Enhancing Renewable Energy Integration:A Gaussian-Bare-Bones Levy Cheetah Optimization Approach to Optimal Power Flow in Electrical Networks

In the contemporary era,the global expansion of electrical grids is propelled by various renewable energy sources(RESs).Efficient integration of stochastic RESs and optimal power flow(OPF)management are critical for network optimization.This study introduces an innovative solution,the Gaussian Bare-Bones Levy Cheetah Optimizer(GBBLCO),addressing OPF challenges in power generation systems with stochastic RESs.The primary objective is to minimize the total operating costs of RESs,considering four functions:overall operating costs,voltage deviation management,emissions reduction,voltage stability index(VSI)and power loss mitigation.Additionally,a carbon tax is included in the objective function to reduce carbon emissions.Thorough scrutiny,using modified IEEE 30-bus and IEEE 118-bus systems,validates GBBLCO’s superior performance in achieving optimal solutions.Simulation results demonstrate GBBLCO’s efficacy in six optimization scenarios:total cost with valve point effects,total cost with emission and carbon tax,total cost with prohibited operating zones,active power loss optimization,voltage deviation optimization and enhancing voltage stability index(VSI).GBBLCO outperforms conventional techniques in each scenario,showcasing rapid convergence and superior solution quality.Notably,GBBLCO navigates complexities introduced by valve point effects,adapts to environmental constraints,optimizes costs while considering prohibited operating zones,minimizes active power losses,and optimizes voltage deviation by enhancing the voltage stability index(VSI)effectively.This research significantly contributes to advancing OPF,emphasizing GBBLCO’s improved global search capabilities and ability to address challenges related to local minima.GBBLCO emerges as a versatile and robust optimization tool for diverse challenges in power systems,offering a promising solution for the evolving needs of renewable energy-integrated power grids.

Optimizing Power Flow in Northern Cameroon’s Interconnected Grid: Challenges and Solutions

This paper presents an analysis of the power flow within the Northern Interconnected Grid of Cameroon. The Newton-Raphson method has been performed, known for its accuracy, under MATLAB software, to model and solve complex power flow equations. This study simulates a series of outage scenarios to evaluate the responsiveness of the grid. The results obtained underline the crucial importance of reactive power management and highlight the urgent need to consolidate the grid infrastructure of North Cameroon. To increase grid resilience and stability, the paper recommends the strategic integration of renewables and the development of interconnections with other power grids. These measures are presented as viable solutions to meet current and future energy distribution challenges, ensuring a reliable and sustainable power supply for Cameroon.

Mathematical Modeling and Control Algorithm Development for Bidirectional Power Flow in CCS-CNT System

As the demand for more efficient and adaptable power distribution systems intensifies, especially in rural areas, innovative solutions like the Capacitor-Coupled Substation with a Controllable Network Transformer (CCS-CNT) are becoming increasingly critical. Traditional power distribution networks, often limited by unidirectional flow capabilities and inflexibility, struggle to meet the complex demands of modern energy systems. The CCS-CNT system offers a transformative approach by enabling bidirectional power flow between high-voltage transmission lines and local distribution networks, a feature that is essential for integrating renewable energy sources and ensuring reliable electrification in underserved regions. This paper presents a detailed mathematical representation of power flow within the CCS-CNT system, emphasizing the control of both active and reactive power through the adjustment of voltage levels and phase angles. A control algorithm is developed to dynamically manage power flow, ensuring optimal performance by minimizing losses and maintaining voltage stability across the network. The proposed CCS-CNT system demonstrates significant potential in enhancing the efficiency and reliability of power distribution, making it particularly suited for rural electrification and other applications where traditional methods fall short. The findings underscore the system's capability to adapt to varying operational conditions, offering a robust solution for modern power distribution challenges.

