Based on risk theory, considering the probability of an accident and the severity of the sequence, combining N-1 and N-2 security check, this paper puts forward a new risk index, which uses the amount of optimal load ...Based on risk theory, considering the probability of an accident and the severity of the sequence, combining N-1 and N-2 security check, this paper puts forward a new risk index, which uses the amount of optimal load shedding as the severity of an accident consequence to identify the critical lines in power system. Taking IEEE24-RTS as an example, the simulation results verify the correctness and effectiveness of the proposed index.展开更多
It is shown that any polynomial written as an infinite product with all positive real roots may be split in two steps into the product of four infinite polynomials: two with all imaginary and two with all real roots. ...It is shown that any polynomial written as an infinite product with all positive real roots may be split in two steps into the product of four infinite polynomials: two with all imaginary and two with all real roots. Equations between such infinite products define adjoint infinite polynomials with roots on the adjoint roots (real and imaginary). It is shown that the shifting of the coordinates to a parallel line of one of the adjoint axes does not influence the relative placement of the roots: they are shifted to the parallel line. General relations between original and adjoint polynomials are evaluated. These relations are generalized representations of the relations of Euler and Pythagoras in form of infinite polynomial products. They are inherent properties of split polynomial products. If the shifting of the coordinate system corresponds to the shifting of the imaginary axes to the critical line, then the relations of Euler take the form corresponding to their occurrence in the functional equation of the Riemann zeta function: the roots on the imaginary axes are all shifted to the critical line. Since it is known that the gamma and the zeta functions may be written as composed functions with exponential and trigonometric parts, this opens the possibility to prove the placement of the zeta function on the critical line.展开更多
Starting with the binomial coefficient and using its infinite product representation, the infinite product representation of the gamma function and of the zeta function are composed of an exponential and of a trigonom...Starting with the binomial coefficient and using its infinite product representation, the infinite product representation of the gamma function and of the zeta function are composed of an exponential and of a trigonometric component and proved. It is proved, that all these components define imaginary roots on the critical line, if written in the form as they are in the functional equation of the zeta function.展开更多
Voltage instability is a serious phenomenon that can occur in a power system because of critical or stressed condi-tions.To prevent voltage collapse caused by such instability,accurate voltage collapse prediction is n...Voltage instability is a serious phenomenon that can occur in a power system because of critical or stressed condi-tions.To prevent voltage collapse caused by such instability,accurate voltage collapse prediction is necessary for power system planning and operation.This paper proposes a novel collapse prediction index(NCPI)to assess the volt-age stability conditions of the power system and the critical conditions of lines.The effectiveness and applicability of the proposed index are investigated on the IEEE 30-bus and IEEE 118-bus systems and compared with the well-known existing indices(Lmn,FVSI,LQP,NLSI,and VSLI)under several power system operations to validate its practicability and versatility.The study also presents the sensitivity assumptions of existing indices and analyzes their impact on voltage collapse prediction.The application results under intensive case studies prove that the proposed index NCPI adapts to several operating power conditions.The results show the superiority of the proposed index in accurately estimating the maximum load-ability and predicting the critical lines,weak buses,and weak areas in medium and large networks during various power load operations and contingencies.A line interruption or generation unit outage in a power system can also lead to voltage collapse,and this is a contingency in the power system.Line and generation unit outage contingencies are examined to identify the lines and generators that significantly impact system stability in the event of an outage.The contingencies are also ranked to identify the most severe outages that significantly cause voltage collapse because of the outage of line or generator.展开更多
基金Technology Major Project of China Southern Power Grid Co.,Ltd.(GZ2014-2-0049).
文摘Based on risk theory, considering the probability of an accident and the severity of the sequence, combining N-1 and N-2 security check, this paper puts forward a new risk index, which uses the amount of optimal load shedding as the severity of an accident consequence to identify the critical lines in power system. Taking IEEE24-RTS as an example, the simulation results verify the correctness and effectiveness of the proposed index.
文摘It is shown that any polynomial written as an infinite product with all positive real roots may be split in two steps into the product of four infinite polynomials: two with all imaginary and two with all real roots. Equations between such infinite products define adjoint infinite polynomials with roots on the adjoint roots (real and imaginary). It is shown that the shifting of the coordinates to a parallel line of one of the adjoint axes does not influence the relative placement of the roots: they are shifted to the parallel line. General relations between original and adjoint polynomials are evaluated. These relations are generalized representations of the relations of Euler and Pythagoras in form of infinite polynomial products. They are inherent properties of split polynomial products. If the shifting of the coordinate system corresponds to the shifting of the imaginary axes to the critical line, then the relations of Euler take the form corresponding to their occurrence in the functional equation of the Riemann zeta function: the roots on the imaginary axes are all shifted to the critical line. Since it is known that the gamma and the zeta functions may be written as composed functions with exponential and trigonometric parts, this opens the possibility to prove the placement of the zeta function on the critical line.
文摘Starting with the binomial coefficient and using its infinite product representation, the infinite product representation of the gamma function and of the zeta function are composed of an exponential and of a trigonometric component and proved. It is proved, that all these components define imaginary roots on the critical line, if written in the form as they are in the functional equation of the zeta function.
基金supported by the National Natural Science Foundation of China under Grant 52007032National Key R&D Program of China(2022YFB2703502)Basic Research Program of Jiangsu province under Grant BK20200385,China.
文摘Voltage instability is a serious phenomenon that can occur in a power system because of critical or stressed condi-tions.To prevent voltage collapse caused by such instability,accurate voltage collapse prediction is necessary for power system planning and operation.This paper proposes a novel collapse prediction index(NCPI)to assess the volt-age stability conditions of the power system and the critical conditions of lines.The effectiveness and applicability of the proposed index are investigated on the IEEE 30-bus and IEEE 118-bus systems and compared with the well-known existing indices(Lmn,FVSI,LQP,NLSI,and VSLI)under several power system operations to validate its practicability and versatility.The study also presents the sensitivity assumptions of existing indices and analyzes their impact on voltage collapse prediction.The application results under intensive case studies prove that the proposed index NCPI adapts to several operating power conditions.The results show the superiority of the proposed index in accurately estimating the maximum load-ability and predicting the critical lines,weak buses,and weak areas in medium and large networks during various power load operations and contingencies.A line interruption or generation unit outage in a power system can also lead to voltage collapse,and this is a contingency in the power system.Line and generation unit outage contingencies are examined to identify the lines and generators that significantly impact system stability in the event of an outage.The contingencies are also ranked to identify the most severe outages that significantly cause voltage collapse because of the outage of line or generator.
