security assessment of a reliable power system. However, its computational requirements rise with the growth of distributed generations in the interconnected power system. As CA is a complex and computationally intensive problem, it requires a fast and accurate calculation to ensure the secure operation. Therefore, efficient mathematical modelling and parallel programming are key to efficient static security analysis. This paper proposes a parallel algorithm for static CA that uses both central processing units (CPUs) and graphical processing units (GPUs). To enhance the accuracy, AC load flow is used, and parallel computation of load flow is done simultaneously, with efficient screening and ranking of the critical contingencies. We perform extensive experiments to evaluate the efficacy of the proposed algorithm. As a result, we establish that the proposed parallel algorithm with high-performance computing (HPC) computing is much faster than the traditional algorithms. Furthermore, the HPC experiments were conducted using the national supercomputing facility, which demonstrates the proposed algorithm in the context of N−1 and N−2 static CA with immense power systems, such as the Indian northern regional power grid (NRPG) 246-bus and the polish 2383-bus networks.

Compensation Admittance Load Flow: A Computational Tool for the Sustainability of the Electrical Grid

Compensation Admittance Load Flow (CALF) is a power flow analysis method that was developed to enhance the sustainability of the power grid. This method has been widely used in power system planning and operation, as it provides an accurate representation of the power system and its behavior under different operating conditions. By providing a more accurate representation of the power system, it can help identify potential problems and improve the overall performance of the grid. This paper proposes a new approach to the load flow (LF) problem by introducing a linear and iterative method of solving LF equations. The aim is to obtain fast results for calculating nodal voltages while maintaining high accuracy. The proposed CALF method is fast and accurate and is suitable for the iterative calculations required by large energy utilities to solve the problem of quantifying the maximum grid acceptance capacity of new energy from renewable sources and new loads, known as hosting capacity (HC) and load capacity (LC), respectively. Speed and accuracy are achieved through a properly designed linearization of the optimization problem, which introduces the concept of compensation admittance at the node. The proposed method was validated by comparing the results obtained with those coming from state-of-the-art methods.

Analysis of Power System Transient Stability of the Nigerian 330-kV Electricity Grid

Faults on power system are inevitable and can occur at any time resulting into transient instability. Transient instability can cause loss of synchronism and possible damage to power equipment and consumer loads. Therefore, this study analyzed the transient stability (TS) of the Nigerian 330-kV, 34-bus power network. Power flow and swing equations describing the system steady and transient states were respectively analyzed using Newton-Rahpson and Runge-Kutta, fourth order numerical techniques to provide linear solution due to their non-linearity. Simulations were done and swing curves for different fault conditions obtained. The critical clearing time at which the simulated faults were cleared was determined. The results of load flow analyses revealed that buses 6, 10, 13, 14, and 17 with respective voltage magnitude of 0.937, 0.921, 0.938, 0.829 and 0.780 per unit violated voltage tolerance limit of 0.95 to 1.05 p.u. The system total active and reactive power losses were 57.62 MW and -70.62 MVar respectively. The obtained swing curve showed that for fault on bus 11 [line 9-11] generators 2, 3 and 7 lost synchronism after 1.0 s but other generators retained their stability. Similarly, for fault on bus 13 [line 10-14] generators 3 and 7 lost synchronism but other generators retained stability after 0.4 s. These results indicate that faults occurrence on generating stations of power system is unavoidable, but the clearance time must be short (few seconds) to avert total system collapse and loss of synchronism.

