鲁棒化理论线损计算技术研究与系统构建_英文_李文博

·专题论述·ＲｅｓｅａｒｃｈｏｎＲｏｂｕｓｔＣｏｍｐｕｔｉｎｇＴｅｃｈｎｉｑｕｅａｎｄＳｙｓｔｅｍＣｏｎｓｔｒｕｃｔｉｏｎｆｏｒＴｈｅｏｒｅｔｉｃａｌＬｉｎｅＬｏｓｓＡｎａｌｙｓｉｓLI Wenbo，MA Changhui（State Grid Shandong Electric Power Research Institute，Jinan250002，China）Abstract:The theoretical line loss calculation is related to a huge amount of data for power grid.In traditional line loss analysis system data manipulation and power flow adjustment are mainly depended on human experiences，by which the correctness of data maintenance and the reasonableness of the power flow statement cannot be guaranteed.The problem will be more serious when the power flow cannot converge during the line loss calculation for the huge transmission network，which wastes lots of energy and time of analyst.In allusion to the problems mentioned above，a robust computing system for the theoretical line losses calculation is established based on the computation experience of line losses and the theories of power flow and optimal power flow，which is made up of data preprocessing，localization of the suspicious data，identification of the bad data，zeroing boundary mismatch.The robust system proposed can run through all the computation process and gives the efficiency and reasonable of the line losses analysis a powerful guarantee.Finally examples illustrate the effectiveness of the method for bad redundant data eliminating and suspect data identification when power flow cannot converge.Key words:theoretical line loss；robust computing system；power flow；data justification；data adjustment鲁棒化理论线损计算技术研究与系统构建李文博，麻常辉（国网山东省电力公司电力科学研究院，济南250002）摘要：理论线损计算中涉及电网数据量庞大，传统方法完全依赖人工经验进行数据操作和潮流调整，数据正确性和潮流断面合理性难以保证，尤其在大型输电网理论线损计算中经常遇到的潮流不收敛问题，给线损计算带来极大困难。

针对线损理论计算中出现的上述问题，总结理论线损计算经验，借助潮流理论和优化潮流理论，通过数据预处理、可疑数据分区定位、错误数据辨识及边界失配量归零模块，构建了鲁棒化理论线损计算系统，该系统贯穿理论线损计算全过程，能有力保障理论线损计算的高效性和合理性。

最后，通过算例阐述冗余数据筛选方法以及潮流不收敛情况下可疑数据定位方法的原理并验证其有效性。

关键词：理论线损；鲁棒计算系统；潮流计算；数据辨识；数据调整中图分类号：TM744文献标志码：A文章编号：1007－9904（2015）04－0026－070IntroductionAs an important tool to improve management of line loss，theoretical computation of line losses can authen-ticate the economy of the structure and the operation of the power grid.It also can provide scientific founda-tions for the development and plan of power grid by revealing the reason of high losses and determining ef-fective measures to decrease the losses.So the research of theoretical computation of line losses is always paid close attention to worldwide.Since the30′in the last century，the foreign re-searchers have studied the power loss in transmission process in distribution network by theoretical compu-tation of line loss.After the fast development of com-puter technology，various theoretical line losses calcu-lation method utilizing the computer as accessibility tools are proposed and are increasingly applied to practice projects.Until late20th century，methods of energy losses calculation have become very mature［1-4］and are widely used in field application.In addition，measures to reduce line losses is another research em-26phasis，such as network reconfiguration，reactive power optimization，location of reactive compensation equip-ment［5-7］.In our country，number of experts and scholars have applied themselves to investigating the suitable method to analysis line loss for Chinese patients［8-11］.For in-stance，several methods were proposed in reference ［12］to improve the precision of the result of the transmission network loss.Reference［13］proposed a method for calculating the line losses utilizing the data of state estimation to decrease the artificial errors and improve calculation efficiency.In reference［14-15］，a loss calculation method for distribution network based on the information from field terminal units is pro-posed.While，the automation equipment could not ful-fill the requirement of the method in many real cases，so reference［16］proposed a method based on the quasi real-time data to calculate the line loss，which could get more precise result with fewer measurements.In reference［17］，state estimation is adopted to find the doubtable data and obtain the missing data for net loss calculation.Reference［18］presents a new data pro cessing method，which can use more accurate data achieved to obtain more accurate and convincing re-sult.In the1990s，the appearance of a variety of ana-lytic systems for theoretical line losses marks the ma-turity of computing technology of theoretical line losses in our country.After years of consistent improvement，a mature analysis system has been formed for theoretical line losses in Shandong province.Not only the tools for computation and analyze but also the analysts have very high standing，which provided a strong technical support to the line-loss management and the develop-ment of power grid.However，basic data with high quality is the precondition of the development of the work mentioned above.With the rapid development of power grid and network interconnection，the precondi-tion has become too tough for analyst，especially dur-ing the line loss analysis of the large-scale transmis-sion network.Firstly，the uncertainty of the