CN116937698A - Small signal modeling method for power system with heterogeneous power supply - Google Patents
Small signal modeling method for power system with heterogeneous power supply Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
- H02J3/40—Synchronising a generator for connection to a network or to another generator
- H02J3/44—Synchronising a generator for connection to a network or to another generator with means for ensuring correct phase sequence
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/01—Arrangements for reducing harmonics or ripples
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/12—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load
- H02J3/16—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load by adjustment of reactive power
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- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
- H02J3/241—The oscillation concerning frequency
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- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
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Abstract
The application relates to a small signal modeling method of an electric power system with a heterogeneous power supply, which comprises the following steps: respectively constructing a grid-structured converter small signal model, a follow-grid converter small signal model, a synchronous generator small signal model, a circuit and a filter small signal model; and constructing a small signal model of the power system based on the small signal model of the grid-connected converter, the small signal model of the follow-up grid converter, the small signal model of the synchronous generator, the small signal model of the circuit and the small signal model of the filter. Compared with the prior art, the application has the advantages of being suitable for an electric power system comprising a synchronous generator, a grid-connected converter and a grid-following converter, and the like.
Description
Technical Field
The application relates to the field of power electronics, in particular to a novel small signal modeling method for a power system with heterogeneous power sources such as a grid-structured converter, a grid-following converter and the like.
Background
In the electric power system, a high proportion of new energy is connected to an electric network point through a current transformer, and more current transformers are used as grid-following type current transformers. The phase angle of the power grid can be tracked in real time by the phase-locked loop with the grid type converter, so that the synchronization with the power grid can be realized quickly, but the voltage and frequency support cannot be provided for the system, so that the system is in a low inertia state, and the stable operation of the power grid is not facilitated. Therefore, a grid-built converter is introduced, which is similar to a synchronous generator, and when disturbance occurs in the system, the grid-built converter can increase or decrease the output power of the grid-built converter so as to balance the load and keep the voltage and frequency stable, and can also provide reference voltage and frequency for the load and other elements in the system and provide voltage and frequency support for the system. Based on the better dynamic characteristics of the grid-connected converters, part of the grid-connected converters in the power system are gradually replaced by the grid-connected converters, so as to provide necessary voltage and frequency support for the power system. Thus, the power system presents a new architecture comprising simultaneously synchronous generators, grid-connected converters and grid-following converters.
At present, small signal stability researches on converters are mostly focused on 100% new energy power systems, a single converter of a grid type or a grid structure type is integrated into an infinite system, small signal stability analysis of a power system comprising two converters at the same time is performed, and small signal stability of a power system comprising a synchronous generator and the single converter is also little researched. However, in an actual power system, three power supplies including a synchronous generator, a grid-connected converter and a grid-connected converter are included at the same time, and the capability of the three power supplies for providing voltage and frequency support for the system is different, so that a small signal modeling method for the power system including the synchronous generator, the grid-connected converter and the grid-connected converter is not available at the present stage.
Disclosure of Invention
The application aims to overcome the defects of the prior art and provide a small-signal modeling method of an electric power system comprising a heterogeneous power source, which is applicable to an electric power system comprising a synchronous generator, a grid-connected converter and a grid-connected converter.
The aim of the application can be achieved by the following technical scheme:
the application provides a small signal modeling method of an electric power system containing heterogeneous power sources, wherein the electric power system comprises a synchronous generator, a grid-connected converter and a grid-following converter, and the small signal modeling method comprises the following steps:
respectively constructing a grid-structured converter small signal model, a follow-grid converter small signal model, a synchronous generator small signal model, a circuit and a filter small signal model;
and constructing a power system small signal model based on the grid-structured converter small signal model, the grid-following converter small signal model, the synchronous generator small signal model and the line and filter small signal model.
As a preferred technical solution, the small signal model of the grid-structured converter includes: a power computation sub-model, a VSG outer loop control sub-model, a virtual impedance link sub-model, and an inner loop control link sub-model.
As a preferred technical solution, the power calculation sub-model includes:
wherein omega c Is the filter cut-off frequency; p (P) e1 And Q e1 The output values of the electromagnetic power and the reactive power are respectively; u (u) o1 And i o1 The output voltage and the output current of the grid-formed converter are respectively; i od1 And U od1 Respectively outputting steady-state values of the current and the voltage in the d-axis component; i oq1 And U oq1 Steady state values of the output current and the output voltage in the q-axis component, respectively;
the VSG outer loop control submodel includes:
wherein θ 1 Is the virtual internal potential phase angle; omega n And omega 1 Rated angular frequency and virtual rotor angular frequency respectively; j is virtual moment of inertia; d is a damping coefficient; k (K) f Is the active power-frequency droop coefficient; e, e d And e q The components of the instantaneous values in the d-axis and q-axis, respectively, obtained from the virtual internal potential phase angle and the effective value; k is an integral coefficient; k (K) v Is the reactive power-voltage sag factor;
the virtual impedance link submodel comprises:
wherein u' od1 And u' oq1 The components of the output voltage of the virtual impedance link in the d axis and the q axis are respectively; r is (r) v And L v Is a virtual impedance;
the inner ring control link sub-model comprises:
voltage loop portion:
wherein χ is d And χ (x) q All are intermediate state variables introduced by the voltage inner loop; i' ld1 And i' lq1 Respectively are provided withOutputting components of current values in d axis and q axis for the voltage inner loop; k (K) pv And K iv The proportional coefficient and the integral coefficient of the voltage ring are respectively;
current loop portion:
wherein, gamma d And gamma q All are intermediate state variables introduced by the current inner loop; u's' d1 And u' q1 The components of the output voltage value of the current inner loop in the d axis and the q axis are respectively; k (K) ii And K iv Is the proportional coefficient and the integral coefficient of the current loop.
