CN112214905A - Broadband modeling analysis and simulation method and system for power system - Google Patents
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Abstract
The invention discloses a broadband modeling analysis and simulation method and system for a power system, wherein the method comprises the following steps: establishing a multi-element equipment DQ unified frequency coordinate system of the power system; establishing DQ dynamic models of the synchronous generator and the new energy equipment under respective independent DQ coordinate systems; converting interface variables of the synchronous generator and the new energy equipment into a DQ unified frequency coordinate system; establishing a DQ dynamic model of a unified frequency of the power transmission network, and performing systematic integration of the synchronous generator, the new energy equipment and the power transmission network under the DQ unified frequency to form a system-level DQ dynamic model; carrying out broadband small interference stability analysis through a full-system linearization state equation established by a linearization method based on a DQ unified frequency coordinate system; and carrying out broadband electromagnetic transient simulation by adopting an implicit trapezoidal integration method of a DQ unified frequency coordinate system. The invention realizes the small interference stability analysis of the broadband oscillation of the power system; the simulation time consumption and the memory occupation are obviously reduced.
Description
Technical Field
The invention relates to the technical field of power system simulation and analysis, in particular to a power system broadband modeling analysis and simulation method and system.
Background
With the continuous improvement of new energy ratio and the continuous expansion of power grid scale, the problem of broadband oscillation caused by the large-scale access of high-proportion and low-inertia power electronic devices to a power system is increased, and the broadband modeling simulation of the power system is increasingly difficult. The traditional quasi-steady-state modeling cannot meet the requirement of stability analysis, an electromagnetic transient simulation model cannot perform small-interference stability calculation, the simulation step length is small, the simulation speed is slow, and the modeling method is not suitable for large-scale high-proportion new energy power systems. Therefore, a broadband modeling analysis and simulation method capable of realizing systematization and integrated modeling of a new energy power system, and completing eigenvalue calculation and efficient simulation is needed.
Disclosure of Invention
The invention provides a broadband modeling analysis and simulation method and system for a power system, and the method can be used for calculating small-interference characteristic values and efficiently simulating the power system.
Aiming at the advantages, the technical scheme adopted by the invention comprises the following steps:
the embodiment of the description provides a broadband modeling analysis and simulation method for a power system, which comprises the following steps:
establishing a multi-element equipment DQ unified frequency coordinate system of the power system; the multi-element device includes: a synchronous generator, new energy equipment and a power transmission network;
establishing a refined DQ dynamic model of each element of a synchronous generator, a new energy source and the like under the respective independent DQ coordinate system;
converting each element interface variable into a DQ unified frequency coordinate system;
establishing a DQ dynamic model of a uniform frequency of the power transmission network, and performing systematic integration of each element device under the DQ uniform frequency to form a system-level nonlinear refined DQ dynamic model;
carrying out broadband small interference stability analysis through a full-system linearization state equation established by a linearization method based on a DQ unified frequency coordinate;
and realizing broadband electromagnetic transient simulation by adopting an implicit trapezoidal integration method of a DQ unified frequency coordinate.
Preferably, the above-mentioned multivariate device DQ unified frequency coordinate system for establishing the power system is as follows:
and a DQ unified frequency conversion method is adopted to convert the multi-element equipment into a system DQ unified frequency coordinate system for system integration modeling, so that the problem of pilot frequency caused by weak coupling of the multi-element equipment is solved. The established uniform frequency coordinate system of the multi-element equipment DQ of the power system is a fixed frequency omegasRotating DQ coordinate system, where ωsThe steady-state operation frequency of the power system can be selected, any element frequency can be selected, and the frequency constant can be defined by a user.
Preferably, the establishing of a refined DQ dynamic model of each element such as a synchronous generator and a new energy under a respective independent DQ coordinate system includes the following steps:
establishing independent DQ coordinates of each element device by using the tide result data;
according to the structural characteristics of the multi-element equipment, the main circuit structure, the control structure and the control logic relation of each element are subjected to refined modeling, and independent dynamic equations and interface variables of the multi-element equipment such as a synchronous generator and new energy are respectively established;
and optimizing and adjusting typical parameters of each element device, and establishing a refined DQ dynamic model of each device.
(1) Synchronous generator model
The synchronous generator model adopts a generator dynamic equation in a flux linkage form to solve the problem of serious frequency deviation of a high-frequency component of a generator stator circuit under the power frequency synchronous rotating speed of the traditional voltage type generator model, and the differential expression of the generator stator circuit is
pψd＝ωψq+raid+ud
pψq＝-ωψd+raiq+uq
pψf＝-rfif+uf
pψD＝-rDiD
pψg＝-rgig
pψQ＝-rQiQ
pδ＝ω-ωs
pω＝[Tm-1.5(ψdiq-ψqid)]/TJ
The algebraic equation is:
ψd＝Ldid+Mdfif+MdDiD
ψq＝Lqiq+Mqgig+MqQiQ
ψf＝3Mdfid/2+Lfif+MfDiD
ψD＝3MdDid/2+MfDif+LDiD
ψg＝3Mqgiq/2+Lgig+MgQiQ
ψQ＝3MqQiq/2+MgQig+LgiQ
in the formula, subscripts D, Q, f, D, g and Q respectively represent D-axis, Q-axis, excitation f, direct-axis damping D, quadrature-axis damping g and quadrature-axis damping Q windings; Ψ is a flux linkage; r is the winding resistance; i is the winding current and u is the winding voltage; l is the winding self-inductance; m is winding mutual inductance; omega is the synchronous generator rotor speed; delta is the power angle.
(2) New energy model
Taking a doubly-fed wind generator model as an example, a high-order transient model is adopted, a rotor-side frequency converter adopts stator flux linkage directional control, and a grid-side frequency converter adopts stator voltage directional control.
The high-order transient state differential equation of the doubly-fed wind generator is
pψsd＝usd+ωeψsq-Rsisd
pψsq＝usq+ωeψsd-Rsisq
pψrd＝urd+ωslψrq-Rrird
pψrq＝urq+ωslψrd-Rrirq
in the formula ,usd、usq、urd、urqD-axis and q-axis components of the stator and the rotor; i.e. isd、isq、ird、irqD-axis and q-axis components of the stator and the rotor; psisd、ψsq、ψrd、ψrqD-axis and q-axis components of the stator and the rotor; omegaeThe synchronous rotating speed is adopted; omegaslIs the slip angular velocity.
