Power flow calculation for a distribution system with multi-port PETs:an improved AC-DC decoupling iterative method

Recently,power electronic transformers(PETs)have received widespread attention owing to their flexible networking,diverse operating modes,and abundant control objects.In this study,we established a steady-state model of PETs and applied it to the power flow calculation of AC-DC hybrid systems with PETs,considering the topology,power balance,loss,and control characteristics of multi-port PETs.To address new problems caused by the introduction of the PET port and control equations to the power flow calculation,this study proposes an iterative method of AC-DC mixed power flow decoupling based on step optimization,which can achieve AC-DC decoupling and effectively improve convergence.The results show that the proposed algorithm improves the iterative method and overcomes the overcorrection and initial value sensitivity problems of conventional iterative algorithms.

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.

A Hybrid Decoupled Power Flow Method for Balanced Power Distribution Systems

This paper proposes a hybrid decoupled power flow method for balanced power distribution systems with distributed generation sources. The method formulates the power flow equations in active power and reactive power decoupled form with polar coordinates. Second-order terms are included in the active power mismatch iteration, and constant Jacobian and Hessian matrices are used. A hybrid direct and indirect solution technique is used to achieve efficiency and robustness of the algorithm. Active power correction is solved by means of a sparse lower triangular and upper triangular （LU） decomposition algorithm with partial pivoting, and the reactive power correction is solved by means of restarted generalized minimal residual algorithm with an incomplete LU pre-conditioner. Typical distribution generation models and distribution load models are included. The impact of zero-impedance branches is explicitly modeled through reconfiguring of the adjacent branches with impedances. Numerical examples on a sample distribution system with widespread photovoltaic installations are given to demonstrate the effectiveness of the proposed method.

Power Flow Model for Medium-voltage Distribution Systems Considering Measurement and Structure Characteristics

Medium-voltage distribution systems(MVDSs)mainly consist of a feeder head,lines,distribution transformers,and the equivalent load or power supply interfaced with the distribution transformers.The information of such load or power supply can be measured via the three-wattmeter method(THM)and the two-wattmeter method(TWM).The measurements can be used to perform the control of the power supply and simulate the characteristics of the load,so the models of the load and the power supply need to consider the measurement characteristics.Existing research works on three-phase power flow(PF)just consider the measurement characteristics of THM.Hence,the PF equation of the bus measured via TWM is firstly built.Based on conventional measurements,an accurate and general model of the grounded and ungrounded slack bus is proposed.Furthermore,the influence arising from the connection type and angle shift of distribution transformers on the admittance matrix is considered,and thus a general three-phase transformer model is summarized,which is applicable for all the transformers mentioned herein.Finally,Newton's method is adopted to solve the PF calculation,and the performance of the proposed PF model is demonstrated through designed tests.

Interdependence between transportation system and power distribution system: a comprehensive review on models and applications

The rapidly increasing penetration of electric vehicles(EVs) in modern metropolises has been witnessed during the past decade, inspired by financial subsidies as well as public awareness of climate change and environment pro-tection. Integrating charging facilities, especially highpower chargers in fast charging stations, into power distribution systems remarkably alters the traditional load flow pattern, and thus imposes great challenges on the operation of distribution network in which controllable resources are rare. On the other hand, provided with appropriate incentives, the energy storage capability of electric vehicle offers a unique opportunity to facilitate the integration of distributed wind and solar power generation into power distribution system. The above trends call for thorough investigation and research on the interdependence between transportation system and power distribution system. This paper conducts a comprehensive survey on this line of research. The basic models of transportation system and power distribution system are introduced,especially the user equilibrium model, which describes the vehicular flow on each road segment and is not familiar to the readers in power system community. The modelling of interdependence across the two systems is highlighted.Taking into account such interdependence, applications ranging from long-term planning to short-term operation are reviewed with emphasis on comparing the description of traffic-power interdependence. Finally, an outlook of prospective directions and key technologies in future research is summarized.

A hybrid multi-objective optimization method considering optimization problems in power distribution systems

Various kinds of new engineering technologies have been studied to realize the low-carbon and sustainable power supply systems all over the world.In actual implementation of these technologies,mostly,there are multiple objectives with trade off relationships among each other,and also various constraints in the achievement of these objectives.Therefore,it should be essential to solve multiobjective optimization problems effectively in the applications of these new technologies in power systems.This paper proposes an improved method to realize multiobjective optimization for critical challenges in advanced power systems.To realize that,in an optimal dispersed generation installation problem,that is,one of effective measures for low-carbon power systems,various optimization methods and their combination methods are evaluated and a hybrid method for evolutionary algorithms was developed.The method can provide improved results compared with other state-of-the-art multi-objective optimization methods.

