CN112491017A - Method and device for obtaining optimal parameters of current limiter of direct current transmission system - Google Patents
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Abstract
The embodiment of the application provides a method and a device for obtaining optimal parameters of a current limiter of a direct current transmission system, wherein the method comprises the following steps: firstly, carrying out fault analysis on a direct current transmission system with a current limiter to obtain a fault current model; establishing a mathematical model of the superconducting current limiter according to the superconducting characteristic of the superconducting current limiter; wherein the mathematical model comprises a resistance model and a thermal model; then, obtaining a current limiter optimal configuration model in the direct current system according to the mathematical model of the superconducting current limiter and the fault current model; and finally, obtaining the optimal parameters of the current limiter according to the optimal configuration model of the current limiter. The scheme is adopted. The optimal parameters obtained by the scheme can effectively reduce the maximum fault removal capacity of the direct current circuit breaker, increase the fault reaction time of the system, ensure the correctness and the reliability of the action of the direct current circuit breaker, and have important significance on a direct current transmission system.
Description
Technical Field
The application relates to the technical field of direct current transmission, in particular to a method and a device for obtaining optimal parameters of a current limiter of a direct current transmission system.
Background
The direct-current transmission technology has the advantages of active and reactive independent control, no phase commutation failure danger and the like, so the direct-current transmission technology has wide application in the aspects of new energy grid connection, regional power grid interconnection and the like. However, because the damping and response coefficient of the dc power transmission system are small, when a short-circuit fault occurs on the dc side of the dc power transmission system, the fault will develop rapidly, generating a short-circuit current ten times or even several tens times as high as the rated current of the system, and seriously threatening the operation of power electronic devices and the ac system in the dc system, so the rapid removal of the fault on the dc side becomes a difficult point for the research on the dc power transmission technology.
At present, one of the main schemes adopted for a dc side fault is to configure a converter and a dc breaker with fault isolation capability on a dc line, and the converter with the fault isolation function not only increases the construction cost of a converter station, but also needs to lock all converters in a dc network, which affects the stable operation of the dc network, and because the fault detection and the action of the dc breaker require time, the fault current often rises rapidly, which will further increase the requirement of the dc breaker on the breaking capacity, therefore, the application of the dc breaker is limited by the breaking capacity, especially in a multi-terminal dc transmission system with a complicated capacitor discharge path, the design difficulty and cost of the dc breaker are increased, and for this reason, a proper current limiting scheme needs to be selected to avoid the above problems.
In view of the above problems, current limiters are usually installed to achieve the current limiting purpose, and more advanced current limiters include superconducting current limiters, polymer current limiters, and power electronic current limiters. The superconducting current limiter has extremely low resistance in normal operation, does not influence the operation of a direct current power grid, and loses the superconductivity when a fault occurs, so that larger resistance is generated, the increase of fault current is effectively limited, and the configuration of the superconducting current limiter in a direct current transmission system is an ideal current limiting scheme which is researched more at present.
However, when configuring a superconducting current limiter in a direct current transmission system, a model of the superconducting current limiter is often simplified, only steady-state resistance of the superconducting current limiter is considered, and coupling relation between current and resistance and cost of a superconducting material in a resistance conversion process are ignored, so that it is difficult to obtain optimal parameters of the superconducting current limiter according with superconducting characteristics, and therefore how to obtain optimal parameter configuration of the current limiter of the direct current transmission system is an urgent problem to be solved at present.
Disclosure of Invention
The application provides a method and a device for obtaining optimal parameters of a current limiter of a direct current transmission system, so as to obtain optimal parameter configuration of the current limiter of the direct current transmission system, and solve the problem that when a superconducting current limiter is configured in the direct current transmission system at present, a model of the superconducting current limiter is often simplified, only steady-state resistance of the superconducting current limiter is considered, and coupling relation and cost of current and resistance of a superconducting material in a resistance conversion process are ignored, so that optimal parameters of the superconducting current limiter conforming to superconducting characteristics are difficult to obtain.
In a first aspect, an embodiment of the present application provides a method for obtaining an optimal parameter of a current limiter of a dc power transmission system, including:
carrying out fault analysis on a direct current transmission system with a current limiter to obtain a fault current model;
establishing a mathematical model of the superconducting current limiter according to the superconducting characteristic of the superconducting current limiter; wherein the mathematical model comprises a resistance model and a thermal model;
obtaining a current limiter optimal configuration model in the direct current system according to the mathematical model and the fault current model of the superconducting current limiter;
and obtaining the optimal parameters of the current limiter according to the optimal configuration model of the current limiter.
With reference to the first aspect, in an implementation manner, the resistance model is a resistance of the superconducting tape, and is obtained according to a resistance of the superconducting layer and a resistance of the composite metal layer, and is obtained by using the following formula:
wherein R isSCIs a superconducting layer resistance; e is the electric field strength in the superconductor; l isSIs the length of the superconducting tape; j is the current density in the superconductor; rhoMeIs the resistivity of the composite metal layer; sMeThe sectional area of the composite metal layer; rMeIs a composite metal layer resistance, RTypeIs the resistance of the superconducting tape.
