Line Loss Analysis and Calculation of Electric Power Systems

Anguan Wu, North China Electric Power University, ChinaBaoshan Ni, Zhejiang University, China

• Foreword xiiiPreface xviiIntroduction xix1 Overview 11.1 Active Power Loss and Electric Energy Loss 11.1.1 Main Types of Active Power Loss 11.1.2 Calculation of Electric Energy Loss 21.1.3 Electricity Line Loss and Line Loss Rate 31.1.4 Calculation and Analysis of Line Loss 51.2 Calculation of AC Resistance 71.3 Influence of Temperature and Voltage Changes on Line Loss in the Measuring Period 71.3.1 Influence of Temperature Change on Line Loss in the Measuring Period 71.3.2 Influence of Voltage Change on Line Loss in the Measuring Period 91.4 Influence of Load Curve Shape on Line Loss 101.4.1 Load Curve and Load Duration Curve 101.4.2 Parameters of Characterization Load Curve 121.4.3 Relationship Between Loss Factor and Load Factor 151.5 Influence of Load Power Factor and Load Distribution on Line Loss 161.5.1 Influence of Load Power Factor 161.5.2 Influence of Load Distribution of Multi-Branch Line 171.6 Influence of Measuring Instrument Error on Line Loss 181.6.1 Composition of Electric Energy Metering System and Constitution of Metering Error 181.6.2 Composition of Electronic Watt-Hour Meter Error 181.6.3 Influence of Metering System Error on the Calculation of Line Loss Rate 192 Calculation of Line Loss by Current Load Curve 212.1 RMS Current Method and Loss Factor Method 212.1.1 RMS Current Method 212.1.2 Loss Factor Method 222.1.3 Other Calculation Methods 222.2 Derivation of Functional Relationship F( f ) by Ideal Load Curve 232.2.1 Derivation of F( f ) Formula by Ideal Load Curve with Two Variables 232.2.2 Derivation of F( f ) Curve by Ideal Load Curve with Four Variables 262.3 Derivation of Approximate Formula of F( f ) by Statistical Mathematical Method 282.3.1 Binomial Approximate Formula of F( f) 292.3.2 Trinomial Approximate Formula of F( f) 302.3.3 Approximate Formula of Family of F( f ) Curves with Four Variables 302.4 Derivation of F( f ) Formula by Mathematical Analysis Method 312.4.1 Direct Integration Method 312.4.2 Subsection Integration Method 323 Probability Theory Analysis of Current Load Curve 333.1 Probability Meanings of Load Curve and Its Parameters 333.1.1 Probability Meaning of Load Duration Curve 333.1.2 Probability Meanings of Minimum Load Rate and Load Rate 343.1.3 Barth Formula of Loss Factor 353.2 Analysis of Rossander Formula as Distribution Function 353.2.1 Rossander Formula of Load Duration Curve 353.2.2 Exponential Distribution Function 363.2.3 Derivation of Loss Factor Formula 373.2.4 Comparison of Direct Integration Method and Distribution Function Analysis Method 403.3 Comparison of Various Loss Factor Formulas 403.3.1 Loss Factor Formula Comparison Procedures Prepared by Monte Carlo Method 413.3.2 Comparison Results of Various Loss Factor Formulas 413.4 Three-Mode Division of Active Load Duration Curve 423.4.1 Three Modes of Load Management in the Electric Power System 423.4.2 Differences and Relations of the Three Operation Modes 433.4.3 Probability Division of Three Operation Modes 434 Calculation of Line Loss by Power Load Curve 494.1 Line Loss Calculation Considering Power Factor 494.1.1 The Maximum Apparent Power is Caused by the Maximum Active Power 494.1.2 The Maximum Apparent Power is Caused by the Maximum Reactive Power 504.2 Maximum Load Power Factor Method of Tröger 514.3 Annual Average Power Factor Method of Glazynov 514.4 Equivalent Load Curve Method 534.4.1 Equivalent Load Curve Method of Cweink 534.4.2 Improvement and Extension of the Cweink Method 544.4.3 Equal Time Equivalent Load Curve Method 554.4.4 Unequal Time Equivalent Load Curve Method 574.5 Analysis of Errors of Various Line Loss Calculation Methods 644.5.1 Analysis of Relative Error in Line Loss Calculated by rms Current Method 644.5.2 Analysis of Relative Error in Line Loss Calculated by Loss Factor Method 665 Line Loss