Parallel-Path Power Flows in Magnetic-Geared Permanent Magnet Machines with Sandwiched Armature Stator

Due to the large torque density of magnetic gears(MGs),magnetic-geared permanent magnet machines(MGPMs)have become promising competitors in the family of direct-drive machines.According to the deployment of armature stators,MGPMs can be generally classified into three types,viz.,MGPM with inner armature stator(MGPM-IAS),MGPM with outer armature stator(MGPM-OAS),and MGPM with sandwiched armature stator(MGPM-SAS).Our investigation finds out that the MGPM-SAS can achieve parallel-path power flows better than the MGPM-OAS,while the MGPM-IAS is with serial power flow paths.Therefore,the torque capability of MGPM-IAS is limited by the torque transmission capability of its integrated MG.However,the MGPM-SAS has the possibility to offer even higher output torque than its integrated MG.This paper focuses on the MGPM-SAS.And three typical MGPMs and their power flow paths are introduced;the interaction of electromagnetic fields in MGPM-SAS is analyzed;simulation calculation and experimental verification are conducted to demonstrate the validity of the theoretical analysis.

Power flows of three non-conservatively series-coupled oscillators, Part Ⅱ: Numerical analysis

The direct and indirect power flows among three non-conservatively series-coupled oscillators subjected to random forces have been investigated by the numerical method. The relationship between the power flows and the parameters of the oscillators and couplings have been studied. It is shown that the indirect power flow is caused by the resonant transmission between the indirectly coupled oscillators. Once the parameters of the oscillator elements have been settled, the indirect power flow is mainly determined by the coupling stiffness k3 and k4, and is less infiuenced by coupling dampings c3 and c4. The indirect power flow cannot be ignored in strong coupling conditions. Because of the resonant transmission between the indirectly coupled oscillators, the indirect power flow still cannot be neglected even if the coupling stiffness is relatively small and the coupling damping is relatively great

Power flows of three non-conservatively series-coupled oscillators,Part Ⅰ:Theory

The formulae of power flows among three non-conservatively series-coupled oscillators have been derived. It is shown that the power flows among the three non-conservatively series-coupled oscillators, similar to that of the three conservatively series-coupled oscillators,include the direct and indirect power flows. The direct and indirect power flows are proportional to the differences of the stored energies in the directly coupled and indirectly coupled oscillators. The proportionality constants are functions of parameters of the oscillators and couplings

A Data Driven Security Correction Method for Power Systems with UPFC

The access of unified power flow controllers(UPFC)has changed the structure and operation mode of power grids all across the world,and it has brought severe challenges to the traditional real-time calculation of security correction based on traditionalmodels.Considering the limitation of computational efficiency regarding complex,physical models,a data-driven power system security correction method with UPFC is,in this paper,proposed.Based on the complex mapping relationship between the operation state data and the security correction strategy,a two-stage deep neural network(DNN)learning framework is proposed,which divides the offline training task of security correction into two stages:in the first stage,the stacked auto-encoder(SAE)classification model is established,and the node correction state(0/1)output based on the fault information;in the second stage,the DNN learningmodel is established,and the correction amount of each action node is obtained based on the action nodes output in the previous stage.In this paper,the UPFC demonstration project of NanjingWest Ring Network is taken as a case study to validate the proposed method.The results show that the proposed method can fully meet the real-time security correction time requirements of power grids,and avoid the inherent defects of the traditional model method without an iterative solution and can also provide reasonable security correction strategies for N-1 and N-2 faults.

Analysis and Power Quality Improvement in Hybrid Distributed Generation System with Utilization of Unified Power Quality Conditioner

This paper presents a comprehensive study that includes the sizing and power flow by series and parallel inverters in a distributed generation system(DGs)that integrates the system of hybrid wind photovoltaic with a unified power quality conditioner(UPQC).In addition to supplying active power to the utility grid,the system of hybrid wind photovoltaic functions as a UPQC,compensating reactive power and suppressing the harmonic load currents.Additionally,the load is supplied with harmonic-free,balanced and regulated output voltages.Since PVWind-UPQC is established on a dual compensation scheme,the series inverter works like a sinusoidal current source,while the parallel inverter works like a sinusoidal voltage source.Consequently,a smooth alteration from interconnected operating modes to island operating modes and vice versa can be achieved without load voltage transients.Since PV-Wind-UPQC inverters handle the energy generated through the hybrid wind photovoltaic system and the energy demanded through the load,the converters should be sized cautiously.A detailed study of the flow of power via the PV-Wind-UPQC is imperative to gain a complete understanding of the system operation and the proper design of the converters.Thus,curves that allow the sizing of the power converters according to the power flow via the converters are presented and discussed.Simulation results are presented to assess both steady state and dynamic performances of the grid connected hybrid system of PV-Wind-UPQC.This investigation is verified by simulating and analyzing the results with Matlab/Simulink.