Connecting Wind Turbine Generator to Distribution Power Grid--A Preload Flow Calculation Stage

A distribution grid is generally characterized by a high R/X （resistance/reactance） ratio and it is radial in nature. By design, a distribution grid system is not an active network, and it is normally designed in such a way that power flows from transmission system via distribution system to consumers. But in a situation when wind turbines are connected to the distribution grid, the power source will change from one source to two sources, in this case, network is said to be active. This may probably have an impact on the distribution grid to whenever the wind turbine is connected. The best way to know the impact of wind turbine on the distribution grid in question is by carrying out load flow analysis on that system with and without the connection of wind turbines. Two major fundamental calculations： the steady-state voltage variation at the PCC （point of common coupling） and the calculation of short-circuit power of the grid system at the POC （point of connection） are necessary before carrying out the load flow study on the distribution grid. This paper, therefore, considers these pre-load flow calculations that are necessary before carrying out load flow study on the test distribution grid. These calculations are carded out on a test distribution system.

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.

An Algorithm for Short-Circuit Current Interval in Distribution Networks with Inverter Type Distributed Generation Based on Affine Arithmetic

During faults in a distribution network,the output power of a distributed generation(DG)may be uncertain.Moreover,the output currents of distributed power sources are also affected by the output power,resulting in uncertainties in the calculation of the short-circuit current at the time of a fault.Additionally,the impacts of such uncertainties around short-circuit currents will increase with the increase of distributed power sources.Thus,it is very important to develop a method for calculating the short-circuit current while considering the uncertainties in a distribution network.In this study,an affine arithmetic algorithm for calculating short-circuit current intervals in distribution networks with distributed power sources while considering power fluctuations is presented.The proposed algorithm includes two stages.In the first stage,normal operations are considered to establish a conservative interval affine optimization model of injection currents in distributed power sources.Constrained by the fluctuation range of distributed generation power at the moment of fault occurrence,the model can then be used to solve for the fluctuation range of injected current amplitudes in distributed power sources.The second stage is implemented after a malfunction occurs.In this stage,an affine optimization model is first established.This model is developed to characterizes the short-circuit current interval of a transmission line,and is constrained by the fluctuation range of the injected current amplitude of DG during normal operations.Finally,the range of the short-circuit current amplitudes of distribution network lines after a short-circuit fault occurs is predicted.The algorithm proposed in this article obtains an interval range containing accurate results through interval operation.Compared with traditional point value calculation methods,interval calculation methods can provide more reliable analysis and calculation results.The range of short-circuit current amplitude obtained by this algorithm is slightly larger than those obtained using the Monte Carlo algorithm and the Latin hypercube sampling algorithm.Therefore,the proposed algorithm has good suitability and does not require iterative calculations,resulting in a significant improvement in computational speed compared to the Monte Carlo algorithm and the Latin hypercube sampling algorithm.Furthermore,the proposed algorithm can provide more reliable analysis and calculation results,improving the safety and stability of power systems.

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.

Research and Practice of Flexibility in Distribution Systems:A Review

Flexibility in energy systems can support the operation of the electricity grid by providing active and reactive power to avoid voltage limit violations or congestion.Active distribution networks can provide this flexibility by implementing systems to control distributed generators,storage or loads.Additionally,power flow controlling devices can be used to implement operational flexibility in the energy system.This paper presents concepts for planning and forecasting of flexibility,monitoring of energy systems and control of flexibility from active distribution networks(ADNs)to enable the use of flexibility in future power systems.

Performance Enhancement of Distribution Systems via Distribution Network Reconfiguration and Distributed Generator Allocation Considering Uncertain Environment

The emergence of dispersed generation,smart grids,and deregulated electricity markets has increased the focus on enhancing the performance of distribution systems.This paper proposes a method to reduce the energy loss and improve the reliability of distribution systems by performing distribution network reconfiguration(DNR)and distributed generator(DG)allocation.In this study,the intermittent nature of renewable-based DGs and the load profile are considered using a probabilistic method.The study investigates different annual plans based on the seasonal power profiles of DGs and the load to minimize the combined cost function of annual energy loss and annual energy not served.The proposed method is implemented using the firefly algorithm(FA),which is one of the meta-heuristic optimization algorithms.Several case studies are investigated using the IEEE 33-bus distribution system to highlight the effectiveness of the method.

Security Constrained Distributed Optimal Power Flow of Interconnected Power Systems

The security constrained distributed optimal power flow （DOPF） of interconnected power systems is presented. The centralized OPF problem of the multi-area power systems is decomposed into independent DOPF subproblems, one for each area. The dynamic security region （DSR） to guarantee the transient stability constraints and static voltage stability region （SVSR） constraints, and line current limits are included as constraints. The solutions to the DOPF subproblems of the different areas are coordinated through a pricing mechanism until they converge to the centralized OPF solution. The nonlinear DOPF subproblem is solved by predictor-corrector interior point method （PClPM）. The IEEE three-area RTS-96 system is worked out in order to demonstrate the effectiveness of the proposed method.