Flexible operation of Post-combustion CO2 capture process enabled by NARX-MPC using neural network

Post-combustion CO2 capture (PCC) process is expected to serve as the role of a bridge solution during the transition from fossil-based to renewable energy, but extensive energy consumption is a significant hurdle to its widespread commercial adoption. Operating a PCC process economically often requires large operating condition changes in response to power plant load changes and time-varying energy prices. The ‘flexible’ operation requires a controller that aids in such a dynamic operating environment of the PCC process. To balance model complexity with prediction accuracy, we adopt NARX-MPC which employs a neural network-based NARX model as a prediction model for MPC. Under various dynamic operation scenarios, the proposed NARX-MPC is evaluated and compared with a linear MPC (LMPC) controller. Our observations indeed reveal that the NARX-MPC delivers significantly superior closed-loop control performance over the LMPC, especially in scenarios involving large changes in the power plant load or inlet flue gas flow rate and simultaneous changes in the flue gas flow rate and the CO2 capture rate.

1D elastic viscoplastic consolidation analysis of bi‐layered soft ground under time‐dependent drainage boundary and ramp load

AbstractThe elastic viscoplastic properties are non‐negligible factors of clays that cause the deviation between the theoretical and the measured values, which were rarely incorporated in layered consolidation problems. Thus, this paper extended a generalized bi‐layered one‐dimensional (1D) consolidation model for soft ground under ramp load, simultaneously incorporating elastic viscoplastic deformation, non‐Darcy flow (NDF), and time‐dependent drainage boundary (TDB) condition. The finite volume technique was employed to numerically solve the control equation. Then, the proposed method solutions were verified by comparing with degenerated cases, including oedometer experimental results, analytical and semi‐analytical solutions with different boundary conditions. Furthermore, parametric studies were conducted on the bi‐layered clay creep consolidation characteristics by investigating the effect of the loading rate, interface and flow parameters, and the relative soil layer properties. The results demonstrate that the entire dissipation rate of the excess pore‐water pressure (EPWP) and settlement rate in the bi‐layered ground become faster as the soil thickness with high permeability or low compressibility increases. When considering the viscosity of soft clay, the EPWP exceeding the overlying construction load value can occur in poorly drained locations. Neglecting loading rate, time‐dependent drainage boundary (TDB), and NDF can result in a significant overestimation of consolidation and settlement proceedings.

Comparative Analysis of the Particle Swarm Optimization and Primal-Dual Interior-Point Algorithms for Transmission System Volt/VAR Optimization in Rectangular Voltage Coordinates

Optimal power flow (OPF) is one of the most widely studied problems in the field of operations research, as it applies to the optimal and efficient operation of the electric power system. Both the problem formulation and solution techniques have attracted significant research interest over the decades. A wide range of OPF problems have been formulated to cater for the various operational objectives of the power system and are mainly expressed either in polar or rectangular voltage coordinates. Many different solution techniques falling into the two main categories of classical/deterministic optimization and heuristic/non-deterministic optimization techniques have been explored in the literature. This study considers the Volt/VAR optimization (VVO) variant of the OPF problem formulated in rectangular voltage coordinates, which is something of a departure from the majority of the studies, which tend to use the polar coordinate formulation. The heuristic particle swarm optimization (PSO) and the classical primal-dual interior-point method (PDIPM) are applied to the solution of the VVO problem and a comparative analysis of the relative performance of the two algorithms for this problem is presented. Four case studies based on the 6-bus, IEEE 14-bus, 30-bus, and 118-bus test systems are presented. The comparative performance analysis reveals that the two algorithms have complementary strengths, when evaluated on the basis of the solution quality and computational efficiency. Particularly, the PSO algorithm achieves greater power loss minimization, whereas the PDIPM exhibits greater speed of convergence (and, thus, better computational efficiency) relative to the PSO algorithm, particularly for higher-dimensional problems. An additional distinguishing characteristic of the proposed solution is that it incorporates the Newton–Raphson load flow computation, also formulated in rectangular voltage coordinates, which adds to the efficiency and effectiveness of the presented solution method.

Water quality management by enhancing assimilation capacity with flow augmentation: a case study for the Yamuna River, Delhi.