measured data，such as the errors of measuring instruments，transmission errors，deficiency of the measuring data，can directly influence the quality of the basic data. Secondly，the basic data include the changes of power network structure and power injection on every node，which is too much for human to handle，so that mistakes will be inevitable.It is very difficult for analysts to find these mistakes out again，especially for the situation that the power flow cannot converge because of them. The analysts have to carry out a carpet-style investi-gation depended on the artificial experience，which is a very aimless and inefficient way.At last，even the pow-er flow converge after modifications，the statement of power flow may not be consistent with the actual situ-ation because of the errors still exist，which also re-duce the significance of the theoretic calculation.In allusion to the problems mentioned above and on the basis of the existing methods for theoretic line lose calculation，we summary the working experience in line loss analysis and proposed a robust computing system for the theoretical line losses calculation，which can assist analyst in modifying bad basic data and ad-justing power flow.With the aid of this system，the an-alyst can accomplish the job with high efficiency and quality.At last，two simple examples are adopted to ex-pound the principle of bad data localization and adjust ment.1Structure of Robust Computing System for Theoretical Line Loss CalculationStructure of robust computing system proposed is shown in Figure 1.The system is constituted of two parts：traditional power flow module and assisted module for robust computation.The former is generally applied in many network loss analysis systems.It can operation well only when the quality of basic data is good enough.The latter can help user to check data，adjust power flow and improve accuracy of the results. That is why the system is called robust.At the beginning，the basic data must be put into the system.The term“basic data”here means the data27needed to execute power flow ，which include the pa -rameters of the electrical network structure and power injection on each node.Then a topology analysis is im plemented to form the network structure.During the pro -cess above ，some data detection programs are carried out at the same time to realize initial processing of the raw data.The term “redundant data ”represents the ac -tual measured data which is not must needed for the power flow program but very helpful for correction of bad basic data and adjustment of power flow ，such as power though lines and the amplitude of bus nodevoltage.Traditional power Assisted module for flow modulerobust computationFig.1Structure of robust computing systemIn general ，the power flow for the whole network cannot converge at first because of bad basic data.Then the “Location of Abnormal Data ”is used to find the restricted space the bad data most lies in and the“Accurate Identification of bad data ”will suggest theuser to modify the data which is most likely to be wrong.After all data is amended and all power flow for each region is correct ，the data in each region will be spliced together again to form the data of the whole network.At last ，to improve the accuracy and the truth of the result ，the “zeroing boundary mismatch ”is implemented to make the boundary parameters equal ，which lie in different computational area.2Function and Principle of Auxiliary Modules2.1Rationality checking of the parameters In this module ，the criterions based on common sense are adopted to check the data which is obvious wrong and is disadvantageous to the converge of the power flow ：A min ≤A ≤A max（1）where A is each input parameter ；A min and A max are theparameter ’s up and down limit respectively.Criterion （1）could be established for each input parameter based on the actual situation and the computational requirements.For example ，the per unit value of the generator terminal voltage must between 0.95to 1.15；transmission lines in various voltage classes have different length scales ；power injections on each node are also have a reasonable range.It is also important to note that the length of the transmission line must not be too small ，because it will seriously influence the numerical stability of the power flow.With the criterions ，the correctness of the parameters which is put into the system through artificial waycould be improved effectively.2.2Rationality checking of the topologyThere too many buses and branches in transmission network and the connecting relationship of them are complicated.To avoid obvious mistakes ，criterions such as follows will be checked ：For transmission network loss calculation ，there are usually only one standalone network.So if more than one isolated network exists in the computational system ，28the user will be prompted to review the related basic data.Check whether the voltage class of the component connected to each other is the same.If not，an error message will be presented.Check whether the connecting points of