tối ưu hóa trong hệ thống điện
- 1. University of technical education HCMC Faculty of Electrical and Electronics Engineering Power System Optimization www.hcmute.edu.vn Chapter 9 STEADY-STATE SECURITY REGIONS Nguyễn Anh Toàn
- 2. FEEE University of technical education HCMC POWER SYSTEM OPTIMIZATION Faculty of Electrical and Electronics Engineering Ensuring Enhanced Education Group No 5 www.hcmute.edu.vn/feee/ Chapter 9: STEADY-STATE SECURITY REGIONS 1. Introduction Objectives 2.Model Presenting the concept and definition of security region 3. Numerical Example Explaint various methods to contruct steady state 4. Appendix security regions of power system 5. Conclusion
- 3. FEEE University of technical education HCMC POWER SYSTEM OPTIMIZATION Faculty of Electrical and Electronics Engineering Ensuring Enhanced Education Group No 5 www.hcmute.edu.vn/feee/ Chapter 9: STEADY-STATE SECURITY REGIONS 1. Introduction Agenda 1 Introduction 2.Model 2 Model 3 Numerical Example 3. Numerical Example 4 Appendix 5 4. Appendix Conclusion 5. Conclusion
- 4. FEEE University of technical education HCMC POWER SYSTEM OPTIMIZATION Faculty of Electrical and Electronics Engineering Ensuring Enhanced Education Group No 5 www.hcmute.edu.vn/feee/ Chapter 9: STEADY-STATE SECURITY REGIONS 1. Introduction Introduction Used to find the best or optimal solution 2.Model Requires that all the mathematical functions in the model be linear functions. 3. Numerical Example The linear model consists of the following components: 4. Appendix • A set of decision variables. • An objective function. 5. Conclusion • A set of constraints.
- 5. FEEE University of technical education HCMC POWER SYSTEM OPTIMIZATION Faculty of Electrical and Electronics Engineering Ensuring Enhanced Education Group No 5 www.hcmute.edu.vn/feee/ Chapter 9: STEADY-STATE SECURITY REGIONS 1. Introduction Models Objective Function: n 1 M m 2.Model MaxZ Wi ( PGi PGi ) (9.72) i nd 1 Subject to constrains 3. Numerical Example n 1 M m (P Gi P ) Gi ( PGi max PGi min ) (9.90) ij min ( Aik Ajk ) PGk ij max (9.95) i nd 1 m PGi PGi PGi min i=n d +1,..,n-1 (9.91) m PGk when Aik -A jk 0 PGi M PGi PGi max i=n d +1,..,n-1 (9.92) PGk ={ M (9.96) 4. Appendix PGk when Aik -A jk 0 nd n 1 M ( Pi - PGi )=PGnm (9.93) PM G P0 + G P0 G (9.97) i 1 i nd 1 nd n 1 m Pm G P0 + G P0 G (9.98) ( Pi - P )=PGnM Gi (9.94) i 1 i nd 1 5. Conclusion
- 6. FEEE University of technical education HCMC POWER SYSTEM OPTIMIZATION Faculty of Electrical and Electronics Engineering Ensuring Enhanced Education Group No 5 www.hcmute.edu.vn/feee/ Chapter 9: STEADY-STATE SECURITY REGIONS 1. Introduction Models X2 1000 Let’s take a closer look at 2.Model the optimal point 800 Infeasible 3. Numerical Example 600 4. Appendix Feasible Feasible region region X1 5. Conclusion 400 600 800
- 7. FEEE University of technical education HCMC POWER SYSTEM OPTIMIZATION Faculty of Electrical and Electronics Engineering Ensuring Enhanced Education Group No 5 www.hcmute.edu.vn/feee/ Chapter 9: STEADY-STATE SECURITY REGIONS 1. Introduction Numerical Examples To assess or compare the size of Ωp for 2.Model different means, the following performance index is introduced: n 1 (PM Gi Pm ) Gi i nd 1 3. Numerical Example PI= n 1 (9.99) ( P max Gi P min ) Gi i nd 1 4. Appendix or M m PGi PGi PI= i=n d +1,.....,n-1 (9.100) PGi max PGi min 5. Conclusion
- 8. FEEE University of technical education HCMC POWER SYSTEM OPTIMIZATION Faculty of Electrical and Electronics Engineering Ensuring Enhanced Education Group No 5 www.hcmute.edu.vn/feee/ Chapter 9: STEADY-STATE SECURITY REGIONS 1. Introduction Numerical Examples Table 9.14 Comparison of security region results for IEEE 6-bus system. 2.Model Security Generator Generator Total Method regions PG4 PG5 PI% PM Gi 4.200 2.200 3. Numerical Example m PGi Method 1 0.184 1.378 71% PI i % 96% 31% PM Gi 3.750 2.649 4. Appendix m Method 2 PGi 2,449 1.400 37% PI i % 31% 47% Method 1: optimization method. 5. Conclusion Method 2: the expanding method.
