电力市场中可用传输容量的计算
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摘要
在电力市场环境下,电力系统的可用传输容量(ATC-Available Transfer Capability)是衡量输电网传输能力,反映系统安全的一种重要指标。ATC反映出输电网对电力市场还能提供的最大传输容量。随着电力市场运营的深入,双边交易剧增,ATC受到广泛关注。
论文基于光滑化函数理论,建立了光滑化的ATC计算新模型,并依据新模型对双边交易ATC进行了实际计算,最后还在解耦计算理论的基础上对模型进行了改进。在这过程中并不考虑鞍节分岔点。论文主要成果是:克服了系统大量不等式约束条件所带来的半光滑问题。
传统的ATC模型是含参数的等式-不等式约束方程组。系统规模越大,等式和不等式约束的数目就越多,ATC问题的求解也越困难。在不考虑鞍节分岔点的情况下,ATC问题的解主要受制于不等式约束。由于不等式约束众多,确定最终起作用的不等式约束往往成为ATC计算的关键。处理不等式约束的难点在于:将不等式转化为等式或将等式松弛为不等式时所引起的半光滑性,以及由此而引起的求解过程的振荡。为了克服这一困难,论文基于光滑化函数理论,建立了光滑化的ATC新模型。该模型将所有不等式约束的信息浓缩于一个等式中,从而避免了处理众多不等式约束而引起的半光滑性及由此产生的困难。论文采用牛顿法对光滑化的ATC模型进行求解,对IEEE 9母线、30母线及118母线标准测试系统进行了试算并加以详细分析,将算法与传统的延拓潮流方法作了比较。计算结果表明,论文的模型和方法能快速可靠地识别出边界上的不等式约束,编程简单,是一种有效的ATC计算方法。
In power market environment, Available Transfer Capability (ATC) of power system is important index of transfer capability and system security. ATC refers to the maximum transfer capability of transmission network to power market. With development of power market, bilateral trade increase greatly. Study on ATC is a significant topic with much attention.
In dissertation, a new smooth model for ATC calculation is developed base on smooth function theory. According to the new model, experimental studies on ATC computation of bilateral trade are carried out. Theoretical analysis confirmed that without considering the Saddle-node Bifurcation problem, this model could handle most of the non-smooth problem caused by enormous inequation constraints in power system.
Traditional model of ATC consists of a set of equations with constraints. The larger the system is, the more enormous equations and inequations it consists of, and the harder to solve the ATC problem. Without considering the Saddle-node Bifurcation problem, the solution of ATC is mainly decided by those inequation constrains. There are too many inequation constraints and the one which is on the boundary is the key of ATC calculation. It is difficult to deal with those inequation constrains: the non-smooth property caused by transferring inequation constrains to equation ones and consequential vibration during solving process. To overcome it, based on the theory of smooth function, a new smooth ATC model is presented in this dissertation. The model gathers information of all inequation constrains into one equation. Non-smooth problem caused by inequation constrains can be avoided. Newton method is adopted in present dissertation to solve smooth ATC model. Numerical tests have been done on the standard IEEE-9/30/118 buses power systems and compared to traditional incremental method (one type of CPF
methods). Results show that the new model and algorithm of this dissertation can find the boundary constraint reliably and quickly. It can easily be programmed and used in practical. It is efficient algorithm of ATC problem.
论文基于光滑化函数理论,建立了光滑化的ATC计算新模型,并依据新模型对双边交易ATC进行了实际计算,最后还在解耦计算理论的基础上对模型进行了改进。在这过程中并不考虑鞍节分岔点。论文主要成果是:克服了系统大量不等式约束条件所带来的半光滑问题。
传统的ATC模型是含参数的等式-不等式约束方程组。系统规模越大,等式和不等式约束的数目就越多,ATC问题的求解也越困难。在不考虑鞍节分岔点的情况下,ATC问题的解主要受制于不等式约束。由于不等式约束众多,确定最终起作用的不等式约束往往成为ATC计算的关键。处理不等式约束的难点在于:将不等式转化为等式或将等式松弛为不等式时所引起的半光滑性,以及由此而引起的求解过程的振荡。为了克服这一困难,论文基于光滑化函数理论,建立了光滑化的ATC新模型。该模型将所有不等式约束的信息浓缩于一个等式中,从而避免了处理众多不等式约束而引起的半光滑性及由此产生的困难。论文采用牛顿法对光滑化的ATC模型进行求解,对IEEE 9母线、30母线及118母线标准测试系统进行了试算并加以详细分析,将算法与传统的延拓潮流方法作了比较。计算结果表明,论文的模型和方法能快速可靠地识别出边界上的不等式约束,编程简单,是一种有效的ATC计算方法。
In power market environment, Available Transfer Capability (ATC) of power system is important index of transfer capability and system security. ATC refers to the maximum transfer capability of transmission network to power market. With development of power market, bilateral trade increase greatly. Study on ATC is a significant topic with much attention.