the component are all connected to the proper position.If not，an error message will be presented.For high voltage side of the220kV substation，if there is only one line connected，review of related basic data is recommended.For low voltage side of the500kV substation，if there are only a few lines connected，review of related basic data is recommended.2.3Eliminating bad redundant dataOnly good redundant data could be used as the reference to correct bad basic data，while bad measured data always appear because of measurement and transmission errors.Kirchhoff’s first law is applied to check for correctness of the redundant data.Neglecting the transmission loss and measurement errors，the sum of the power flow thought the branches belonging to a cut sets is definitely zero.So if there are no bad redundant data，the follow inequality will holds：G·Z′≤C（2）where G is the cut sets in which the sum of the branch power will be checked；Z′is the measured data of the branch power；C is a threshold value which could distinguish whether there are bad data or not. Specific steps are as follows：1）Initializing minimal cut sets.If two measurements on both end of the line l are available，the line l between points of measurement will be regarded as a node and the two measurements will form a cut sets.If no measurement along the line l is available，l will be shorten out and all measurements along the lines connected to l will form a cut sets.2）A measurement can be considered reliable if two cut sets related to it both fulfill inequality（2）.While，it will be called suspect if both of related cut sets cannot fulfill inequality（2）and undetermined if only one cut sets can fulfill inequality（2）.3）Two cut sets related to a suspect measurement m ij are merged into a new big cut sets G ij.If G ij fullfills inequality（2），all undetermined measurements related G new will be recognized as available and m ij is an abnormal data which needs to be eliminated.4）For the cut sets related to the rest undetermined and suspect data，shorten out all the lines connect to the cut sets to form new extension cut sets G new respectively.If G new fullfills inequality（2），the data in the original cut sets is bad data and need to be eliminated.3L ocation and Identification of Abnormal Basic DataThe most troublesome problem in line loss calculation is that the power flow cannot converge.In the theory，it mainly resulted from two reasons：1）the boundary condition is unreasonable and the actual power system cannot operate under such conditions. 2）bad numerical stability affects the convergence property.Considering that bad numerical stability could be avoid because small branch cannot be put into the system，and the actual power system indeed have operated in the past，so the problem is mainly caused by bad input basic data undiscovered.In traditional calculation system，no available information is offered if the power flow cannot converge and the analyst have to check the bad data out carrying out a carpet-style investigation which is very aimless and inefficiency.In our robust system，we subdivided the whole power network into many mutually independent sub-network by using the measurements of the tie lines between them.Any sub-network，of which power flow cannot converge or the statement is not reasonable，will be applied a optimal power flow to identify the bad data. Specific steps for location function are as follows：1）Using clustering algorithm and measurements，the whole network is divided into many sub-networks.2）Equivalent models are added to the sub-networks29to simulate the act of the rest network utilizing the measurements along the tie lines.For example，if there are power flow into the sub-network though the cut-ting-off tie line，an PQ generation is added to the re-sponsive node，and if power flows out though the cut-ting-off tie line，a load will be added.3）The biggest active power resource is selected as the slack bus and the magnitude of the voltage also comes from the corresponding measurement.This node maybe a real generation or an equivalent generation.4）Power flow calculation is executed in each sub-network separately.A optimal power flow will be ap-plied to any sub-network to identify the reasons if the power flow cannot converge or the statement is unrea-sonable.The OPF model can be represented abstractly as follows：minΣ（Z cal（x+Δx）-Z′）2+‖Δx‖（3）s.t.f（x+Δx）=0（4）where x are basic data needed to calculate theoretical line loss；Δx are corrections of x，and they are the de-cision variables in this optimal model；Z′is redundant data such as measurements of power flow though lines and the amplitude of voltage；Z cal（x+Δx）is calculated by the new statement of power flow obtained from the corrected basic data.The objective function of the model is that the statement of power flow obtained from the corrected basic data must almost the same as that is presented by the actual measured data with the smallest adjust-mentΔx.The restriction conditions，as shown in equa-tion（4），are the power flow equations with the correct-ed basic data.In practical