With reference to the first aspect, in one implementation manner, the relationship between the electric field intensity and the current density of the superconducting material in the superconducting state, the magnetic flux flow dynamic state, and the normal resistance state is obtained by using the following formula:
wherein E is the electric field in the superconductorStrength; j is the current density in the superconductor; t is the current temperature of the superconductor; j. the design is a squareC(T) is the critical current density at temperature T; t isCIs the critical temperature of the superconductor; eCCritical electric field strength; n is a characteristic constant of the superconducting tape; rho is the critical temperature T of the superconductorCResistivity of the substrate.
With reference to the first aspect, in one implementation, the thermal model is established according to the following formula:
QSC＝I2RType
QSC＝ε(TRe-TSC)
wherein Q isSCThe heating power of the superconductor; i is current; rTypeIs the resistance of the superconducting tape; t isReTemperature of the refrigerant medium, TSCThe temperature of the superconducting tape is shown, and epsilon is the heat conduction coefficient between the refrigerating medium and the superconducting tape; t represents the temperature of the superconducting tape, T0Indicating the initial temperature of the superconducting tape; cSCIs the bulk thermal capacity of the superconducting tape; qReT represents time, which is the conductive thermal power of the superconductor and the cooling medium.
With reference to the first aspect, in an implementation manner, the method for obtaining the optimal configuration model of the flow restrictor includes: establishing an objective function, proposing constraint conditions and obtaining an optimal solution.
With reference to the first aspect, in one implementation manner, the objective function refers to a cost of a current limiter, and is obtained according to the following formula:
CYC＝kSC·MSC＝kSC·NSC·LSC；
Crefrigation＝kre1·LSC+kre1(a·Tsc 2+b·Tsc+c)；
Cmaintain＝kmain·Crefrigration·D；
CSFCL＝Csc+Crefrigration+Cmaintain；
wherein, CYCCost of superconducting material, kSCBeing a unit price of superconducting tape, MSCFor the total amount of superconducting tape, NSCThe number of parallel superconducting tapes, LSCIs the length of a single superconducting tape, CrefrigationFor the size of superconducting current limiters, kre1Is the Dewar cost coefficient, a, b, C are the fitting parameters of the refrigeration cost, CmainFor the cost of operation and maintenance, KmainThe refrigeration coefficient of the superconducting current limiter, D represents the operating life of the superconducting current limiter, CSFCLThe cost of the superconducting current limiter.
With reference to the first aspect, in one implementation, the constraints include a maximum fault current, a maximum fault clearing time, a voltage sag constraint, and a temperature constraint of the superconducting tape; wherein,
the maximum fault current in a short-circuit fault must not exceed the maximum current;
the fault clearing time of the direct current line does not exceed the maximum fault clearing time;
the voltage of the failed direct-current bus cannot drop to 80% of the rated direct-current voltage;
the temperature of the superconducting current limiter tape must not exceed the maximum allowable temperature.
With reference to the first aspect, in one implementation, the method of obtaining the optimal solution is obtaining by using a genetic algorithm.
In a second aspect, an embodiment of the present application provides an apparatus for obtaining optimal parameters of a current limiter of a dc power transmission system, including:
the fault current model acquisition model is fast, and is used for carrying out fault analysis on a direct current transmission system with a current limiter to obtain a fault current model;
the mathematical model acquisition module is used for establishing a mathematical model of the superconducting current limiter according to the superconducting characteristic of the superconducting current limiter; wherein the mathematical model comprises a resistance model and a thermal model;
the current limiter optimal configuration model obtaining module is used for obtaining a current limiter optimal configuration model in the direct current system according to the mathematical model and the fault current model of the superconducting current limiter;
and the current limiter optimal parameter obtaining module is used for obtaining the current limiter optimal parameters according to the current limiter optimal configuration model.
With reference to the second aspect, in an implementation manner, the resistance model is a resistance of the superconducting tape, and is obtained according to a resistance of the superconducting layer and a resistance of the composite metal layer, and is obtained by using the following formula:
wherein R isSCIs a superconducting layer resistance; e is the electric field strength in the superconductor; l isSIs the length of the superconducting tape; j is the current density in the superconductor; rhoMeIs the resistivity of the composite metal layer; sMeThe sectional area of the composite metal layer; rMeIs a composite metal layer resistance, RTypeIs the resistance of the superconducting tape.
With reference to the second aspect, in one implementation manner, the relationship between the electric field intensity and the current density of the superconducting material in the superconducting state, the magnetic flux flow dynamic state and the normal resistance state is obtained by using the following formula:
wherein E is the electric field strength in the superconductor; j is the current density in the superconductor; t is the current temperature of the superconductor; j. the design is a squareC(T) is the critical current density at temperature T; t isCIs the critical temperature of the superconductor; eCCritical electric field strength; n is a characteristic constant of the superconducting tape; rho is the critical temperature T of the superconductorCResistivity of the substrate.
With reference to the second aspect, in one implementation, the thermal model is established according to the following formula:
QSC＝I2RType
QSC＝ε(TRe-TSC)
wherein Q isSCThe heating power of the superconductor; i is current; rTypeIs the resistance of the superconducting tape; t isReTemperature of the refrigerant medium, TSCThe temperature of the superconducting tape is shown, and epsilon is the heat conduction coefficient between the refrigerating medium and the superconducting tape; t represents the temperature of the superconducting tape, T0Indicating the initial temperature of the superconducting tape; cSCIs the bulk thermal capacity of the superconducting tape; qReT represents time, which is the conductive thermal power of the superconductor and the cooling medium.