This paper aims to assess the requirement of load reductions and flow augmentation to enhance the assimilation yield of the Yamuna River, Delhi. The framework QUAL2kw was used to predict river quality. The model was calibrated and confirmed in critical flow conditions of pre-monsoon periods. Three strategies were established for varying pollutant loads. The DO concentration was predicted with changing BOD and COD loads. The 16 outfalling drains were considered pollutant sources between the 22 km stretch of the river. Four cases with 41 scenarios were studied with varying flow augmentation upstream and varying load. It has been observed that with 80 cumecs of upstream flow, the reach can assimilate 31.33 tonnes per day of BOD and 142.85 tonnes per day of COD load, maintaining the desired level of DO (≥4 mg/L) and BOD (≤3 mg/L) throughout the reach.

Loading characteristics of streptavidin on polypropylene capillary channeled polymer fibers and capture performance towards biotinylated proteins.

The development of higher-throughput, potentially lower-cost means to isolate proteins, for a variety of end uses, is of continuing emphasis. Polypropylene (PP) capillary-channeled polymer (C-CP) fiber columns are modified with the biotin-binding protein streptavidin (SAV) to capture biotinylated proteins. The loading characteristics of SAV on fiber supports were determined using breakthrough curves and frontal analysis. Based on adsorption data, a 3-min on-column loading at a flow rate of 0.5 mL min-1 (295.2 cm h-1) with a SAV feed concentration of 0.5 mg mL-1 produces a SAV loading capacity of 1.4 mg g-1 fiber. SAV has an incredibly high affinity for the small-molecule biotin (10-14 M), such that this binding relationship can be exploited by labeling a target protein with biotin via an Avi-tag. To evaluate the capture of the biotinylated proteins on the modified PP surface, the biotinylated versions of bovine serum albumin (b-BSA) and green fluorescent protein (b-GFP) were utilized as probe species. The loading buffer composition and flow rate were optimized towards protein capture. The non-ionic detergent Tween-20 was added to the deposition solutions to minimize non-specific binding. Values of 0.25-0.50% (v/v) Tween-20 in PBS exhibited better capture efficiency, while minimizing the non-specific binding for b-BSA and b-GFP, respectively. The C-CP fiber platform has the potential to provide a fast and low-cost method to capture targeted proteins for applications including protein purification or pull-down assays.

Optimal allocation of distributed generation in active distribution power network considering HELM-based stability index

Traditionally, assessment of static voltage stability for distribution power networks with distributed generation (DG) utilizes the continuous power flow (CPF) method by calculating load margin index (LMI) at various load levels, which suffers from slow calculation speed and low accuracy when power flow calculation becomes ill-conditioned. To overcome this issue, this paper presents a novel holomorphic embedding load flow method (HELM)-based approach that calculates voltage stability indices for various types of nodes in a distribution network. Different orders of sensitivity information are calculated using the HELM method, and the criteria for assessing voltage stability are derived, which are used as constraints to optimize the location and capacity of DG. Such formulation of the optimization problem does not need to calculate the maximum load margin using CPF. Moreover, it can be effectively solved using the Genetic Algorithm and easily adaptable to various operating conditions of DG, which improve the calculation speed of the stability index. The effectiveness of the proposed approach is verified on IEEE 33-node and IEEE 69-node distribution power network models. Results show that considering the HELM VSI, the location, and capacity of DG in the distribution network can be better optimized. For the IEEE 33-node model, the total cost is reduced by approximately 2.33%, the network loss is reduced by 1.2%, and the HELM voltage stability criteria index is increased by about 4.23%; while for the IEEE 69-node system, the total cost is reduced by about 2.98%.