In dissertation, a new smooth model for ATC calculation is developed base on smooth function theory. According to the new model, experimental studies on ATC computation of bilateral trade are carried out. Theoretical analysis confirmed that without considering the Saddle-node Bifurcation problem, this model could handle most of the non-smooth problem caused by enormous inequation constraints in power system.
Traditional model of ATC consists of a set of equations with constraints. The larger the system is, the more enormous equations and inequations it consists of, and the harder to solve the ATC problem. Without considering the Saddle-node Bifurcation problem, the solution of ATC is mainly decided by those inequation constrains. There are too many inequation constraints and the one which is on the boundary is the key of ATC calculation. It is difficult to deal with those inequation constrains: the non-smooth property caused by transferring inequation constrains to equation ones and consequential vibration during solving process. To overcome it, based on the theory of smooth function, a new smooth ATC model is presented in this dissertation. The model gathers information of all inequation constrains into one equation. Non-smooth problem caused by inequation constrains can be avoided. Newton method is adopted in present dissertation to solve smooth ATC model. Numerical tests have been done on the standard IEEE-9/30/118 buses power systems and compared to traditional incremental method (one type of CPF
methods). Results show that the new model and algorithm of this dissertation can find the boundary constraint reliably and quickly. It can easily be programmed and used in practical. It is efficient algorithm of ATC problem.
引文
Available transmission capability definitions and determination. North American Electric Reliability Council, Princeton, New Jersey, June 1996.
Transmission Transfer Capability Task Force, ”Transmission Transfer Capability”, North American Electric Reliability Council, Princeton, New Jersey, May. 1995.
Transmission Transfer Capability Task Force, ”Transmission Transfer Capability”, North American Electric Reliability Council, Princeton, New Jersey, May 1996.
Promoting Utility Competition Through Open Access, Non-Discriminatory Transmission Service By Public Utilities; Recovery Of Stranded Costs By Public Utilities And Transmitting Utilities, Order No. 888, Final Rule, FERC, April 24, 1996.
Open Access Same-Time Information System And Standards Of Conduct, Order No. 889, Final Rule, FERC, April 24, 1996.
H.D. Chiang, A. Flueck, K.S. Shah, N. Balu. CPFLOW: A practical tool for tracing power system steady-state stationary behavior due to load and generation variations. IEEE Transactions on Power Systems. vol. 10, no. 2, May 1995, pp.623-634.
C.A. Canizares, F.L. Alvarado. Point of collapse and continuation methods for large AC/DC systems. IEEE Transactions on Power Systems. vol.7, no.1, Feb.1993, pp.1-8.
V. Ajjarapu, C. Christy. The continuation power flow: a tool for steady state voltage stability analysis, IEEE Transactions on Power Systems. vol.7, no.1, Feb.1992,pp.416-423.
Alexander J. Flueck, Hsiao-Dong Chiang, Kirit S. Shah, Investigating the Installed Real Power Transfer Capability of a Large Scale Power System Undedr a Proposed Multiarea Interchange Schedule Using CPFLOW, IEEE Transaction on Power System, Vol.11, No.2, May 1996.
J.A. Momoh, M.E. El-Hawary, R. Adapa. A review of selected optimal power flow literature to 1993, Part I. Newton, linear programming and interior point methods, IEEE Transactions on Power Systems, vol. 14, no. 1, pp. 96 -104, Feb.1999.
J.A. Momoh, M.E. El-Hawary, R. Adapa. A review of selected optimal power flow literature to 1993, Part II. Newton, linear programming and interior point methods, IEEE Transactions on Power Systems, vol. 14, no. 1, pp. 105 -111,Feb. 1999.
G.C. Ejebe, J.G. Waight, M. Sanots-Nieto, W.F. Tinney. Fast calculation of linear available transfer capability. IEEE Transactions on Power Systems, Vol: 15 Issue: 3 , Aug. 2000. pp: 1112 –1116.
