Abstract: A linear asymmetric method for examining branch-outage-type steady-state security of AC power networks is provided. Two linear expressions of bus injection active and reactive powers in terms of translation voltages and voltage angles of all buses are established. Then a linear asymmetric matrix-equation model for the steady state of the network is built considering the reference bus number. Manipulating this model produces the matrix expression of branch-not-outage-type translation voltages and voltage angles of non-reference buses and the bus impedance matrix with the reference bus discarded. The branch-outage-type translation-voltage increments and voltage-angle increments of non-reference buses are then obtained by the bus impedance matrix and the outage branch using the calculation formula of ordinary inverse of a modified matrix. The examination of the steady-state security of the network is achieved using these increments.

Abstract: A symmetric method for obtaining branch-mean-square-current components induced by sources and loads at individual buses in AC power networks is invented. Two linear expressions of bus injection active and reactive powers in terms of translation voltages and voltage angles of all buses are established at first. Then a linear symmetric matrix-equation model for the steady state of the network is built. Manipulating this model by Moore-Penrose pseudoinverse produces a linear symmetric matrix expression of translation voltages and voltage angles of all buses in terms of bus injection powers. Expressing the branch mean-square current in terms of source's and load's powers by this matrix expression, a symmetric algebraic calculation formula for obtaining the branch-mean-square-current components is produced after manipulating by Shapley value theorem, by which the obtaining of branch-mean-square-current components are achieved.

Abstract: A symmetric method for obtaining network-power-loss components induced by sources and loads at individual buses in AC power networks is invented. Two linear expressions of bus injection active and reactive powers in terms of translation voltages and voltage angles of all buses are established at first. Then a linear symmetric matrix-equation model for the steady state of the network is built. Manipulating this model by Moore-Penrose pseudoinverse produces a linear symmetric matrix expression of translation voltages and voltage angles of all buses in terms of bus injection powers. Expressing the network power loss in terms of source's and load's powers by this matrix expression, a symmetric algebraic calculation formula for obtaining the network-power-loss components is produced after manipulating by Shapley value theorem, by which the obtaining of network-power-loss components are achieved. The set of network-power-loss components provides a new efficient tool for economic operation of AC power networks.

Abstract: A symmetric method for obtaining network-power-loss components induced by sources and loads at individual buses in AC power networks is invented. Two linear expressions of bus injection active and reactive powers in terms of translation voltages and voltage angles of all buses are established at first. Then a linear symmetric matrix-equation model for the steady state of the network is built. Manipulating this model by Moore-Penrose pseudoinverse produces a linear symmetric matrix expression of translation voltages and voltage angles of all buses in terms of bus injection powers. Expressing the network power loss in terms of source's and load's powers by this matrix expression, a symmetric algebraic calculation formula for obtaining the network-power-loss components is produced after manipulating by Shapley value theorem, by which the obtaining of network-power-loss components are achieved. The set of network-power-loss components provides a new efficient tool for economic operation of AC power networks.

Abstract: A linear asymmetric method for examining branch-outage-type steady-state security of AC power networks is provided. Two linear expressions of bus injection active and reactive powers in terms of translation voltages and voltage angles of all buses are established. Then a linear asymmetric matrix-equation model for the steady state of the network is built considering the reference bus number. Manipulating this model produces the matrix expression of branch-not-outage-type translation voltages and voltage angles of non-reference buses and the bus impedance matrix with the reference bus discarded. The branch-outage-type translation-voltage increments and voltage-angle increments of non-reference buses are then obtained by the bus impedance matrix and the outage branch using the calculation formula of ordinary inverse of a modified matrix. The examination of the steady-state security of the network is achieved using these increments.

Abstract: A symmetric method for obtaining bus-translation-voltage components induced by sources and loads at individual buses in AC power networks is invented. Two linear expressions of bus injection active and reactive powers in terms of translation voltages and voltage angles of all buses are established according to branch admittances and bus injection powers of sources and loads. Then a linear symmetric matrix-equation model for the steady state of the network is built. Manipulating this model by Moore-Penrose pseudoinverse produces a linear symmetric matrix expression of translation voltages and voltage angles of all buses in terms of bus injection powers. Finally a linear symmetric algebraic calculation formula for obtaining the bus-translation-voltage components is extracted from this matrix expression to achieve obtaining of the bus-translation-voltage components.

