Group-based BCU methods for on-line dynamical security assessments and energy margin calculations of practical power systems

A method of determining boundary condition of unstable equilibrium points (UEPs) in BCU system, comprising:

• classifying UEPs into UEP groups of coherent contingencies based on predetermined condition;
• selecting one UEP group from the classified UEP groups;
• obtaining UEP having predetermined condition from the selected UEP group;
• and
• determining boundary condition of the selected UEP group based on the obtained UEP having predetermined condition.

A method of determining stability of unstable equilibrium points (UEPs) computed by using BCU method, comprising:

• classifying UEPs into UEP groups of coherent contingencies based on predetermined condition;
• selecting one UEP group from the classified UEP groups;
• obtaining UEP having predetermined condition from the selected UEP group;
• obtaining a test vector Xtest for the obtained UEP, say XUEP using the following equation:
• Xtest=Xspost+0.99(XUEP−Xspost)
• where Xspost is the SEP, and
• checking boundary condition of XUEP by simulating system trajectory of post-fault original system starting from Xtest, thereby determining boundary condition of the selected UEP group.

A method of obtaining controlling unstable equilibrium point (CUEP) satisfying a boundary condition in a BCU system, comprising:

• obtaining a group of coherent contingencies which violates boundary condition;
• computing UEP from the obtained group of coherent contingencies which violates boundary condition;
• selecting the computed UEP which has the largest SEP separation, say XlUEP with respect to contingency, say Ll, and selecting the computed UEP which has the smallest SEP separation, say XsUEP, with respect to contingency, say Ls;
• and
• computing corresponding BCU-Exit points for XlUEP and XsUEP respectively;
• where BCU-Exit points for XlUEP and XsUEP are denoted as Xlbcu and sbcu respectively, thereby using an energy at Xlbcu, denoted as Vsbcu, as critical energy for the contingency Ls and an energy at Xsbcu, denoted as Vsbcu, as the critical energy for the contingency Ls,
• wherein the SEP separation of a contingency, say Li, in the group of coherent contingencies be SEPi. and the critical energy for the contingency Li is the following equation:
• V
• i
• cr
• =
• a
• ×
• SEP
• i
• +
• b
• where
• a
• =
• V
• l
• bcu
• -
• V
• s
• bcu
• SEP
• l
• -
• SEP
• s
• b
• =
• V
• s
• bcu
• ×
• SEP
• l
• -
• V
• l
• bcu
• ×
• SEP
• s
• SEP
• l
• -
• SEP
• s

A method for group-based BCU method, comprising:

• computing controlling unstable equilibrium point (UEP) and post-fault SEP of each study contingency of a contingency list until the contingency list is finished by using BCU method;
• and
• classifying the computed UEPs associated with each contingency into groups of coherent contingencies based on predetermined condition,
• wherein each classified group of UEPs performs the following steps:
• selecting UEP with the greatest SEP separation when the SEP separation of each contingency in the group is predetermined amount or less, otherwise selecting UEP with the greatest SEP separation and UEP with the smallest SEP separation;
• checking boundary property of the selected UEP or UEPs in accordance with a predetermined method;
• determining UEPs of entire group lie on stability boundary of an original system based on the checking result;
• performing a direct stability assessment and calculate an energy margin for each study contingency in the group of coherent contingencies based on a critical energy when the determining steps determines that UEPs of entire group lie on stability boundary of the original system, wherein the critical energy value each study contingency in the groups of coherent contingencies is energy value at the computed UEP;
• computing corresponding BCU-Exit point for XlUEP and XsUEP respectively, wherein the corresponding BCU-Exit point for XlUEP and XsUEP are denoted as Xlbcu and Xsbcu respectively, the selected UEP which has the largest SEP separation is denoted as XlUEP with respect to contingency, say Ll, and the selected UEP which has the smallest SEP separation is denoted as XsUEP, with respect to contingency, say Ls;
• computing critical energy for contingency Li based on the following equations:
• V
• i
• cr
• =
• a
• ×
• SEP
• i
• +
• b
• where
• a
• =
• V
• l
• bcu
• -
• V
• s
• bcu
• SEP
• l
• -
• SEP
• s
• b
• =
• V
• s
• bcu
• ×
• SEP
• l
• -
• V
• l
• bcu
• ×
• SEP
• s
• SEP
• l
• -
• SEP
• s
• , wherein the energy at Xlbcu is denoted as Vlbcu, as the critical energy for the contingency Ls and the energy at Xsbcu is denoted as Vsbcu, as the critical energy for the contingency Ls;
• and
• performing a direct stability assessment and calculate an energy margin for each study contingency in the group of coherent contingencies based on the computed critical energy when the determining steps determines that UEPs of entire group do not lie on stability boundary of the original system.

A revised BCU classifiers used in BCU system, comprising:

• first BCU classifier for detecting problem of network islanding problem based on contingency;
• second BCU classifier for detecting problem with regard to computed pre-fault SEP and post-fault SEP of the contingency when the first BCU classifier does not detect the problem;
• third BCU classifier for detecting problem with regard to computed exit point of the contingency when the second BCU classifier does not detect the problem;
• fourth BCU classifier for detecting problem with regard to computed minimal gradient point of the contingency when the third classifies does not detect the problem;
• fifith BCU classifier for detecting problem with regard to computed controlling unstable equilibrium point (CUEP) of the contingency when the fourth classifies does not detect the problem;
• and
• sixth BCU classifier for determining stability of the contingency based on energy margin which is computed based on energy value at the computed CUEP when the fifth classifies does not detect the problem.