CN112165114A - Alternating current-direct current hybrid system transient stability analysis method considering commutation failure - Google Patents

Alternating current-direct current hybrid system transient stability analysis method considering commutation failure Download PDF

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CN112165114A
CN112165114A CN202011083828.XA CN202011083828A CN112165114A CN 112165114 A CN112165114 A CN 112165114A CN 202011083828 A CN202011083828 A CN 202011083828A CN 112165114 A CN112165114 A CN 112165114A
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direct current
transient
fault
alternating current
hybrid system
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王彤
王增平
胡加伟
刘刚
段方维
范维
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North China Electric Power University
Electric Power Research Institute of State Grid Liaoning Electric Power Co Ltd
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Electric Power Research Institute of State Grid Liaoning Electric Power Co Ltd
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/36—Arrangements for transfer of electric power between ac networks via a high-tension dc link
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
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Abstract

The invention discloses an alternating current-direct current hybrid system transient stability analysis method considering commutation failure, aiming at an alternating current-direct current hybrid system of a high-voltage direct current transmission line containing a power grid commutation type, establishing a network structure maintenance model of the alternating current-direct current hybrid system by equivalently using a direct current converter station as a dynamic load on a corresponding converter bus, and constructing an energy function of the alternating current-direct current hybrid system through first integration; secondly, a trapezoidal integral path is adopted to approximately calculate a transient energy function of the system after the fault, a transient stability criterion based on the energy function is provided, and meanwhile, the dichotomy is utilized to quickly calculate the limit removal time of the system; and finally, an improved IEEE-39 node alternating current-direct current hybrid system is built, and the correctness of the theoretical analysis method is verified through simulation. When the alternating current-direct current hybrid system fails in an alternating current system and causes phase commutation failure on the inversion side of a direct current line, transient stability margin analysis can be rapidly carried out.

Description

Alternating current-direct current hybrid system transient stability analysis method considering commutation failure
Technical Field
The invention relates to an alternating current and direct current hybrid system transient stability analysis technology, in particular to an alternating current and direct current hybrid system transient stability analysis method considering commutation failure.
Background
At present, large primary energy bases and load centers are generally distributed in a reverse direction. In order to optimize resource allocation and improve energy utilization efficiency, a Line Commutated Converter High Voltage Direct Current (LCC-HVDC) Converter type High Voltage Direct Current (LCC-HVDC) power transmission is rapidly developed by virtue of advantages in the aspects of long-distance and large-capacity power transmission and the like. The alternating current-direct current hybrid system has the characteristics of high direct current occupation ratio and large capacity on a power grid structure. When an alternating current system in the near area of a converter station at the inversion side of a direct current line fails, the phase change failure at the inversion side of the direct current line is caused at the same time, the short-time large-range transfer of the power flow is caused, and the safe and stable operation of the system is seriously threatened. Alternating current side faults in the alternating current-direct current hybrid system and direct current line commutation failure are accompanied, transient stability of the system is greatly influenced, and on-line transient stability analysis of the alternating current-direct current hybrid system containing LCC-HVDC is necessary to be studied deeply.
In the field of transient stability analysis of alternating current and direct current hybrid systems, a great deal of research has been carried out by scholars at home and abroad. Compared with a time domain simulation method, the energy function method judges the transient stability of the system from the energy perspective, can give the stability margin of the system and determine the instability trend of the system, and is widely applied to the transient stability analysis of the power system. Ni and Fouaad define corresponding transient energy functions by neglecting dynamic processes of direct current lines and control and adopting a quasi-steady state direct current model for the first time, and realize direct transient stability analysis by using an RUEP method.
In the prior art, n.fernandopulle and r.t.h.alden, "integration of cascaded HVDC dynamics in transient energy functions," IEEE trans.power system ", vol.20, No.2, pp.1043-1052, and may.2005, a differential equation is introduced to characterize the dynamic characteristics of HVDC when a transient energy function is constructed, so that the prediction accuracy of the transient stability of the alternating current/direct current hybrid system is improved, and the calculation time is also saved.
In the second prior art, based on a network structure maintenance Model, a transient Energy Function considering Detailed dynamic characteristics of a direct current line is constructed, and a numerical algorithm for constructing the Energy Function is provided, wherein the "Energy Function for Power System with Detailed DC Model" Construction and Analysis, "IEEE trans.
The existing technology has the disadvantages that when an alternating current system of the alternating current-direct current hybrid system fails and causes a phase commutation failure on an inversion side of a direct current line, the transient stability of the system is seriously impacted, and a fast transient stability margin analysis method under the current scene has few literature reports.
Disclosure of Invention
The invention aims to provide an alternating current-direct current hybrid system transient stability analysis method considering commutation failure.
The purpose of the invention is realized by the following technical scheme:
the invention discloses an alternating current-direct current hybrid system transient stability analysis method considering commutation failure, which aims at an alternating current-direct current hybrid system of a high-voltage direct current transmission line containing a power grid commutation type, constructs a transient energy function containing a direct current line, and carries out transient stability analysis on the alternating current-direct current hybrid system under the scene of commutation failure on a direct current inversion side caused by an alternating current fault, and comprises the following steps:
firstly, establishing a network structure maintenance model of an alternating current-direct current hybrid system by equivalently using a direct current convertor station as a dynamic load on a corresponding convertor bus, and constructing an energy function of the alternating current-direct current hybrid system through first integration;
secondly, a trapezoidal integral path is adopted to approximately calculate a transient energy function of the system after the fault, a transient stability criterion based on the energy function is provided, and meanwhile, the dichotomy is utilized to quickly calculate the limit cut-off time of the system;
and finally, an improved IEEE-39 node alternating current-direct current hybrid system is built, and the correctness of the theoretical analysis method is verified through simulation.