Greene, S.; Dobson, I.; Alvarado, F.L. Sensitivity of transfer capability margins with a fast formula. Power Systems, IEEE Transactions on Power Systems, Volume: 17 Issue: 1, Feb. 2002 Page(s): 34 –40.
T. Wu, R. Fischl. An algorithm for detecting the contingencies which limit the inter-area megawatt transfer. Proceedings 1993 North American Power Symposium. Washington D.C., pp.222-227, October 11-12, 1993.
F.H. Clarke, Optimization and Nonsmooth Analysis, John Wiley, New York, 1983.
Venkataramana Ajjarapu, Colin Christy, The Continuation Power Flow: A Tool For Steady State Voltage Stability Analysis, Transaction on Power Systems, Vol.7, No.1, Feberary 1992.
王成山,李国庆,余贻鑫,江伟,《电力系统区域间功率交换能力的研究(一)连续型方法的基本理论及应用》,《电力系统自动化》,第23卷 第3期。
江伟,王成山,《电力系统输电能力研究中PV曲线的求取》,《电力系统自动化》,2001年02期。
L. Qi, Convergence analysis of some algorithms for solving nonsmooth equations, Mathematics Of Operations Research, 18(1993), 227-244.
D.Sun, R.S. Womersley and H. Qi, A feasible semismooth asymptotically Newton method for mixed complementarity problems, Math.Prog., 94(2002)167-187.
柴庆宣,《用协调惩罚技术改善牛顿法最优潮流收敛性》,《哈尔滨工业大学学报》,第27卷 第2期。
侯芳,吴政球,王良缘,《基于内点法的快速解耦最优潮流算法》,《电力系统及其自动化学报》,第13卷 第6期。
杨建华,《快速解耦法潮流计算的一种初值确定方法》,《华中电力》,第9卷 第6期。
刘梓洪,陈守雄,王秋梅,《基于一维搜索的电力系统潮流快速解耦法》,《华东电力》,2003年第1期。
P.W. Sauer. Technical challenges of computing available transfer capability (ATC) in electric power systems. Maui, Hawaii: 30th Hawaii International Conference on System Science. January 1997. 5pp.
I. Dobson, S. Greene, R. Rajaraman, C.L. DeMarco, F.L. Alvarado, M. Glavic, J. Zhang, R. Zimmerman. Electric power transfer capability: concepts, applications, sensitivity, uncertainty. Power Systems Engineering Research Center publication 00-34, November 2001. available from http://www.pserc.wisc.edu/.
W.W. Hogan. Contract networks for electric power transmission. Journal of Regulatory Economics. Sep, 1992. vol. 4, pp. 211–242.
P.W. Sauer, S. Grijalva. Error analysis in electric power system available transfer capability computation. Decision Support Systems. vol. 24, 1999, pp. 321-330.
T.V. Cutsem, C. Vournas. Voltage stability of electric power systems. Kluwer Academic Publishers. Boston, 1998.
S. Hao, G.A. Angelidis, H. Singh, A.D. Papalexopoulos. Consumer payment minimization in power pool auctions, IEEE Transactions on Power Systems, vol. 13, no. 3 , pp. 986 -991, Aug. 1998.
M.D. Ilic, J.R. Lacalle-Melero, F. Nishimura, W. Schenler, D. Shirmohammadi, A. Crough, A. Catelli. Short-term economic energy management in a competitive utility environment, IEEE Transactions on Power Systems, vol. 8, no. 1, pp. 198 -206, Feb. 1993.
H. Singh, S. Hao, A. Papalexopoulos. Transmission congestion management in competitive electricity markets, IEEE Transactions on Power Systems, vol. 13. no. 2 , pp. 672 -680, May 1998.
G.C. Ejebe, J. Tong, J.G. Waight J.G. Frame X. Wang, W.F. Tinney, Available Transfer Capability Calculations, IEEE Transactions on Power Systems, Vol.13, No.4, November 1998.
Hsiao-Dong Chiang, Alexander J. Flueck, Kirit S. Shah, Neal Balu, CPFLOW: A Practical Tool for Tracing Power System Steady-State Stationary Behavior Due to Load and Generation Variations, IEEE Transactions on Power Systems, Vol.10, No.2, May 1995.