With reference to the second aspect, in an implementation manner, the method for obtaining the optimal configuration model of the flow restrictor includes: establishing an objective function, proposing constraint conditions and obtaining an optimal solution.
With reference to the second aspect, in one implementation, the objective function refers to a cost of the current limiter, and is obtained according to the following formula:
CYC＝kSC·MSC＝kSC·NSC·LSC；
Crefrigation＝kre1·LSC+kre1(a·Tsc 2+b·Tsc+c)；
Cmaintain＝kmain·Crefrigration·D；
CSFCL＝Csc+Crefrigration+Cmaintain；
wherein, CYCCost of superconducting material, kSCBeing a unit price of superconducting tape, MSCFor the total amount of superconducting tape, NSCThe number of parallel superconducting tapes, LSCIs the length of a single superconducting tape, CrefrigationFor the size of superconducting current limiters, kre1Is the Dewar cost coefficient, a, b, C are the fitting parameters of the refrigeration cost, CmainFor the cost of operation and maintenance, KmainThe refrigeration coefficient of the superconducting current limiter, D represents the operating life of the superconducting current limiter, CSFCLThe cost of the superconducting current limiter.
With reference to the second aspect, in one implementation, the constraints include a maximum fault current, a maximum fault clearing time, a voltage sag constraint, and a temperature constraint of the superconducting tape; wherein,
the maximum fault current in a short-circuit fault must not exceed the maximum current;
the fault clearing time of the direct current line does not exceed the maximum fault clearing time;
the voltage of the failed direct-current bus cannot drop to 80% of the rated direct-current voltage;
the temperature of the superconducting current limiter tape must not exceed the maximum allowable temperature.
With reference to the second aspect, in one implementation, the method of obtaining the optimal solution is obtaining by using a genetic algorithm.
The embodiment of the application provides a method and a device for obtaining optimal parameters of a current limiter of a direct current transmission system, wherein the method comprises the following steps: firstly, carrying out fault analysis on a direct current transmission system with a current limiter to obtain a fault current model; establishing a mathematical model of the superconducting current limiter according to the superconducting characteristic of the superconducting current limiter; wherein the mathematical model comprises a resistance model and a thermal model; then, obtaining a current limiter optimal configuration model in the direct current system according to the mathematical model of the superconducting current limiter and the fault current model; and finally, obtaining the optimal parameters of the current limiter according to the optimal configuration model of the current limiter. By adopting the scheme of the method, the device,
the optimal parameters obtained by the scheme can effectively reduce the maximum fault removal capacity of the direct current circuit breaker, increase the fault reaction time of the system, ensure the correctness and the reliability of the action of the direct current circuit breaker, and have important significance on a direct current transmission system.
In addition, the design of the current limiter can be effectively guided by adopting the scheme, and the economical efficiency in the application process of the current limiter is improved.
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In order to more clearly explain the technical solution of the present application, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious to those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a schematic flowchart of a method for obtaining optimal parameters of a current limiter of a dc power transmission system according to an embodiment of the present application;
FIG. 2 is a discharge circuit diagram of MMC interpolar short circuit in an embodiment of the present application;
fig. 3 is a topology of a hybrid dc circuit breaker according to an embodiment of the present application;
fig. 4 is a flow chart of the operation of the hybrid dc circuit breaker of fig. 3;
fig. 5 is a fault procedure of a dc power transmission system including a superconducting current limiter according to an embodiment of the present application;
FIG. 6 is a diagram illustrating the variation of system fault current when the current limiting resistors are different in the embodiment of the present application;
FIG. 7 is a diagram illustrating a variation of a DC bus voltage of a system when a current-limiting resistor is different in an embodiment of the present application;
FIG. 8 is a flow chart of solving an optimal solution using a genetic algorithm in an embodiment of the present application;
fig. 9 is a graph showing the resistance value of a superconducting current limiter to be configured and the cost variation of the superconducting current limiter when the maximum fault-cutting current of the circuit breaker is from 12kA to 20kA in simulation calculation;
fig. 10 is a graph showing the variation in cost of a superconducting current limiter of a desired configuration at different failure reaction times in simulation calculation.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present application more comprehensible, the present application is described in further detail with reference to the accompanying drawings and the detailed description.
The application provides a method and a device for obtaining optimal parameters of a current limiter of a direct current transmission system, so as to obtain optimal parameter configuration of the current limiter of the direct current transmission system, and solve the problem that when a superconducting current limiter is configured in the direct current transmission system at present, a model of the superconducting current limiter is often simplified, only steady-state resistance of the superconducting current limiter is considered, and coupling relation and cost of current and resistance of a superconducting material in a resistance conversion process are ignored, so that optimal parameters of the superconducting current limiter conforming to superconducting characteristics are difficult to obtain.
The application takes a superconducting current limiter as an example, and firstly, the fault in the flexible direct current power grid is analyzed in detail. Then, an optimal configuration scheme considering the factors such as the current carrying capacity of the superconducting current limiter, the resistance conversion speed, the design cost and the like is provided when the maximum cut-off current of the direct current breaker is constant.
The embodiment of the application provides a method for acquiring optimal parameters of a current limiter of a direct current transmission system, and referring to fig. 1, the method for acquiring optimal parameters of the current limiter of the direct current transmission system comprises the following steps:
and step S10, carrying out fault analysis on the direct current transmission system with the current limiter to obtain a fault current model.