Abstract: An equilibrium-conductance-compensated eccentric method for obtaining power transfer coefficients of a direct current (DC) power network, including: establishing an equilibrium-conductance-compensated globally-linear function that relates all bus translation voltages to a bus injection power according to given bus load parameters and given bus source parameters of the DC power network; establishing an equilibrium-conductance-compensated globally-linear eccentric matrix-equation model for steady state of the DC power network; establishing an equilibrium-conductance-compensated globally-linear eccentric matrix relation between non-reference bus injection powers and non-reference bus translation voltages by using ordinary inversion of matrices; establishing an equilibrium-conductance-compensated globally-linear eccentric expression of a branch-transferred power in terms of the non-reference bus injection powers; and obtaining power transfer coefficients of the DC power network according to the equilibrium-conduc

Abstract: An equivalent-conductance-compensated globally-linear symmetric method for obtaining power flows in a DC power network, including: establishing an equivalent-conductance-compensated globally-linear function that relates all bus translation voltages to a bus injection power according to given bus load parameters and given bus source parameters of the DC power network; establishing an equivalent-conductance-compensated globally-linear symmetric matrix-equation model for power flows in the DC power network according to the equivalent-conductance-compensated globally-linear function and a given slack bus serial number; establishing an equivalent-conductance-compensated globally-linear symmetric matrix relation between non-slack bus injection powers and all the bus translation voltages by using M-P inversion of matrices according to the equivalent-conductance-compensated globally-linear symmetric matrix-equation model; and calculating each bus per-unit voltage and each branch-transferred power in the DC power netw

Abstract: An equilibrium-conductance-compensated globally-linear symmetric method for obtaining power flows in a DC power network, including: establishing an equilibrium-conductance-compensated globally-linear function that relates all bus translation voltages to a bus injection power according to given bus load parameters and given bus source parameters of the DC power network; establishing an equilibrium-conductance-compensated globally-linear symmetric matrix-equation model for power flows in the DC power network according to the equilibrium-conductance-compensated globally-linear function and a given slack bus serial number; establishing an equilibrium-conductance-compensated globally-linear symmetric matrix relation between non-slack bus injection powers and all the bus translation voltages by using M-P inversion of matrices according to the equilibrium-conductance-compensated globally-linear symmetric matrix-equation model; and calculating each bus per-unit voltage and each branch-transferred power in the DC powe

Abstract: An equivalent-conductance-compensated eccentric method for obtaining power transfer coefficients of a direct current (DC) power network, including: establishing an equivalent-conductance-compensated globally-linear function that relates all bus translation voltages to a bus injection power according to given bus load parameters and given bus source parameters of the DC power network; establishing an equivalent-conductance-compensated globally-linear eccentric matrix-equation model for steady state of the DC power network; establishing an equivalent-conductance-compensated globally-linear eccentric matrix relation between non-reference bus injection powers and non-reference bus translation voltages by using ordinary inversion of matrices; establishing an equivalent-conductance-compensated globally-linear eccentric expression of a branch-transferred power in terms of the non-reference bus injection powers; and obtaining power transfer coefficients of the DC power network according to the equivalent-conductance-

Abstract: An equilibrium-conductance-compensated eccentric method for obtaining power transfer coefficients of a direct current (DC) power network, including: establishing an equilibrium-conductance-compensated globally-linear function that relates all bus translation voltages to a bus injection power according to given bus load parameters and given bus source parameters of the DC power network; establishing an equilibrium-conductance-compensated globally-linear eccentric matrix-equation model for steady state of the DC power network; establishing an equilibrium-conductance-compensated globally-linear eccentric matrix relation between non-reference bus injection powers and non-reference bus translation voltages by using ordinary inversion of matrices; establishing an equilibrium-conductance-compensated globally-linear eccentric expression of a branch-transferred power in terms of the non-reference bus injection powers; and obtaining power transfer coefficients of the DC power network according to the equilibrium-conduc

