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.

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.

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.

Linear OPF-based Robust Dynamic Operating Envelopes with Uncertainties in Unbalanced Distribution Networks

Dynamic operating envelopes(DOEs),as key enablers to facilitate distributed energy resource(DER)integration,have attracted increasing attention in the past years.However,uncertainties,which may come from load forecasting errors or inaccurate network parameters,have been rarely discussed in DOE calculation,leading to compromised quality of the hosting capacity allocation strategy.This letter studies how to calculate DOEs that are immune to such uncertainties based on a linearised unbalanced three-phase optimal power flow(UTOPF)model.With uncertain parameters constrained by norm balls,formulations for calculating robust DOEs(RDOEs)are presented along with discussions on their tractability.Two cases,including a 2-bus illustrative network and a representative Australian network,are tested to demonstrate the effectiveness and efficiency of the proposed approach.

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.

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.

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.

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.

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.

Day-Ahead Probabilistic Load Flow Analysis Considering Wind Power Forecast Error Correlation

Short-term power flow analysis has a significant influence on day-ahead generation schedule. This paper proposes a time series model and prediction error distribution model of wind power output. With the consideration of wind speed and wind power output forecast error’s correlation, the probabilistic distributions of transmission line flows during tomorrow’s 96 time intervals are obtained using cumulants combined Gram-Charlier expansion method. The probability density function and cumulative distribution function of transmission lines on each time interval could provide scheduling planners with more accurate and comprehensive information. Simulation in IEEE 39-bus system demonstrates effectiveness of the proposed model and algorithm.

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.

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.

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.

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.

主动配电网潮流的全纯嵌入计算方法

配电网潮流计算是进行配电网规划和运行的重要基础。目前,配电网潮流求解方法主要有牛拉(Newton Raphson,NR)法和前推回代(forward backward substitution,FBS)法两大类,但NR法和FBS法在潮流收敛性和计算效率等方面均存在一定的不足。全纯嵌入法(holomorphic embedding method,HEM)是一种求解非线性潮流方程的新方法,它可以有效避免NR法和FBS法在配电网潮流求解过程中出现的上述问题,但现有HEM未充分考虑配电网中各类型分布式电源(distributed generation,DG)和智能软开关(soft open point,SOP)控制方式的多样性,且未构建计及负荷电压特性和频率特性的潮流模型,难以适用于不同运行模式下配电网潮流计算。针对上述问题,提出一种可求解含多类型DG和SOP且可运行在并网/孤岛模式的主动配电网统一全纯嵌入潮流计算方法。首先,根据负荷静态电压和频率特性,构建计及配电网频率和节点电压影响的负荷节点全纯嵌入潮流模型;其次,根据DG不同的控制方式以及配电网不同的运行模式,将DG所连节点等效为不同节点类型,构建各类DG的全纯嵌入潮流模型;再次,考虑SOP不同控制方式,构建SOP全纯嵌入潮流模型;从次,依据全纯嵌入潮流模型等式左右两侧同次幂级数系数相等原则,推导配电网各全纯函数幂级数系数的求解递推关系式,进而计算各全纯函数的各项幂级数系数,借助解析延拓理论求取电压和频率逼近值,实现配电网潮流的准确求解;最后,通过修改的IEEE-33节点测试系统和IEEE-123节点测试系统验证所提方法准确性和有效性。

基于分布式潮流控制器的海上风电系统谐波治理方法和控制策略

由于电力电缆的电容效应,海上风电经电缆汇集系统极易出现谐波谐振放大的现象,造成电能质量的下降。分布式潮流控制器属于基于电压源换流器的装置,在进行潮流调节的同时也能进行谐波治理。文中首先构建了海上风电系统的频域相关模型,基于该模型分析了谐波谐振放大的原因;随后,采用了将分布式潮流控制器串入海上风电系统的谐波治理方式,推导并得到了含分布式潮流控制器的海上风电系统的谐波特性。基于该谐波特性,设计了一种控制策略。该策略通过控制分布式潮流控制器实时跟踪使并网点谐波电压幅值为零的谐波补偿电压,从而降低并网点的谐波电压含量。仿真结果表明,所提出的基于分布式潮流控制器的海上风电系统谐波治理方法和控制策略能够有效地降低并网点的谐波电压,改善电能质量。