According to the technical scheme provided by the invention, the transient stability analysis method of the alternating current-direct current hybrid system considering the commutation failure provided by the embodiment of the invention can be used for quickly analyzing the transient stability margin under the condition that the alternating current-direct current hybrid system fails and causes the commutation failure on the inversion side of the direct current line.
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FIG. 1 is a schematic diagram of a model of an AC/DC hybrid system according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of an equivalent model of a converter station in an embodiment of the invention;
FIG. 3 is a schematic diagram of a CEPRI-7 AC/DC system model according to an embodiment of the present invention;
FIG. 4 is a diagram illustrating a critical stability scenario in an embodiment of the present invention; in the figure: (a) gamma curve of turn-off angle, (b) Pd curve of direct current power, (c) theta curve of relative rotor angle, (d) murayA curve;
FIG. 5 is a schematic diagram of an unstable scenario in an embodiment of the present invention; in the figure: (a) gamma curve of turn-off angle, (b) Pd curve of direct current power, (c) theta curve of relative rotor angle, (d) murayA curve;
FIG. 6 is a schematic diagram illustrating a transient stability margin evaluation process according to an embodiment of the invention;
FIG. 7 is a schematic diagram of an improved IEEE-39 AC/DC hybrid system in an embodiment of the present invention;
FIG. 8 is a schematic diagram illustrating a stable equilibrium point unchanged in a stable scene according to an embodiment of the present invention; in the figure: (a) gamma curve of turn-off angle, (b) theta curve of relative rotor angle, (c) V curve of energy function, and (d) murayA curve;
FIG. 9 is a schematic diagram illustrating a stable equilibrium point unchanged under an unstable scenario in an embodiment of the present invention; in the figure: (a) gamma curve of turn-off angle, (b) theta curve of relative rotor angle, (c) V curve of energy function, and (d) murayA curve;
FIG. 10 is a schematic diagram illustrating a stable equilibrium point change in a stable scene according to an embodiment of the present invention; in the figure: (a) gamma curve of turn-off angle, (b) theta curve of relative rotor angle, (c) V curve of energy function, and (d) murayA curve;
FIG. 11 is a schematic diagram illustrating a stable equilibrium point change in an unstable scenario according to an embodiment of the present invention; in the figure: (a) gamma curve of turn-off angle, (b) theta curve of relative rotor angle, (c) V curve of energy function, and (d) murayCurve line.
Detailed Description
The embodiments of the present invention will be described in further detail below. Details which are not described in detail in the embodiments of the invention belong to the prior art which is known to the person skilled in the art.
The invention relates to an alternating current-direct current hybrid system transient stability analysis method considering commutation failure, which has the preferred specific implementation mode that:
to containing electric wire netting commutation type high voltage direct current transmission line's alternating current-direct current series-parallel connection system, construct the transient state energy function that contains the direct current circuit, under alternating current fault causes the direct current contravariant side and takes place commutation failure scene, carry out transient state stability analysis to alternating current-direct current series-parallel connection system, include:
firstly, establishing a network structure maintenance model of an alternating current-direct current hybrid system by equivalently using a direct current convertor station as a dynamic load on a corresponding convertor bus, and constructing an energy function of the alternating current-direct current hybrid system through first integration;
secondly, a trapezoidal integral path is adopted to approximately calculate a transient energy function of the system after the fault, a transient stability criterion based on the energy function is provided, and meanwhile, the dichotomy is utilized to quickly calculate the limit cut-off time of the system;
and finally, an improved IEEE-39 node alternating current-direct current hybrid system is built, and the correctness of the theoretical analysis method is verified through simulation.
The method specifically comprises the following steps:
step 1: constructing a network structure maintenance model of the AC-DC hybrid system:
for an alternating current-direct current hybrid system with n nodes and l direct current lines (LCC-HVDC), wherein i is 1,2, the node is connected with a generator, the synchronous generator adopts E' q constant representation, the voltage characteristic of a load is considered, the resistance of the high voltage line is ignored, two ends of the direct current lines are equivalent to the injection power of the corresponding bus, and an equivalent model based on a system network structure holding model is obtained;
in the inertial Center (COI) reference coordinate, the system equation is:
1) characteristic equation of synchronous generator
Figure BDA0002719646380000031
Figure BDA0002719646380000041
Figure BDA0002719646380000042
Figure BDA0002719646380000043
In the formula: 1,2, ·, m; theta i and omega i are respectively the power angle and the angular speed of the ith synchronous generator relative to an inertia Center (COI); ui and phi i are respectively the amplitude and phase angle of the ith node; pmi, Pei and Di are respectively the mechanical input power, active power output and damping of the ith generator; mi and PCOI are respectively an inertia time constant and an acceleration power of an inertia Center (COI) of the ith synchronous generator;
2) load equation taking into account voltage characteristics
Taking into account the voltage characteristics of the load at node i, the following relationship is obtained:
Figure BDA0002719646380000044
Figure BDA0002719646380000045
in the formula: i is 1,2, n, PLi and QLi are the active and reactive sizes of the load on the ith node, and a, b, c, d, e and f are constant coefficients;
3) dc line power equation
Taking a converter station at the rectification side of a direct current line (LCC-HVDC) as an example, the relationship between the direct current voltage and the direct current of the converter station at the rectification side of the direct current line (LCC-HVDC) in the equivalent model of the converter station in the alternating current-direct current hybrid system is as follows:
Figure BDA0002719646380000046
in the formula: udr is the DC voltage of the rectifier side converter station; id is direct current; xr is the equivalent commutation reactance of the rectification side; ktr is the transformation ratio of the converter transformer at the rectifying side; ulr is the AC bus voltage of the rectifier side converter station; alpha is a commutation side trigger delay angle;