An algebraic equation of
ψsd＝Lsisd+Lmird
ψsq＝Lsisq+Lmirq
ψrd＝Lmisd+Lrird
ψrq＝Lmisq+Lrirq
in the formula ,LmEquivalent mutual inductance between the stator winding and the rotor winding under a synchronous coordinate system; l issThe self-inductance of the stator winding under the synchronous coordinate system; l isrIs the self-inductance of the rotor windings in a synchronous coordinate system.
Preferably, the method for transforming the interface variables of each element into the DQ uniform frequency coordinate system is as follows:
based on a geometric algebra method, an isomorphic group algebra structure of unified frequency transformation is established, conversion of an interface algebra variable to a unified frequency variable under independent frequency is realized by utilizing park transformation, and a full-system DQ dynamic model under a DQ unified frequency coordinate is integrally realized. Taking a synchronous generator as an example, the included angle of the DQ coordinates of generator interface variables in a unified frequency coordinate system is thetarAnd the included angle of DQ coordinates in a generator frequency coordinate system is thetaeThen, pass throughAnd after the DQ unified frequency conversion type processing, the conversion from the interface variable to the DQ unified coordinate frequency can be realized.
wherein ,
representing interface variables under respective independent coordinate systems; x is the number ofdq0The interface variable is transformed into an interface variable under a uniform frequency coordinate system.
The converted interface variables are brought into the element equations to realize interconnection and intercommunication among the devices, so that a broadband fine DQ dynamic model of the complex power system can be built in a plug-in module mode on the basis of independent building of subsystems and combining with unified frequency conversion.
The DQ unified frequency variable transformation is provided, so that the full system DQ dynamic model has the small-interference stable computing capability.
Preferably, the method for establishing a uniform frequency DQ dynamic model of the power transmission network and performing systematic integration of each component device under a DQ uniform frequency is as follows:
the built DQ dynamic model of the power transmission network takes high-frequency state variables into account, and the network consists of a resistance inductor series RL branch and a conductance capacitor parallel GC branch. Wherein, the DQ dynamic model of the resistor-inductor series branch circuit is
The DQ dynamic model of the linear capacitor and the conductance parallel GC branch circuit is
The following network model simplification method is provided, the model order is reduced, and the problem of high dimensionality caused by multiple buses and complex circuits in system simulation analysis is solved. The following 3 cases can eliminate partial bus implementation simplification:
(1) the bus which is not connected with the generator or the load has zero injection current;
(2) and the load connected with the bus is a constant impedance load and is integrated into a DQ dynamic model. In this case, the load bus appears as a zero current disconnect bus;
(3) when the dynamic stability of a unit subset connected with the network is mainly concerned, the load model in the network can be merged into the network model, and then the common bus is eliminated to form a simplified network model.
Assuming that the transmission network consists of G generators, M buses, N branches, and L loads (the loads are represented by impedance branches), the differential algebraic equation describing the system network can be represented by the following equation
x＝Ax+Bu
y＝Cx
Wherein, a is a 2(N + L) order state matrix, B is a 2(N + L) × 2M order input matrix, C is a 2 mx 2(N + L) order output matrix, x is a state variable of each line and load, u is each bus voltage, and y is a bus injection current.
Through further simplification, the obtained reduced-order network model after eliminating unnecessary buses is as follows:
x2＝Anx2+Bnu2
y2＝Cnx2
wherein ：An＝PAQ+PBJ1(CrP1AQ+P2AQ),Bn＝PBJ2,Cn＝C3CQ。
Preferably, the method for performing the broadband small-interference stability analysis through the full-system linearized state equation established by the DQ unified frequency coordinate-based linearization method is as follows:
based on a system-level nonlinear refined DQ dynamic model, linearization processing is carried out under a DQ unified frequency coordinate, and a linearization state equation suitable for small interference stability analysis is established, wherein the linearization state equation is in the form of:
Δx＝AΔx
in the formula, Δ x is a state variable in the form of system increment, and a is a state matrix of the system. For a system comprising three parts, namely a synchronous generator, a new energy source and a power network, the specific representation form of the state variable is as follows:
x＝[xG xw xl]T
wherein ,xG、xw、xlAnd state variables of the synchronous generator, the doubly-fed wind generator and the power transmission network under a unified DQ coordinate are represented.
The characteristic value analysis is carried out by utilizing the state matrix A, so that the broadband small interference stability analysis can be realized, and attention is paid to: based on the characteristic value obtained by the characteristic calculation, the absolute oscillation frequency of the characteristic value is subtracted by the rotation frequency of the DQ unified frequency coordinate, so that the oscillation frequency of the small interference stability analysis under the traditional definition is obtained.
The characteristic utilizes the characteristic that a full-system DQ dynamic model has a DQ unified frequency coordinate, realizes broadband small-interference stability analysis, and overcomes the defect that the small-interference stability calculation cannot be carried out by the traditional electromagnetic simulation.
Preferably, the method for realizing the broadband electromagnetic transient simulation by using the implicit trapezoidal integration method of the DQ uniform frequency coordinate comprises the following steps:
a system-level nonlinear fine DQ dynamic model, wherein the equation expression is as follows under DQ unified frequency coordinate
g(y,z,t)＝0
Where y is the state vector, z is the algebraic vector, and f and g are functions of the appropriate dimensions.
Non-linear differential equation of each element in system as t according to trapezoidal methodn～tn+1The difference algebraic equation of time step:
in the formula, h is a simulation step length. It is combined with an algebraic equation:
g(yn+1,zn+1,tn+1)＝0
simultaneous solution, which essentially solves a set of nonlinear algebraic equations and uses newton's method to calculate.
The transient simulation based on the characteristics has the same simulation precision as the high-precision traditional electromagnetic simulation on the premise of the same dynamic model prototype; meanwhile, transient simulation is carried out by adopting dq uniform frequency coordinates according to the characteristic, and the simulation step length can be selected to be 10-3～10-2Second, the step size of the conventional electromagnetic transient simulation is usually 10-6The time consumption and the memory occupation of the simulation are obviously reduced by the characteristics, and the simulation efficiency is improved.