Towards sparse matrix operations:graph database approach for power grid computation

The construction of new power systems presents higher requirements for the Power Internet of Things(PIoT)technology.The“source-grid-load-storage”architecture of a new power system requires PIoT to have a stronger multi-source heterogeneous data fusion ability.Native graph databases have great advantages in dealing with multi-source heterogeneous data,which make them suitable for an increasing number of analytical computing tasks.However,only few existing graph database products have native support for matrix operation-related interfaces or functions,resulting in low efficiency when handling matrix calculations that are commonly encountered in power grids.In this paper,the matrix computation process is expressed by a strategy called graph description,which relies on the natural connection between the matrix and structure of the graph.Based on that,we implement matrix operations on graph database,including matrix multiplication,matrix decomposition,etc.Specifically,only the nodes relevant to the computation and their neighbors are concerned in the process,which prunes the influence of zero elements in the matrix and avoids useless iterations compared to the conventional matrix computation.Based on the graph description,a series of power grid computations can be implemented on graph database,which reduces redundant data import and export operations while leveraging the parallel computing capability of graph database.It promotes the efficiency of PIoT when handling multi-source heterogeneous data.An comprehensive experimental study over two different scale power system datasets compares the proposed method with Python and MATLAB baselines.The results reveal the superior performance of our proposed method in both power flow and N-1 contingency computations.

Reactive Power Flow Convergence Adjustment Based on Deep Reinforcement Learning

Power flow calculation is the basis of power grid planning and many system analysis tasks require convergent power flow conditions.To address the unsolvable power flow problem caused by the reactive power imbalance,a method for adjusting reactive power flow convergence based on deep reinforcement learning is proposed.The deep reinforcement learning method takes switching parallel reactive compensation as the action space and sets the reward value based on the power flow convergence and reactive power adjustment.For the non-convergence power flow,the 500 kV nodes with reactive power compensation devices on the low-voltage side are converted into PV nodes by node type switching.And the quantified reactive power non-convergence index is acquired.Then,the action space and reward value of deep reinforcement learning are reasonably designed and the adjustment strategy is obtained by taking the reactive power non-convergence index as the algorithm state space.Finally,the effectiveness of the power flow convergence adjustment algorithm is verified by an actual power grid system in a province.

Model Predictive Control Strategy of Multi-Port Interline DC Power Flow Controller

There are issues with flexible DC transmission system such as a lack of control freedom over power flow.In order to tackle these issues,a DC power flow controller(DCPFC)is incorporated into a multi-terminal,flexible DC power grid.In recent years,a multi-port DC power flow controller based on a modular multi-level converter has become a focal point of research due to its simple structure and robust scalability.This work proposes a model predictive control(MPC)strategy for multi-port interline DC power flow controllers in order to improve their steady-state dynamic performance.Initially,the mathematical model of a multi-terminal DC power grid with a multi-port interline DC power flow controller is developed,and the relationship between each regulated variable and control variable is determined;The power flow controller is then discretized,and the cost function and weight factor are built with numerous control objectives.Sub module sorting method and nearest level approximation modulation regulate the power flow controller;Lastly,theMATLAB/Simulink simulation platformis used to verify the correctness of the establishedmathematicalmodel and the control performance of the suggestedMPC strategy.Finally,it is demonstrated that the control strategy possesses the benefits of robust dynamic performance,multiobjective control,and a simple structure.

Modeling load distribution for rural photovoltaic grid areas using image recognition

Expanding photovoltaic(PV)resources in rural-grid areas is an essential means to augment the share of solar energy in the energy landscape,aligning with the“carbon peaking and carbon neutrality”objectives.However,rural power grids often lack digitalization;thus,the load distribution within these areas is not fully known.This hinders the calculation of the available PV capacity and deduction of node voltages.This study proposes a load-distribution modeling approach based on remote-sensing image recognition in pursuit of a scientific framework for developing distributed PV resources in rural grid areas.First,houses in remote-sensing images are accurately recognized using deep-learning techniques based on the YOLOv5 model.The distribution of the houses is then used to estimate the load distribution in the grid area.Next,equally spaced and clustered distribution models are used to adaptively determine the location of the nodes and load power in the distribution lines.Finally,by calculating the connectivity matrix of the nodes,a minimum spanning tree is extracted,the topology of the network is constructed,and the node parameters of the load-distribution model are calculated.The proposed scheme is implemented in a software package and its efficacy is demonstrated by analyzing typical remote-sensing images of rural grid areas.The results underscore the ability of the proposed approach to effectively discern the distribution-line structure and compute the node parameters,thereby offering vital support for determining PV access capability.