The method comprises the following steps of firstly considering the fault analysis after a current limiter is added into a direct current transmission system, and specifically comprises the following steps:
(1) fault model analysis for DC power transmission systems
In this embodiment, for example, a superconducting current limiter and an MMC (modular multilevel converter), an inter-electrode short-circuit fault of a flexible dc power transmission system is analyzed:
for a traditional half-bridge MMC, when an inter-electrode short-circuit fault occurs, the sub-modules are not locked, and the fault will develop through three stages: firstly, the module capacitor discharges to a fault point, at the moment, the alternating current power supply does not discharge to the fault point, then, when the direct current voltage drops to a certain degree, the diode is conducted in a reversing way in an uncontrolled rectification way, at the moment, the alternating current power supply starts to discharge to the fault point, finally, the fault is further developed into the way that the diode is completely conducted, the alternating current side discharges to the fault point in a three-phase short circuit way, and at the moment, the short circuit current greatly threatens the safety of the power electronic device. Therefore, it is generally required to remove the fault before the dc voltage drops to 80% during the module capacitor discharge phase.
FIG. 2 is a discharge circuit diagram of MMC interelectrode short-circuiting. In fig. 2, SM1, sm2armFor bridge arm inductance, RarmIs a bridge arm resistance; u shapedcThe total voltage on the direct current capacitor; rsEquivalent resistance, L, for MMCsEquivalent inductance, C for MMCsThe equivalent capacitance is MMC; rSFCLIs the resistance of the superconducting current limiter; l isdcThe inductance of a current-limiting reactor in the direct-current circuit breaker; in the application, the condition of bipolar short circuit fault at the most serious outlet is considered, namely the resistance and the inductance on a line are 0, the SFCL is a superconducting current limiter, and Ua, Ub and Uc are three-phase voltages.
During the fault period, the equivalent capacitance, inductance and resistance of the converter are respectively:
wherein N is the number of submodules on each bridge arm, CSMIs the capacitance value of the sub-module.
(2) Operating mode analysis for DC circuit breakers
The present application takes a hybrid circuit breaker as an example for analysis. Fig. 3 is a topology of a hybrid dc circuit breaker. When the system normally operates, the current only flows through a branch circuit 1 consisting of a transfer switch and a mechanical isolating switch, and when a fault occurs, the fault current is transferred to a branch circuit 2 to cut off the fault current, K1And K2Showing a mechanical isolating switch. The working flow is shown in FIG. 4, which is firstly failure detection, and locking is performed after the failure is detectedTransfer switch and disconnecting mechanical isolating switch K2Diverting the fault current to the main breaker, i.e. opening the main breaker and opening the mechanical disconnector K1And finally, the fault is cut off.
The main parameter of the operation of a dc circuit breaker is the maximum breaking capacity of the circuit breaker, i.e. the maximum cut-off fault current Ic, and the circuit breaker can only operate if the fault current decays below this value. The other parameter of the direct current breaker is fault reaction time tc, and since the action of the direct current breaker requires a fault detection original to detect and make a judgment, when a fault occurs in a complex direct current network, the fault reaction time is required to make a judgment and order the fault to be removed.
(3) DC line fault calculation taking current limiter into account
The present application assumes that the dc circuit breaker can remove the fault during the capacitor discharge phase, and the fault process considering the superconducting current limiter can be represented by fig. 5, where in fig. 5, t0To t1The moment is the normal operation stage of the system, t1To t2The moment is the resistance transition phase, t2To t3The moment is the resistive current limiting phase, t3To t4The moment is the fault removal stage of the direct current breaker.
At t0At the moment, the system normally operates, and the operating current at the moment is set as I0；
At t1At the moment, the system is in failure, the fault current is rapidly increased, and the resistance of the superconducting current limiter is changed along with the change of the current;
at t2At the moment, the resistance of the superconducting current limiter reaches a stable value, the system enters an over-damping state, and the fault current begins to attenuate;
at t3At that moment, the fault current decays to the maximum cut-off value of the direct current breaker, and the direct current breaker is put into operation. In this case, let Δ T be T3-t1Δ T is the fault handling time of the system;
at t4At that moment, the fault of the dc line is completely cleared by the dc breaker.
Of primary interest to the present application is t1To t3Fault current i between momentsfResistance R with superconducting current limiterSFCLA coupling change process. In the process, firstly, a line model of the superconducting current limiter is established, the line model is used for calculating the direct current line fault in the process of coupling and changing the fault current and the superconducting resistance, so that the fault characteristic of a direct current transmission system of the current limiter is analyzed, and the line model of the superconducting current limiter is expressed as follows:
solving the second order equation of state yields:
1) when the system is underdamped, a pair of characteristic roots of equation 2 is:
wherein,
the fault current and the direct current voltage satisfy the following conditions:
wherein,
2) when the system is over-damped, the characteristic root of equation 2 satisfies the following condition:
the fault current and the direct current voltage satisfy the following conditions: :
wherein,
(4) analysis of influence of current limiting resistor on fault current and DC voltage
The application takes a certain direct current transmission system as an example, neglects the transient process of a current limiter, and carries out RSFCLThe failure conditions at 0 Ω, 10 Ω, 20 Ω, and 30 Ω were analyzed.