Abstract: An equivalent-conductance-compensated globally-linear symmetric method for obtaining power flows in a DC power network, including: establishing an equivalent-conductance-compensated globally-linear function that relates all bus translation voltages to a bus injection power according to given bus load parameters and given bus source parameters of the DC power network; establishing an equivalent-conductance-compensated globally-linear symmetric matrix-equation model for power flows in the DC power network according to the equivalent-conductance-compensated globally-linear function and a given slack bus serial number; establishing an equivalent-conductance-compensated globally-linear symmetric matrix relation between non-slack bus injection powers and all the bus translation voltages by using M-P inversion of matrices according to the equivalent-conductance-compensated globally-linear symmetric matrix-equation model; and calculating each bus per-unit voltage and each branch-transferred power in the DC power netw

Abstract: The present invention belongs to electric power engineering field, and provides a symmetric method for obtaining line-transferred linear active power flows in Multi-Terminal Direct Current (MTDC) power networks, which comprises: firstly establishing a system of symmetric linear indeterminate equations of buses' injection active powers in terms of buses' voltage offsets; then establishing a symmetric linear matrix equation of buses' voltage offsets in terms of buses' injection active powers and obtaining each bus' voltage offset and bus' voltage of the MTDC power network according to the system of symmetric linear indeterminate equations; finally establishing a symmetric linear relationship that expresses a line-transferred linear active power flow in terms of buses' injection active powers and obtaining each line-transferred linear active power flow of the MTDC power network according to the symmetric linear matrix equation of buses' voltage offsets in terms of buses' injection active powers, known line-trans

Abstract: The present invention belongs to electric power engineering field, relates to a method for obtaining a set of symmetric power transfer coefficients under simultaneous change of sources and loads in AC power networks, which comprises the steps of: firstly establishing a linear function of a lossy branch transferred power in terms of buses voltage angles according to a nonlinear function of a branch transferred power, parameters and operation features of the AC power network; then establishing symmetric linear functions of buses injection powers of power sources and loads in terms of buses voltage angles by combining the linear function of the lossy branch transferred power in terms of buses voltage angles and buses injection powers of power sources and loads, in turn establishing symmetric linear functions of buses voltage angles in terms of buses injection powers of power sources and loads; and finally obtaining the symmetric power transfer coefficients from buses injection powers of power sources and loads t

Abstract: The present invention belongs to electric power engineering field, and provides a symmetric method for obtaining line-transferred linear active power flows in Multi-Terminal Direct Current (MTDC) power networks, which comprises: firstly establishing a system of symmetric linear indeterminate equations of buses' injection active powers in terms of buses' voltage offsets; then establishing a symmetric linear matrix equation of buses' voltage offsets in terms of buses' injection active powers and obtaining each bus' voltage offset and bus' voltage of the MTDC power network according to the system of symmetric linear indeterminate equations; finally establishing a symmetric linear relationship that expresses a line-transferred linear active power flow in terms of buses' injection active powers and obtaining each line-transferred linear active power flow of the MTDC power network according to the symmetric linear matrix equation of buses' voltage offsets in terms of buses' injection active powers, known line-trans

Abstract: The present invention belongs to electric power engineering field, relates to a method for obtaining a set of symmetric power transfer coefficients under simultaneous change of sources and loads in AC power networks, which comprises the steps of: firstly establishing a linear function of a lossy branch transferred power in terms of buses voltage angles according to a nonlinear function of a branch transferred power, parameters and operation features of the AC power network; then establishing symmetric linear functions of buses injection powers of power sources and loads in terms of buses voltage angles by combining the linear function of the lossy branch transferred power in terms of buses voltage angles and buses injection powers of power sources and loads, in turn establishing symmetric linear functions of buses voltage angles in terms of buses injection powers of power sources and loads; and finally obtaining the symmetric power transfer coefficients from buses injection powers of power sources and loads t