when active loss in the phase commutation process is ignored, the power characteristic equation between the rectifier station and the alternating current system is expressed as:
Figure BDA0002719646380000047
in the formula, Pd and Qd are respectively the active power and the reactive power transmitted to the rectifier station by the alternating current system; pdr is the transmission active power of the rectifier side converter station; cr is equivalent capacitance of a parallel capacitor on an alternating current bus of the rectifier side converter station, and Qcr is reactive output of the parallel capacitor; qdr is the total reactive power consumption of the converter station at the rectifying side; omega is the angular speed of the alternating current system; phi r is the equivalent power factor angle of the rectification side of the direct current system;
4) network equation
Based on the equivalent model of the AC-DC hybrid system and according to the power balance relationship, the active power and the reactive power injected into the network by the node i are respectively as follows:
Figure BDA0002719646380000051
Figure BDA0002719646380000052
in the formula: qei is the reactive output of the ith generator; bij is the imaginary part of the system network node admittance array Y;
further obtaining according to the power balance relation:
Pi+PLi+ξPdi＝0 (11)
Qi+QLi+ξQdi＝0 (12)
in the formula: pdi and Qdi are respectively the equivalent active and reactive power of the converter station on the corresponding node, and if the node i has direct current line access, zeta is 1; if the node i has no direct line access, zeta is 0;
step 2: theoretical derivation and analysis of the system transient energy function:
the alternating current-direct current hybrid system containing the direct current circuit (LCC-HVDC) can describe the whole dynamic process of the system including a phase-change failure scene of the inversion side of the direct current circuit and can reduce the construction difficulty of an energy function by equivalently constructing the converter stations at two ends of the direct current circuit as the dynamic load of corresponding buses, and the transient energy function of the ith converter station is expressed as follows through the first integral construction:
Figure BDA0002719646380000053
in the formula: xs is a stable balance point after the fault; x is a current operating point, and in energy function analysis, all transient energy of the direct current system is used as potential energy to be processed;
for the AC-DC hybrid system, the transient energy of the system after the fault is divided into transient kinetic energy and transient potential energy, wherein the transient potential energy consists of AC system potential energy and DC system potential energy, and the value is (theta)s,ωs,Us,Φs,ts) For stable equilibrium point of system equation after faultThe energy function is constructed by first integrating the system equation:
Figure BDA0002719646380000054
Figure BDA0002719646380000055
Figure BDA0002719646380000061
Figure BDA0002719646380000062
the physical interpretation in the formula is: vpkIs the transient kinetic energy of the system; vpeIs the transient potential energy of the system, and, VacIs the transient potential energy of an AC system, VdIs the transient potential energy of the dc system;
the transient energy function V is derived with respect to time t, and the result is shown in equations (18), (19), (20):
Figure BDA0002719646380000063
Figure BDA0002719646380000064
Figure BDA0002719646380000065
from the formulae (18), (19), (20):
Figure BDA0002719646380000066
according to the formula (21), based on a network structure maintenance model, along the trajectory after the fault, the derivative of the constructed transient energy function V with respect to the time t is less than or equal to zero, which indicates that the transient energy of the system after the fault of the AC-DC hybrid system is gradually attenuated, and whether a lower bound exists depends on the stable state of the system after the fault;
based on equations (11), (12) and the implicit integral theorem, U, Φ of the system network node is expressed as a function of θ, that is, there are:
Figure BDA0002719646380000067
the transient potential energy Vpe of the AC-DC hybrid system is rewritten to
Figure BDA0002719646380000068
Similarly, equation (14) is rewritten as:
Figure BDA0002719646380000069
wherein: the transient kinetic energy Vpk and the transient potential energy Vpe after the fault are mutually converted to define dVpcThe frequency of 0/dt is m, which represents the frequency of complete mutual conversion between the transient kinetic energy Vpk and the transient potential energy Vpe of the system after the fault;
performing transient stability analysis on the AC-DC hybrid system by using a Potential Energy Boundary Surface (PEBS) method based on an energy function, and judging whether a current system operating point is separated from the Potential Energy Boundary Surface (PEBS) by using a formula (25) which is popularized from a classical power system model to a network structure maintenance model;
Figure BDA0002719646380000071
if the μ ray is less than 0 after the fault, representing that the current system operation trajectory is in the PEBS; if the mu ray is greater than 0, the current system operation trajectory is outside the PEBS;
and step 3: transient stability analysis based on energy function:
1) transient stability criterion proposition
An alternating current fault occurs near the direct current inversion station, so that the inversion side has phase commutation failure; when the AC fault disappears, the DC returns to the normal operation state, the relative rotor angle of the generator gradually converges along with the damping of the system, which shows that the system is in the stable state after the fault and the system mu after the faultrayWhen the voltage is constant negative, an alternating current fault occurs near the inverter station, so that the phase change failure occurs on the direct current inverter side;
when the AC fault disappears, the generator diverges relative to the rotor angle, namely the system is in an unstable state after the fault, the DC is always in the dynamic regulation process, and the mu of the system after the fault is detectedrayChanges from negative to positive at t-0.49 s;
on the basis, a transient stability criterion based on an energy function is provided:
criterion I: if after failure murayChanging from negative to positive indicates that the system is in an unstable state;
criterion II: if after failure murayThe constant is negative until m is 3, which indicates that the system is in a stable state;
2) transient stability margin evaluation
And (3) approximately calculating an energy function curve by adopting a trapezoidal integral path, and quickly obtaining the Critical Clearing Time (CCT) of the AC-DC hybrid system by utilizing a dichotomy (BM), wherein the Critical Clearing Time (CCT) is used as a transient stability margin index.
The invention relates to an alternating Current-Direct Current hybrid system transient stability analysis method considering commutation failure, which aims at an alternating Current-Direct Current hybrid system containing a power grid commutation type High-Voltage Direct Current (LCC-HVDC), constructs a transient energy function containing a Direct Current Line, and carries out transient stability analysis on the alternating Current-Direct Current hybrid system under the scene of commutation failure on a Direct Current inversion side caused by alternating Current fault. Firstly, establishing a network structure maintenance model of an alternating current-direct current hybrid system by equivalently converting a direct current converter station into a dynamic load on a corresponding converter bus, and constructing an energy function of the alternating current-direct current hybrid system through first integration; secondly, a trapezoidal integral path is adopted to approximately calculate a transient energy function of the system after the fault, a transient stability criterion based on the energy function is provided, and meanwhile, a binary clear Time (CCT) of the system is quickly calculated by using a Binary Method (BM); and finally, an improved IEEE-39 node alternating current-direct current hybrid system is set up, and the correctness of the theoretical analysis method is verified through simulation.
The specific embodiment is as follows:
step 1: construction of network structure maintenance model of alternating current-direct current hybrid system
For n nodes, an alternating-direct current hybrid system with l direct current lines (LCC-HVDC) is combined, wherein i is 1,2, and m nodes are connected with generators. The synchronous generator is represented by constant E' q, the voltage characteristic of the load is considered, the resistance of the high-voltage line is ignored, two ends of the direct-current line are equivalent to the injection power of the corresponding bus, and an equivalent model based on a system network structure holding model is obtained, as shown in fig. 1.
In the Center of Inertia (COI) reference coordinate, the system equation is:
1) characteristic equation of synchronous generator
Figure BDA0002719646380000081
Figure BDA0002719646380000082
Figure BDA0002719646380000083
Figure BDA0002719646380000084
In the formula: 1,2, ·, m; theta i and omega i are respectively the power angle and the angular speed of the ith synchronous generator relative to an inertia Center (COI); ui and phi i are respectively the amplitude and phase angle of the ith node; pmi, Pei and Di are respectively the mechanical input power, active power output and damping of the ith generator; mi and PCOI are the inertia time constant and the acceleration power of the inertia Center (COI) of the ith synchronous generator respectively.
2) Load equation taking into account voltage characteristics
Taking into account the voltage characteristics of the load at node i, the following relationship can be obtained:
Figure BDA0002719646380000085
Figure BDA0002719646380000086
in the formula: 1,2, n. PLi and QLi are the real and reactive magnitudes of the load on the ith node, respectively. a. b, c, d, e and f are constant coefficients respectively.
3) Dc line power equation
Taking the converter station at the rectification side of the LCC-HVDC converter as an example, the equivalent model of the converter station in the alternating current-direct current hybrid system is shown in fig. 2.
From fig. 2, the relationship between the dc voltage and the current of the LCC-HVDC rectifier side converter station is as follows:
Figure BDA0002719646380000087
in the formula: udr is the DC voltage of the rectifier side converter station; id is direct current; xr is the equivalent commutation reactance of the rectification side; ktr is the transformation ratio of the converter transformer at the rectifying side; ulr is the AC bus voltage of the rectifier side converter station; α is the commutation side triggered delay angle.
When active loss in the phase commutation process is ignored, the power characteristic equation between the rectifier station and the alternating current system can be expressed as:
Figure BDA0002719646380000091
in the formula, Pd and Qd are respectively the active power and the reactive power transmitted to the rectifier station by the alternating current system; pdr is the transmission active power of the rectifier side converter station; cr is equivalent capacitance of a parallel capacitor on an alternating current bus of the rectifier side converter station, and Qcr is reactive output of the parallel capacitor; qdr is the total reactive power consumption of the converter station at the rectifying side; omega is the angular speed of the alternating current system; phi r is the equivalent power factor angle of the rectifying side of the direct current system.
4) Network equation
Based on the equivalent model of the AC-DC hybrid system and according to the power balance relationship, the active power and the reactive power injected into the network by the node i are respectively as follows:
Figure BDA0002719646380000092
Figure BDA0002719646380000093
in the formula: qei is the reactive output of the ith generator; bij is the imaginary part of the admittance array Y of the network node of the system.
Further derived from the power balance relationship:
Pi+PLi+ξPdi＝0 (11)
Qi+QLi+ξQdi＝0 (12)
in the formula: and Pdi and Qdi are respectively the equivalent active and reactive sizes of the converter stations on the corresponding nodes. If the node i has a direct current line access, zeta is 1; when the i-node has no direct line access, ζ is 0.
Step 2: theoretical derivation and analysis of system transient energy function
The direct current circuit has the characteristics of complex control, high dynamic regulation speed, phase change failure of a converter station at the inversion side and the like, so that the energy function for constructing and calculating the detailed dynamic process of direct current at two ends is very difficult and tedious, and the direct current circuit alternating current-direct current series-parallel connection system cannot be applied to the scene of phase change failure of the inversion side of the direct current circuit caused by alternating current faults. The transient energy function is constructed by equivalent of the converter stations at the two ends of the direct current line as the dynamic load of the corresponding bus, so that the dynamic overall process of the system including the scene of phase change failure on the inversion side of the direct current line can be described, and the construction difficulty of the energy function can be reduced. Through the first integration construction, the transient energy function of the ith converter station can be expressed as:
Figure BDA0002719646380000101
in the formula: xs is a stable balance point after the fault; and x is the current operating point. In the energy function analysis, all transient energy of the direct current system is treated as potential energy.
For an alternating current-direct current hybrid system, the transient state energy of the system after the fault can be divided into transient state kinetic energy and transient state potential energy, wherein the transient state potential energy is composed of alternating current system potential energy and direct current system potential energy. Let (theta)s,ωs,Us,Φs,ts) And constructing an energy function for a stable balance point of the system equation after the fault by integrating the system equation for the first time to obtain:
Figure BDA0002719646380000102
Figure BDA0002719646380000103
Figure BDA0002719646380000104
Figure BDA0002719646380000105
the physical interpretation in the formula is: vpkIs the transient kinetic energy of the system; vpeIs the transient potential of the system. And, VacIs a transient state bit of an AC systemCan, VdIs the transient potential energy of the dc system.
The transient energy function V is derived with respect to time t, and the result is shown in equations (18), (19), (20):
Figure BDA0002719646380000106
Figure BDA0002719646380000107
Figure BDA0002719646380000108
the following equations (18), (19) and (20) can be obtained:
Figure BDA0002719646380000109
from equation (21), based on the network structure maintenance model, along the trajectory after the fault, the derivative of the constructed transient energy function V with respect to time t is less than or equal to zero, which indicates that the transient energy of the system after the fault of the ac/dc hybrid system gradually decays, and whether a lower bound exists will depend on the steady state of the system after the fault.
Based on equations (11), (12) and implicit integration theorem, U, Φ of the system network node can be expressed as a function of θ, that is, there are:
Figure BDA0002719646380000111
the transient potential Vpe of the AC/DC hybrid system can be rewritten to
Figure BDA0002719646380000112
Similarly, equation (14) can be rewritten as:
Figure BDA0002719646380000113
wherein: the transient kinetic energy Vpk and the transient potential energy Vpe after the fault are mutually converted to define dVpeThe number of times when/dt is 0 is m, which represents the number of times that the system transient kinetic energy Vpk and the transient potential energy Vpe complete one-time mutual conversion after the fault.
Transient stability analysis of the AC/DC hybrid system is performed by using a Potential Energy Boundary Surface (PEBS) based on an Energy function, and whether a current system operating point is separated from a Potential Energy Boundary Surface (PEBS) is judged by using a formula (25) which is popularized from a classical power system model to a network structure retention model.
Figure BDA0002719646380000114
If the μ ray is less than 0 after the fault, representing that the current system operation trajectory is in the PEBS; if μ ray >0, it represents that the current system operation trajectory is outside the PEBS.
And step 3: transient stability analysis based on energy function
1) Transient stability criterion proposition
Taking the CEPRI-7 system as an example, the network structure is shown in FIG. 3. Critical cut-off angle gamma of DC inversion sideminThe generator in the system has uniform damping at 7 deg., i.e., Di/Mi. Three-phase short circuit fault occurs at the Bus-6 position, so that commutation failure occurs at the direct current inversion side, and the system is in critical stable and unstable states after the fault.
The calculation results are shown in fig. 4 and 5, respectively. In fig. 4(a) and 5(a), the blue solid line and the red solid line represent the real-time off angle and the critical off angle of the dc link, respectively. The solid blue line in fig. 4(b) and 5(b) represents the dc power. The solid blue lines in fig. 4(c) and 5(c) indicate the relative rotor angle of the generator. The solid blue line in FIGS. 4(d) and 5(d) depicts μrayCurve line. As can be seen from fig. 4(a) and 4(b), an ac fault occurs near the dc inverter station, which results in a phase change failure on the inverter side(ii) a And when the alternating current fault disappears, the direct current restores to a normal operation state. As can be seen from fig. 4(c), the relative rotor angle of the generator gradually converges with the damping of the system, indicating that the system is in a steady state after a fault; as shown in FIG. 4(d), post-fault system μrayAnd is always negative. As can be seen from fig. 5(a) and 5(b), an ac fault occurs near the inverter station, which results in a phase change failure on the dc inverter side. When the ac fault disappears, the dc is always in the dynamic regulation process because the generator in fig. 5(c) diverges with respect to the rotor angle, i.e., the system is in an unstable state after the fault. As shown in FIG. 5(d), μ of post-fault systemrayChanges from negative to positive at t-0.49 s.
On the basis, a transient stability criterion based on an energy function is provided:
criterion I: if after failure murayChanging from negative to positive indicates that the system is in an unstable state;
criterion II: if after failure murayAnd constant negative until m is 3, indicating that the system is in a stable state.
2) Transient stability margin evaluation
Fig. 6 shows a flow chart of transient stability margin evaluation of the ac/dc hybrid system, where h is a simulation step length. "[ ]" denotes a rounding function. An energy function curve is approximately calculated by adopting a trapezoidal integral path, and the Critical Clearing Time (CCT) of the AC-DC hybrid system is quickly obtained by utilizing a dichotomy (BM), wherein the CCT can be used as a transient stability margin index.
The technical effects are as follows:
1) simulation verification
An improved IEEE-39 node alternating current and direct current hybrid system is built, and the correctness and the effectiveness of the theoretical method provided by the text are verified. The network topology is as shown in fig. 7, and on the premise of not changing the power flow of the system, the alternating current connecting line between the Bus-16 and the Bus-15 is changed into LCC-HVDC, wherein the Bus-16 is a rectifying station Bus, and the Bus-15 is an inverting station Bus. And, critical off angle gamma of DC inversion sideminAnd 7 degrees, the generator in the alternating current and direct current system has uniform damping, namely, the lambda is Di/Mi.
AC system in the vicinity of a DC inverter stationIn the system, a three-phase short-circuit fault which causes commutation failure on a direct current inversion side is set. The simulation step h is 0.01s, and the simulation time T is 5 s. Selecting xcIs potential energy VpeThe start of integration of (a). Under the following four scenes, transient stability evaluation is performed on the AC/DC hybrid system after the fault by adopting a transient stability criterion based on an energy function.
Scene I: a three-phase short circuit fault occurs at the Bus-14 of the ac system. The fault starts at t-0 and has a fault duration of 0.20 s.
The simulation results are shown in fig. 8. The blue solid line and the red solid line in fig. 8(a) respectively depict the real-time off-angle and critical off-angle variation curves of the dc line. The blue solid lines in fig. 8(b) respectively show the relative angle change curves of the generator rotor. In FIG. 8(c), the blue solid line, the red solid line and the black solid line respectively represent the post-failure system potential VpeKinetic energy VpkAnd total energy change curve. The solid blue line in FIG. 8(d) depicts μ after failurerayA curve of variation.
As can be seen from fig. 8(a), the ac system near the inverter station fails, and the dc inverter side fails to perform commutation. And after the AC fault disappears, the DC line is restored to a normal operation state under the regulation of the DC control system. As shown in fig. 8(b), under the effect of system damping, the relative rotor angle of the generator gradually converges to the stable equilibrium point before failure, which indicates that the system is in a stable state after failure. As can be seen from fig. 8(c), the derivative of the energy function V of the post-fault system is always non-positive, and when the post-fault system is in a steady state, the energy function V has a lower bound, which proves the correctness of the energy function proposed herein. As shown in FIG. 8(d), μ of post-fault systemrayAnd is constantly negative during the period when m is 3. According to the transient stability criterion, the system after the fault is in a stable state, and the analysis result is matched with the simulation result.
And scene II: a three-phase short circuit fault occurs at the Bus-14 of the ac system. The fault starts at t-0 and has a fault duration of 0.29 s.
As can be seen from fig. 9(a), an ac system near the inverter station fails, and a commutation failure occurs on the dc inverter side. Exchange of electricityAfter the fault disappears, the generator gradually diverges from the rotor angle as shown in fig. 9(b), i.e., the system is in an unstable state after the fault, and the dc line is always in the dynamic adjustment process. As can be seen from fig. 9(c), the derivative of the post-fault system energy function V is always non-positive, and when the post-fault system is in an unstable state, the energy function V is unbounded, proving the correctness of the energy function proposed herein. As shown in FIG. 9(d), μ of post-fault systemrayAnd the t is changed from negative to positive in 1.23 s. According to the transient stability criterion, the system after the fault is in an unstable state, and the analysis result is matched with the simulation result.
Scene III: a three-phase short circuit fault occurs at the Bus-14 of the ac system. The fault starts at t-0 and has a fault duration of 0.20 s. Furthermore, when t is 0.20s, the ac line between Bus-4 and Bus-14 is cut off.
As can be seen from fig. 10(a), an ac system near the inverter station fails, and a commutation failure occurs on the dc inverter side. And after the AC fault disappears, the DC line is restored to a normal operation state under the regulation of the DC control system. As shown in fig. 10(b), under the effect of system damping, the relative rotor angle of the generator gradually converges to a new stable equilibrium point, which indicates that the system is in a stable state after a fault. As can be seen from fig. 10(c), the derivative of the energy function V of the post-fault system is always non-positive, and when the post-fault system is in a steady state, the energy function V has a lower bound, which proves the correctness of the energy function proposed herein. As shown in FIG. 10(d), post-fault system μrayAnd is constantly negative during the period when m is 3. According to the transient stability criterion, the system after the fault is in a stable state, and the analysis result is matched with the simulation result. Compared to scenario I, the proposed method will be effective regardless of whether the system stable equilibrium point changes after a fault.
Scene iv: a three-phase short circuit fault occurs at the Bus-14 of the ac system. The fault starts at t-0 and has a fault duration of 0.20 s. Furthermore, when t is 0.28s, the ac line between Bus-4 and Bus-14 is cut off.
As can be seen from fig. 11(a), the ac system in the vicinity of the inverter station fails, resulting in a dc reverseAnd a commutation fault occurs at the transformation side. After the ac fault disappears, the generator shown in fig. 11(b) gradually diverges from the rotor angle, i.e., it is described that the system is in an unstable state after the fault, and the dc line is always in the dynamic adjustment process. As can be seen from fig. 11(c), the derivative of the post-fault system energy function V is always non-positive, and when the post-fault system is in an unstable state, the energy function V is unbounded, which proves the correctness of the energy function proposed herein. As shown in FIG. 11(d), μ of post-fault systemrayAnd the t is changed from negative to positive in 1.17 s. According to the transient stability criterion, the system after the fault is in an unstable state, and the analysis result is matched with the simulation result. Compared with the scenario II, the proposed method is effective no matter whether the stable balance point of the system changes after the fault.
2) Comparative analysis
Aiming at different positions of an alternating current system near an inverter station, a three-phase short-circuit fault which can cause a direct current commutation fault is set to simulate an alternating current fault accompanied with a commutation fault scene in an improved IEEE-39 node alternating current and direct current hybrid system. The CCT of the ac/dc hybrid system is calculated by using an Energy Function Criterion (EFC) and a Time Domain Simulation (TDS), respectively, and the result is shown in table 1.
TABLE 1 comparison of CCTs calculated by different methods under different scenarios
Figure BDA0002719646380000141
"/" indicates that no wires are cut.
According to table 1, it can be seen that, when an ac fault and a commutation fault occur in the ac/dc hybrid system, the transient stability evaluation result of the theoretical method provided herein is substantially consistent with the time domain simulation result. Under 20 scenes, CCT calculation results obtained by adopting EFC are about 0-0.01 s more than TDS conservation, and the effectiveness and the practicability of the method are verified.
Then, the time spent on calculating the CCT of the AC-DC hybrid system by respectively adopting EFC and TDS in different scenes is researched. The computation time of the CCT varies from hardware environment to hardware environment, and the computation time is mainly the time spent in simulation. Thus, in the comparison of Table 2, the total simulation duration is taken to represent the time taken to calculate the CCT, rather than the actual calculation time. When the alternating current-direct current hybrid system CCT is rapidly obtained by using the BM, the upper limit and the lower limit of the BM are respectively set to be 0.1s and 0.9 s. The simulation time was 5s, and the simulation results are shown in table 2.
TABLE 2 time comparison of CCT calculations by different methods under different scenarios
Figure BDA0002719646380000142
Figure BDA0002719646380000151
"/" indicates that no wires are cut.
As shown in table 2, in 20 scenarios, the time spent on calculating the CCT of the ac/dc hybrid system by using EFC is shorter than TDS. The CCT calculation speed by adopting EFC is 2-3 times faster than that of TDS, and the efficiency of dynamic security evaluation of the AC-DC hybrid system is greatly improved. In addition, when the CCT is calculated by TDS, it is impossible to quantitatively determine whether the system is stable after a fault by observing the relative rotor angle of the generator, and the EFC can solve this problem.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (2)

1. The method for analyzing the transient stability of the alternating current-direct current hybrid system in consideration of the commutation failure is characterized in that a transient energy function containing a direct current line is constructed for the alternating current-direct current hybrid system containing a power grid commutation type high-voltage direct current transmission line, and the transient stability analysis is performed on the alternating current-direct current hybrid system under the situation that the commutation failure occurs on a direct current inversion side caused by an alternating current fault, and comprises the following steps:
firstly, establishing a network structure maintenance model of an alternating current-direct current hybrid system by equivalently using a direct current convertor station as a dynamic load on a corresponding convertor bus, and constructing an energy function of the alternating current-direct current hybrid system through first integration;
secondly, a trapezoidal integral path is adopted to approximately calculate a transient energy function of the system after the fault, a transient stability criterion based on the energy function is provided, and meanwhile, the dichotomy is utilized to quickly calculate the limit cut-off time of the system;
and finally, an improved IEEE-39 node alternating current-direct current hybrid system is built, and the correctness of the theoretical analysis method is verified through simulation.
2. The alternating current-direct current hybrid system transient stability analysis method considering commutation failure according to claim 1, specifically comprising the steps of:
step 1: constructing a network structure maintenance model of the AC-DC hybrid system:
for an alternating current-direct current hybrid system with n nodes and l direct current lines (LCC-HVDC), wherein i is 1,2, the node is connected with a generator, the synchronous generator adopts E' q constant representation, the voltage characteristic of a load is considered, the resistance of the high voltage line is ignored, two ends of the direct current lines are equivalent to the injection power of the corresponding bus, and an equivalent model based on a system network structure holding model is obtained;
in the inertial Center (COI) reference coordinate, the system equation is:
1) characteristic equation of synchronous generator
Figure FDA0002719646370000011
Figure FDA0002719646370000012
Figure FDA0002719646370000013
Figure FDA0002719646370000014
In the formula: 1,2, ·, m; theta i and omega i are respectively the power angle and the angular speed of the ith synchronous generator relative to an inertia Center (COI); ui and phi i are respectively the amplitude and phase angle of the ith node; pmi, Pei and Di are respectively the mechanical input power, active power output and damping of the ith generator; mi and PCOI are respectively an inertia time constant and an acceleration power of an inertia Center (COI) of the ith synchronous generator;
2) load equation taking into account voltage characteristics
Taking into account the voltage characteristics of the load at node i, the following relationship is obtained:
Figure FDA0002719646370000021
Figure FDA0002719646370000022
in the formula: i is 1,2, n, PLi and QLi are the active and reactive sizes of the load on the ith node, and a, b, c, d, e and f are constant coefficients;
3) dc line power equation
Taking a converter station at the rectification side of a direct current line (LCC-HVDC) as an example, the relationship between the direct current voltage and the direct current of the converter station at the rectification side of the direct current line (LCC-HVDC) in the equivalent model of the converter station in the alternating current-direct current hybrid system is as follows:
Figure FDA0002719646370000023
in the formula: udr is the DC voltage of the rectifier side converter station; id is direct current; xr is the equivalent commutation reactance of the rectification side; ktr is the transformation ratio of the converter transformer at the rectifying side; ulr is the AC bus voltage of the rectifier side converter station; alpha is a commutation side trigger delay angle;
when active loss in the phase commutation process is ignored, the power characteristic equation between the rectifier station and the alternating current system is expressed as:
