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.

Applying Convex Optimal Power Flow to Combined Economic and Emission Dispatch

This paper addresses the problem of reducing CO2 emissions by applying convex optimal power flow model to the combined economic and emission dispatch problem. The large amount of CO2 emissions in the power industry is a major source of global warming effect. An efficient and economic approach to reduce CO2 emissions is to formulate the emission reduction problem as emission dispatch problem and combined with power system economic dispatch (ED). Because the traditional optimal power flow (OPF) model used by the economic dispatch is nonlinear and nonconvex, current nonlinear solvers are not able to find the global optimal solutions. In this paper, we use the convex optimal power flow model to formulate the combined economic and emission dispatch problem. The advantage of using convex power flow model is that global optimal solutions can be obtained by using mature industrial strength nonlinear solvers such as MOSEK. Numerical results of various IEEE power network test cases confirm the feasibility and advantage of convex combined economic and emission dispatch (CCEED).

Optimal Power Flow Using Firefly Algorithm with Unified Power Flow Controller

Firefly algorithm is the new intelligent algorithm used for all complex engineering optimization problems. Power system has many complex optimization problems one of which is the optimal power flow (OPF). Basically, it is minimizing optimization problem and subjected to many complex objective functions and constraints. Hence, firefly algorithm is used to solve OPF in this paper. The aim of the firefly is to optimize the control variables, namely generated real power, voltage magnitude and tap setting of transformers. Flexible AC Transmission system (FACTS) devices may used in the power system to improve the quality of the power supply and to reduce the cost of the generation. FACTS devices are classified into series, shunt, shunt-series and series-series connected devices. Unified power flow controller (UPFC) is shunt-series type device that posses all capabilities to control real, reactive powers, voltage and reactance of the connected line in the power system. Hence, UPFC is included in the considered IEEE 30 bus for the OPF solution.

Calculation and Evaluation of Ecological Flow of Hydropower Station Based on Fuzzy Evaluation Model

The reasonable determination of ecological flow is of great significance for the efforts to promote the transformation of water ecological environmental protection from pollution management to synergistic management of water resources,water ecology and water environment,and to promote them in an integrated manner.This paper analyzed and calculated the ecological flow process of the Bangsha River diversion power station using the minimum ecological flow method,the annual spreading method,the improved annual spreading method,the NGPRP method,and the month-by-month frequency method,and evaluated the reasonableness of the process and results of the ecological flow calculations by using the fuzzy evaluation model established.The study showed that the minimum ecological flow rate determined by improving the coupling of the spreading method and the NGPRP method was the best,and the suitable ecological flow rate determined by the month-by-month frequency method was the best;the minimum ecological flow rate of the Bangsha River diversion power station was at 0.43-4.21 m 3/s,and the suitable ecological flow rate was at 0.56-4.94 m 3/s,and the trend of its change showed the trend of first increasing and then decreasing,and the trend of change from January to July showed the trend of first increasing and then decreasing.Its trend of change showed an increasing and then decreasing trend,from January to July showed a gradually increasing trend,from August to December showed a gradually decreasing trend.It aimed to provide a theoretical basis for the reasonable determination of the ecological flow of the river hydropower station.

Convexification of Hybrid AC-DC Optimal Power Flow with Line-Commutated Converters

Line-commutated converter (LCC)-based high-voltage DC (HVDC) systems have been integrated with bulk AC power grids for interregional transmission of renewable power. The nonlinear LCC model brings additional nonconvexity to optimal power flow (OPF) of hybrid AC-DC power grids. A convexification method for the LCC station model could address such nonconvexity but has rarely been discussed. We devise an equivalent reformulation for classical LCC station models that facilitates second-order cone convex relaxation for the OPF of LCC-based AC-DC power grids. We also propose sufficient conditions for exactness of convex relaxation with its proof. Equivalence of the proposed LCC station models and properties, exactness, and effectiveness of convex relaxation are verified using four numerical simulations. Simulation results demonstrate a globally optimal solution of the original OPF can be efficiently obtained from relaxed model.

Uniformity evaluation and optimization of fluid flow characteristics in a seven-strand tundish

The effect of flow control devices（FCDs） on the uniformity of flow characteristics in a seven-strand symmetrical trapezoidal tundish was studied using both an experimental 1：2.5 hydraulic model and a numerical simulation of a 1：1 geometric model.The variation coefficient（CV） was defined to evaluate the flow uniformity of the seven-strand tundish.An optimized FCD configuration was proposed on the basis of the evaluation of experimental results.It is concluded that a turbulence inhibitor（TI） and U-type dam are essential to improve the uniformity of fluid flow in the seven-strand tundish.In addition,the configuration of inclination T-type dams with a height of 200 mm between the second and third strands and with a height of 300 mm between the third and fourth strands can minimize the proportion of dead zone.After optimizing the configuration of FCDs,the variation coefficient reduces below 20%of the mean value,and the average proportion of dead zone is just 14.6%;in addition,the temperature fluctuation between the strands could be controlled within 0.6 K.In summary,the uniformity of flow and temperature in the seven-strand tundish is greatly improved.