The embodiment of the present description further provides a broadband modeling analysis and simulation system for an electric power system, where the system includes:
the first establishing module is used for establishing a multi-element equipment DQ unified frequency coordinate system of the power system; the multi-element device includes: a synchronous generator, new energy equipment and a power transmission network;
the second establishing module is used for establishing DQ dynamic models of the synchronous generator and the new energy equipment under respective independent DQ coordinate systems;
the variable transformation module is used for transforming the interface variables of the synchronous generator and the new energy equipment to the DQ unified frequency coordinate system;
the system integration module is used for establishing a uniform frequency DQ dynamic model of the power transmission network, performing systematic integration of the synchronous generator, the new energy equipment and the power transmission network under a DQ uniform frequency, and forming a system-level DQ dynamic model;
the stability analysis module is used for carrying out broadband small-interference stability analysis through a full-system linearization state equation established by a linearization method based on the DQ unified frequency coordinate system;
and the transient simulation module is used for performing broadband electromagnetic transient simulation by adopting an implicit trapezoidal integration method of the DQ unified frequency coordinate system.
The embodiment of the specification adopts at least one technical scheme which can achieve the following beneficial effects:
the method has higher accuracy on the reproduction capability of the system, can reproduce the dynamic response of the system on a relatively wide frequency band, has a constant steady-state operating point, is convenient for carrying out small-interference characteristic value calculation, greatly improves the simulation efficiency, and can be used for high-efficiency simulation of a large-scale power system.
Drawings
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
Fig. 1 is a schematic flow chart of a broadband modeling analysis and simulation method for a power system according to an embodiment of the invention;
FIG. 2 is a block diagram of a resistive-reactive series branch according to an embodiment of the present invention;
FIG. 3 is a diagram of a conductance susceptance series branch in accordance with an embodiment of the present invention;
FIG. 4 is a diagram of a DFIG-containing 3-machine 9-node system architecture;
FIG. 5 is a graph of a distribution of eigenvalues calculated based on a dq model and a quasi-static model according to an embodiment;
FIG. 6 is a graph comparing simulation curves in the case of instability based on three models according to the embodiment;
FIG. 7 is a graph comparing an identification curve with an original oscillation curve;
FIG. 8 is a graph of the participation factor distribution of a destabilizing feature root;
FIG. 9 is a Bode plot of a dq model and a quasi-static model;
FIG. 10 is a graph comparing simulation curves of three models under subsynchronous oscillation;
FIG. 11 is a graph of distribution of characteristic values calculated by dq and quasi-static models in a subsynchronous mode;
FIG. 12 is a graph comparing a subsynchronous oscillation curve and an identification curve;
FIG. 13 is a graph comparing simulation curves of three models under super-synchronous oscillation;
FIG. 14 is a graph of distribution of eigenvalues calculated for dq and quasi-static models in super-synchronous mode;
FIG. 15 is a graph comparing a super-synchronous oscillation curve and an identification curve;
fig. 16 is a schematic structural diagram of a broadband modeling analysis and simulation system of a power system according to an embodiment of the present invention.
Detailed Description
The embodiments of the present invention will be described in further detail below with reference to the drawings of the embodiments of the present invention, and it should be understood that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Fig. 1 is a schematic flow chart of a broadband modeling analysis and simulation method for a power system according to an embodiment of the present invention. As shown in fig. 1, the method comprises the steps of:
s101: establishing a multi-element equipment DQ unified frequency coordinate system of the power system; the multi-element device includes: a synchronous generator, new energy equipment and a power transmission network;
s102: establishing a refined DQ dynamic model of each element of a synchronous generator, a new energy source and the like under the respective independent DQ coordinate system;
s103: establishing an isomorphic group algebraic structure for uniform frequency conversion of each element, and converting interface variables of each element into a DQ uniform frequency coordinate system;
s104: establishing a DQ dynamic model of a uniform frequency of the power transmission network, and performing systematic integration of each element device under the DQ uniform frequency to form a system-level nonlinear refined DQ dynamic model;
s105: establishing a full-system linearization state equation by a linearization method based on a DQ unified frequency coordinate, and performing broadband small-interference stability analysis;
s106: and realizing broadband electromagnetic transient simulation by adopting an implicit trapezoidal integration method of a DQ unified frequency coordinate.
The step S101 of establishing a unified frequency coordinate system of the multivariate equipment DQ of the power system includes the following steps:
step S1011: dq0 transformation
For wide-band dynamic simulation of a large-scale power system, in order to accelerate the simulation speed and provide small-interference stable computing capacity, dq0 transformation is adopted, and three-phase components of abc are projected onto a direct axis (d axis), a quadrature axis (q axis) and a zero axis (0 axis) perpendicular to a dq plane along with the rotation of a rotor. The classical form of dq0 transformation is in the form
Where θ is the transformation angle.
After transformation, the original signal frequency is reduced, large-step simulation can be adopted, and the simulation calculation speed is effectively improved. Moreover, since the model accuracy is determined by the degree of model detail, the abc-dq0 transformation does not degrade the modeling simulation accuracy.
Step S1012: establishing DQ unified frequency coordinate system
And a DQ unified frequency conversion method is adopted to convert the multi-element equipment into a system DQ unified frequency coordinate system for system integration modeling, so that the problem of pilot frequency caused by weak coupling of the multi-element equipment is solved. The established uniform frequency coordinate system of the multi-element equipment DQ of the power system is a fixed frequency omegasRotating DQ coordinate system, where ωsThe steady-state operation frequency of the power system can be selected, any element frequency can be selected, and the frequency constant can be defined by a user.
In step S102, establishing a refined DQ dynamic model of each component such as a synchronous generator and a new energy in a respective independent DQ coordinate system includes the following steps:
s1021: establishing independent DQ coordinates of each element device by using the tide result data;
s1022: according to the structural characteristics of the multi-element equipment, the main circuit structure, the control structure and the control logic relation of each element are subjected to refined modeling, and independent dynamic equations and interface variables of the multi-element equipment such as a synchronous generator and new energy are respectively established;
s1023: and optimizing and adjusting typical parameters of each element device, and establishing a refined DQ dynamic model of each device.
(1) Synchronous generator DQ dynamic model
The synchronous generator model adopts a generator dynamic equation in a flux linkage form to solve the problem of serious frequency deviation of a high-frequency component of a generator stator circuit under the power frequency synchronous rotating speed of the traditional voltage type generator model, and the differential expression of the generator stator circuit is
Algebraic equation:
in the formula, subscripts D, Q, f, D, g and Q respectively represent D-axis, Q-axis, excitation f, direct-axis damping D, quadrature-axis damping g and quadrature-axis damping Q windings; Ψ is a flux linkage; r is the winding resistance; i is the winding current and u is the winding voltage; l is the winding self-inductance; m is winding mutual inductance; omega is the synchronous generator rotor speed; delta is the power angle.
(2) Multi-scale simulation model of doubly-fed wind generator
The doubly-fed wind generator model adopts a high-order transient model. The rotor side frequency converter adopts stator flux linkage directional control, and the network side frequency converter adopts stator voltage directional control.
The high-order transient state differential equation of the doubly-fed wind generator is
in the formula ,usd、usq、urd、urqD-axis and q-axis components of the stator and the rotor; i.e. isd、isq、ird、irqD-axis and q-axis components of the stator and the rotor; psisd、ψsq、ψrd、ψrqD-axis and q-axis components of the stator and the rotor; omegaeTo synchronize forA rotational speed; omegaslIs the slip angular velocity.
An algebraic equation of
in the formula ,LmEquivalent mutual inductance between the stator winding and the rotor winding under a synchronous coordinate system; l issThe self-inductance of the stator winding under the synchronous coordinate system; l isrIs the self-inductance of the rotor windings in a synchronous coordinate system.
The method for converting the interface variables of each component to the DQ uniform frequency coordinate system in step S103 is specifically as follows:
based on a geometric algebra method, an isomorphic group algebra structure of unified frequency transformation is established, conversion of an interface algebra variable to a unified frequency variable under independent frequency is realized by utilizing park transformation, and a full-system DQ dynamic model under a DQ unified frequency coordinate is integrally realized. Taking a synchronous generator as an example, the included angle of the DQ coordinates of generator interface variables in a unified frequency coordinate system is thetarAnd the included angle of DQ coordinates in a generator frequency coordinate system is thetaeThen, after the processing of the following DQ uniform frequency conversion formula, the conversion of the interface variable to the DQ uniform coordinate frequency can be realized.
wherein ,
representing interface variables under respective independent coordinate systems; x is the number ofdq0The interface variable is transformed into an interface variable under a uniform frequency coordinate system.
The converted interface variables are brought into the element equations to realize interconnection and intercommunication among the devices, so that a broadband fine DQ dynamic model of the complex power system can be built in a plug-in module mode on the basis of independent building of subsystems and combining with unified frequency conversion.
Here, the proposal of DQ unified frequency variable transformation enables the full system DQ dynamic model to have the calculation capability of small interference stability
Specifically, the dq model is linked and distinguished from the quasi-static phasor model:
the dq model is a natural extension of the phasor model. Suppose that the voltage abc of the generator terminal is three-phase signal
Wherein the maximum value Am(t) is:
in the formula, p is a differential operator,
is the steady state terminal voltage peak. Under the quasi-static assumption, the signal amplitude Am(t) and phase amplitude delta (t) variation with respect to frequency omegasThe change is very slow (e.g., low frequency oscillation number change speed). Under this assumption, the phase angle δ is approximately constant, its derivative is 0,
thus, the voltage signal can be represented by a phasor model as
U＝Aejδ (9)
Wherein, A ═ V is an effective value, and when the quasi-static assumption is not satisfied, the amplitude A ismThe derivative term of equation (8) cannot be ignored in the case of high-frequency changes of (t) and phase amplitude δ (t), so that the phasor form (9) no longer accurately reflects the actual voltage (7).
At this time, if abc-dq0 transformation is performed on equation (7) to establish a voltage model under dq0 coordinate system:
according to the analytical formula (10), the dq0 voltage model abandons the quasi-steady-state constant assumption, and the amplitude adopts an accurate expression, so that the high-frequency mode characteristics of the system can be accurately reflected. Assuming the system is balanced in three phases, the 0-axis component can be ignored, and equation (10) can be simplified to dq model:
V(t)＝A(t)(cos(δ(t))+jsin(δ(t)))＝ud(t)+juq(t) (11)
in step S104, a uniform frequency DQ dynamic model of the power transmission network is established, and a method for performing systematic integration of each component device at a DQ uniform frequency is as follows:
the built DQ dynamic model of the power transmission network takes high-frequency state variables into account, and the network consists of a resistance inductor series RL branch and a conductance capacitor parallel GC branch. Wherein, the DQ dynamic model of the resistor-inductor series branch circuit is
Will [ i ]a,ib,ic]T＝Tθ -1[id,iq,i0]TSubstituting the above formula, one can obtain:
expand using the derivative product formula:
and the derivative of the dq transformation is
p(Tθ -1)＝-Tθ -1W (15)
In which W is
Formula (13) is a co-product of two sides Tθ -1To give formula (17):
wherein ,ud,1，uq,1，ud,2，uq,2，u0,1，u0,2Respectively dq0 transformed line end voltage dq0 components.
The resistance-inductance series branch dq is therefore modeled as
As with the model formation of the resistor-inductor series branch dq, the constraint equation for the GC branch shown in FIG. 3 is
By the same token, the model of the linear capacitance and conductance parallel GC branch under dq0 is obtained
The following network model simplification method is provided, the model order is reduced, and the problem of high dimensionality caused by multiple buses and complex circuits in system simulation analysis is solved. In general, the following 3 cases may eliminate partial bus implementation simplifications:
(1) the bus which is not connected with the generator or the load has zero injection current;
(2) and the load connected with the bus is a constant impedance load and is integrated into a DQ dynamic model. In this case, the load bus appears as a zero current disconnect bus;
(3) when the dynamic stability of a unit subset connected with the network is mainly concerned, the load model in the network can be merged into the network model, and then the common bus is eliminated to form a simplified network model.