Figure FDA0002719646370000025
in the formula, Pd and Qd are respectively the active power and the reactive power transmitted to the rectifier station by the alternating current system; pdr is the transmission active power of the rectifier side converter station; cr is equivalent capacitance of a parallel capacitor on an alternating current bus of the rectifier side converter station, and Qcr is reactive output of the parallel capacitor; qdr is the total reactive power consumption of the converter station at the rectifying side; omega is the angular speed of the alternating current system; phi r is the equivalent power factor angle of the rectification side of the direct current system;
4) network equation
Based on the equivalent model of the AC-DC hybrid system and according to the power balance relationship, the active power and the reactive power injected into the network by the node i are respectively as follows:
Figure FDA0002719646370000024
Figure FDA0002719646370000031
in the formula: qei is the reactive output of the ith generator; bij is the imaginary part of the system network node admittance array Y;
further obtaining according to the power balance relation:
Pi+PLi+ξPdi＝0 (11)
Qi+QLi+ξQdi＝0 (12)
in the formula: pdi and Qdi are respectively the equivalent active and reactive power of the converter station on the corresponding node, and if the node i has direct current line access, zeta is 1; if the node i has no direct line access, zeta is 0;
step 2: theoretical derivation and analysis of the system transient energy function:
the alternating current-direct current hybrid system containing the direct current circuit (LCC-HVDC) can describe the whole dynamic process of the system including a phase-change failure scene of the inversion side of the direct current circuit and can reduce the construction difficulty of an energy function by equivalently constructing the converter stations at two ends of the direct current circuit as the dynamic load of corresponding buses, and the transient energy function of the ith converter station is expressed as follows through the first integral construction:
Figure FDA0002719646370000032
in the formula: xs is a stable balance point after the fault; x is a current operating point, and in energy function analysis, all transient energy of the direct current system is used as potential energy to be processed;
for the AC-DC hybrid system, the transient energy of the system after the fault is divided into transient kinetic energy and transient potential energy, wherein the transient potential energy consists of AC system potential energy and DC system potential energy, and the value is (theta)s,ωs,Us,Φs,ts) And constructing an energy function for a stable balance point of the system equation after the fault by integrating the system equation for the first time to obtain:
V(θ,ω,U,φ,t)＝Vpk(ω)+Vpe(θ,U,φ,t)
＝Vpk(ω)+Vac(θ,U,φ,t)+Vd(U,t) (14)
Figure FDA0002719646370000033
Figure FDA0002719646370000034
Figure FDA0002719646370000035
the physical interpretation in the formula is: vpkIs the transient kinetic energy of the system; vpeIs the transient potential energy of the system, and, VacIs the transient potential energy of an AC system, VdIs the transient potential energy of the dc system;
the transient energy function V is derived with respect to time t, and the result is shown in equations (18), (19), (20):
Figure FDA0002719646370000041
Figure FDA0002719646370000042
Figure FDA0002719646370000043
from the formulae (18), (19), (20):
Figure FDA0002719646370000044
according to the formula (21), based on a network structure maintenance model, along the trajectory after the fault, the derivative of the constructed transient energy function V with respect to the time t is less than or equal to zero, which indicates that the transient energy of the system after the fault of the AC-DC hybrid system is gradually attenuated, and whether a lower bound exists depends on the stable state of the system after the fault;
based on equations (11), (12) and the implicit integral theorem, U, Φ of the system network node is expressed as a function of θ, that is, there are:
Figure FDA0002719646370000045
the transient potential energy Vpe of the AC-DC hybrid system is rewritten to
Figure FDA0002719646370000046
Similarly, equation (14) is rewritten as:
Figure FDA0002719646370000047
wherein: the transient kinetic energy Vpk and the transient potential energy Vpe after the fault are mutually converted to define dVpeThe frequency of 0/dt is m, which represents the frequency of complete mutual conversion between the transient kinetic energy Vpk and the transient potential energy Vpe of the system after the fault;
performing transient stability analysis on the AC-DC hybrid system by using a Potential Energy Boundary Surface (PEBS) method based on an energy function, and judging whether a current system operating point is separated from the Potential Energy Boundary Surface (PEBS) by using a formula (25) which is popularized from a classical power system model to a network structure maintenance model;
Figure FDA0002719646370000048
if the μ ray is less than 0 after the fault, representing that the current system operation trajectory is in the PEBS; if the mu ray is greater than 0, the current system operation trajectory is outside the PEBS;
and step 3: transient stability analysis based on energy function:
1) transient stability criterion proposition
An alternating current fault occurs near the direct current inversion station, so that the inversion side has phase commutation failure; when the AC fault disappears, the DC returns to the normal operation state, the relative rotor angle of the generator gradually converges along with the damping of the system, which shows that the system is in the stable state after the fault and the system mu after the faultrayConstantly negative, near the inverter stationGenerating an alternating current fault to cause phase commutation failure on a direct current inversion side;
when the AC fault disappears, the generator diverges relative to the rotor angle, namely the system is in an unstable state after the fault, the DC is always in the dynamic regulation process, and the mu of the system after the fault is detectedrayChanges from negative to positive at t-0.49 s;
on the basis, a transient stability criterion based on an energy function is provided:
criterion I: if after failure murayChanging from negative to positive indicates that the system is in an unstable state;
criterion II: if after failure murayThe constant is negative until m is 3, which indicates that the system is in a stable state;
2) transient stability margin evaluation
And (3) approximately calculating an energy function curve by adopting a trapezoidal integral path, and quickly obtaining the Critical Clearing Time (CCT) of the AC-DC hybrid system by utilizing a dichotomy (BM), wherein the Critical Clearing Time (CCT) is used as a transient stability margin index.
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