李国庆,董存,《电力市场下区域间输电能力的定义和计算》,《电力系统自动化》,2001年05期。
李国庆,王成山,余贻鑫. 《大型互联电力系统区域间功率交换能力研究综述》, 《中国电机工程学报》,第21卷 第4期。
杨洪明,荆朝霞,段献忠. 《电力市场下电网的可传输容量》,《电力自动化设备》,2002.2.vol22(2). p34-37
默哈莫德·夏班,刘皓明,李卫星,严正,倪以信,吴复立,《静态安全约束下基于Benders分解算法的可用传输容量计算》,《中国电机工程学报》,2003年08期。
焦连伟,默哈莫德·夏班,倪以信,《可用传输容量计算的分层算法研究》,《中国电力》,第35卷 第1期。
刁勤华,默哈莫德·夏班,倪以信,《运用连续二次规划法计区域间极限传输容量算》,《电力系统自动化》2000年24期。
倪以信,陈寿孙,张宝霖. 《动态电力系统的理论和分析》,北京:清华大学出版社. 第一版.2002.5
张伯明,陈寿孙. 《高等电力网络分析》,北京:清华大学出版社。第一版. 1996.8
Transmission Transfer Capability Task Force, ”Transmission Transfer Capability”, North American Electric Reliability Council, Princeton, New Jersey, May. 1995.
Transmission Transfer Capability Task Force, ”Transmission Transfer Capability”, North American Electric Reliability Council, Princeton, New Jersey, May 1996.
Promoting Utility Competition Through Open Access, Non-Discriminatory Transmission Service By Public Utilities; Recovery Of Stranded Costs By Public Utilities And Transmitting Utilities, Order No. 888, Final Rule, FERC, April 24, 1996.
Open Access Same-Time Information System And Standards Of Conduct, Order No. 889, Final Rule, FERC, April 24, 1996.
H.D. Chiang, A. Flueck, K.S. Shah, N. Balu. CPFLOW: A practical tool for tracing power system steady-state stationary behavior due to load and generation variations. IEEE Transactions on Power Systems. vol. 10, no. 2, May 1995, pp.623-634.
C.A. Canizares, F.L. Alvarado. Point of collapse and continuation methods for large AC/DC systems. IEEE Transactions on Power Systems. vol.7, no.1, Feb.1993, pp.1-8.
V. Ajjarapu, C. Christy. The continuation power flow: a tool for steady state voltage stability analysis, IEEE Transactions on Power Systems. vol.7, no.1, Feb.1992,pp.416-423.
Alexander J. Flueck, Hsiao-Dong Chiang, Kirit S. Shah, Investigating the Installed Real Power Transfer Capability of a Large Scale Power System Undedr a Proposed Multiarea Interchange Schedule Using CPFLOW, IEEE Transaction on Power System, Vol.11, No.2, May 1996.
J.A. Momoh, M.E. El-Hawary, R. Adapa. A review of selected optimal power flow literature to 1993, Part I. Newton, linear programming and interior point methods, IEEE Transactions on Power Systems, vol. 14, no. 1, pp. 96 -104, Feb.1999.
J.A. Momoh, M.E. El-Hawary, R. Adapa. A review of selected optimal power flow literature to 1993, Part II. Newton, linear programming and interior point methods, IEEE Transactions on Power Systems, vol. 14, no. 1, pp. 105 -111,Feb. 1999.
G.C. Ejebe, J.G. Waight, M. Sanots-Nieto, W.F. Tinney. Fast calculation of linear available transfer capability. IEEE Transactions on Power Systems, Vol: 15 Issue: 3 , Aug. 2000. pp: 1112 –1116.
Greene, S.; Dobson, I.; Alvarado, F.L. Sensitivity of transfer capability margins with a fast formula. Power Systems, IEEE Transactions on Power Systems, Volume: 17 Issue: 1, Feb. 2002 Page(s): 34 –40.
T. Wu, R. Fischl. An algorithm for detecting the contingencies which limit the inter-area megawatt transfer. Proceedings 1993 North American Power Symposium. Washington D.C., pp.222-227, October 11-12, 1993.
F.H. Clarke, Optimization and Nonsmooth Analysis, John Wiley, New York, 1983.
Venkataramana Ajjarapu, Colin Christy, The Continuation Power Flow: A Tool For Steady State Voltage Stability Analysis, Transaction on Power Systems, Vol.7, No.1, Feberary 1992.