applications，Δx can be ob-tained respectively.For example，only the corrections of power injected into the nodes are studied to see if it is enough to obtain the reasonable result，if not，then the corrections of branches will be checked again.Due to the number of bad basic data is definite very small in sub-network，most of elements inΔx is very small.Few elements with large value inΔx corresponding to the suspect basic data need to be checked by analyst.That is how the bad basic data to be identified.It’s worth noting that the objection function wound not get to zero because of the errors of the measure-ment.There is also no need to modify all the x accord-ing toΔx，because it will make the theoretical line loss calculation meaningless.4Zeroing Boundary MismatchIn traditional power system，there are so many large centralized power plants accessing to the transmission grid that the transmission grid could act as a strong power source.At the same time，there are almost only loads in distribution network，so，the distribution net-work looks like a pure load.Under this kind of situa-tion，power flow of transmission grid and distribution are calculated respectively.It can fulfill the require-ment of line loss analysis because the mismatch on boundary of the two classes of network is small enough to be neglected.In recent years，with the rapid development of dis-tributed generators，there is an increasing regulation a-bility in distributed network，especially in the respect of the reactive power and voltage.Under such in-stances，the results of the separating calculation will not satisfactory because the boundary mismatch of the reactive power will be too large and it will affects the line loss analysis seriously.So the boundary mismatch must be eliminated to realize the seamless mosaic be-tween the transmission grid and the distribution net-works.The iteration method proposed in reference［19］is adopted to eliminate this boundary mismatch.Itera-tion steps are briefly introduced as follows：1）Each power network adjusts its own power flow properly.2）Given the voltage amplitude of the boundary node，each distribution network builds a linear equiva-lent model by itself and sends it to the transmission network.3）Transmission network executes a power flow pro-gram taking the linear equivalent model of the distri-30bution network into consideration ，and send the voltage amplitude of the boundary node to each related distri -bution network.4）The iterative process will go on until the bound -ary mismatches are eliminated.5Numerical Examples5.1Example of eliminating bad redundant data A simple example is analyzed in this section to illus -trate how to eliminate bad redundant data by Kirch -hoff's first low.The topological structure and the sever -al measurement points are shown in Figure 2.The measured values are displayed in Table 1.The thresh -old valve C in inequality （2）is set to be15.Fig.2The topological structure and measurement points.TABLE 1The measured values of the plow flowReactive power /Mvar MeasurementpointM3e20Active power ／MW 98M1s 6032M1e -62-40Active power ／MW -60134-132Reactive power /Mvar 37-37-37MeasurementpointM3s M4e Mt2M2s 624360-31M4s M2e 9438Mt19731The initialized minimal cut sets are as follows ：L1＝｛M1s ，M1e ｝，L2＝｛M2s ，M2e ｝，S ＝｛M1e ，M2e ，M3e ，M4e ，Mt1，Mt2｝，L3＝｛M3e ，M3s ｝，L4=｛M4s ，M4e ｝.Then calculate the sum of the measurement value for each set.As a result ，all the cut sets fulfill the in -equality （2）except L2and S when the sum of the ac -tive power is calculated.The sum of active power mea -surement in L2is 34and that in S is-35.When L2and S are merged into a new big cut sets LS ，the sum will be -1for LS .So the measurement M2e is identified to be a bad measurement.5.2Identification of abnormal basic data The IEEE39node system is used to test the effect of bad data location and identification of the robust computing system.The structure of the system is shown in Figure 3.The network partition parameters and the nodal injection power （including load and generation power ）are all known and 80%of the branch power measurement data are reliable redundant data.The measurement value equals the sum of accurate branch power and a random quantity of 1%in order to simu -late the difference between the measurement value and the true data.Assume that the reactive power of node 8is 10times of its true value and the branch 28-29is missing because of the operational mistake which re -sults in the non-convergence of the power flow.In that case ，we must check the measurementdata.Fig.3The partition result of IEEE 39bus systemsFirst of all ，according to the reliable redundant data and the network partition method ，divide the power system into 4sub-systems as shown in Figure 3.After the equivalence in each sub-system based on the tie-31line power，calculate the power flow of the four sub-systems independently.It is shown that there is a greater difference between the calculation result and the measurement in sub-system I and the power flow can not converge in sub-system IV.Therefore，the