Fig. 6 is a diagram illustrating a change situation of a system fault current when a current-limiting resistor is different, wherein an abscissa t represents time, and an ordinate If represents the fault current; fig. 7 shows the change of the dc bus voltage of the system when the current-limiting resistors are different, where the abscissa t represents time and the ordinate Udc represents the dc bus voltage. It can be seen that when the current-limiting resistance is increased, the fault current of the system is effectively controlled, and the drop of the direct-current voltage is restrained. In fig. 6, the breaking current of the circuit breaker is 15kA, and when the current limiting resistance reaches 20 Ω, the requirement of the circuit breaker can be barely met.
Step S11, establishing a mathematical model of the superconducting current limiter according to the superconducting characteristics of the superconducting current limiter; wherein the mathematical model includes a resistance model and a thermal model.
Resistance R of superconducting current limiterSFCLAnd fault current ifThere is a complex nonlinear coupling relationship, and this step is to analyze the characteristics of the current limiter, and to establish a mathematical model of the superconducting current limiter according to the superconducting characteristics of the superconducting current limiter.
Firstly, establishing a resistance model:
the resistance model is expressed by the resistance of the superconducting strip, is obtained according to the resistance of the superconducting layer and the resistance of the composite metal layer, and is obtained by adopting the following formula:
wherein R isSCIs a superconducting layer resistance; e is the electric field strength in the superconductor; l isSIs the length of the superconducting tape; j is the current density in the superconductor; rhoMeIs the resistivity of the composite metal layer; sMeThe sectional area of the composite metal layer; rMeIs a composite metal layer resistance, RTypeIs the resistance of the superconducting tape.
In the above formula, the relationship between the electric field intensity and the current density of the superconducting material is obtained in three states, namely, in the superconducting state, the flux flow state and the normal resistance state, the following formula is adopted:
wherein E is the electric field strength in the superconductor; j is the current density in the superconductor; t is the current temperature of the superconductor; j. the design is a squareC(T) is the critical current density at temperature T; t isCIs the critical temperature of the superconductor; eCCritical electric field strength; n is a characteristic constant of the superconducting tape; rho is the critical temperature T of the superconductorCResistivity of the substrate.
In addition, after the superconducting tape quenches, the temperature of the superconducting tape can be greatly increased, and the resistance change of the superconducting tape meets the relationship of resistance-temperature as follows:
RMe(T)＝RMe(T0)(1+ηMe(T-T0)) (17)
wherein eta isMeThe temperature coefficient of resistance of the composite metal layer.
Then a thermal model is established:
the transformation process of the resistance of the superconducting tape is driven by the temperature change of the superconducting tape, and thus it is required to establish a thermal model of the superconducting tape. In addition, the layered structure of the superconducting tape enables the mechanical property of the superconducting tape to be poor, the superconducting tape is easy to layer under the high-temperature condition, the superconducting tape is irreversibly damaged at the moment, and the superconducting property cannot be recovered, so that the limit working condition of the superconducting current limiter can be researched by establishing a thermal model of the superconducting material.
The thermal model is built according to the following formula:
QSC＝I2RType
QSC＝ε(TRe-TSC)
wherein Q isSCThe heating power of the superconductor; i is current; rTypeIs the resistance of the superconducting tape; t isReTemperature of the refrigerant medium, TSCThe temperature of the superconducting tape is shown, and epsilon is the heat conduction coefficient between the refrigerating medium and the superconducting tape; t represents the temperature of the superconducting tape, T0Indicating the initial temperature of the superconducting tape; cSCIs the bulk thermal capacity of the superconducting tape; qReT represents time, which is the conductive thermal power of the superconductor and the cooling medium.
In the process of quenching of the superconducting tape, the tape generates a large amount of heat for a short time, and the leidenfrost effect is generated, at the moment, the cooling power of the cooling medium is difficult to estimate and is small relative to the generated heat, so that the cooling power can be ignored in the simulation, and the cooling power of the cooling medium is only considered in the process of stable operation and quenching recovery.
And step S12, obtaining a current limiter optimal configuration model in the direct current system according to the mathematical model of the superconducting current limiter and the fault current model.
The method for acquiring the optimal configuration model of the current limiter comprises the following steps: establishing an objective function, proposing constraint conditions and obtaining an optimal solution.
The optimal configuration of the current limiter needs to consider the requirement of the direct current breaker on the maximum breaking current and the use cost of the current limiter. The method takes a superconducting current limiter as an example, and considers the optimal configuration scheme of the current limiter when the maximum cut-off current of the direct current breaker is constant, and because the resistance of the superconducting current limiter and the fault current have a complex nonlinear coupling relation, the current limiting characteristic of the superconducting current limiter needs to be analyzed first, and then the fault current can be iteratively solved. Therefore, a mathematical model of the superconducting current limiter is established according to the superconducting characteristics of the superconducting current limiter, and then the requirement of the direct current breaker on the maximum cut-off current and the use cost of the current limiter are considered on the basis, so that an optimal configuration model of the current limiter in the direct current power grid is obtained.