Calculation after Reactive Compensation 695.1 Calculation of Load Curve Parameters after Reactive Compensation 695.1.1 Calculation of Reactive Load Curve Parameters at Under-Compensation 695.1.2 Calculation of Reactive Load Curve Parameters at Weak Over-Compensation 705.1.3 Calculation of Reactive Load Curve Parameters at Strong Over-Compensation 725.2 Calculation of Loss Reduction Effect of Reactive Compensation 725.2.1 Calculation of Compensation Effect at High Natural Power Factor 735.2.2 Calculation of Reactive Compensation Effect at Low Natural Power Factor 755.3 Calculation Curves of Annual Electric Energy Losses for Power Grid Planning and Design 795.3.1 Calculation Curves of Annual Electric Energy Losses of 35–110 kV Transmission Lines 795.3.2 Calculation Curves of Annual Electric Energy Losses of 220 kV Transmission Lines 815.3.3 Calculation Curves of Annual Electric Energy Losses of Agricultural Electric Lines Consuming Electricity on a Quarterly Basis 826 Change Law for the Electric Energy Losses of Power Grids 876.1 Basis of Analysis of Line Loss Changes 876.1.1 Line Loss Binomial 876.1.2 Condition of Minimum Line Loss Rate 886.2 Calculation and Analysis of No-load Loss 896.2.1 Higher-Order Expression 896.2.2 Square Expression 916.2.3 Quasi Square Expression 916.3 Calculation and Analysis of Load Loss Coefficient C 926.3.1 Calculation of Load Loss Coefficient 926.3.2 Inclusion of Load Loss Coefficient 946.4 Determination of Voltage Level by Loss Reduction Requirement 1056.4.1 Voltage Characteristics of Various Loads and Comprehensive Loads of Distribution Lines 1056.4.2 Control of Voltage Level and Reduction of Electric Energy Loss 1067 Analysis and Control of Line Loss Rate Indicators of Power Grids 1097.1 Analysis of Line Loss Rate Composition 1097.1.1 Line Loss Rates and Total Line Loss Rate of Different Voltage Grids 1097.1.2 No-load Line Loss Rate and Load Line Loss Rate 1107.2 Analysis of Influence of Grid Electric Supply Structure on Line Loss Rate 1137.2.1 Repeated Electric Supply Rate 1137.2.2 Calculation of Loss Reduction Effect of Reducing Repeated Electric Supply Rate 1157.3 Analysis of Power Sales Quantity Composition 1177.3.1 Influence of Power Sales Quantity without Loss or Power Sales Quantity with Loss on Line Loss Rate 1177.3.2 Calculation of Influence of Transit Electric Supply on Line Loss Rate 1197.4 Multiple-factor Analysis of Changes in Electricity Line Losses 1227.4.1 Loss Structure Coefficient and Electricity Line Loss Increase Rate Function 1227.4.2 Loss Structure Function and Calculation of Increase in Electricity Line Losses 1257.5 Marginal Line Loss Rate and Optimal Distribution of Increase in Electric Supply 1267.5.1 Marginal Line Loss Rate 1267.5.2 Optimal Distribution of Increase in Electric Supply 1268 Theoretical Calculation of Electric Energy Losses of Power Grid Units 1318.1 Classification of Electric Energy Losses 1318.1.1 Classification of Electric Energy Losses by Whether Theoretical Calculation is Feasible 1318.1.2 Classification of Calculable Technical Losses by Change Law 1318.1.3 Classification of Electric Energy Losses by Different Power Grid Units 1318.2 Calculation of Electric Energy Losses of Overhead Lines 1328.2.1 Calculation of Corona Losses of Power Transmission Lines 1328.2.2 Calculation of Resistance Heat Losses of Overhead Lines 1368.2.3 Calculation of Electric Energy Losses of Low-voltage Lines 1378.3 Calculation of Electric Energy Losses of Cable Lines 1418.3.1 Calculation of No-load Losses (Dielectric Losses in Insulating Layers) of Cable Lines 1418.3.2 Calculation of Load Losses of Cable Lines 1418.4 Calculation of Electric Energy Losses of Main Transformers 1458.4.1 Active Power Losses of Main Transformers 1458.4.2 Calculation of Electric Energy Losses of Main Transformers 1468.4.3 Calculation of Electric Energy Losses of Main Transformers in Parallel Operation 1478.5 Calculation of Electric Energy Losses of Other Electrical Equipment 