侧式进/出水口各孔道流量分配差异及影响因素

对于抽水蓄能电站侧式进/出水口各孔道流量分配,现有设计规范规定进/出水口相邻中边孔道的流量不均匀程度不宜超过10%,但实际工程设计难以达到此要求.本文以某抽水蓄能电站侧式进/出水口为例,通过优化进/出水口各体型参数,利用数值模拟方法研究各孔道流量等水力参数,重点分析分流墩布置对各孔道流量分配的影响及其规律,试图使进流工况和出流工况相邻中边孔道的流量不均匀程度均最小.研究表明,改变扩散段分流墩布置能有效改善流量不均匀程度.对于3墩4孔侧式进/出水口,相邻中边孔道的流量不均匀程度在出流工况下随中边孔宽度比增大而增大,在进流工况下随中边孔宽度比增大而减小;当中边孔宽度比增大且中墩后移距离减小时,出流工况和进流工况下的流量不均匀程度均减小.对于2墩3孔侧式进/出水口,相邻中边孔道的流量不均匀程度不论在出流工况下还是在进流工况下,均随中边孔宽度比增大呈先减小后增大的规律.优化后的3墩4孔侧式进/出水口的中边孔宽度比取0.228∶0.272,中墩后移距离取0.36D(D为隧洞直径),其相邻中边孔道的流量不均匀程度均较优,在出流工况下为18.47%~19.43%,在进流工况下为19.82%~19.83%;优化后的2墩3孔侧式进/出水口的中边孔宽度比取0.310∶0.345,其相邻中边孔道的流量不均匀程度均较优,在出流工况下为19.47%~19.63%,在进流工况下为18.66%~18.67%.相邻中边孔道的流量不均匀程度较难满足不宜超过10%的设计规范要求.研究成果将有助于《抽水蓄能电站设计规范》中关于进/出水口水力指标要求的完善.

考虑风光出力不确定性及相关性的配电网规划方法

新能源在电力系统中的渗透率日益提高,大大增加了电网中的不确定因素,对配电网的规划运行和控制提出了更高的要求。配电网规划是电力系统安全稳定运行的重要基石,传统配电网规划中各参数都已确定,缺乏对不确定因素的适应性。因此,提出一种基于概率潮流的配电网规划方法,首先对配电网中的不确定因素定量建模,建立源荷出力模型,其次将风速、太阳辐射与用电负荷之间的相关性用秩相关系数矩阵表征,建立计及相关性的半不变量概率潮流计算方法,最后构建以规划成本最小为目标函数,以潮流平衡、馈线容量、节点电压、网架辐射型结构为约束条件的配电网规划模型,并通过改进惯性参数与引入变异操作对粒子群算法进行改进,利用改进后的算法求解规划模型。以33节点系统为例进行仿真,结果验证了该方法能够有效降低网损,减少网络规划费用。

考虑光伏随机性的交直流混合配电网鲁棒机会约束安全域模型

为实现高比例光伏接入下交直流混合配电网的安全评估,构建了交直流混合配电网的鲁棒机会约束安全域模型。首先,提出一种基于区间划分的自适应带宽核密度估计方法,以获取光伏预测误差概率分布,构建光伏出力机会约束不确定集合;其次,采用功率与节点电压幅值比值为状态变量,在已有交流线性化潮流模型的基础上推导一种交直流混合配电网线性化潮流模型;然后,提出交直流混合配电网鲁棒机会约束安全域的概念和模型,结合列与约束生成算法和径向迭代搜索算法生成可观测的鲁棒机会约束安全域空间。最后,算例分析验证了所提模型能够在鲁棒机会约束安全域上准确、直观的反映光伏出力的随机性,进而为交直流混合配电网的准确安全评估提供支撑。

基于电压补偿的双端直流配电网电压就地协调控制

双端直流配电网是一种双端电源供电的网络结构,可为直流负荷提供更加稳定和可靠的电源电压。然而,负荷的功率波动和不平衡使线路电压跌落增大,可能导致直流负荷的电压不平衡度和电压偏差指标越限,影响直流负荷的正常运行。文中基于电压源型换流器(VSC)外环电压控制,考虑中线电压补偿,提出基于电压补偿等效模型的直流配电网电压偏差及不平衡度联合抑制策略,实现直流配电网电压就地协调控制。首先,建立双端直流配电网潮流模型,将VSC电压下垂控制引入潮流模型,分析不同控制策略下的电压偏差和不平衡度的特性。其次,在此基础上,以电压最低点为分点获得双端电源供电回路压降的简化等效模型,并利用最小二乘法实现等效阻抗参数辨识,构建双端直流配电网的电压补偿等效模型。以参数辨识结果作为电压外环控制输入,提出考虑中线电压补偿的双端直流配电网电压就地协调控制策略。最后,在MATLAB/Simulink中搭建仿真模型,验证了双端直流配电网潮流模型的正确性和控制策略的有效性。