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Materials for current monitoring of the course "Power Engineering Systems Simulation and Research" Module 1. Principles of simulation 1. Voltage of power grid and its application 2. Neutral point connections of power grid 3. Impact of short-circuit current on power supply system components 4. Initial short-circuit current and its detection 5. Physical meaning and calculation of periodic and aperiodic component of short- circuit current 6. Selection of short-circuit current protection devices to protect power grid 7. Characteristics of three-phase and single-phase short-circuit current dependent on neutral point connection of power grid 8. Definition of an ordinary differential equation 9. What problems could be solved by means of algebraic and differential equations in mathematical models 10. Necessity for simulation methods application when analyzing power supply systems 11. The main difference between physical and mathematical simulation 12. Common sense of mathematical simulation when designing power supply systems 13. Classification of simulation types 14. Classification of mathematical simulation 15. The main types of simulation Module 2. Simulation of components and operation of industrial electric power supply 16. The main characteristics of mathematical models in power supply 17. Application of analysis and numerical computation to solve differential equation 18. The main advantages and disadvantages of numerical computation to solve differential equations 19. Basic requirements for mathematical models 20. Equations of the simplest mathematical models of electrical components 21. Characteristics of various modes of power supply system simulation 22. The main advantages of mathematical simulation 23. Model existence conditions 24. Forced component of a differential equation and its origin 25. Transient component of a differential equation and its origin 26. Simulation 27. Solution of a differential equation 28. The main purpose of power supply system mathematical simulation 29. Mathematical model of power source for power supply systems and characteristics of their simulation 30. Simulation of power grid components when calculating the operating modes of power supply systems 31. The main methods of electrical loads simulation, their advantages and disadvantages Module 3. Optimization problems of electric power supply 32. Graphical solution of linear programming problem 33. Simplex method for solving linear programming problem 34. Optimization problems referred to linear programming problems 35. Mathematical model of optimization problem 36. Criterion of optimality 37. Classification of optimization mathematical models by the type of input information 38. Methods for solving optimization problems 39. Transportation problem and its particular reference to problems of power supply 40. Characteristics of transportation problem in view of transmission line capability 41. Characteristics of transportation problem in view of transit facilities 42. Methods for solving optimization problems with random and uncertain input information Module 4. Correlation and Regression data analysis 43. Scope of correlation and regression analysis 44. Least square method 45. Concept of functional and statistical relation between phenomena, their formalization 46. Necessary conditions for correlation and regression analysis 47. The main tasks of correlation and regression analysis 48. Concept of regression, types and forms of regression 49. Linear coefficient of pair correlation (how to define, variation limits, what characterizes) 50. Why and how test significance of correlation coefficient 51. Coefficient of determination (how to define, variation limits, what characterizes) 52. What parameters evaluate quality of regression model 53. Why to conduct dispersion analysis to construct regression model 54. T-test and Fisher (purpose, definition, application) 55. Significance test of regression equation 56. Significance test of regression coefficients 57. Concept of point and interval predictions Tasks for intermediate monitoring of the course "Power Engineering Systems Simulation and Research" Task 1 By means of Euler method find the value of circuital current after switch closure within the time interval from 0 to 1 second, taking t = 0.2 sec. Determine an analytic expression for the circuital current after switching, find the general and particular solution of a differential equation. Task 2 For the following circuit diagram of power supply draw a equivalent circuit and determine short-circuit current at the points P1 and P2 in view of feed to the fault from electric motor. TMN –6300/110 System ~ AS - 70 TS-1 AS - 50 L = 0,64 km L =1,77 km Uн = 110 kW P2 P1 AS - 95 AVBeShv-(3х25) L = 0,84 km L = 0,02 km Uн = 6 kW TS-2 AVBeShv-(3х35) L = 0,02 km DE-4 AD AK4-4-400, Uн=6 kW Task 3 For the following diagram draw equivalent circuit of the loop "phaseneutral" and choose pickup setting of magnetic-only circuit breaker CB 4. АВ1 Inom=1000 А TS-1 ТА1 ТМZ-630/6 АВ2 Inom=630 А ТShP-1000/5 ТА2 ТShP-600/5 AVBeShv2(3х185+1х65) L = 225 m ShSU-2 VBeShv-(3х70+1х35) L = 140 m АВ3 АВ4 Inom=400 А Inom=100 А AD Рnom=37 kV Task 4 To the steel plant as raw material is supplied brass (alloy of copper and zinc) of four types containing 10, 20, 25 and 40% of zinc that costs 10, 30, 40 and 60 rub. per 1 kg, respectively. In what proportions raw material should be melted to get the alloy (brass) containing 30% of zinc, and thus the cheapest? Task 5 Sc=600 МВА Хс=0,8 115 kV 4000 kVА Usc=17.5 % 35 kV L-1 АС-70 L=4 sm Хl rl P-3 Хт MSS SC Sн=1600 kVA Usc=8% P-1 Хl rl DE-1 CL1 ASB-3*240 P-2 CL2 ASB-3*150 TS-3 Draw equivalent crcuit and determine short-circuit current at the points P-1 and P-2. Task 6 As a result of the calculation dependence of reduced annual costs Ci on cable section Si is obtained: Si mm2 10 16 25 35 50 70 95 120 150 185 Зi ths.rub/year 360 340 320 290 280 270 300 340 400 470 Required: to approximate and interpolate table function by known methods (method of least squares); to find an extremum (extrema) of obtained function and compare methods; to compare values of obtained functions at the midpoints of intervals (4, 5 points); to compare accuracy of methods (approximation and interpolation of 4.5 points) and draw conclusion. Task 7 Determine similarity criteria of electric circuit with mutual inductance M12, which consists of two fixed relative to each other circuits formed by connected in series elements with the active resistance R and inductance L, and the second circuit is short-circuited, and the first is under constant voltage u1. Task 8 Calculate supply and distribution mains of the shop in accordance with the condition of inconsequential voltage loss and draw diagrams of voltage deviation for lines from the busbar of main step-down substation to the terminals of one of the most powerful electric load for the modes of maximum and minimum loads. 1 2 ST2 3 АСБ -2(3120) 4 ASB –8(1120) 5 ASG- 4(1 150) APV-3(1 35) 6 MSS 10 kV Zone designation Type of cable or wire section, mm2 length, m Loads Р+jQ at min max modes DE 0,38кВ DistrCentr1 CD5 Р=37kW 1-2 2-3 3-4 4-5 5-6 ASB 2(3120) 500 TMN-1600/10 ASB 8(1120) 20 ASG4(1150) 20 APV3(135) 50 2215,5+1500,0 2215,5+1500,0 2951,5+1996,9 2951,5+1996,9 640+350,2 817+564,3 150,2+110,6 176,9+135,3 26,5+19,9 26,5+19,9