- 9. FEEE University of technical education HCMC POWER SYSTEM OPTIMIZATION Faculty of Electrical and Electronics Engineering Ensuring Enhanced Education Group No 5 www.hcmute.edu.vn/feee/ Chapter 9: STEADY-STATE SECURITY REGIONS 1. Introduction Numerical Examples Table 9.15 Comparison of security region results for IEEE 30-bus system Gen Gen Security Gen Gen Gen Total method PG PG regions PG2 PG5 PG8 PI% 2.Model 11 13 PM Gi 0.800 0.500 0.350 0.300 0.384 Method m PGi 0.439 0.150 0.100 0.100 0.120 85% 1 3. Numerical Example PI i % 80% 100% 100% 100% 94% PM Gi 0.712 0.402 0.350 0.300 0.400 4. Appendix Method m PGi 0.428 0.150 0.148 0.100 0.177 70% 2 PI i % 47% 72% 81% 100% 80% 5. Conclusion Method 1: optimization method. Method 2: the expanding method.
- 10. FEEE University of technical education HCMC POWER SYSTEM OPTIMIZATION Faculty of Electrical and Electronics Engineering Ensuring Enhanced Education Group No 5 www.hcmute.edu.vn/feee/ Chapter 9: STEADY-STATE SECURITY REGIONS 1. Introduction Numerical Examples 2.Model Table 9.16 Results for security regions on IEEE 6-bus system (p.u.) Security -cut PG4 PG5 PG6 regions M 3. Numerical Example PGi 4.200 2.2240 3.8990 1 P m Gi 0.1840 1.3700 0.0000 M PGi 4.0050 202245 4.5480 0.6 m PGi 0.1701 1.1500 0.0000 m PGi 4.0050 2.2245 4.7100 0.5 m PGi 4. Appendix 0.1620 1.0693 0.0000 M PGi 3.9755 2.4245 5.1849 0 m PGi 0.1215 1.000 0.0000 5. Conclusion
- 11. FEEE University of technical education HCMC POWER SYSTEM OPTIMIZATION Faculty of Electrical and Electronics Engineering Ensuring Enhanced Education Group No 5 www.hcmute.edu.vn/feee/ Chapter 9: STEADY-STATE SECURITY REGIONS 1. Introduction Appendix Standard Form of LP 2.Model Max/min z = c1x1 + c2x2 + ... + cnxn subject to: a11x1 + a12x2 + ... + a1nxn (≤, =, ≥) b1 3. Numerical Example a21x1 + a22x2 + ... + a2nxn (≤, =, ≥) b2 : am1x1 + am2x2 + ... + amnxn (≤, =, ≥) bm 4. Appendix xj = decision variables bi = constraint levels cj = objective function coefficients 5. Conclusion aij = constraint coefficients
- 12. FEEE University of technical education HCMC POWER SYSTEM OPTIMIZATION Faculty of Electrical and Electronics Engineering Ensuring Enhanced Education Group No 5 www.hcmute.edu.vn/feee/ Chapter 9: STEADY-STATE SECURITY REGIONS 1. Introduction Infeasibility No point, simultaneously, 2.Model lies both above line 1 and below lines 2 and 3. 3. Numerical Example 2 4. Appendix 5. Conclusion 1 3
- 13. FEEE University of technical education HCMC POWER SYSTEM OPTIMIZATION Faculty of Electrical and Electronics Engineering Ensuring Enhanced Education Group No 5 www.hcmute.edu.vn/feee/ Chapter 9: STEADY-STATE SECURITY REGIONS 1. Introduction Unbounded solution 2.Model 3. Numerical Example 4. Appendix 5. Conclusion
- 14. FEEE University of technical education HCMC POWER SYSTEM OPTIMIZATION Faculty of Electrical and Electronics Engineering Ensuring Enhanced Education Group No 5 www.hcmute.edu.vn/feee/ Chapter 9: STEADY-STATE SECURITY REGIONS 1. Introduction Unbounded solution Primal Dual 2.Model Objective max cTx min bTy Variables x1, …, xn y1,…, ym Constraint matrix A AT 3. Numerical Example Right-hand vector b c Constraints ith constraint: · yi ¸ 0 versus ith constraint: ¸ yi · 0 Variables ith constraint: = yi unrestricted 4. Appendix , xj ¸ 0 jth constraint: ¸ xj · 0 jth constraint: · xj unrestricted jth constraint: = 5. Conclusion
- 15. FEEE University of technical education HCMC POWER SYSTEM OPTIMIZATION Faculty of Electrical and Electronics Engineering Ensuring Enhanced Education Group No 5 www.hcmute.edu.vn/feee/ Chapter 9: STEADY-STATE SECURITY REGIONS 1. Introduction 2.Model 3. Numerical Example 4. Appendix GROUP 5 5. Conclusion
Editor's Notes
- #4: Nội dung trình bày: