CN113270868A - Dynamic load flow calculation method for power supply system of alternating current electrified railway train - Google Patents
Dynamic load flow calculation method for power supply system of alternating current electrified railway train Download PDFInfo
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- H—ELECTRICITY
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- H—ELECTRICITY
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- H—ELECTRICITY
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Abstract
The invention belongs to the technical field of rail transit power supply, and particularly relates to a dynamic load flow calculation method for an alternating current electrified railway train power supply system. The method comprises the steps of dividing external power supplies, power transmission lines, traction substations, feeders and traction networks in a power supply system into sections based on train positions and train power, so as to construct chain circuits of the power transmission lines, the feeders and the traction networks, and then constructing power source iterative models based on node voltage equations of the chain circuits, so as to obtain voltages of each section node. The method can better integrate dynamic power flow solution of the train power supply system, simultaneously considers the condition of multiple loads at the common connecting point, can realize direct solution of the PV node, and is suitable for power flow calculation of the rail transit power supply alternating current power supply system in various occasions.
Description
Technical Field
The invention belongs to the technical field of rail transit power supply, and particularly relates to a dynamic load flow calculation method for an alternating current electrified railway train power supply system.
Background
The method has the advantages that dynamic load flow calculation is carried out on the power supply system of the alternating current electrified railway train, the train load process is obtained, and the method has important engineering practical significance for optimization and design of the train power supply system, safe line operation, reasonable and efficient resource utilization and the like [1 ]. The load of the train is a single-phase high-power dynamic load, and has the characteristics of random volatility, quick mobility and the like; according to different line conditions, different traction network power supply modes exist, such as a direct supply mode with a return wire and an autotransformer power supply mode, so that the topological structure of the traction network is more special and complex. Therefore, the conventional load flow calculation method cannot be completely used to obtain the load process of the electrified railway.
The current research does not consider the situation of multiple loads at a common connection point, and the external power supply is generally equivalent, and the emphasis is placed on modeling of a traction power supply system. In order to better integrate dynamic power flow solving of a train power supply system, particularly in a weak power grid area, combined modeling and simulation of an external power supply and a traction power supply system need to be considered. In addition, with the development of research and application of new energy resources and the like in a rail transit power supply system, control modes are different, and node types are different when load flow calculation is performed, for example, a PQ node, a PV node and the like, a PV node cannot be directly solved by adopting a current source iterative model, and a general solution model of a power source iterative model needs to be constructed.
Disclosure of Invention
Aiming at the problems, the invention aims to provide a dynamic load flow calculation method for an alternating current electrified railway train power supply system, which can realize direct solution of PV nodes by considering the condition of multiple loads at a common connecting point and is suitable for load flow calculation of the alternating current electrified railway train power supply system in various occasions.
The technical scheme of the invention is as follows:
the dynamic load flow calculation method for the power supply system of the alternating current electrified railway train comprises the following steps:
s1, inputting original data including line parameters, train parameters and driving strategies, and obtaining a train operation diagram, train positions at corresponding moments and train power through traction calculation;
s2, the train power supply system comprises an external power supply, a power transmission line, a traction substation, a feeder line and a traction network which are connected in sequence; the method comprises the following steps that an upper-level transformer substation of a traction substation is used as an equivalent demarcation point of an external power supply, the external power supply is equivalent to an ideal voltage source in series equivalent impedance, and the equivalent external power supply is located in the upper-level transformer substation of the traction substation and is connected with the traction substation through a power transmission line; dividing the section of an equivalent train power supply system, and constructing chain circuits of a transmission line, a feeder line and a traction network, wherein the interval of dividing the section of the traction network is determined according to parallel elements in the traction network and the position of a train, the constructed chain circuit of the transmission line is defined as a first chain circuit, the constructed chain circuit of the feeder line is defined as a second chain circuit, and the constructed chain circuit of the traction network is defined as a third chain circuit, namely, interfaces at two ends of the first chain circuit are respectively connected with an external power supply and a traction substation, interfaces at two ends of the second chain circuit are respectively connected with the traction substation and the traction network, and interfaces at two ends of the third chain circuit are respectively connected with the feeder line and the train; the section numbers corresponding to the first chain circuit are marked as 1-N1The section number corresponding to the second chain circuit is marked as N1+1~N2And the section number corresponding to the third chain circuit is marked as N2+1~N3(ii) a The equivalent external power supply is positioned at the section 1; the primary winding and the secondary winding of the traction transformer are respectively positioned on the tangent plane N1And section N1+ 1; section N of the third chain circuit2+p2And N2+p2+1 is the section, p, corresponding to the two power supply arm ports2And p2+1 is the tangent plane N between the port of the two power supply arms and the third chain circuit2The section distance of (a); section N in chain circuit 22From section N of the chain circuit 32+p2And N2+p2+1 formed together, i.e. section N2Is a public section; according to the connection relation among the sections, a train supply formed by a first chain circuit, a second chain circuit and a third chain circuit is constructedThe node voltage equation of the electrical system is:
I1=Y1U1 (1)
wherein, I1Injecting a current matrix into nodes of all nodes in a train power supply system, wherein the current of the injected nodes of the section of the train in the third chained circuit is obtained according to the train power and the port voltage of the train, and U is1Node voltage matrix, Y, for all nodes in a train power supply system1A node admittance matrix formed by admittance between nodes in the train power supply system;
s3, a feeder connected with a contact line in a direct supply mode or an autotransformer power supply mode is called a positive power supply line, and a feeder connected with a steel rail in the direct supply mode or a feeder connected with a negative feeder in the autotransformer power supply mode is called a negative power supply line; reordering the nodes in formula (1) to obtain another expression of formula (1):
wherein,I21from section 1 to N in the first chain circuit1The node current of (1); i is22From the middle section N of the second chain circuit1+1~N2-a positive supply line node current of 1 and a contact line node current in the third chain circuit; i is23From the middle section N of the second chain circuit1+1~N2-1 negative supply line node current and rail node current in the third chain circuit; u shape21From section 1 to N in the first chain circuit1The node voltage of (1); u shape22From the middle section N of the second chain circuit1+1~N2-a positive supply line node voltage of 1 and a contact line node voltage in the third chain circuit; u shape23From the middle section N of the second chain circuit1+1~N2-1 negative supply line node voltage and rail node in third chain circuitVoltage formation; u shape3A matrix formed by node voltages of the remaining nodes; y is11Is U2Admittance matrixes between the middle corresponding nodes and the nodes; y is12Is U2Middle corresponding node and U3Admittance matrices between the middle corresponding nodes; y is21Is U3Middle corresponding node and U2Admittance matrices between the middle corresponding nodes; y is22Is U3Admittance matrixes between the middle corresponding nodes and the nodes;
s4, combining the equations of part 1 and part 2 of the block matrix of equation (2):
Wherein,Z11is U21The impedance matrix between the middle corresponding node and the node; z12Is U21Middle corresponding node and U22An impedance matrix between the corresponding nodes; z13Is U21Middle corresponding node and U23An impedance matrix between the corresponding nodes; z22Is U22The impedance matrix between the middle corresponding node and the node; z21Is U22Middle corresponding node and U21An impedance matrix between the corresponding nodes; z23Is U22Middle corresponding node and U23An impedance matrix between the corresponding nodes; z33Is U23The impedance matrix between the middle corresponding node and the node; z31Is U23Middle corresponding node and U21An impedance matrix between the corresponding nodes; z32Is U23Middle corresponding node and U22An impedance matrix between the corresponding nodes;
let IL=I22=-I23,UL=U22-U23Is shown byLAnd ULIn the formula (4), the node voltage equation solved by adopting the power source iterative model basic model is obtained as
Wherein, ILA node current matrix formed by node currents corresponding to a positive power supply line node and a contact line node; u shapeLA node voltage matrix formed by the voltage between the positive power supply line node and the negative power supply line node and the voltage between the contact line and the steel rail; z'11=Z11Is U21The impedance matrix between the middle corresponding node and the node; z'12=Z12+Z13Is U21Middle corresponding node and ULAn impedance matrix between the corresponding nodes; z'21=Z12-Z13Is ULMiddle corresponding node and U21An impedance matrix between the corresponding nodes; z'22=Z23+Z32-Z22-Z33Is ULThe impedance matrix between the middle corresponding node and the node;
s5, where the total number of nodes in the setting formula (5) is f, and the injection power of any node c is assumed to be Pc+jQc,c=1,2,···,f,PcIs active power, QcIf j is a complex unit, the injection power equation of the node c is obtained from equation (5):
wherein d is the number of the corresponding node, d is 1,2, f,andnode voltage phasor forms of nodes c and d, YcdCalculating the conjugation for the admittance between the nodes c and d;
the active power P at the node c under the polar coordinate is obtained by the formula (5)cAnd reactive power QcIs given by the equation
Wherein, deltacAnd deltadThe voltage phase angles of nodes c and d, respectively; deltacd=δc-δd;UcAnd UdVoltage modulus values of nodes c and d, respectively; gcdAnd bcdIs YcdThe real and imaginary parts of (c); Σ denotes summation;
the iteration equation of the basic model of the power source iteration model after k times of calculation is obtained by the formula (6)
Wherein (C)(k)Representing the k-th calculation result of the variable, wherein when k is 0, the value of the variable is an initial value;
s6, orderSetting convergence accuracy to epsilon, setting k-th and k + 1-th iteration voltages toAndto be provided withAs a convergence criterion, based onAnd (4) forming a correction equation of all the nodes by the formula (8), solving by using a Newton Raphson method, updating the voltage value of each node, and solving the voltage of each tangent plane node.
A method for carrying out load flow calculation by improving a power source iterative model is provided as follows:
dividing the tangent planes in the first chain circuit, the second chain circuit and the third chain circuit into a common connection point tangent plane, a load node tangent plane and a connection node tangent plane, wherein the tangent plane 1 is the common connection point tangent plane; the load node section refers to a section in which node current injection exists; the connection node section is a section without current injection; when reordering the nodes of formula (1) in step S3 of claim 1, I2And U2In the node, only the load node section is reserved, and the load node section is classified into U in the node3In (1), the rest of the solving processes are unchanged.
A method for carrying out load flow calculation by improving a power source iterative model is provided as follows:
dividing nodes in the first chained circuit, the second chained circuit and the third chained circuit into a balance node, a load node and a connection node, wherein the node at the section 1 in the train power supply system is regarded as the balance node, the voltage amplitude and the phase of the node are known, and the node with current injection in the train power supply system is called the load node; the remaining nodes in the train power supply system are contact nodes, and when reordering the nodes in formula (1) in step S3 of claim 1, I2And U2Only the load node is reserved, and the load node is classified into U in the node3In (1), the rest of the solving processes are unchanged.
The invention has the beneficial effects that: 1) the condition of multiple loads at the common connecting point is considered, dynamic load flow solving can be better integrally carried out on the train power supply system, and the calculation result is more complex to the actual condition; 2) the PV node can be directly solved, and the application range is wider; 3) the invention has simple result, reliable technology, excellent performance and convenient implementation.
Drawings
Fig. 1 is a schematic structural diagram of a train power supply system according to an embodiment of the present invention.
Fig. 2 is a schematic diagram of a chain circuit of the train power supply system in the embodiment of the invention.
Fig. 3 is a schematic structural diagram of the chain circuit 3 in the embodiment of the present invention.
Detailed Description
The technical scheme of the invention is described in detail below with reference to the accompanying drawings and embodiments:
example 1
As shown in fig. 1, which is a schematic structural diagram of the train power supply system of this example, a public power grid substation transmits electric energy to a traction substation through a three-phase power transmission line, the traction substation is provided with a traction transformer, the electric energy with a high voltage level of 110 kV, 220 kV or 330kV is converted into electric energy with a voltage level of 27.5kV, 55 kV or 2 × 27.5kV, and the electric energy is transmitted to the traction grid through a feeder line to supply power to trains. In fig. 1, the traction transformer is a three-phase two-phase connection transformer, and includes an YNd11 connection wire, a Vv connection wire, a Scott connection wire, etc., and the secondary side of the traction transformer forms two ports, which are respectively connected to an α power supply arm port and a β power supply arm port, or a single-phase connection transformer, which has only one port; in fig. 1, the traction network may adopt a direct supply mode, a direct supply mode with a return line, an AT power supply mode, and the like.
The transmission line, the feeder line and the traction network are parallel multi-conductor transmission lines, and are respectively divided into sections to form chain circuits 1,2 and 3, as shown in figure 2, the numbers corresponding to the sections are respectively 1-N1、N1+1~N2And N2+1~N3. The chain circuit 1 is connected with a public power grid transformer substation and a traction transformer through interfaces 1 and 2 respectively; the chain circuit 2 is connected with a traction transformer and a traction network through interfaces 2 and 3 respectively; the chain circuit 3 is connected to the feeder and the train via interfaces 4 and 5, respectively.
The chain circuit 3 is more complex and consists of parallel elements and series elements, as shown in fig. 3. Z in FIG. 3iAn impedance matrix for the transverse element between sections i and i + 1; i isiA node current matrix at a tangent plane i; y isiA node admittance matrix at a tangent plane i; the series elements comprise a traction network circuit, a series compensation device and the like; parallel elements having transverse connecting wires, AT-supplied autotransformer and in traction substationA joint compensation device and the like; the port of the alpha power supply arm and the port of the beta power supply arm are respectively connected to two ports of the secondary side of the traction transformer; section N of the third chain circuit2+p2And N2+p2+1 is the section, p, corresponding to the two power supply arm ports2And p2+1 is the tangent plane N between the port of the two power supply arms and the third chain circuit2The interface 4 is a common connection section of the chain circuits 2 and 3, so that the section N in the chain circuit 22Can be regarded as a tangent plane N in the chain circuit 32+p2And N2+p2+1 together.
The embodiment specifically comprises the following steps:
s1, inputting original data including line parameters, train parameters and driving strategies, and obtaining a train operation diagram, train positions at corresponding moments and train power through traction calculation;
s2, the train power supply system comprises an external power supply, a power transmission line, a traction substation, a feeder line and a traction network which are connected in sequence; the method comprises the following steps that an upper-level transformer substation of a traction substation is used as an equivalent demarcation point of an external power supply, the external power supply is equivalent to an ideal voltage source in series equivalent impedance, and the equivalent external power supply is located in the upper-level transformer substation of the traction substation and is connected with the traction substation through a power transmission line; dividing the section of an equivalent train power supply system, and constructing chain circuits of a transmission line, a feeder line and a traction network, wherein the interval of dividing the section of the traction network is determined according to parallel elements in the traction network and the position of a train, the constructed chain circuit of the transmission line is defined as a first chain circuit, the constructed chain circuit of the feeder line is defined as a second chain circuit, and the constructed chain circuit of the traction network is defined as a third chain circuit, namely, interfaces at two ends of the first chain circuit are respectively connected with an external power supply and a traction substation, interfaces at two ends of the second chain circuit are respectively connected with the traction substation and the traction network, and interfaces at two ends of the third chain circuit are respectively connected with the feeder line and the train; the section numbers corresponding to the first chain circuit are marked as 1-N1The section number corresponding to the second chain circuit is marked as N1+1~N2And the section number corresponding to the third chain circuit is marked as N2+1~N3(ii) a The equivalent external power supply is positioned at the section 1; the primary winding and the secondary winding of the traction transformer are respectively positioned on the tangent plane N1And section N1+ 1; section N of the third chain circuit2+p2And N2+p2+1 is the section, p, corresponding to the two power supply arm ports2And p2+1 is the tangent plane N between the port of the two power supply arms and the third chain circuit2The section distance of (a); section N in chain circuit 22From section N of the chain circuit 32+p2And N2+p2+1 formed together, i.e. section N2Is a public section; according to the connection relation among the sections, a node voltage equation of a train power supply system formed by the first chain circuit, the second chain circuit and the third chain circuit is constructed as follows:
I1=Y1U1 (1)
wherein, I1Injecting a current matrix into nodes of all nodes in a train power supply system, wherein the current of the injected nodes of the section of the train in the third chained circuit is obtained according to the train power and the port voltage of the train, and U is1Node voltage matrix, Y, for all nodes in a train power supply system1A node admittance matrix formed by admittance between nodes in the train power supply system;
s3, a feeder connected with a contact line in a direct supply mode or an autotransformer power supply mode is called a positive power supply line, and a feeder connected with a steel rail in the direct supply mode or a feeder connected with a negative feeder in the autotransformer power supply mode is called a negative power supply line; reordering the nodes in formula (1) to obtain another expression of formula (1):
wherein,I21from section 1 to N in the first chain circuit1The node current of (1); i is22From the middle section N of the second chain circuit1+1~N2-a positive supply line node current of 1 and a contact line node current in the third chain circuit; i is23From the middle section N of the second chain circuit1+1~N2-1 negative supply line node current and rail node current in the third chain circuit; u shape21From section 1 to N in the first chain circuit1The node voltage of (1); u shape22From the middle section N of the second chain circuit1+1~N2-a positive supply line node voltage of 1 and a contact line node voltage in the third chain circuit; u shape23From the middle section N of the second chain circuit1+1~N2-1 negative supply line node voltage and rail node voltage in the third chain circuit; u shape3A matrix formed by node voltages of the remaining nodes; y is11Is U2Admittance matrixes between the middle corresponding nodes and the nodes; y is12Is U2Middle corresponding node and U3Admittance matrices between the middle corresponding nodes; y is21Is U3Middle corresponding node and U2Admittance matrices between the middle corresponding nodes; y is22Is U3Admittance matrixes between the middle corresponding nodes and the nodes;
s4, combining the equations of part 1 and part 2 of the block matrix of equation (2):
Wherein,Z11is U21The impedance matrix between the middle corresponding node and the node; z12Is U21Middle corresponding node and U22An impedance matrix between the corresponding nodes; z13Is U21Middle corresponding node and U23An impedance matrix between the corresponding nodes; z22Is U22The impedance matrix between the middle corresponding node and the node; z21Is U22Middle corresponding node and U21An impedance matrix between the corresponding nodes; z23Is U22Middle corresponding node and U23An impedance matrix between the corresponding nodes; z33Is U23The impedance matrix between the middle corresponding node and the node; z31Is U23Middle corresponding node and U21An impedance matrix between the corresponding nodes; z32Is U23Middle corresponding node and U22An impedance matrix between the corresponding nodes;
let IL=I22=-I23,UL=U22-U23Is shown byLAnd ULIn the formula (4), the node voltage equation solved by adopting the power source iterative model basic model is obtained as
Wherein, ILA node current matrix formed by node currents corresponding to a positive power supply line node and a contact line node; u shapeLA node voltage matrix formed by the voltage between the positive power supply line node and the negative power supply line node and the voltage between the contact line and the steel rail; z'11=Z11Is U21The impedance matrix between the middle corresponding node and the node; z'12=Z12+Z13Is U21Middle corresponding node and ULAn impedance matrix between the corresponding nodes; z'21=Z12-Z13Is ULMiddle corresponding node and U21An impedance matrix between the corresponding nodes; z'22=Z23+Z32-Z22-Z33Is ULMiddle corresponding jointAn impedance matrix between the points and the nodes;
s5, where the total number of nodes in the setting formula (5) is f, and the injection power of any node c is assumed to be Pc+jQc,c=1,2,···,f,PcIs active power, QcIf j is a complex unit, the injection power equation of the node c is obtained from equation (5):
wherein d is the number of the corresponding node, d is 1,2, f,andnode voltage phasor forms of nodes c and d, YcdCalculating the conjugation for the admittance between the nodes c and d;
the active power P at the node c under the polar coordinate is obtained by the formula (5)cAnd reactive power QcIs given by the equation
Wherein, deltacAnd deltadThe voltage phase angles of nodes c and d, respectively; deltacd=δc-δd;UcAnd UdVoltage modulus values of nodes c and d, respectively; gcdAnd bcdIs YcdThe real and imaginary parts of (c); Σ denotes summation;
the iteration equation of the basic model of the power source iteration model after k times of calculation is obtained by the formula (6)
Wherein (C)(k)K number of times of representing variableCalculating a result, wherein when k is 0, the value of the variable is an initial value;
s6, orderSetting convergence accuracy to epsilon, setting k-th and k + 1-th iteration voltages toAndto be provided withAnd (3) forming a correction equation of all nodes according to the formula (8) as a convergence criterion, solving by using a Newton Raphson method, updating the voltage value of each node, and obtaining the voltage of each tangent plane node.
Claims (3)
1. The dynamic power flow calculation method for the power supply system of the alternating current electrified railway train is characterized by comprising the following steps of:
s1, inputting original data including line parameters, train parameters and driving strategies, and obtaining a train operation diagram, train positions at corresponding moments and train power through traction calculation;
s2, the train power supply system comprises an external power supply, a power transmission line, a traction substation, a feeder line and a traction network which are connected in sequence; the method comprises the following steps that an upper-level transformer substation of a traction substation is used as an equivalent demarcation point of an external power supply, the external power supply is equivalent to an ideal voltage source in series equivalent impedance, and the equivalent external power supply is located in the upper-level transformer substation of the traction substation and is connected with the traction substation through a power transmission line; dividing the equivalent train power supply system into sections, and constructing chain circuits of a transmission line, a feeder line and a traction network, wherein the interval of dividing the section of the traction network is determined according to parallel elements in the traction network and the position of a train, the constructed chain circuit of the transmission line is defined as a first chain circuit, the constructed chain circuit of the feeder line is defined as a second chain circuit, and the constructed chain circuit of the traction network is defined as a second chain circuitThe circuit is defined as a third chain circuit, namely, interfaces at two ends of the first chain circuit are respectively connected with an external power supply and a traction substation, interfaces at two ends of the second chain circuit are respectively connected with the traction substation and a traction network, and interfaces at two ends of the third chain circuit are respectively connected with a feeder line and a train; the section numbers corresponding to the first chain circuit are marked as 1-N1The section number corresponding to the second chain circuit is marked as N1+1~N2And the section number corresponding to the third chain circuit is marked as N2+1~N3(ii) a The equivalent external power supply is positioned at the section 1; the primary winding and the secondary winding of the traction transformer are respectively positioned on the tangent plane N1And section N1+ 1; section N of the third chain circuit2+p2And N2+p2+1 is the section, p, corresponding to the two power supply arm ports2And p2+1 is the tangent plane N between the port of the two power supply arms and the third chain circuit2The section distance of (a); section N in chain circuit 22From section N of the chain circuit 32+p2And N2+p2+1 formed together, i.e. section N2Is a public section; according to the connection relation among the sections, a node voltage equation of a train power supply system formed by the first chain circuit, the second chain circuit and the third chain circuit is constructed as follows:
I1=Y1U1 (1)
wherein, I1Injecting a current matrix into nodes of all nodes in a train power supply system, wherein the current of the injected nodes of the section of the train in the third chained circuit is obtained according to the train power and the port voltage of the train, and U is1Node voltage matrix, Y, for all nodes in a train power supply system1A node admittance matrix formed by admittance between nodes in the train power supply system;
s3, a feeder connected with a contact line in a direct supply mode or an autotransformer power supply mode is called a positive power supply line, and a feeder connected with a steel rail in the direct supply mode or a feeder connected with a negative feeder in the autotransformer power supply mode is called a negative power supply line; reordering the nodes in formula (1) to obtain another expression of formula (1):
wherein,I21from section 1 to N in the first chain circuit1The node current of (1); i is22From the middle section N of the second chain circuit1+1~N2-a positive supply line node current of 1 and a contact line node current in the third chain circuit; i is23From the middle section N of the second chain circuit1+1~N2-1 negative supply line node current and rail node current in the third chain circuit; u shape21From section 1 to N in the first chain circuit1The node voltage of (1); u shape22From the middle section N of the second chain circuit1+1~N2-a positive supply line node voltage of 1 and a contact line node voltage in the third chain circuit; u shape23From the middle section N of the second chain circuit1+1~N2-1 negative supply line node voltage and rail node voltage in the third chain circuit; u shape3A matrix formed by node voltages of the remaining nodes; y is11Is U2Admittance matrixes between the middle corresponding nodes and the nodes; y is12Is U2Middle corresponding node and U3Admittance matrices between the middle corresponding nodes; y is21Is U3Middle corresponding node and U2Admittance matrices between the middle corresponding nodes; y is22Is U3Admittance matrixes between the middle corresponding nodes and the nodes;