The objective function mainly considers the cost of the current limiter, and the cost of the superconducting current limiter mainly consists of the cost of the superconducting tape, the cost of the refrigeration system and the operation and maintenance cost, namely: obtaining the objective function according to the following formula:
CYC＝kSC·MSC＝kSC·NSC·LSC (19)；
Crefrigation＝kre1·LSC+kre1(a·Tsc 2+b·Tsc+c) (20)；
Cmaintain＝kmain·Crefrigration·D (21)；
CSFCL＝Csc+Crefrigration+Cmaintain (22)；
wherein, CYCCost of superconducting material, kSCBeing a unit price of superconducting tape, MSCFor the total amount of superconducting tape, NSCThe number of parallel superconducting tapes, LSCIs the length of a single superconducting tape, CrefrigationFor the size of superconducting current limiters, kre1Is the Dewar cost coefficient, a, b, C are the fitting parameters of the refrigeration cost, CmainFor the cost of operation and maintenance, KmainThe refrigeration coefficient of the superconducting current limiter, D represents the operating life of the superconducting current limiter, CSFCLThe cost of the superconducting current limiter.
Cost C of superconducting materialYCThe operation and maintenance cost is obtained by multiplying the usage amount of the superconducting tape by the unit price of the superconducting tape, and mainly comprises the energy consumed by refrigeration of the superconducting current limiter and the consumption of refrigerant, which are mainly determined by a refrigeration system of the superconducting current limiter.
Constraints are then proposed, including: maximum fault current, maximum fault clearing time, voltage sag constraint and temperature constraint of the superconducting tape; wherein:
the maximum fault current is the maximum fault current i in the short-circuit fault for ensuring that the power element is not damagedfMust not exceed a maximum value, i.e.:
if≤If,max (23)；
wherein, If，maxIs the current maximum.
The maximum fault clearing time is to prevent the original from overheating, and the clearing time t of the fault of the direct current line4Must not exceed a maximum value, i.e.:
t4≤tc,max (24)；
wherein, tc，maxThe maximum value of the fault clearing time.
The voltage sag constraint is to prevent the discharge of the ac power supply to a short-circuit point on the dc link, and therefore the voltage u at the failed dc busDC(t) must not drop to 80% of the rated dc voltage, i.e.:
uDC(t)≥0.8·UDC_R (25)；
wherein, UDC_RIs rated dc voltage.
The temperature constraint of the superconducting tape is to prevent the superconducting tape of the superconducting current limiter from irreversible damage during the current limiting process, so that the temperature of the superconducting current limiter tape must not exceed the maximum allowable temperature, namely:
K(t)≤KSC_max (26)；
wherein, KSC_maxIs the maximum allowable temperature.
Finally, the optimal solution is optimized and solved, the optimization process involves short-circuit current calculation and the thermal process of the superconducting tape, therefore, the solving of the optimal solution is a complex nonlinear multivariable problem, the problem is solved by adopting a genetic algorithm, as shown in fig. 8, an initial population is generated firstly, and then an evaluation population is generated, and the method comprises the following steps: calculating fault current, calculating the thermal process of the superconducting current limiter and calculating the resistance of the superconducting current limiter, solving an evaluation population fitness value, finally judging whether a termination condition is met, if not, re-executing the evaluation population according to genetic operations such as selection, crossing and variation, and if so, ending the operation.
And step S13, obtaining the optimal parameters of the current limiter according to the optimal configuration model of the current limiter.
In this step, current limiter optimal parameters are obtained according to the current limiter optimal configuration model obtained in step S12, and a current limiter of the dc power transmission system is configured according to the optimal parameters, where the optimal parameters refer to maximum cut-off capacity, that is, current, and fault reaction time.
In order to verify the validity of the above scheme, the embodiment of the present application further performs simulation verification on the above method, and the system parameters adopted during verification are shown in table 1:
TABLE 1 parameter table of certain double-ended MMC system
| Item | Parameter(s) |
| Operating voltage/kV | 200 |
| Delivery power/WM | 400 |
| Equivalent capacitance/. mu.f | 180.26 |
| Equivalent inductance/mL | 66.67 |
| Equivalent resistance/omega | 1.533 |
1) Impact of maximum circuit breaker trip capacity on cost of current limiter
The present embodiment first studies the change in the configuration cost of the superconducting current limiter when the maximum fault current cut-off value of the dc circuit breaker is different. Fig. 9 shows the resistance value of the superconducting current limiter to be arranged and the cost of the superconducting current limiter when the maximum fault interrupting current of the circuit breaker is from 12kA to 20kA, wherein the abscissa R/sfcl represents the resistance of the superconducting current limiter, and the ordinate Ic represents the maximum interrupting current of the circuit breaker, wherein the resistance of the superconducting current limiter is represented by the average value of the resistance stabilizing stage. It can be seen that under the system model, the increase of the stable resistance of the superconducting current limiter can reduce the requirement of the maximum fault clearing capacity of the direct current breaker. However, when the maximum cutoff value of the fault current is small to some extent, the cost for disposing the superconducting current limiter increases sharply, and the economical efficiency is lowered. Therefore, the use of the superconducting current limiter requires a dc breaker with an appropriate breaking capacity, and economic benefits can be achieved.
2) Fault response time and superconducting current limiter configuration
Considering the limitation that the direct current voltage cannot be lower than 80% of the operation voltage, the latest investment time of the circuit breaker is taken as the fault reaction time of the system. The longer the fault response time required by the system, the larger the current limiting resistor is required to limit the drop in current voltage. Therefore, this section studies the relationship between the system fault reaction time and the configuration cost of the superconducting current limiter. Fig. 10 is a graph showing the variation in cost of a superconducting current limiter to be configured at different critical-fault-clearing times (fault-reaction times), where the abscissa R/sfcl represents the resistance of the superconducting current limiter and the ordinate tc represents the critical-fault-clearing time.