A Parallel Approach for Real-Time Power Flow in Distribution Networks

The new reality of smart distribution systems with use of generation sources of small and medium sizes brings new challenges for the operation of these systems. The complexity and the large number of nodes requires use of methods which can reduce the processing time of algorithms such as power flow, allowing its use in real time. This paper presents a known methodology for calculating the power flow in three phases using backward/forward sweep method, and also considering other network elements such as voltage regulators, shunt capacitors and sources of dispersed generation of types PV （active power and voltage） and PQ （active and reactive power）. After that, new elements are introduced that allow the parallelization of this algorithm and an adequate distribution of work between the available processors. The algorithm was implemented using a multi-tiered architecture; the processing times were measured in many network configurations and compared with the same algorithm in the serial version.

Novel Affine Power Flow Method for Improving Accuracy of Interval Power Flow Data in Cyber Physical Systems of Active Distribution Networks

A large number of load power and power output of distributed generation in an active distribution network(ADN)are uncertain,which causes the classical affine power flow method to encounter problems of interval expansion and low efficiency when applied to an AND.This then leads to errors of interval power flow data sources in the cyber physical system(CPS)of an ADN.In order to improve the accuracy of interval power flow data in the CPS of an ADN,an affine power flow method of an ADN for restraining interval expansion is proposed.Aiming at the expansion of interval results caused by the approximation error of non-affine operations in an affine power flow method,the approximation method of the new noise source coefficient is improved,and it is proved that the improved method is superior to the classical method in restraining interval expansion.To overcome the decrease of computational efficiency caused by new noise sources,a novel merging method of new noise sources in an iterative process is designed.Simulation tests are conducted on an IEEE 33-bus,PG&E 69-bus and an actual 1180-bus system,which proves the validity of the proposed affine power flow method and its advantages in terms of computational efficiency and restraining interval expansion.

Fuzzy vs. Probabilistic Techniques to Address Uncertainty for Radial Distribution Load Flow Simulation

For Power distribution system the most important task for distribution engineer is to efficiently simulate the system and address the uncertainty using a suitable mathematical method. This paper presents a comparison of two methods used in analyzing uncertainties. The first method is Montecarlo simulation (MCS) that considers input parameters as random variables and second one is fuzzy alpha cut method (FAC) in which uncertain parameters are treated as fuzzy numbers with given membership functions. Both techniques are tested on a typical Load flow solution simulation, where connected loads are considered as uncertain. In order to provide a basis for comparison between above two approaches, the shapes of the membership function used in the fuzzy method is taken same as the shape of the probability density function used in the Monte Carlo simulations. For more than one uncertain input variable, simulation result indicates that MCS method provides better output results compared to FAC, however takes more time due to number of runs. FAC provides an alternate method to MCS when addressing single or limited input variables and is fast.

Power Law Exponents for Vertical Velocity Distributions in Natural Rivers

While log law is an equation theoretically derived for near-bed region, in most cases, power law has been researched by experimental methods. Thus, many consider it as an empirical equation and fixed power law exponents such as 1/6 and 1/7 are generally applied. However, exponent of power law is an index representing bed resistance related with relative roughness and furthermore influences the shapes of vertical velocity distribution. The purpose of this study is to investigate characteristics of vertical velocity distribution of the natural rivers by testing and optimizing previous methods used for determination of power law exponent with vertical velocity distribution data collected with ADCPs during the years of 2005 to 2009 from rivers in South Korea. Roughness coefficient has been calculated from the equation of Limerinos. And using theoretical and empirical formulae, and representing relationships between bed resistance and power law exponent, it has been evaluated whether the exponents suggested by these equations appropriately reproduce vertical velocity distribution of actual rivers. As a result, it has been confirmed that there is an increasing trend of power law exponent as bed resistance increases. Therefore, in order to correctly predict vertical velocity distribution in the natural rivers, it is necessary to use an exponent that reflects flow conditions at the field.

Development of a Genetic Algorithm for Evaluating the Performance of Overhead Power Distribution Lines and Proposing Solutions to Improve Distribution Line Safety

This paper aims to present and discuss the use of a power flow methodology based on Gauss elimination method to evaluate the performance of distribution network taking into account the neutral conductor absence at specific sections, and a development of a methodology based on GA （genetic algorithm） capable of evaluating alternative solutions in different bars of the feeder, in order to propose appropriate solutions to improve the distribution network safety. Besides the technical aspects, the proposed GA methodology takes into account the economic feasibility analysis. The results of power flow simulations have shown that the presence of single-phase transformers along with the absence of the neutral conductor at specific sections of the MV （medium voltage） network may increase the Vng （neutral-to-ground voltage） levels of the feeders involved, jeopardizing the system＇s safety. On the other hand, the solutions proposed by the GA methodology may reduce the network Vng levels and improve the safety conditions, providing values close to the ones found before the neutral conductor theft.

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.