Stability transfer limit calculation in a power transmission network
First Claim
1. A method for calculating a transient stability or voltage stability transfer limit in a power network, said network having at least two independent AC generators supplying a common load via separate AC transmission lines having at least one bus, the method comprising the steps of:
- a) determining steady state values for variable characteristic electrical parameters of variable elements of said network based on particular values for power transferred by said transmission lines;
b) determining static values for passive characteristic electrical parameters of passive conductive elements of said network;
c) selecting a contingency resulting in a sudden change of at least one of said variable electrical parameters and said passive electrical parameters;
d) calculating using said steady state and said static values a post contingency steady state value for a voltage at one of said at least one bus;
e) calculating using said steady state and said static values a voltage over time during a transition period at said one of said at least one bus, said transition period extending in time from a start of said contingency through a discontinuity during which said voltage at said one bus is abnormally altered, and recovery during which said voltage at said one bus will tend toward a steady state terminal value;
f) calculating an integral sum of squares of a difference between said post contingency steady state voltage and said transition period voltage over said transition period to obtain an energy value;
g) changing one of said power values associated with one of said AC transmission lines and repeating said steps a) b) d) e) and f) to obtain two said energy values, said two energy values being non-substantially-infinite;
h) obtaining a transfer limit estimate for said one transmission line as being an asymptote of said energy values, said energy values being an inverse function of said limit less said one power value.
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Abstract
A transient or voltage stability transfer limit is calculated for a power network having at least two independent AC generators supplying a common load via separate AC transmission lines having at least one bus. Steady state values for variable characteristic electrical parameters of variable elements of the network are determined based on particular values for power transferred by the transmission lines. Static values for passive characteristic electrical parameters of passive conductive elements of the network are determined. A contingency resulting in a sudden change of at least one of the variable electrical parameters and the passive electrical parameters is selected. A post contingency steady state value for a voltage at one of the buses is calculated. A voltage over time during a transition period at the bus is calculated, the transition period extending in time from a start of the contingency through a discontinuity during which the voltage is abnormally altered, and recovery during which the voltage will tend toward a steady state terminal value. An integral sum of squares of a difference between the post contingency steady state voltage and the transition period voltage over the transition period is calculated to obtain an energy value. Using two such energy values from two power values, a transfer limit estimate for the transmission line is obtained as being an asymptote of the energy values, the energy values being an inverse function of the stability limit less the power value.
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Citations
12 Claims
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1. A method for calculating a transient stability or voltage stability transfer limit in a power network, said network having at least two independent AC generators supplying a common load via separate AC transmission lines having at least one bus, the method comprising the steps of:
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a) determining steady state values for variable characteristic electrical parameters of variable elements of said network based on particular values for power transferred by said transmission lines; b) determining static values for passive characteristic electrical parameters of passive conductive elements of said network; c) selecting a contingency resulting in a sudden change of at least one of said variable electrical parameters and said passive electrical parameters; d) calculating using said steady state and said static values a post contingency steady state value for a voltage at one of said at least one bus; e) calculating using said steady state and said static values a voltage over time during a transition period at said one of said at least one bus, said transition period extending in time from a start of said contingency through a discontinuity during which said voltage at said one bus is abnormally altered, and recovery during which said voltage at said one bus will tend toward a steady state terminal value; f) calculating an integral sum of squares of a difference between said post contingency steady state voltage and said transition period voltage over said transition period to obtain an energy value; g) changing one of said power values associated with one of said AC transmission lines and repeating said steps a) b) d) e) and f) to obtain two said energy values, said two energy values being non-substantially-infinite; h) obtaining a transfer limit estimate for said one transmission line as being an asymptote of said energy values, said energy values being an inverse function of said limit less said one power value. - View Dependent Claims (2, 3, 4, 5)
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6. A method for calculating a transient stability or voltage stability transfer limit in a power network, said network having at least two independent AC generators supplying a common load via separate AC transmission lines having at least one bus node, said method comprising the steps of:
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a) determining steady state values for variable characteristic electrical parameters of elements of said network based on particular values for power transferred by one of said transmission lines; b) determining static values for characteristic electrical parameters of passive conductive elements of said network; c) selecting a contingency resulting in a sudden change of at least one of said variable electrical parameters and said passive electrical parameters; d) calculating using said steady state and said static values a voltage over time during a transition period at one of said at least one bus, said transition period extending in time from a start of said contingency through a discontinuity during which said voltage at said one bus is abnormally altered, and recovery during which said voltage at said one bus node will oscillate toward a steady state terminal value; and e) changing one of said power values associated with said one of said transmission lines and repeating said steps a) and d) to determine within a predetermined degree of accuracy a maximum value for power generated at said one of said transmission lines resulting in a stable value of said terminal value, whereby said transfer limit is calculated to be said maximum value. - View Dependent Claims (7, 8, 9, 10)
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11. An apparatus for calculating a stability transfer limit in a power network, said network having at least two independent AC generators supplying a common load via separate groups of AC transmission lines having at least one bus node, said apparatus comprising:
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means for determining steady state values for variable characteristic electrical parameters of elements of said network based on particular values for power generated by said generators, and static values for characteristic electrical parameters of passive conductive elements of said network; means for selecting a contingency resulting in a sudden change of at least one of said variable electrical parameters and said passive electrical parameters; means receiving said steady state and said static values for calculating a voltage over time during a transition period at one of said at least one bus, said transition period extending in time from a start of said contingency through a discontinuity during which said voltage at said one bus is abnormally altered, and recovery during which said voltage at said one bus node will tend toward a steady state terminal value; and means for controlling said determining means and said calculating means to determine within a predetermined degree of accuracy a maximum value for power generated at one of said generators resulting in a stable value of said terminal value, whereby said transfer limit is said maximum value.
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12. An apparatus for calculating a stability transfer limit in a power network, said network having at least two independent AC generators supplying a common load via separate groups of AC transmission lines having at least one bus node, said apparatus comprising:
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means for determining steady state values for variable characteristic electrical parameters of elements of said network based on particular values for power generated by said generators, and static values for characteristic electrical parameters of passive conductive elements of said network; means for selecting a contingency resulting in a sudden change of at least one of said variable electrical parameters and said passive electrical parameters; means for calculating using said steady state and said static values a post contingency steady state value for a voltage at one of said at least one bus node; means receiving said steady state and said static values for calculating a voltage over time during a transition period at one of said at least one bus, said transition period extending in time from a start of said contingency through a discontinuity during which said voltage at said one bus is abnormally altered, and recovery during which said voltage at said one bus node will tend toward a steady state terminal value; means for calculating an integral sum of squares of a difference between said post contingency steady state voltage and said transition period voltage over said transition period to obtain a signal energy value; means for selecting two said power values associated with one of said AC transmission lines and obtaining two non-substantially infinite energy values; means for determining said transfer limit for said one transmission line as being an asymptote of said energy values, said energy values being an inverse function of said limit less said one power value.
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Specification