An Optimal DF Based Method for Transient Stability Analysis

The effect of energy on the natural environment has become increasingly severe as human consumption of fossil energy has increased.The capacity of the synchronous generators to keep working without losing synchronization when the system is exposed to severe faults such as short circuits is referred to as the power system’s transient stability.As the power system’s safe and stable operation and mechanism of action become more complicated,higher demands for accurate and rapid power system transient stability analysis are made.Current methods for analyzing transient stability are less accurate because they do not account formisclassification of unstable samples.As a result,this paper proposes a novel approach for analyzing transient stability.The key concept is to use deep forest(DF)and a neighborhood rough reduction approach together.Using the neighborhood rough sets,the original feature space is obtained by creating many optimal feature subsets at various granularity levels.Then,by deploying the DF cascade structure,the mapping connection between the transient stability state and the features is reinforced.The weighted voting technique is used in the learning process to increase the classification accuracy of unstable samples.When contrasted to current methods,simulation results indicate that the proposed approach outperforms them.

The optimized design of a double-layer flow chamber

Introduction Blood flow provides a mechanical condition for blood cells and vessels,especially for endothelial cells.It is important to understand the mechanical characteristics of

Optimal Dispatch in Power Systems with Intermittent Power Sources

With the increasing integration of intermittent power sources (IPSs) into the power system, the uncertainty of IPSs requires solution and current dispatch system needs improvement. This paper aims to generate the optimal dispatch plan for day-ahead scheduling and real-time dispatch using the proposed model of characteristic optimal power flow (COPF). The integral time period represented by the median load point and the heavy and light load point with simplicity and accuracy. Simulation case studies on a 30-bus system are presented, which shows that COPF is an effective model to generate the optimal dispatch plan for power systems with high penetration of IPSs.

Direct and noisy transitions in a model shear flow

The transition to turbulence in flows where the laminar profile is linearly stable requires perturbations of finite amplitude. ＂Optimal＂ perturbations are distinguished as extrema of certain functionals, and different functionals give different optima. We here discuss the phase space structure of a 2D simplified model of the transition to turbulence and discuss optimal perturbations with respect to three criteria： energy of the initial condition, energy dissipation of the initial condition, and amplitude of noise in a stochastic transition. We find that the states triggering the transition are different in the three cases, but show the same scaling with Reynolds number.

Identification of Critical Lines in Power System Based on Optimal Load Shedding

Based on risk theory, considering the probability of an accident and the severity of the sequence, combining N-1 and N-2 security check, this paper puts forward a new risk index, which uses the amount of optimal load shedding as the severity of an accident consequence to identify the critical lines in power system. Taking IEEE24-RTS as an example, the simulation results verify the correctness and effectiveness of the proposed index.

ODFF: Optimized Dual Fuzzy Flow Controller Based Voltage Sag Compensation for SMES-Based DVR in Power Quality Applications

The booming electronics itself carries an impact on power quality. Superconducting Magnetic Energy Storage (SMES) is proposed to enhance power quality in three-phase systems under various loads. This paper aimed to compensate the voltage sags under various faults in the grid systems. The SMES is selected as an energy storage unit to improve the capability of voltage sag compensation. Optimized Dual Fuzzy Flow (ODFF) logic controller is designed to prevent the voltage sag time during excessive phase voltage variation. Hence the proposed controller strategy reduces the total harmonic distortion during various fault conditions. To regulate the contribution of active power, the least possible value is improved using ODFF. The depth of voltage sags compensation is achieved by the over modulation and an iterative loop is designed in the control block. While protecting sensitive loads from voltage disturbances, and sags initiated by the power system, the proposed configuration is advantageous for an industrial implementation. It is found that the proposed method can result in more than 50% additional sag support time when compared with the previous methods such as PI and PSO. Utilizing MATLAB Simulink, compensation of sag and minimization of THD is established, and the simulation tests are performed to evaluate the performance of the proposed control method.