A Cascading Fault Path Prediction Method for Integrated Energy Distribution Networks Based on the Improved OPA Model under Typhoon Disasters

In recent times,the impact of typhoon disasters on integrated energy active distribution networks(IEADNs)has received increasing attention,particularly,in terms of effective cascading fault path prediction and enhanced fault recovery performance.In this study,we propose a modified ORNL-PSerc-Alaska(OPA)model based on optimal power flow(OPF)calculation to forecast IEADN cascading fault paths.We first established the topology and operational model of the IEADNs,and the typical fault scenario was chosen according to the component fault probability and information entropy.The modified OPA model consisted of two layers:An upper-layer model to determine the cascading fault location and a lower-layer model to calculate the OPF by using Yalmip and CPLEX and provide the data to update the upper-layer model.The approach was validated via the modified IEEE 33-node distribution system and two real IEADNs.Simulation results showed that the fault trend forecasted by the novel OPA model corresponded well with the development and movement of the typhoon above the IEADN.The proposed model also increased the load recovery rate by>24%compared to the traditional OPA model.

An Augmented Jacobian Method for Power Flow Analysis of Weakly Looped Distribution Systems with PV Buses

A power flow analysis method for weakly looped distribution systems with PV buses is proposed in this paper. The proposed method is computationally more efficient and more robust compared with the conventional compensation methods. The robustness is achieved by embedding the boundary conditions of loops and PV buses into the Jacobian matrix. The computational efficiency is achieved by the carefully designed factorization of Jacobian matrix. Test results on a 33 bus system are presented.

Theory and Method of Power System Integrated Security Region Irrelevant to Operation States:An Introduction

How to comprehensively consider the power flow constraints and various stability constraints in a series of power system optimization problems without affecting the calculation speed is always a problem.The computational burden of probabilistic security assessment is even more unimaginable.In order to solve such problems,a security region(SR)methodology is proposed,which is a brand-new methodology developed on the basis of the classical point-wise method.Tianjin University has been studying the SR methodology since the 1980s,and has achieved a series of original breakthroughs that are described in this paper.The integrated SR introduced in this paper is mainly defined in the power injection space,and includes SRs to ensure steady-state security,transient stability,static voltage stability,and smalldisturbance stability.These SRs are uniquely determined for a given network topology(as well as location and clearing process for transient faults)and given system component parameters,and are irrelevant to operation states.This paper presents 11 facts and related remarks to introduce the basic concepts,composition,dynamics nature,and topological and geometric characteristics of SRs.It also provides a practical mathematical description of SR boundaries and fast calculation methods to determine them in a concise and systematic way.Thus,this article provides support for the systematic understanding,future research,and applications of SRs.The most critical finding on the topological and geometric characteristics of SRs is that,within the scope of engineering concern,the practical boundaries of SRs in the power injection space can be approximated by one or a few hyperplanes.Based on this finding,the calculation time for power system probabilistic security assessment(i.e.,risk analysis)and power system optimization with security constraints can be decreased by orders of magnitude.

The wave and vibratory power transmission in a finite L-shaped Mindlin plate with two simply supported opposite edges

In this paper,wave and vibratory power transmission in a finite L-shaped Mindlin plate with two simply supported opposite edges are investigated using the wave approach.The dynamic responses,active and reactive power flow in the finite plate are calculated by the Mindlin plate theory （MPT） and classic plate theory （CPT）.To satisfy the boundary conditions and continuous conditions at the coupled junction of the finite L-shaped plate,the near-field and far-field waves are entirely contained in the wave approach.The in-plane longitudinal and shear waves are also considered.The results indicate that the vibratory power flow based on the MPT is different from that based on the CPT not only at high frequencies but also at low and medium frequencies.The influence of the plate thickness on the vibrational power flow is investigated.From the results it is seen that the shear and rotary inertia correction of the MPT can influence the active and reactive power at the junction of the L-shaped plate not only at high frequencies but also at low and medium frequencies.Furthermore,the effects of structural damping on the active and reactive power flow at the junction are also analyzed.