Assuming that the transmission network consists of G generators, M buses, N branches, and L loads (the loads are represented by impedance branches), the differential algebraic equation describing the system network can be represented by the following equation
Wherein, a is a 2(N + L) order state matrix, B is a 2(N + L) × 2M order input matrix, C is a 2 mx 2(N + L) order output matrix, x is a state variable of each line and load, u is each bus voltage, and y is a bus injection current.
The output matrix C is partitioned, and an algebraic equation can be expressed as
Further, can obtain
02(M-G)×1＝C2,2(M-G)×2(N+L)x2(N+L)×1 (23)
Where I is the bus injection current connected to the external element. As can be seen from equation (23), some of the state variables can be represented by other variables, C for equation (23)2Conversion of elementary rows into a canonical ladder matrix, C2The canonical ladder has the following general form:
C2,2(M-G)×2(N+L)＝[E2(M-G)×2(M-G),Cr,2(M-G)×2(N+L-M+G)] (24)
wherein E is an identity matrix, formula (24) is substituted for formula (23), and the state variables are blocked to obtain
wherein ,x2For the reduced state variable, x is obtained by using the principal element column1And x2Relation and relation with x, thereby obtainingAnd (5) performing state space expression after reduction.
Since u and y are also input/output of all buses, it is necessary to continue to convert u and y to input amounts including only necessary buses. Left-multiplying the reduced state equation by-CrAnd formula (21) is left-multiplied by P to obtain u and x2And (4) relationship. For J in the relation-1And partitioning and bringing the partitioned data into a state space expression after order reduction to obtain a reduced order system (26):
wherein ：An＝PAQ+PBJ1(CrP1AQ+P2AQ),Bn＝PBJ2,Cn＝C3CQ。
In step S105, a method for performing broadband small interference stability analysis by using a full-system linearized state equation established by a DQ uniform frequency coordinate-based linearization method is as follows:
based on a system-level nonlinear refined DQ dynamic model, linearization processing is carried out under a DQ unified frequency coordinate, and a linearization state equation suitable for small interference stability analysis is established, wherein the linearization state equation is in the form of:
Δx＝AΔx (27)
in the formula, Δ x is a state variable in the form of system increment, and a is a state matrix of the system. For a system comprising three parts, namely a synchronous generator, a new energy source and a power network, the specific representation form of the state variable is as follows:
x＝[xG xw xl]T (28)
wherein ,xG、xw、xlAnd state variables of the synchronous generator, the doubly-fed wind generator and the power transmission network under a unified DQ coordinate are represented.
The characteristic value analysis is carried out by utilizing the state matrix A, so that the broadband small interference stability analysis can be realized, and attention is paid to: based on the characteristic value obtained by the characteristic calculation, the absolute oscillation frequency of the characteristic value is subtracted by the rotation frequency of the DQ unified frequency coordinate, so that the oscillation frequency of the small interference stability analysis under the traditional definition is obtained.
The characteristic utilizes the characteristic that a full-system DQ dynamic model has a DQ unified frequency coordinate, realizes broadband small-interference stability analysis, and overcomes the defect that the small-interference stability calculation cannot be carried out by the traditional electromagnetic simulation.
In step S106, the method for implementing the broadband electromagnetic transient simulation by using the implicit trapezoidal integration method of the DQ uniform frequency coordinate includes:
a system-level nonlinear fine DQ dynamic model, wherein the equation expression is as follows under DQ unified frequency coordinate
Where y is the state vector, z is the algebraic vector, and f and g are functions of the appropriate dimensions.
Non-linear differential equation of each element in system as t according to trapezoidal methodn～tn+1The difference algebraic equation of time step:
in the formula, h is a simulation step length. It is combined with an algebraic equation:
g(yn+1,zn+1,tn+1)＝0 (31)
simultaneous solution, which is essentially to solve a set of nonlinear algebraic equations, is usually calculated by using the newton method commonly used in power flow calculation of power systems.
The transient simulation based on the characteristics has the same simulation precision as the high-precision traditional electromagnetic simulation on the premise of the same dynamic model prototype; meanwhile, transient simulation is carried out by adopting dq uniform frequency coordinates according to the characteristic, and the simulation step length can be selected to be 10-3～10-2Second, the step size of the conventional electromagnetic transient simulation is usually 10-6The time consumption and the memory occupation of the simulation are obviously reduced by the characteristics, and the simulation effect is improvedAnd (4) rate.
The method of the present embodiment is further described with reference to the drawings and examples.
The schematic diagram of the IEEE3 machine 9 node test system is shown in FIG. 4: the node 1 is an infinite bus; node 2 is a synchronous generator; the node 3 is 60 equivalent doubly-fed fans adopting a capacity weighting method, and the dq and the quasi-static simulation models of the system both adopt fixed step length of 1 ms; the electromagnetic transient model uses a fixed step size of 5 mus.
And comparing the small-interference stability calculation result of the method and the quasi-static model with the broadband dynamic simulation accuracy by taking the electromagnetic transient simulation result as a verification standard, and verifying the performance of the established dq model in the broadband dynamic simulation and the small-interference stability calculation.
(1) Compared with the calculation of characteristic values of the quasi-static model
Different from electromagnetic transient simulation, the dq model in a steady state has time invariance and has system balance points, and small-interference stable calculation can be applied to calculate a system characteristic mode. According to the quasi-steady-state model concept, the power network under quasi-steady state is an algebraic equation, and the dq model adopts a differential equation. In order to illustrate the defects of the quasi-static model in reflecting the stability of the new energy power system, the rotational inertia of the traditional generator is reduced by half in simulation, and then the difference between the two is compared. Fig. 5 shows the calculated eigenvalues based on the dq model and the quasi-static model. As can be seen in the figure, the eigenvalues calculated based on the dq model appear as positive roots 2.296 + -14575 j, meaning that the system will be destabilized; and the characteristic values calculated based on the quasi-static model are all negative roots, which represents that the system is stable.
Meanwhile, the two models are simulated and compared with the electromagnetic transient model simulation, and the result is shown in fig. 6. Therefore, the dq model simulation and the electromagnetic simulation are basically consistent, the output power of the double-fed fan is gradually oscillated and dispersed, and the instability of a system can be reflected; for the quasi-static model, the output power is a straight line, which represents the balance of the system, and the simulation of the system cannot reflect the instability problem of the system.