NGHIÊN CỨU MỐI TƯƠNG QUAN GIỮA DIỆN TÍCH SỬ DỤNG ĐẤT NÔNG NGHIỆP ĐẾN TẢI LƯỢNG CÁC CHẤT DINH DƯỠNG TRONG MÔI TRƯỜNG NƯỚC TRÊN LƯU VỰC SÔNG CẢ

The purpose of this research is to determine the relationship between the land area in the agricultural watershed and the nutrient load in the Ca River basin. Eight sampling sites in the Ca River basin were chosen for sampling in two phases during the dry season (5/2021) and the rainy season (September-2021). The results show that the measured water flow ranges from 27.7 m3 /s to 206.1 m3 /s in the dry season, with the highest reaching 2696 m3 /s and the lowest at 395 m3 /s in the rainy season. The load results of nutrients TN and, TP show a close relationship with flow and topography. The area of agricultural land in the basins influences nutrient load, which follows two distinct trends, increasing steadily in the northwest side river group and fluctuating in the southeast side river group. The land use process has a more obvious impact on the load during the dry season, whereas natural factors change the variation of nutrient load flows during the rainy season.

A robust crow search algorithm based power system state estimation

The State Estimation (SE) computational procedure plays a crucial role in modern electric power system security control by monitoring and analyzing operational conditions and predicting any emergency. In order to estimate state variables, Power System State Estimation (PSSE) takes into account the magnitudes and phases of voltage on each bus. To address the state estimation challenges in power systems, in this paper, we propose a novel application of the Crow Search Algorithm (CSA) specifically tailored for the state estimation problem. We have assessed the introduced algorithm using the frameworks of both the IEEE 14-bus and IEEE 30-bus test systems. The first formulation is the Weighted Least Square (WLS) method, and the second is the Weighted Least Absolute Value (WLAV) method, both of which are objective function formulations. By comparing the results, it is clear that CSA-based SE is superior to the other metaheuristic algorithms considered, namely Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Artificial Bee Swarm Optimization (ABSO). As a point of comparison, we use the Newton–Raphson method for calculating load flow. It has been shown that the proposed CSA-based SE technique has better accuracy than the other two algorithms in all different test systems. With this study, the power system is operated more accurately and reliably by the operators operating the system.

Multiple distribution networks hosting capacity assessment using a stochastic approach

The stochastic approach is applied to an entire concession area with 1264-LV distribution networks to estimate the hosting capacity. About 15 000-customers are connected to the individual secondary distribution networks supplied through 48-medium voltage 10 kV radial feeders.The hosting capacity assessment uses the end-customer voltage magnitude rise and transformer thermal overload. The hosting capacity is estimated by applying the “stochastic mixed aleatory-epistemic method” to determine the voltage magnitude rise and load flow with solar PV. The minimum power consumption is compared with the solar PV power infeed through the individual transformers.The hosting capacity estimation is done for three-phase connected solar PV sizes from 3 to 18 kW. At moderate PV penetration (25%–50%), the results showed that overvoltage would limit the hosting capacity more often than overload, but it becomes an issue only for LV networks studied with more than 8-customers. Considering all LV networks, most of the customers could install 6 kWp. Even when installing PV systems of 18 kWp (about twice the average size today and about the maximum area of a typical residential roof), two-thirds of houses would not need an upgrade to withstand SS-EN 50160 voltage limits. The latter customers can connect solar PV units with 18 kWp size without overvoltage or overload issues.

Online optimization and tracking control strategy for battery energy storage in DC microgrids

This paper proposes a fast time-varying optimal power flow (OPF) command tracking control algorithm for DC microgrids based on measurement feedback. The algorithm establishes a model by adding power command tracking constraints and considering the power, voltage, and current constraints of the microgrid. A forward-back generation DC power flow sensitivity calculation method is designed to calculate the power output of the energy storage at each node, and charging and discharging decisions are made based on the state of charge (SOC) of the energy storage system, current voltage, and charging and discharging scenarios previous and subsequent. By continuously issuing control decisions, the DC microgrid OPF command tracking solution is achieved. The measurement feedback control scheme used in this algorithm reduces model error and non-iterative calculation error, thus improving calculation and tracking accuracy. The algorithm is tested in a modified 28-node arithmetic system and suppresses voltage fluctuations caused by unstable PV active output effectively, while accurately tracking the power command of the upper level and meeting the voltage safety operation requirements of the microgrid.