Coordinated restoration optimization of power-gas integrated energy system with mobile emergency sources

In an integrated energy system(IES) composed of multiple subsystems, energy coupling causes an energy supply blockage or shutdown in one subsystem, thereby affecting the energy flow distribution optimization of other subsystems.The energy supply should be globally optimized during the IES energy supply restoration process to produce the highest restoration net income. Mobile emergency sources can be quickly and flexibly connected to supply energy after an energy outage to ensure a reliable supply to the system, which adds complexity to the decision. This study focuses on a powergas IES with mobile emergency sources and analyzes the coupling relationship between the gas distribution system and the power distribution system in terms of sources, networks, and loads, and the influence of mobile emergency source transportation. The influence of the transient process caused by the restoration operation of the gas distribution system on the power distribution system is also discussed. An optimization model for power-gas IES restoration was established with the objective of maximizing the net income. The coordinated restoration optimization decision-making process was also built to realize the decoupling iteration of the power-gas IES, including system status recognition, mobile emergency source dispatching optimization, gas-to-power gas flow optimization, and parallel intra-partition restoration scheme optimization for both the power and gas distribution systems. A simulation test power-gas IES consisting of an 81-node medium-voltage power distribution network, an 89-node medium-pressure gas distribution network, and four mobile emergency sources was constructed. The simulation analysis verified the efficiency of the proposed coordinated restoration optimization method.

Estimating Risk-aware Flexibility Areas for Electric Vehicle Charging Pools via AC Stochastic Optimal Power Flow

This paper introduces an AC stochastic optimal power flow(SOPF)for the flexibility management of electric vehicle(EV)charging pools in distribution networks under uncertainty.The AC SOPF considers discrete utility functions from charging pools as a compensation mechanism for eventual energy not served to their charging tasks.An application of the AC SOPF is described where a distribution system operator(DSO)requires flexibility to each charging pool in a day-ahead time frame,minimizing the cost for flexibility while guaranteeing technical limits.Flexibility areas are defined for each charging pool and calculated as a function of a risk parameter involving the uncertainty of the solution.Results show that all players can benefit from this approach,i.e.,the DSO obtains a riskaware solution,while charging pools/tasks perceive a reduction in the total energy payment due to flexibility services.

An Uncertain Optimal Energy Flow Model for CCHP Campus Microgrid Using Parameterized Probability Boxes

Due to the uncertain fluctuations of renewable energy and load power, the state variables such as bus voltages and pipeline mass flows in the combined cooling, heating, and power campus microgrid(CCHP-CMG) may exceed the secure operation limits. In this paper, an optimal energy flow(OEF) model for a CCHP-CMG using parameterized probability boxes(p-boxes) is proposed to describe the higher-order uncertainty of renewables and loads. In the model, chance constraints are used to describe the secure operation limits of the state variable p-boxes, and variance constraints are introduced to reduce their random fluctuation ranges. To solve this model, the chance and variance constraints are transformed into the constraints of interval cumulants(ICs) of state variables based on the p-efficient point theory and interval Cornish-Fisher expansion. With the relationship between the ICs of state variables and node power, and using the affine interval arithmetic method, the original optimization model is finally transformed into a deterministic nonlinear programming model. It can be solved by the CONOPT solver in GAMS software to obtain the optimal operation point of a CCHP-CMG that satisfies the secure operation requirements considering the higher-order uncertainty of renewables and loads. Case study on a CCHP-CMG demonstrates the correctness and effectiveness of the proposed OEF model.

Probabilistic Optimal Power Flow Considering the Dependence of Multiple Wind Farms Using Pair Diffusive Kernel Copula

As wind farms are commonly installed in areas with abundant wind resources,spatial dependence of wind speed among nearby wind farms should be considered when modeling a power system with large-scale wind power.In this paper,a novel bivariate non-parametric copula,and a bivariate diffusive kernel(BDK)copula are proposed to formulate the dependence between random variables.BDK copula is then applied to higher dimension using the pair-copula method and is named as pair diffusive kernel(PDK)copula,offering flexibility to formulate the complicated dependent structure of multiple random variables.Also,a quasi-Monte Carlo method is elaborated in the sampling procedure based on the combination of the Sobol sequence and the Rosen-blatt transformation of the PDK copula,to generate correlated wind speed samples.The proposed method is applied to solve probabilistic optimal power flow(POPF)problems.The effectiveness of the BDK copula is validated in copula definitions.Then,three different data sets are used in various goodness-of-fit tests to verify the superior performance of the PDK copula,which facilitates in formulating the dependence structure of wind speeds at different wind farms.Furthermore,samples obtained from the PDK copula are used to solve POPF problems,which are modeled on three modified IEEE 57-bus power systems.Compared to the Gaussian,T,and parametric-pair copulas,the results obtained from the PDK copula are superior in formulating the complicated dependence,thus solving POPF problems.