王成山,李国庆,余贻鑫,江伟,《电力系统区域间功率交换能力的研究(一)连续型方法的基本理论及应用》,《电力系统自动化》,第23卷 第3期。
江伟,王成山,《电力系统输电能力研究中PV曲线的求取》,《电力系统自动化》,2001年02期。
L. Qi, Convergence analysis of some algorithms for solving nonsmooth equations, Mathematics Of Operations Research, 18(1993), 227-244.
D.Sun, R.S. Womersley and H. Qi, A feasible semismooth asymptotically Newton method for mixed complementarity problems, Math.Prog., 94(2002)167-187.
柴庆宣,《用协调惩罚技术改善牛顿法最优潮流收敛性》,《哈尔滨工业大学学报》,第27卷 第2期。
侯芳,吴政球,王良缘,《基于内点法的快速解耦最优潮流算法》,《电力系统及其自动化学报》,第13卷 第6期。
杨建华,《快速解耦法潮流计算的一种初值确定方法》,《华中电力》,第9卷 第6期。
刘梓洪,陈守雄,王秋梅,《基于一维搜索的电力系统潮流快速解耦法》,《华东电力》,2003年第1期。
P.W. Sauer. Technical challenges of computing available transfer capability (ATC) in electric power systems. Maui, Hawaii: 30th Hawaii International Conference on System Science. January 1997. 5pp.
I. Dobson, S. Greene, R. Rajaraman, C.L. DeMarco, F.L. Alvarado, M. Glavic, J. Zhang, R. Zimmerman. Electric power transfer capability: concepts, applications, sensitivity, uncertainty. Power Systems Engineering Research Center publication 00-34, November 2001. available from http://www.pserc.wisc.edu/.
W.W. Hogan. Contract networks for electric power transmission. Journal of Regulatory Economics. Sep, 1992. vol. 4, pp. 211–242.
P.W. Sauer, S. Grijalva. Error analysis in electric power system available transfer capability computation. Decision Support Systems. vol. 24, 1999, pp. 321-330.
T.V. Cutsem, C. Vournas. Voltage stability of electric power systems. Kluwer Academic Publishers. Boston, 1998.
S. Hao, G.A. Angelidis, H. Singh, A.D. Papalexopoulos. Consumer payment minimization in power pool auctions, IEEE Transactions on Power Systems, vol. 13, no. 3 , pp. 986 -991, Aug. 1998.
M.D. Ilic, J.R. Lacalle-Melero, F. Nishimura, W. Schenler, D. Shirmohammadi, A. Crough, A. Catelli. Short-term economic energy management in a competitive utility environment, IEEE Transactions on Power Systems, vol. 8, no. 1, pp. 198 -206, Feb. 1993.
H. Singh, S. Hao, A. Papalexopoulos. Transmission congestion management in competitive electricity markets, IEEE Transactions on Power Systems, vol. 13. no. 2 , pp. 672 -680, May 1998.
G.C. Ejebe, J. Tong, J.G. Waight J.G. Frame X. Wang, W.F. Tinney, Available Transfer Capability Calculations, IEEE Transactions on Power Systems, Vol.13, No.4, November 1998.
Hsiao-Dong Chiang, Alexander J. Flueck, Kirit S. Shah, Neal Balu, CPFLOW: A Practical Tool for Tracing Power System Steady-State Stationary Behavior Due to Load and Generation Variations, IEEE Transactions on Power Systems, Vol.10, No.2, May 1995.
李国庆,董存,《电力市场下区域间输电能力的定义和计算》,《电力系统自动化》,2001年05期。
李国庆,王成山,余贻鑫. 《大型互联电力系统区域间功率交换能力研究综述》, 《中国电机工程学报》,第21卷 第4期。
杨洪明,荆朝霞,段献忠. 《电力市场下电网的可传输容量》,《电力自动化设备》,2002.2.vol22(2). p34-37
默哈莫德·夏班,刘皓明,李卫星,严正,倪以信,吴复立,《静态安全约束下基于Benders分解算法的可用传输容量计算》,《中国电机工程学报》,2003年08期。
焦连伟,默哈莫德·夏班,倪以信,《可用传输容量计算的分层算法研究》,《中国电力》,第35卷 第1期。
刁勤华,默哈莫德·夏班,倪以信,《运用连续二次规划法计区域间极限传输容量算》,《电力系统自动化》2000年24期。
倪以信,陈寿孙,张宝霖. 《动态电力系统的理论和分析》,北京:清华大学出版社. 第一版.2002.5
张伯明,陈寿孙. 《高等电力网络分析》,北京:清华大学出版社。第一版. 1996.8