The effect of polymeric binder type and concentration on flow and dissolution properties of SMEDDS loaded mesoporous silica-based granules

Self-microemulsifying drug delivery systems (SMEDDS) are lipid-based formulations, designed to improve the solubility of poorly-water soluble drugs. Mesoporous silica is frequently used for SMEDDS solidification by various techniques. One of them is wet granulation, which enables achieving both high SMEDDS load and good flow properties. This study investigated the effect of six polymeric binders’ addition to granulation dispersion (GD) (povidone K30, povidone K90, copovidone, Pharmacoat® 603, Pharmacoat® 615 and Methocel™ K100 Premium LV) on characteristics of produced SMEDDS granules, prepared by wet granulation. By incorporation of polymer in GD, it was possible to produce mesoporous silica-based free-flowing granules, with preserved self-microemulsifying properties, responsible for improved in vitro release of carvedilol. The incorporation of higher molecular weight binders resulted in slower in vitro release, while high binder concentration was related to faster drug release. The highest release rate was achieved with povidone K30 at 7.45 % binder concentration, as corresponding granules exhibited complete drug release already in 5 min. Granulation method (manual vs. high-shear) influenced the release rate of carvedilol as it was released slower from SMEDDS granules prepared using the granulator.Finally, SMEDDS tablet formulation was optimized to achieve maximum granule content and adequate tablet hardness. Increased granule content found to negatively influence tablet hardness, as maximum granule content of 25 % was needed to obtain appropriate hardness. Such tablets exhibited short disintegration time, so this final prototype can be considered as orodispersible tablet.

The work input to saturated porous media undergoing internal erosion

The mechanism of internal erosion in porous media involves the microstructural evolutions induced by washing out of fine particles under different loading and seepage flow actions. Consequently, the effective stress on the solid skeleton is governed by the transition in velocity and stress of fine particles due to their detachment from the skeleton and then transport through pore channels, in addition to pore pressure. This study is to develop a formulation of work input to account for the interactions and mass exchanges between solid and fluid phases. Coupled mechanical-hydraulic erosion processes can be properly reflected through mass, momentum and energy balances based on Biot’s mixture theory of a three-phase model. This leads to three separate stress-like variables, effective stress, erosion force and hydraulic gradient, in conjugation with three strain-like variables, strain, mass loss and seepage velocity, respectively. The effective stress tensor, different from the classical form by Terzaghi due to the effect of erosion, and coupled hydro-mechanical-erosion criteria are naturally derived from the proposed work input. They consider grain scale mechanisms describing the transition of erodible particles from the solid skeleton to the fluidized state. Systematic formulations and discussions are presented to highlight the promising features of our approach.

Probabilistic load flow in distribution networks: An updated and comprehensive review with a new classification proposal

Due to the increased penetration of distributed energy resources and the presence of uncertainties in power networks, it is essential to evaluate the uncertainty of system performance. As a result, effective technologies for load flow analysis are required. The stochastic properties of power systems can be discovered via probabilistic load flow analysis. To model the uncertainties and construct the parametric tools of probabilistic power flow, several works recently utilize ensembles of probability density functions. Nevertheless, the uncertainties may not fit into any of the conventional classes of probability density functions. Thus, nonparametric tools are required. Various studies on uncertainty modeling techniques in probabilistic load flow have recently been undertaken, although there is no single best uncertainty modeling methodology to date. The load flow problem and the type of uncertain input variables determine the best strategy. There have been positive evaluations in this area, but the main focus of this research is firstly to present an overview and classification of the available load flow strategies in distribution networks from various perspectives and also, investigate the stochastic correlation or dependency of a random variable's variation relative to others. Then, based on a fresh perspective, we present a review, taxonomy, and discussion of the strengths and shortcomings of existing uncertainty modeling techniques in stochastic load flow as probability methods (parametric, semi- and non-parametric approaches) and non-probability methods. Moreover, for first time, a comprehensive comparison and assessment between these uncertainty methods based on accuracy, complexity, and simulation time presents in the uncertainties handling of the power system. The authors suggest this review to engineers, scientists and researchers who are doing their research work in this field.