As can be seen from fig. 10, the increase of the current limiting resistance of the superconducting current limiter can increase the fault reaction time of the system, and ensure the correctness and reliability of the action of the dc breaker. The long fault response time required for the system also dramatically increases the cost of configuring the superconducting current limiter.
From the above, the influence of the maximum cut-off capacity of the circuit breaker on the cost of the current limiter, the relation between the fault reaction time and the configuration of the superconducting current limiter are compared, so that the effectiveness of the optimal configuration method disclosed by the application on guiding the design of the current limiter is shown, and the economy in the application process of the current limiter is improved.
The following are embodiments of the apparatus of the present invention that may be used to perform embodiments of the method of the present invention. For details which are not disclosed in the embodiments of the apparatus of the present invention, reference is made to the embodiments of the method of the present invention.
The embodiment of the present application provides a device for obtaining optimal parameters of a current limiter of a dc power transmission system, where the device includes:
the fault current model acquisition model is fast, and is used for carrying out fault analysis on a direct current transmission system with a current limiter to obtain a fault current model;
the mathematical model acquisition module is used for establishing a mathematical model of the superconducting current limiter according to the superconducting characteristic of the superconducting current limiter; wherein the mathematical model comprises a resistance model and a thermal model;
the current limiter optimal configuration model obtaining module is used for obtaining a current limiter optimal configuration model in the direct current system according to the mathematical model and the fault current model of the superconducting current limiter;
and the current limiter optimal parameter obtaining module is used for obtaining the current limiter optimal parameters according to the current limiter optimal configuration model.
Optionally, the resistance model is a resistance of the superconducting tape, and is obtained according to the resistance of the superconducting layer and the resistance of the composite metal layer, and is obtained by using the following formula:
wherein R isSCIs a superconducting layer resistance; e is the electric field strength in the superconductor; l isSIs the length of the superconducting tape; j is the current density in the superconductor; rhoMeIs the resistivity of the composite metal layer; sMeThe sectional area of the composite metal layer; rMeIs a composite metal layer resistance, RTypeIs the resistance of the superconducting tape.
Optionally, in three states of the superconducting state, the flux flow dynamic state and the normal resistance state, the relationship between the electric field strength and the current carrying density of the superconducting material is obtained by using the following formula:
wherein E is the electric field strength in the superconductor; j is the current density in the superconductor; t is the current temperature of the superconductor; j. the design is a squareC(T) is the critical current density at temperature T; t isCIs the critical temperature of the superconductor; eCCritical electric field strength; n is a characteristic constant of the superconducting tape; rho is the critical temperature T of the superconductorCResistivity of the substrate.
Optionally, the thermal model is established according to the following formula:
QSC＝I2RType
QSC＝ε(TRe-TSC)
wherein Q isSCThe heating power of the superconductor; i is current; rTypeIs the resistance of the superconducting tape; t isReTemperature of the refrigerant medium, TSCThe temperature of the superconducting tape is shown, and epsilon is the heat conduction coefficient between the refrigerating medium and the superconducting tape; t represents the temperature of the superconducting tape, T0Indicating the initial temperature of the superconducting tape; cSCIs the bulk thermal capacity of the superconducting tape; qReT represents time, which is the conductive thermal power of the superconductor and the cooling medium.
Optionally, the method for obtaining the optimal configuration model of the flow restrictor includes: establishing an objective function, proposing constraint conditions and obtaining an optimal solution.
Optionally, the objective function refers to the cost of the current limiter, and is obtained according to the following formula:
CYC＝kSC·MSC＝kSC·NSC·LSC；
Crefrigation＝kre1·LSC+kre1(a·Tsc 2+b·Tsc+c)；
Cmaintain＝kmain·Crefrigration·D；
CSFCL＝Csc+Crefrigration+Cmaintain；
wherein, CYCCost of superconducting material, kSCBeing a unit price of superconducting tape, MSCFor the total amount of superconducting tape, NSCThe number of parallel superconducting tapes, LSCIs the length of a single superconducting tape, CrefrigationFor the size of superconducting current limiters, kre1Is the Dewar cost coefficient, a, b, C are the fitting parameters of the refrigeration cost, CmainFor the cost of operation and maintenance, KmainThe refrigeration coefficient of the superconducting current limiter, D represents the operating life of the superconducting current limiter, CSFCLThe cost of the superconducting current limiter.
Optionally, the constraints include a maximum fault current, a maximum fault clearing time, a voltage sag constraint, and a temperature constraint of the superconducting tape; wherein,
the maximum fault current in a short-circuit fault must not exceed the maximum current;
the fault clearing time of the direct current line does not exceed the maximum fault clearing time;
the voltage of the failed direct-current bus cannot drop to 80% of the rated direct-current voltage;
the temperature of the superconducting current limiter tape must not exceed the maximum allowable temperature.
Alternatively, the method of obtaining the optimal solution is to obtain using a genetic algorithm.
The same and similar parts in the various embodiments in this specification may be referred to each other. In particular, as for the apparatus embodiment, since it is substantially similar to the method embodiment, the description is simple, and the relevant points can be referred to the description in the method embodiment.
The present application has been described in detail with reference to specific embodiments and illustrative examples, but the description is not intended to limit the application. Those skilled in the art will appreciate that various equivalent substitutions, modifications or improvements may be made to the presently disclosed embodiments and implementations thereof without departing from the spirit and scope of the present disclosure, and these fall within the scope of the present disclosure. The protection scope of this application is subject to the appended claims.