To further verify the accuracy of the eigenvalue calculation, the electromagnetic transient curve of fig. 6 was identified using the Prony method and compared to the eigenvalues of the proposed method. The identification curve is shown in FIG. 7, and the comparison results are shown in Table 1.
TABLE 1
| Model (model) | frequency/Hz | Damping ratio |
| Quasi-steady state model | —— | —— |
| dq model | 2321.36 | -0.0005 |
| Electromagnetic transient | 2312.54 | -0.0012 |
The identification result shows that the negative damping conjugate positive root calculated by the method is consistent with the mode of the electromagnetic transient simulation expression. To explore the cause of this pattern instability, its participation factor was calculated, as shown in fig. 8. As can be seen from fig. 8 and table 2, the negative damping conjugate positive root is strongly correlated with the grounding capacitance of the outlet bus 3 of the doubly-fed fan, the grounding capacitance of the adjacent bus 9, and the line between the two buses. And (3) comparing the quasi-static model, wherein the line is represented by a constant admittance form, and high-frequency dynamics represented by the mode cannot be reflected, so that the characteristic value is inaccurately calculated, and an incorrect stability conclusion is obtained. The dq model reflects the dynamic state of the line and the grounding capacitor, and can accurately judge the stability of the system.
TABLE 2
| Serial number | Variable of |
| 1 | |
| 2 | |
| 3 | Rotor side q-axis component of DFIG |
| 4 | Stator side q-axis component of |
| 5 | Stator side d-axis component of DFIG |
| 6 | Q-axis component of DFIG network side circuit |
| 7 | Line 3- |
| 8 | Line 3-9q axis component |
| 9 | Bus 9 capacitance d-axis component |
| 10 | Q-axis component of bus 9 capacitance |
(2) Comparison with quasi-static model and electromagnetic transient simulation
Bode plots of the dq model and the quasi-static model are plotted as shown in fig. 9. It can be seen that the bode plots of the two coincide at low frequencies (ω ≈ (0-100) rad/s), producing a large difference at high frequencies. The high-frequency quasi-static model does not take the electromagnetic transient of the generator stator into account, does not model the electromagnetic transient of the power transmission network, and the dq model takes the two electromagnetic transients into account at the same time, so that the amplitude-frequency response and the phase-frequency response of the dq model are finer in the high-frequency section of the Bode diagram. Therefore, the dq model can better reflect the high frequency dynamics of the system. To further illustrate the difference between the two at high frequency, the oscillation curve and the characteristic value are compared below by taking subsynchronous oscillation and supersynchronous oscillation as examples.
(a) Comparison of three models under subsynchronous oscillation
When subsynchronous oscillation is simulated, step input which lasts for 0.01s and has the amplitude of 0.5p.u. is acted on the input power of the generator, and the output power of the doubly-fed wind turbine and a local enlarged view thereof are shown in fig. 10. The quasi-static, dq and electromagnetic transient models were simulated at 14.42s, 254.47s and 1820.04s, respectively. Therefore, the dq model well reflects the dynamic process of the electromagnetic transient curve, the simulation time length is shortened by 86.02%, and the simulation efficiency is high. Although the quasi-static simulation is short, the oscillation process cannot be accurately reflected.
In order to better measure the fitting degree and the difference degree between the three models, the relation of curves of Euclidean measurement (ED) and Dynamic Time Warping (DTW) quantification is introduced. ED measures the distance between two points at the same time, and can measure the overall accuracy of the model. DTW accounts for dynamic changes in time. Using the above method, the accuracy of dq and the quasi-static model over the simulation period of fig. 10(a) was calculated, and the results are shown in table 3. By using an ED method, the dq model under subsynchronous oscillation is closer to an electromagnetic transient model than a quasi-static model, and the accuracy is improved by 5 times. The two methods in the DTW method have 2-time difference, so that the quasi-static model has larger error, and the dq model and the electromagnetic transient model have extremely high similarity of simulation curves and are basically the same. Therefore, the dq model can be effectively used for subsynchronous oscillation simulation of a large-scale power system instead of an electromagnetic transient model.
TABLE 3
| Model (model) | ED | DTW |
| dq model | 0.7178 | 5.2595 |
| Quasi-steady state model | 4.3808 | 10.2293 |
The eigenvalue distribution graph calculated by dq and the quasi-static model in the sub-synchronization mode is shown in fig. 11, the damping ratio and the frequency of the eigenvalue distribution graph are shown in table 4, and it can be seen that the damping ratio calculated by the quasi-static model is high, and the stability of the system is implicitly increased by using the model, so that the stability calculation result is too conservative.
TABLE 4
| Model (model) | frequency/Hz | Damping ratio |
| dq model | 30.87 | 0.0009 |
| Quasi-steady state model | 32.50 | 0.0465 |
| Electromagnetic transient | 30.96 | 0.0003 |
To further verify the accuracy of the pattern calculation, the electromagnetic transient curve of fig. 10 was identified by Prony method, the identification result is shown in table 4, and the identification curve is shown in fig. 12. Therefore, the calculation result of the dq model characteristic value is consistent with the electromagnetic transient simulation curve, and the dq model can be accurately used for subsynchronous oscillation simulation.
(b) Comparison of three models under super-synchronous oscillation
The supersynchronous oscillation curve of the output power of the doubly-fed wind turbine and a partial enlarged view of the supersynchronous oscillation curve are shown in fig. 13. The quasi-static, dq and electromagnetic transient models were simulated at 4.06s, 16.53s and 746.37s, respectively. Compared with an electromagnetic transient model, the dq model has smaller deviation, can ensure good precision, shortens the simulation time length by 97.79 percent compared with the electromagnetic transient simulation, and obviously improves the simulation efficiency; and the quasi-static model has great deviation, and the super-synchronous dynamic state is difficult to accurately reflect.
The simulation accuracy of dq and quasi-static models in fig. 13(a) was calculated using the ED and DTW methods as well, and the results are shown in table 5. It can be seen that under the super-synchronous oscillation, based on the ED method, the dq model is closer to the electromagnetic transient simulation result than the quasi-static model, and the accuracy can be improved by 2 times. There is also a 1.3-fold advantage based on the DTW method. Therefore, the dq model is closer to the electromagnetic transient simulation, the super-synchronous dynamic of the electromagnetic transient simulation is basically described, and meanwhile, the dq model can effectively replace the electromagnetic transient model to be used for large-scale power system simulation to a certain extent in consideration of the simulation acceleration effect of the dq model.