s4, combining the equations of part 1 and part 2 of the block matrix of equation (2):
Wherein,Z11is U21The impedance matrix between the middle corresponding node and the node; z12Is U21Middle corresponding node and U22An impedance matrix between the corresponding nodes; z13Is U21Middle corresponding node and U23An impedance matrix between the corresponding nodes; z22Is U22The impedance matrix between the middle corresponding node and the node; z21Is U22Middle corresponding node and U21An impedance matrix between the corresponding nodes; z23Is U22Middle corresponding node and U23An impedance matrix between the corresponding nodes; z33Is U23The impedance matrix between the middle corresponding node and the node; z31Is U23Middle corresponding node and U21An impedance matrix between the corresponding nodes; z32Is U23Middle corresponding node and U22An impedance matrix between the corresponding nodes;
let IL=I22=-I23,UL=U22-U23Is shown byLAnd ULIn the formula (4), the node voltage equation solved by adopting the power source iterative model basic model is obtained as
Wherein, ILA node current matrix formed by node currents corresponding to a positive power supply line node and a contact line node; u shapeLFor the voltage between positive and negative supply line nodes and contact lineAnd the voltage between the steel rails to form a node voltage matrix; z'11=Z11Is U21The impedance matrix between the middle corresponding node and the node; z'12=Z12+Z13Is U21Middle corresponding node and ULAn impedance matrix between the corresponding nodes; z'21=Z12-Z13Is ULMiddle corresponding node and U21An impedance matrix between the corresponding nodes; z'22=Z23+Z32-Z22-Z33Is ULThe impedance matrix between the middle corresponding node and the node;
s5, where the total number of nodes in the setting formula (5) is f, and the injection power of any node c is assumed to be Pc+jQc,c=1,2,···,f,PcIs active power, QcIf j is a complex unit, the injection power equation of the node c is obtained from equation (5):
wherein d is the number of the corresponding node, d is 1,2, f,andnode voltage phasor forms of nodes c and d, YcdCalculating the conjugation for the admittance between the nodes c and d;
the active power P at the node c under the polar coordinate is obtained by the formula (5)cAnd reactive power QcIs given by the equation
Wherein, deltacAnd deltadThe voltage phase angles of nodes c and d, respectively; deltacd=δc-δd;UcAnd UdVoltage modulus values of nodes c and d, respectively; gcdAnd bcdIs YcdThe real and imaginary parts of (c); Σ denotes summation;
the iteration equation of the basic model of the power source iteration model after k times of calculation is obtained by the formula (6)
Wherein (C)(k)Representing the k-th calculation result of the variable, wherein when k is 0, the value of the variable is an initial value;
s6, orderSetting convergence accuracy to epsilon, setting k-th and k + 1-th iteration voltages toAndto be provided withAnd (3) forming a correction equation of all nodes according to the formula (8) as a convergence criterion, solving by using a Newton Raphson method, updating the voltage value of each node, and obtaining the voltage of each tangent plane node.
2. The method for calculating the dynamic power flow of the alternating current electrified railway train power supply system according to claim 1, wherein the sections in the first chain circuit, the second chain circuit and the third chain circuit are divided into a common connection point section, a load node section and a connection node section, wherein the section 1 is the common connection point section; the load node section refers to a section in which node current injection exists; the connection node section is a section without current injection; in right toWhen reordering of the nodes in formula (1) in step S3 of 1 is required, I2And U2In the node, only the load node section is reserved, and the load node section is classified into U in the node3In (1), the rest of the solving processes are unchanged.
3. The method for calculating the dynamic power flow of the alternating current electrified railway train power supply system according to claim 1, wherein nodes in the first chain circuit, the second chain circuit and the third chain circuit are divided into a balance node, a load node and a contact node, wherein a node at a tangent plane 1 in the train power supply system is regarded as the balance node, the voltage amplitude and the phase of the node are known, and a node with current injection in the train power supply system is called the load node; the remaining nodes in the train power supply system are contact nodes, and when reordering the nodes in formula (1) in step S3 of claim 1, I2And U2Only the load node is reserved, and the load node is classified into U in the node3In (1), the rest of the solving processes are unchanged.
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