1488.5.1 Shunt Capacitors 1488.5.2 Shunt Reactors and Series Current-limiting Reactors 1498.5.3 Synchronous Compensator 1498.5.4 Watt-hour Meter and Other Instruments 1509 Calculation of Electric Energy Losses of Multi-branch Lines 1519.1 Basic Method for Calculating Electric Energy Losses of Multi-branch Lines 1519.1.1 Weighted Average Method 1519.1.2 Point by Point Section Simplification Method 1539.2 Equivalent Resistance Method and Calculation of Electric Energy Losses of Distribution Transformers 1579.2.1 Equivalent Resistance of a Line 1579.2.2 Calculation of Electric Energy Losses of Distribution Transformers 1599.2.3 Equivalent Resistance and Equal Resistance of Common Distribution Transformers 1599.2.4 Calculation of Electric Energy Losses by Equivalent Resistance Method 1619.3 Double Component Balance Method 1629.4 Dispersion Coefficient Method 1689.4.1 Calculation of Power Losses of Typically Distributed Loads 1689.4.2 Dispersion Coefficient 1699.4.3 Conversion of Length Under Different Sectional Areas of Conductors 1709.4.4 Calculation of Power Losses of Complexly Distributed Loads 1709.4.5 Calculation of Electric Energy Losses by Dispersion Coefficient Method 1719.5 Calculation of Electric Energy Losses of Multi-branch Lines by Voltage Drop Method 1739.5.1 Calculation of Line Loss Rate by Proportionality Coefficient Method 1739.5.2 Calculation of Line Losses by Voltage Drop Measurements 1759.6 Comparison and Selection of Calculation Methods of Electric Energy Losses of Multi-branch Lines 1789.7 Calculation of Loss Reduction Benefits after Connection of Distributed Resources to System 1789.7.1 Calculation of Loss Reduction Benefits During Generation Period of Distributed Resources 1799.7.2 Calculation of Line Loss Change During Consumption Period of Distributed Resources 1819.7.3 Calculation of Loss Reduction Benefits During the Full Period of Distributed Resources 1819.7.4 Benefit Evaluation of Distributed Energy System 18110 Calculation of High-voltage Power Grid Losses 18310.1 Characteristics and Requirements of Loss Calculation 18310.1.1 Classification of High-voltage Power Grids 18310.1.2 Characteristics of Regional Power Grids and Requirements of Loss Calculation 18410.1.3 Characteristics of Prefectural Power Grids and Requirements of Loss Calculation 18410.2 Real-time Loss Measuring Method for High-voltage Power Grids 18410.2.1 Function and Method of State Estimation 18510.2.2 Real-time Calculation of Losses by State Estimation Combined with Excel 18610.2.3 Typical Day Method Based on Actual Load Measurement and State Estimation 18710.2.4 Comprehensive Analysis Method of Losses Based on Real-time System Data 18910.3 Equivalent Node Power Method for Calculation of High-voltage Power Grid Losses 19010.3.1 Equivalent Node Power and its Distribution 19010.3.2 Relationship between Power Losses and Electric Energy Losses Under Distribution of Equivalent Node Power 19110.3.3 Analysis of Equivalent Node Power Method 19510.4 Calculation of Losses of High-voltage Power Grids Based on Power Losses under Three Modes 19610.5 Calculation and Analysis of Samples 19710.5.1 Verification of Loss Calculation of Standard Power Grid with 39 Nodes 19710.5.2 Three-mode Calculation Based on Total Loads and Measured Loss Power over 24 h in one Province During 2004 20411 Analysis and Calculation of Loss Allocation 20911.1 Occurrence of Loss Allocation Problem and Possible Solutions 20911.1.1 Analysis of Double Load Power Supply Model 21011.1.2 Analysis of Triple Load Power Supply Model 21111.1.3 Possible Solutions to Loss Allocation 21411.2 Theoretical Preparation for Loss Allocation 21411.2.1 Three-mode Section Division of Active Load Duration Curve 21411.2.2 Calculation of Influence of Transit Electric Supply on Electricity Line Losses 21411.2.3 Calculation of Marginal Line Loss Rate 21511.2.4 Calculation of Optimal Distribution of Increased Electric Supply 21511.3 Analysis and Calculation of