TABLE 5
| Model (model) | ED | DTW |
| dq model | 3.5292 | 24.2750 |
| Quasi-steady state model | 9.4892 | 33.6578 |
Fig. 14 shows a characteristic value distribution diagram calculated by dq and the quasi-static model in the super-synchronous mode, and a damping ratio and a frequency corresponding to the super-synchronous oscillation mode are shown in table 6.
TABLE 6
To further test the accuracy of the pattern calculation, the electromagnetic transient curves of FIG. 13 are identified, the identification curves are shown in FIG. 15, and the identification results are shown in Table 6. Therefore, compared with the identification result, the damping ratio calculated by the quasi-static model is higher, higher stability evaluation is given to the system, if the inertia of the system is reduced due to new unstable factors, the quasi-static model obtains a theoretical analysis result deviating from the reality, and therefore the quasi-static model is not suitable for researching the super-synchronous oscillation. And the frequency and damping ratio calculated by the dq model are extremely consistent with the pattern recognition result, so that the dq model is suitable for super-synchronous oscillation analysis.
The invention provides a power system broadband modeling simulation method based on DQ unified frequency conversion, which has higher accuracy on the reproduction capability of a system, can reproduce the dynamic response of the system on a relatively broadband, has a constant steady-state operating point, is convenient for carrying out small-interference characteristic value calculation, has simulation time far shorter than electromagnetic transient simulation, and can be used for high-efficiency simulation of a large-scale power system.
Fig. 16 is a schematic structural diagram of a broadband modeling analysis and simulation system of a power system according to an embodiment of the present invention. As shown in fig. 16, the system includes:
the first establishing module 1601 is used for establishing a multi-element device DQ unified frequency coordinate system of the power system; the multi-element device includes: a synchronous generator, new energy equipment and a power transmission network;
a second establishing module 1602, configured to establish a DQ dynamic model of the synchronous generator and the new energy device in respective independent DQ coordinate systems;
a variable transformation module 1603, configured to transform the interface variables of the synchronous generator and the new energy device to the DQ uniform frequency coordinate system;
the system integration module 1604 is configured to establish a DQ dynamic model of a unified frequency of the power transmission network, perform systematic integration of the synchronous generator, the new energy device, and the power transmission network at a DQ unified frequency, and form a system-level DQ dynamic model;
a stability analysis module 1605, configured to perform broadband small-interference stability analysis through a full-system linearized state equation established by a linearization method based on the DQ uniform frequency coordinate system;
the transient simulation module 1606 is configured to perform broadband electromagnetic transient simulation by using an implicit trapezoidal integration method of the DQ uniform frequency coordinate system.
Optionally, the established uniform frequency coordinate system of the multi-component device DQ of the power system is a fixed frequency ωsRotating DQ coordinate system, where ωsThe steady-state operation frequency of the power system can be selected, any element frequency can be selected, and the frequency constant can be defined by a user.
Finally, it should be noted that: although the present invention has been described in detail with reference to the above embodiments, those skilled in the art can make modifications and equivalents to the specific embodiments of the present invention, and any modifications and equivalents without departing from the spirit and scope of the present invention are intended to be covered by the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (10)
1. A broadband modeling analysis and simulation method for a power system is characterized by comprising the following steps:
establishing a multi-element equipment DQ unified frequency coordinate system of the power system; the multi-element device includes: a synchronous generator, new energy equipment and a power transmission network;
establishing DQ dynamic models of the synchronous generator and the new energy equipment under respective independent DQ coordinate systems;
converting interface variables of the synchronous generator and the new energy equipment to the DQ unified frequency coordinate system;
establishing a DQ dynamic model of a unified frequency of the power transmission network, and performing systematic integration of the synchronous generator, the new energy equipment and the power transmission network under a DQ unified frequency to form a system-level DQ dynamic model;
carrying out broadband small interference stability analysis through a full-system linearization state equation established by a linearization method based on the DQ unified frequency coordinate system;
and carrying out broadband electromagnetic transient simulation by adopting an implicit trapezoidal integration method of the DQ unified frequency coordinate system.
2. The method of claim 1, wherein the established DQ unified frequency coordinate system of the power system multi-element device is at a fixed frequency ωsRotating DQ coordinate system, where ωsThe steady-state operation frequency of the power system can be selected, any element frequency can be selected, and the frequency constant can be defined by a user.
3. The method according to claim 1, wherein the establishing of the DQ dynamic model of the synchronous generator and the new energy device under respective independent DQ coordinate systems specifically comprises:
establishing independent DQ coordinates of the synchronous generator and the new energy equipment by utilizing the tide result data;
according to the structural characteristics, modeling is carried out on the main circuit structure, the control structure and the control logic relation, and independent dynamic equations and interface variables of the synchronous generator and the new energy equipment are respectively established;
optimizing and adjusting typical parameters of the synchronous generator and the new energy equipment, and establishing respective DQ dynamic models;
the DQ dynamic model of the synchronous generator adopts a generator dynamic equation in a flux linkage form, and a differential expression of the generator dynamic equation is as follows:
pψd＝ωψq+raid+ud
pψq＝-ωψd+raiq+uq
pψf＝-rfif+uf
pψD＝-rDiD
pψg＝-rgig
pψQ＝-rQiQ
pδ＝ω-ωs
pω＝[Tm-1.5(ψdiq-ψqid)]/TJ
the algebraic equation is:
ψd＝Ldid+Mdfif+MdDiD
ψq＝Lqiq+Mqgig+MqQiQ
ψf＝3Mdfid/2+Lfif+MfDiD
ψD＝3MdDid/2+MfDif+LDiD
ψg＝3Mqgiq/2+Lgig+MgQiQ
ψQ＝3MqQiq/2+MgQig+LgiQ
in the formula, subscripts D, Q, f, D, g and Q respectively represent D-axis, Q-axis, excitation f, direct-axis damping D, quadrature-axis damping g and quadrature-axis damping Q windings; Ψ is a flux linkage; r is the winding resistance; i is the winding current and u is the winding voltage; l is the winding self-inductance; m is winding mutual inductance; omega is the synchronous generator rotor speed; delta is the power angle.