A multi-objective gravitational search algorithm based approach of power system stability enhancement with UPFC

On the basis of the theoretical analysis of a single-machine infinite-bus （SMIB）, using the modified linearized Phil- lips-Heffron model installed with unified power flow controller （UPFC）, the potential of the UPFC supplementary controller to enhance the dynamic stability of a power system is evaluated by measuring the electromechanical controllability through singular value decomposition （SVD） analysis. This controller is tuned to simultaneously shift the undamped electromeehanical modes to a prescribed zone in the s-plane. The problem of robust UPFC based damping controller is formulated as an optimization problem according to the eigenvalue-based multi-objective function comprising the damping factor, and the damping ratio of the undamped electromechanical modes to be solved using gravitational search algorithm （GSA） that has a strong ability to find the most optimistic results. The different loading conditions are simulated on a SMIB system and the rotor speed deviation, internal voltage deviation, DC voltage deviation and electrical power deviation responses are studied with the effect of this flexible AC transmission systems （FACTS） controller. The results reveal that the tuned GSA based UPFC controller using the proposed multi-objective function has an excellent capability in damping power system with low frequency oscillations and greatly enhances the dynamic stability of the power systems.

Analysis of cascading failures of power cyber-physical systems considering false data injection attacks

This study considers the performance impacts of false data injection attacks on the cascading failures of a power cyber-physical system,and identifies vulnerable nodes.First,considering the monitoring and control functions of a cyber network and power flow characteristics of a power network,a power cyber-physical system model is established.Then,the influences of a false data attack on the decision-making and control processes of the cyber network communication processes are studied,and a cascading failure analysis process is proposed for the cyber-attack environment.In addition,a vulnerability evaluation index is defined from two perspectives,i.e.,the topology integrity and power network operation characteristics.Moreover,the effectiveness of a power flow betweenness assessment for vulnerable nodes in the cyberphysical environment is verified based on comparing the node power flow betweenness and vulnerability assessment index.Finally,an IEEE14-bus power network is selected for constructing a power cyber-physical system.Simulations show that both the uplink communication channel and downlink communication channel suffer from false data attacks,which affect the ability of the cyber network to suppress the propagation of cascading failures,and expand the scale of the cascading failures.The vulnerability evaluation index is calculated for each node,so as to verify the effectiveness of identifying vulnerable nodes based on the power flow betweenness.

Power Flow Response Based Dynamic Topology Optimization of Bi-material Plate Structures

Work on dynamic topology optimization of engineering structures for vibration suppression has mainly addressed the maximization of eigenfrequencies and gaps between consecutive eigenfrequencies of free vibration, minimization of the dynamic compliance subject to forced vibration, and minimization of the structural frequency response. A dynamic topology optimization method of bi-material plate structures is presented based on power flow analysis. Topology optimization problems formulated directly with the design objective of minimizing the power flow response are dealt with. In comparison to the displacement or velocity response, the power flow response takes not only the amplitude of force and velocity into account, but also the phase relationship of the two vector quantities. The complex expression of power flow response is derived based on time-harmonic external mechanical loading and Rayleigh damping. The mathematical formulation of topology optimization is established based on power flow response and bi-material solid isotropic material with penalization(SIMP) model. Computational optimization procedure is developed by using adjoint design sensitivity analysis and the method of moving asymptotes(MMA). Several numerical examples are presented for bi-material plate structures with different loading frequencies, which verify the feasibility and effectiveness of this method. Additionally, optimum results between topological design of minimum power flow response and minimum dynamic compliance are compared, showing that the present method has strong adaptability for structural dynamic topology optimization problems. The proposed research provides a more accurate and effective approach for dynamic topology optimization of vibrating structures.

POWER FLOW ANALYSIS FOR THE FINITE CONTINUOUS ISOLATION SYSTEMS

A universal expression for the transmitted power to the flexible foundation via the finite continuous isolation system of asymmetry is derived where the concept of effective mobility for the coupled system with continuous contact points is put forward. On the basis of the theoretic calculation and analysis, effects of structure parameters of the system on the power flow transmission as well as on the isolation efficiency are fully investigated.