Allocation of Increased Losses in Regional Power Grids 21611.3.1 Allocation of Losses in the Main Part of Regional Power Grids to Provincial Power Grids 21611.3.2 Allocation of Increased Losses Caused by Power Transmission and Reception in Inter-Provincial Power Grids 21611.4 Calculation of Loss Allocation Under Complex Trading Setup 22311.4.1 Loss Allocation for Pilot Project of Direct Electricity Purchase by Large Customers Under “One to Many” Model 22311.4.2 Shapley Method of “Many to Many” Loss Allocation 22411.4.3 Marginal Loss Coefficient-Based GMM Method 22812 Technical Measures for the Reduction of Line Losses 23112.1 Selection of Reasonable Connection Mode and Operation Mode 23112.1.1 Introduction of High-voltage Grids to Large Cities or Load Centers 23112.1.2 Stepping up of Power Grid Voltage, Simplification of Voltage Class, and Reduction of Repeated Substation Capacity 23212.1.3 Reasonable Determination of Closed Loop Operation or Open Loop Operation of Loop Net, or Change of Break Points of Loop Net 23212.1.4 Realization of Economic Power Distribution by Longitudinal and Transverse Voltage Regulating Transformer or Series Capacitor 23512.1.5 Prevention of Remote Supply by Nearby Power or Round about Power Supply 23612.1.6 Reasonable Arrangement of Equipment Overhaul and Practice of Live-Line Overhaul 23712.1.7 Replacement of Conductors, Installation of Composite Conductors, or Construction of Secondary Loop Lines 23812.2 Reasonable Determination of Voltage Level of Power Grids 23812.3 Utilization of Reactive Power Compensation Equipment and Increase in Power Factor 23912.3.1 Calculation of Loss Reduction Effect of Reactive Compensation 24012.3.2 Optimal Configuration of Reactive Compensation Equipment in Power Grids 24412.3.3 Exploitation of Reactive Potential and Reduction of Reactive Consumption 24512.4 Economical Operation of Transformers 24512.4.1 Economical Operation of Two-Winding Transformers of the Same Model 24512.4.2 Economical Operation of Two-Winding Transformers of Different Models 24712.4.3 Economical Operation of Three-Winding Transformers of Different Models 25112.5 Adjustment and Balancing of Loads 25512.5.1 Adjustment of Load Curves 25512.5.2 Balancing the Loads of Lines or Transformers, and Adjusting the Power Sources of Dual Power Customers 25612.5.3 Balancing Three-Phase Loads 25812.6 Strengthen Power Grid Maintenance 25812.7 Strengthen Power Consumption Management and Measuring Management 25912.8 Application of New Designs, New Materials, and New Technologies 25912.8.1 New Design for Loss Reduction in Ground Wires of High-voltage Transmission Line 26012.8.2 Application of Energy-saving Hardware and Energy-saving Conductors 26012.8.3 Application of Harmonic Control Technology and High-Temperature Superconducting Technology 26113 Line Loss Prediction and Loss Reduction Plan for Power Grids 26313.1 Univariate Prediction of Electricity Line Losses and Line Loss Rate 26313.1.1 Basis for Predicting the Indicator of Line Loss Rate 26313.1.2 Univariate Prediction of Electricity Line Losses 26613.1.3 Univariate Prediction of Line Loss Rate 26613.2 Multivariable Prediction of Electricity Line Losses and Line Loss Rate 26713.2.1 Multivariable Prediction of Electricity Line Losses 26813.2.2 Multivariable Prediction of Line Loss Rate 26813.2.3 Rolling Prediction Method 27213.3 Main Content and Preparation Process of Loss Reduction Plan 27613.3.1 Content and Preparation Basis of the Loss Reduction Plan 27613.3.2 Preparation of the Loss Reduction Plan 27713.3.3 Implementation and Monitoring of the Loss Reduction Plan 27913.3.4 Introduction of an Example of the Loss Reduction Plan 28014 Analysis of the Influence of Power Grid Line Losses on Power Grid Enterprises 28114.1 Influence of Line Losses on the Profits of Power Grid Enterprises 28114.1.1 Calculating the Profits of Power Grid Enterprises 28114.1.2 Break-Even Point Power Sales Quantity 28214.1.3 Profit and Tax Amount per Unit