Claims (10)
1. A method for obtaining optimal parameters of a current limiter of a direct current transmission system is characterized by comprising the following steps:
carrying out fault analysis on a direct current transmission system with a current limiter to obtain a fault current model;
establishing a mathematical model of the superconducting current limiter according to the superconducting characteristic of the superconducting current limiter; wherein the mathematical model comprises a resistance model and a thermal model;
obtaining a current limiter optimal configuration model in the direct current system according to the mathematical model and the fault current model of the superconducting current limiter;
and obtaining the optimal parameters of the current limiter according to the optimal configuration model of the current limiter.
2. The method according to claim 1, wherein the resistance model is a resistance of the superconducting tape, obtained from a superconducting layer resistance and a composite metal layer resistance, obtained using the following equation:
wherein R isSCIs a superconducting layer resistance; e is the electric field strength in the superconductor; l isSIs the length of the superconducting tape; j is the current density in the superconductor; rhoMeIs the resistivity of the composite metal layer; sMeThe sectional area of the composite metal layer; rMeIs a composite metal layer resistance, RTypeIs the resistance of the superconducting tape.
3. The method of claim 2, wherein the relationship between the electric field intensity and the current density of the superconducting material in the superconducting state, the flux flow dynamic state and the normal resistance state is obtained by using the following formula:
wherein E is the electric field strength in the superconductor; j is the current density in the superconductor; t is the current temperature of the superconductor; j. the design is a squareC(T) is the critical current density at temperature T; t isCIs the critical temperature of the superconductor; eCCritical electric field strength; n is a characteristic constant of the superconducting tape; rho is the critical temperature T of the superconductorCResistivity of the substrate.
4. The method of claim 2, wherein the thermal model is established according to the following formula:
QSC＝I2RType
QSC＝ε(TRe-TSC)
wherein Q isSCThe heating power of the superconductor; i is current; rTypeIs the resistance of the superconducting tape; t isReTemperature of the refrigerant medium, TSCThe temperature of the superconducting tape is shown, and epsilon is the heat conduction coefficient between the refrigerating medium and the superconducting tape; t represents the temperature of the superconducting tape, T0Indicating the initial temperature of the superconducting tape; cSCIs the bulk thermal capacity of the superconducting tape; qReT represents time, which is the conductive thermal power of the superconductor and the cooling medium.
5. The method according to claim 1, wherein the method for obtaining the model of the optimal configuration of the flow restrictor comprises: establishing an objective function, proposing constraint conditions and obtaining an optimal solution.
6. The method of claim 5, wherein the objective function is a cost of the flow restrictor, the objective function being obtained according to the following formula:
CYC＝kSC·MSC＝kSC·NSC·LSC；
Crefrigation＝kre1·LSC+kre1(a·Tsc 2+b·Tsc+c)；
Cmaintain＝kmain·Crefrigration·D；
CSFCL＝Csc+Crefrigration+Cmaintain；
wherein, CYCCost of superconducting material, kSCBeing a unit price of superconducting tape, MSCFor the total amount of superconducting tape, NSCThe number of parallel superconducting tapes, LSCIs the length of a single superconducting tape, CrefrigationFor the size of superconducting current limiters, kre1Is the Dewar cost coefficient, a, b, C are the fitting parameters of the refrigeration cost, CmainFor the cost of operation and maintenance, KmainThe refrigeration coefficient of the superconducting current limiter, D represents the operating life of the superconducting current limiter, CSFCLThe cost of the superconducting current limiter.
7. The method of claim 5, wherein the constraints include a maximum fault current, a maximum fault clearing time, a voltage sag constraint, and a temperature constraint of the superconducting tape; wherein,
the maximum fault current in a short-circuit fault must not exceed the maximum current;
the fault clearing time of the direct current line does not exceed the maximum fault clearing time;
the voltage of the failed direct-current bus cannot drop to 80% of the rated direct-current voltage;
the temperature of the superconducting current limiter tape must not exceed the maximum allowable temperature.
8. The method of claim 5, wherein the optimal solution is obtained using a genetic algorithm.
9. An apparatus for obtaining optimal parameters of a current limiter of a direct current transmission system, comprising:
the fault current model acquisition model is fast, and is used for carrying out fault analysis on a direct current transmission system with a current limiter to obtain a fault current model;
the mathematical model acquisition module is used for establishing a mathematical model of the superconducting current limiter according to the superconducting characteristic of the superconducting current limiter; wherein the mathematical model comprises a resistance model and a thermal model;
the current limiter optimal configuration model obtaining module is used for obtaining a current limiter optimal configuration model in the direct current system according to the mathematical model and the fault current model of the superconducting current limiter;
and the current limiter optimal parameter obtaining module is used for obtaining the current limiter optimal parameters according to the current limiter optimal configuration model.
10. The apparatus according to claim 9, wherein the resistance model is a resistance of the superconducting tape, obtained from a superconducting layer resistance and a composite metal layer resistance, obtained by using the following equation:
wherein R isSCIs a superconducting layer resistance; e is the electric field strength in the superconductor; l isSIs the length of the superconducting tape; j is the current density in the superconductor; rhoMeIs the resistivity of the composite metal layer; sMeThe sectional area of the composite metal layer; rMeIs a composite metal layer resistance, RTypeIs the resistance of the superconducting tape.
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