Analysis and Detection of Power System Network Faults with Wavelet Transform

Fault detection technique is important for enhancing protection, stability, reliability and continuity of supply. There are many fault detection techniques implemented in power system such as Fourier transform, wavelet transform, neural networks, etc. This research presents the fault identification and analysis using wavelet transform method as well as estimation of circuit breaker rating. The discrete wavelet transform is implemented for the fault identification in five bus system. Various types of line and ground faults have been considered and studied using Daubechies wavelet function. The first level decomposition is used for the fault analysis. The maximum detailed coefficients for various faults currents are analysed for the fault identification. The wavelet transform algorithm is implemented using MATLAB programming. The five-bus system is modelled in MATLAB Simulink and various faults are simulated. The switching time of fault is taken as 0.05 to 0.1 seconds. The faults have been studied at different points in the system. The fault identification method gives accurate results for different types of faults. The load flow analysis is also done for five bus system and appropriate rating of circuit breaker is estimated.

Small signal stability and dynamic performance investigation on multi-machines power system including DFIG wind farm

<p>The boundless potential of wind power in augmenting global energy production is a promising prospect. The efficient design and cost-effectiveness of doubly fed induction generator (DFIG) wind systems make them an optimistic solution for incorporating wind power on a massive scale. However, integrating these systems into power grids poses several challenges, including power system stability. This study examines the small signal stability and dynamic performance of a modified Western System Coordinating Council (WSCC) 9-bus system including a DFIG wind farm using load flow analysis, and both electromechanical oscillations and eigenvalue analysis. Three case studies were conducted based on the DFIG location and power increment.The simulation is carried out with the aid of the power system analysis toolbox (PSAT) that operates within the MATLAB environment. The study’s findings suggest that the perturbation and location of the DFIG relative to the system’s load have a minimal influence on the overall system’s stability and efficiency. However, when considering damping ratio, power angle, and rotor speed deviations, generators 1 and 2 with the perturbed DFIG installed on bus 8 are the most sensitive units to instability. Hence, larger perturbations and different DFIG’s location influence on power systems necessitates further analysis.</p>

Reactive Capability Sizing of HPR1000 NPP in the UK Grid

To address the voltage profile, the reactive power requirements in the UK Grid Code have risen due to increasing power flows and the wind turbine system volume. This study strives to figure out the reactive capability of HPR1000 NPP in the UK grid and presents ETAP-based modeling and simulation of the demonstration. The paper first introduces the UK grid’s reactive capability requirements, then analyses the theory of synchronous generator reactive capability and unit transformer tap changer sizing, and finally demonstrates the sizing of reactive generator capability and unit transformer tap changer via load flow studies. The reactive capability requirements of the UK grid are more severe than China, causing the synchronous generator with a larger reactive capability [0.83PF(lagging), 0.98PF(leading)] and the unit transformer with a larger range of on-load tap changer[-10×1.25% / +4×1.25%], which should be concerned during HPR1000 NPP exportation.

Holomorphic Embedding Load Flow Method in Three-Phase Distribution Networks With ZIP Loads

The Holomorphic Embedding Load flow Method (HELM) employs analytic continuation of complex analytic functions to calculate the practical (high voltage) load flow solution and provides promising convergence guarantees. Although HELM has been applied to various types of power systems, the literature has not thoroughly investigated three-phase distribution networks with common load types/connections. In this paper, we extend HELM to three-phase distribution networks with ZIP loads, while preserving its prominent convergence promises. Specifically, we introduce a HELM formulation, which emphasizes on accurate modeling of constant-current loads (and the voltage dependence of current injections) for both wye and delta connections. We perform extensive numerical experiments on standard test systems with various equipment/connection types to demonstrate the accuracy and efficacy of the proposed HELM compared with the existing literature.