Robust N−k Security-constrained Optimal Power Flow Incorporating Preventive and Corrective Generation Dispatch to Improve Power System Reliability

As extreme weather events have become more frequent in recent years,improving the resilience and reliability of power systems has become an important area of concern.In this paper,a robust preventive-corrective security-constrained optimal power flow(RO-PCSCOPF)model is proposed to improve power system reliability under N−k outages.Both the short-term emergency limit(STL)and the long-term operating limit(LTL)of the post-contingency power flow on the branch are considered.Compared with the existing robust corrective SCOPF model that only considers STL or LTL,the proposed ROPCSCOPF model can achieve a more reliable generation dispatch solution.In addition,this paper also summarizes and compares the solution methods for solving the N−k SCOPF problem.The computational efficiency of the classical Benders decomposition(BD)method,robust optimization(RO)method,and line outage distribution factor(LODF)method are investigated on the IEEE 24-bus Reliability Test System and 118-bus system.Simulation results show that the BD method has the worst computation performance.The RO method and the LODF method have comparable performance.However,the LODF method can only be used for the preventive SCOPF and not for the corrective SCOPF.The RO method can be used for both.

Constraint Learning-based Optimal Power Dispatch for Active Distribution Networks with Extremely Imbalanced Data

Transition towards carbon-neutral power systems has necessitated optimization of power dispatch in active distribution networks(ADNs)to facilitate integration of distributed renewable generation.Due to unavailability of network topology and line impedance in many distribution networks,physical model-based methods may not be applicable to their operations.To tackle this challenge,some studies have proposed constraint learning,which replicates physical models by training a neural network to evaluate feasibility of a decision(i.e.,whether a decision satisfies all critical constraints or not).To ensure accuracy of this trained neural network,training set should contain sufficient feasible and infeasible samples.However,since ADNs are mostly operated in a normal status,only very few historical samples are infeasible.Thus,the historical dataset is highly imbalanced,which poses a significant obstacle to neural network training.To address this issue,we propose an enhanced constraint learning method.First,it leverages constraint learning to train a neural network as surrogate of ADN's model.Then,it introduces Synthetic Minority Oversampling Technique to generate infeasible samples to mitigate imbalance of historical dataset.By incorporating historical and synthetic samples into the training set,we can significantly improve accuracy of neural network.Furthermore,we establish a trust region to constrain and thereafter enhance reliability of the solution.Simulations confirm the benefits of the proposed method in achieving desirable optimality and feasibility while maintaining low computational complexity.

Multi-period integrated natural gas and electric power system probabilistic optimal power flow incorporating power-to-gas units

The increasing adoption of gas-fired power plants directly strengthens the coupling between electric power and natural gas systems. Current industrial practice in optimal power flow for electric power systems has not taken the security constraints of gas systems into consideration, resulting in an overly-optimistic solution. Meanwhile, the operation of electric power and natural gas systems is coupled over multiple periods because of the ramp rate limits of power generators and the slow dynamical characteristics of gas systems. Based on these motivations, we propose a multi-period integrated natural gas and electric power system probabilistic optimal power flow(M-GEPOPF) model, which includes dynamic gas flow models. To address the uncertainties originating from wind power and load forecasting, a probabilistic optimal power flow(POPF) calculation based on a three-point estimate method(3 PEM) is adopted. Moreover, power-togas(Pt G) units are employed to avoid wind power curtailment and enable flexible bi-directional energy flows between the coupled energy systems. An integrated IEEE RTS 24-bus electric power system and the Belgian 20-node natural gas system are employed as a test case to verify the applicability of the proposed M-GEPOPF model, and to demonstrate the potential economic benefits of Pt G units.

Optimal Energy Flow and Nodal Energy Pricing in Carbon Emission-embedded Integrated Energy Systems

Green energy is driving the evolutions of energy industry and carbon emission is becoming an important concern.Considering the increasing couplings among various energy sectors,this paper investigates multi-period optimal energy flow and energy pricing in carbon-emission embedded integrated energy systems,including electricity,natural gas,and district heating networks.Firstly,an optimal scheduling model of integrated energy systems was proposed in this paper.The models of DC power flow,natural gas pipeline flow and heating network energy flow are presented and linearized for the optimization problem.Natural gas-fired generators and combined heat and power(CHP)units are modeled as coupling components of electricitygas and electricity-heating networks.Then,based on the optimal scheduling model,the locational marginal prices(LMP)for electricity,natural gas and heating network are determined.Moreover,the carbon emission caused by energy production has been taken into account in the optimal scheduling and energy pricing process.Finally,case studies on a combined network consisting of IEEE 39-bus system,Belgium 20-node natural gas system and 6-node heating system demonstrate the effectiveness of the proposed model and the impacts of carbon emission on system scheduling and LMP.