bad data can be located in sub-system I and IV.Based on the model described in section3.3and the redundant data known，build and calculate the optimal power flow model of sub-system I and IV.In the calcula-tion of sub-system I，if we use the nodal injection power as the adjustable variables，there will be big adjustments of all the4nodes which indicate some other problems in this region.If we use the structure of the system as the adjustable variables，there will be a big adjustment （0.0139）in the reactance value of branch28-29which indicates that the branch parameters of28-29need to be checked.In the calculation of sub-system IV，if we use the nodal injection power as the adjustable variables，there will be a big adjustment（15.63）of the reactive power in node4which indicates that the reactive pow-er in node4needs to be checked.From the analysis above，we can see that the method proposed in this paper can provide reliable guidance for the bad data identification and power flow regula-tion，therefore，it can effectively improve the fault cor-rection and tolerance of the calculation system.6ConclusionsIn allusion to the common problems in theoretical line loss calculation，a robust computing system based on power flow and optimal power flow is proposed in this paper.The structure and function of each module are de-scribed and the effect of the system is analyzed.Numeri-cal examples show that the robust computing system can improve the accuracy of calculation data and provide guidance for bad data identification and power flow reg-ulation.Application of the system will effectively improve the efficiency and accuracy of line loss calculation.References［1］Yung-Chung Chang，Wei-Tzen Yang and Chun-Chang Liu.ANew Method for Calculation Loss Coefficients.IEEE Transactions on Power Systems，1994，9（3）：1665-1671.［2］Suechoey B，Ekburanaway J，Kraisnachinda N，et al.An Analysis and Selection of Distribution Transformer for Losses Reduction.Power Engineering Society Winter Meeting，2000：2290-2293.［3］Metor Poveda.A New Method to Calculate Power Distribution Losses in an Environment of High Unregistered Loads.IEEE Transmission and Distribution Conference，1999.［4］Anguan Wu，Baoshan Ni.Analysis and Calculation on Power Sys-tem Line Loss.China Electric Power Press，2013.［5］Rubin Taleski，Dragoslav Rajicic.Distribution Network Reconfigu-ration For Energy Loss Reduction.IEEE Transaction On Power System，1997，12（1）：398－406.［6］G Levitin，A Kakyuzhny and A M Chertkov.Optimal Capacitor Al-location in Distribution Systems Using a Genetic Algorithm and a Fast Energy Loss.IEEE Transaction on Power Delivery，2000，15（2）：623-628.［7］Joanicjusz Nazarko，Zbigniew Styezynski，Miroosalw Poplawski.The Fuzzy Approach to Energy Losses Calculations in Low Voltage Distribution Networks，IEEE Power Engineering Society Winter Meeting，2000.［8］LI Wenbo，HAN Xueshan，ZHANG Bo.A Closed Format Power Flow Algorithm Based on Branch Models.Power System Technolo-gy，2012，36（03）：113-119.［9］YU Weiguo，XIONG Youjing，ZHOU Xinfeng，et al.Analysis on Technical Line Lossed of Power Grids and Countermeasures to Re-duce Line Losses.Power System Technology，2006，30（18）：54-63.［10］TANG Guangyu，ZHOU Buxiang.The Special Application of Re-serve Power Supply Automatic Connection Device.Relay，2002，30（08）：50-54.［11］CHEN Dezhi，GUO Zhizhong.Distribution System Theoretical Line Loss Calculation Based on Load Obtaining and Matching Power Flow.Power System Technology，2005，29（01）：80-84.［12］FU Hao，ZHOU Bu-xiang，CHEN Shi.Methods to Improve the Precision of Calculation of Power System Line Losses.Relay.2007，35（07）：28-36.［13］XU Han-ping，HOU Jin-feng，SHI Liu-zhong，et al.Calculation Method of Power System Line Lossed Based on Data of State Esti-mation.Power System Technology.2003，27（03）：59-62.［14］Liu Wei，Li Heng，Zhang Jiang，et al.Topology Analysis Method for Loss Calculation of Distribution Network Based on Feeder Sec-tions and GIS.Relay，2002，30（08）：10-13.［15］Zhu Faguo.Loss Calculation Method for Distribution Network with Information from Filed Terminal Using.Power System Technoloyg，2001，25（05）：38-40.［16］LI Bin，DU Mengyuan，WEI Wei，et al.Calculation of Theoretical Line Loss Based on Quasi Real-time Data of Smart Distribution Network.Electric Power Automation Equipment.2014，34（11）：122-128.（下转第37页）32［17］LU Zhi-gang ，LI Shuang.Theoretical Network Loss Calculation ofWhole Power System under Incomplete Injected Measured Data of Partial Plants and Substations.Power System Technology.2007，31（16）：83-87.［18］SONG Yi-bing ，LOU Bei.Theoretical Computation of Network LossBased on New Data Processing Method.2001，21（05）：15-17.［19］GUO Zhihong ，HAN Xueshan ，LI Wenbo ，et al.A CoordinationPower Flow Algorithm for Power Transmission -Distribution GridAccommodate Distributed Generations.Shandong Electric Power ，2014.Accepted date ：2015-04-10Li Wenbo （1984）received the B.E.and Ph.D.degrees from Shandong University in 2007and 2013，respectively.He is now an engineer in State Grid Shandong Electric Power Research Institute.His research interests include power system operation and control.为-0.221%，标准差为0.730%。