Power Sales Quantity 28214.1.4 Analysis of Factors Affecting Profits 28214.2 Link Cost and Link Electricity Price 28314.2.1 Significance of Division of Internal Links of Power Grid Enterprises 28314.2.2 Calculation Model of Link Electricity Price Under a Simple Electric Supply Structure 28314.2.3 Calculation Model of Link Electricity Price Under a Complicated Electric Supply Structure 28414.2.4 Equivalent Merging of Parallel Electric Supply Structure 28514.3 Influence of Line Losses on the Composition of Multi-section Electricity Prices 28914.3.1 Type of Electricity Price and Comparison of Calculation Methods 28914.3.2 Analysis of Composition of Two-Section Electricity Prices Under the Single Electricity Purchaser Model 29014.3.3 Recursive Calculation of Multi-Section Electricity Prices 29214.3.4 Controlling the Aggregate Level of Electricity Price 29414.3.5 Analysis and Discussion 29614.4 Analysis of Coal–Electricity Price Linkage 29714.4.1 Interpretation of the Existing Policy of Coal–Electricity Price Linkage 29714.4.2 Analysis of the Linkage between On-Grid Price and Coal Price 30014.4.3 Linkage between Sales Price and On-Grid Price 30214.5 Analysis of Electricity Price Factor in Post Project Evaluation 30314.5.1 Reverse Calculation of Mark-Up in Link Output End 30414.5.2 Calculation of Mark-Up Allocation Coefficient of Simplified Electric Supply Network 30414.5.3 Mark-Up Calculation of Complicated Electric Supply Structure 30514.5.4 Calculation of Annual Power Sales Mark-Up Revenue of a Single Transmission and Transformation Project 30715 Management and Utilization of Line Loss Mass Information for an Electric Power System 30915.1 Evaluation and Functions of Two Management Information Systems Under the Guidelines 30915.1.1 Functional Design Requirements for Two Types of Software 30915.1.2 Functions of Line Loss Calculation and Management Information Systems Developed by Provincial Power Grid Enterprises 31015.1.3 Integrated Management System for Theoretical Calculation of Line Losses Developed by Regional Power Grid Enterprise 31115.1.4 New Management Requirements 31215.2 Value Creation and Support Processes for Power Grid Enterprises 31315.2.1 Information-Oriented Development of Large Enterprises and Application of Enterprise Resource Planning 31315.2.2 Value Creation and Support Processes of Power Grid Enterprises 31415.3 Composition of Model Driven Decision Support System 31515.3.1 Structure and Functions of Decision Support System 31515.3.2 Intelligent Decision Support System and Group Decision Support System 31815.3.3 Conceptual Model of Power Grid Enterprise 31915.3.4 Business Conceptual Model of Power Grid Enterprise 32015.4 Utilization of Line Loss Mass Information 32215.4.1 Basic Concept of Data Warehouse 32215.4.2 Basic Concepts of Data Mining and Online Analysis 32315.4.3 Application of Data Warehouse Technology in Electric Power Dispatching and Marketing Systems 32415.4.4 In-Depth Utilization of Line Loss Mass Information – Integration of Data in Dispatching and Marketing Systems 328Appendix A Calculation Curve of Corona Loss Power ΔPcor 335Appendix B Calculation of Electrical Parameters of Power Grid Units 341B.1 Parameters of Overhead Lines 341B.1.1 Parameters of Overhead Transmission Lines 341B.1.2 Parameters of Steel Conductor Overhead Lines 343B.1.3 Parameters of Two-Wire One-Ground Overhead Lines 343B.2 Parameters of Transformer 343B.2.1 Parameters of Two-Winding Transformer 343B.2.2 Parameters of Three-Winding Transformer 344Appendix C Derivation of Loss Factor Formula by Subsection Integration Method 347Appendix D Actual Measurement Analysis of No-load Power Losses and Relationship between No-load Current and Voltage of Distribution Transformers 351D.1 Actual Measurement Analysis of ΔP0(U) of General Transformers 351D.2 Actual Measurement Analysis of ΔP0(U) of Low Loss Transformers 351D.3 Actual Measurement Analysis of I0(U) of General Transformers 352References 353Index 357