4. The method according to claim 1, wherein transforming the interface variables of the synchronous generator and the new energy device to the DQ unified frequency coordinate system comprises:
based on a geometric algebra method, establishing a homogeneous group algebra structure of unified frequency transformation, and realizing the conversion of an interface algebra variable under independent frequency to a unified frequency variable by utilizing park transformationAngle thetarAnd the included angle of DQ coordinates in a generator frequency coordinate system is thetaeThen, after the processing of the following DQ unified frequency conversion formula, the conversion of the interface variable to the DQ unified coordinate frequency can be realized:
wherein ,
representing interface variables under respective independent coordinate systems; x is the number ofdq0The interface variable is transformed into an interface variable under a uniform frequency coordinate system.
And the interconnection and intercommunication among the devices can be realized by substituting the converted interface variables into the element equations.
5. The method according to claim 1, wherein the established DQ dynamic model of the power transmission network involves high frequency state variables, and the network consists of a resistor-inductor series RL branch and a conductance-capacitor parallel GC branch, wherein the DQ dynamic model of the resistor-inductor series branch is:
the DQ dynamic model of the linear capacitor and the conductance capacitor in parallel connection with the GC branch circuit is as follows:
6. the method of claim 1, wherein the DQ dynamics model of the power transmission network is further simplified as follows:
(1) the bus which is not connected with the generator or the load has zero injection current;
(2) the load connected with the bus is a constant impedance load and can be integrated into a DQ dynamic model, and under the condition, the load bus appears in a zero-current disconnection bus mode;
(3) when the dynamic stability of the unit subsets connected with the power transmission network is concerned, the load model in the power transmission network can be merged into the power transmission network model, and then the common bus is eliminated to form a simplified network model;
assuming that the transmission network consists of G generators, M buses, N branches, and L loads, the loads are represented by impedance branches, the differential algebraic equation describing the system network can be represented by:
x＝Ax+Bu
y＝Cx
wherein, A is a 2(N + L) order state matrix, B is a 2(N + L) × 2M order input matrix, C is a 2 Mx2 (N + L) order output matrix, x is a state variable of each line and load, u is each bus voltage, and y is bus injection current;
through further simplification, the obtained reduced-order network model after eliminating unnecessary buses is as follows:
x2＝Anx2+Bnu2
y2＝Cnx2
wherein ：An＝PAQ+PBJ1(CrP1AQ+P2AQ),Bn＝PBJ2,Cn＝C3CQ。
7. The method according to claim 1, wherein the performing a wide-band small interference stability analysis through a full-system linearized state equation established by a linearization method based on the DQ uniform frequency coordinate system specifically comprises:
based on a system-level DQ dynamic model, carrying out linearization processing under a DQ unified frequency coordinate system, and establishing a linearization state equation suitable for small interference stability analysis, wherein the linearization state equation is in the form of:
Δx＝AΔx
in the formula, Δ x is a state variable in the form of system increment, a is a state matrix of the system, and for a system comprising three parts, namely a synchronous generator, a new energy source and a power network, the specific representation form of the state variable is as follows:
x＝[xG xw xl]T
wherein ,xG、xw、xlRepresenting state variables of the synchronous generator, the doubly-fed wind generator and the power transmission network under a unified DQ coordinate;
and (4) analyzing the characteristic value by using the state matrix A, so that the broadband small-interference stability analysis can be realized.
8. The method according to claim 1, wherein the performing the wide-band electromagnetic transient simulation by using the implicit trapezoidal integration method of the DQ uniform frequency coordinate system specifically comprises:
the system level DQ dynamic model has the equation expression as follows under DQ unified frequency coordinate:
g(y,z,t)＝0
where y is a state vector, z is an algebraic vector, and f and g are functions of appropriate dimensions;
non-linear differential equation of each element in system as t according to trapezoidal methodn～tn+1The difference algebraic equation of time step:
in the formula, h is a simulation step length. It is combined with an algebraic equation:
g(yn+1,zn+1,tn+1)＝0
simultaneous solution, which essentially solves a set of nonlinear algebraic equations and uses newton's method to calculate.
9. A broadband modeling analysis and simulation system for a power system, the system comprising:
the first establishing module is used for establishing a multi-element equipment DQ unified frequency coordinate system of the power system; the multi-element device includes: a synchronous generator, new energy equipment and a power transmission network;
the second establishing module is used for establishing DQ dynamic models of the synchronous generator and the new energy equipment under respective independent DQ coordinate systems;
the variable transformation module is used for transforming the interface variables of the synchronous generator and the new energy equipment to the DQ unified frequency coordinate system;
the system integration module is used for establishing a uniform frequency DQ dynamic model of the power transmission network, performing systematic integration of the synchronous generator, the new energy equipment and the power transmission network under a DQ uniform frequency, and forming a system-level DQ dynamic model;
the stability analysis module is used for carrying out broadband small-interference stability analysis through a full-system linearization state equation established by a linearization method based on the DQ unified frequency coordinate system;
and the transient simulation module is used for performing broadband electromagnetic transient simulation by adopting an implicit trapezoidal integration method of the DQ unified frequency coordinate system.
10. The system of claim 9, wherein the established DQ unified frequency coordinate system of the power system multi-element device is at a fixed frequency ωsRotating DQ coordinate system, where ωsThe steady-state operation frequency of the power system can be selected, any element frequency can be selected, and the frequency constant can be defined by a user.
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| CN113326673A (en) * | 2021-06-23 | 2021-08-31 | 华北电力大学 | VBR model electromagnetic transient simulation method and system of synchronous motor |
| CN113326673B (en) * | 2021-06-23 | 2023-08-22 | 华北电力大学 | VBR model electromagnetic transient simulation method and system of synchronous motor |
| CN113868859A (en) * | 2021-09-27 | 2021-12-31 | 国网天津市电力公司 | Method for establishing small interference model of synchronous motor to system |
| CN116722563A (en) * | 2023-05-30 | 2023-09-08 | 杭州盛星能源技术有限公司 | Electromagnetic transient simulation frequency domain expansion method and device based on dynamic phasors |
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