As an preferable technical solution, the following-net type converter small signal model includes: a phase-locked loop sub-model, a power outer loop sub-model, and a current inner loop sub-model.
As a preferred technical solution, the phase-locked loop submodel includes:
wherein θ 2 Is the electrical angle of the converter; omega 2 The angular frequency of the converter; k (K) p,PLL And K i,PLL The phase-locked loop proportional link coefficient and the integral link coefficient are respectively; u (u) oq2 The voltage q-axis component is output by the following-net type converter;
the power outer loop sub-model includes:
wherein x is 1 And x 2 Are all introduced intermediate state variables; p (P) e2 And Q e2 Respectively is real active powerThe actual value of the reactive power and the actual value of the reactive power; i.e dref And i qref D-axis and q-axis components of the power outer loop output current, respectively; k (K) pp And K ip The proportional coefficient and the integral coefficient of the active loop are respectively; k (K) pq And K iq The proportional coefficient and the integral coefficient of the reactive ring are respectively;
the current inner loop sub-model includes:
wherein x is 3 And x 4 Are all intermediate state variables of the current inner loop; k (K) p1 And K i1 The proportional coefficient and the integral coefficient of the d axis of the current inner loop are respectively; k (K) p2 And K i2 The proportional coefficient and the integral coefficient of the q-axis of the current inner loop; u's' d2 And u' q2 The components of the current inner loop output value in the d axis and the q axis are respectively; u (u) o2 And i o2 The output voltage and the output current of the follow-net type converter are respectively.
As a preferable technical solution, the synchronous generator small signal model includes:
wherein omega r Is the angular velocity deviation; h is an inertia constant; t (T) m And T e Mechanical torque and acceleration torque, respectively; k (K) D Is a damping torque coefficient; delta r Is the rotor angle; omega 0 Is the reference rotor angular velocity; psi phi type fd Is magnetic field winding flux linkage; r is R fd A rotor circuit resistance; l (L) adu Unsaturated mutual inductance of the stator and the rotor; e (E) fd Is the output voltage of the exciter; i.e fd Is the magnetic field winding current;
the small signal model of the synchronous generator can be obtained by the method:
wherein A is SG For a state matrix of a synchronous generator, the small-signal model has 3 state variables including Deltaomega r 、Δδ r And Deltapsi fd 。
As a preferred technical solution, the line and filter small signal model includes:
wherein i is l1,2 Filtering inductance current for a grid-type follow-grid converter filter; l (L) f1,2 And C f1,2 The filter capacitor and the filter inductance are respectively a filter capacitor and a filter inductance of an output port LC filter of the grid-type and grid-type converter; r is (r) f1,2 Parasitic resistance of filtering inductance of the net-structured and net-connected converter; r is (r) c1,2 And L c1,2 The equivalent resistance and the equivalent inductance of the line from the grid-structured and grid-connected converter to the PCC are obtained; u (u) g Is the common connection point voltage.
As a preferable technical solution, before the constructing a small signal model of the electric power system based on the small signal model of the grid-connected converter, the small signal model of the synchronous generator, and the small signal model of the line and the filter, the method further includes:
converting the voltage of the converter connected with the PCC from a common rotation coordinate system to the respective coordinate system of the converter, specifically:
wherein delta is the phase angle difference; omega 1，2 The angular frequency of the grid-structured and grid-following type converter is set; omega com Angular frequency of the common rotation coordinate system;
the voltage at which the converter is connected into the PCC is u under the common rotation coordinate system gDQ Should be converted into u in the respective coordinate system of the converter gdq ：
As a preferred technical solution, the small signal model of the electric power system includes:
the small signal model of the network-structured converter is as follows:
wherein A is GFM A state matrix for the grid-formed converter;
the small signal model of the grid-built converter comprises 14 state variables including delta theta 1 、Δω 1 、ΔP e1 、ΔQ e1 、Δχ dq 、Δγ dq 、Δi ldq1 、Δu odq1 And Δi odq1 ；
The small signal model of the follow-net type converter is as follows:
wherein A is GFL A state matrix for the heel-net type converter;
the small signal model of the following net type converter comprises 11 state variables, wherein the state variables comprise delta omega 2 、Δx 1 、Δx 2 、Δx 3 、Δx 4 、Δi ldq2 、Δu odq2 And Δi odq2 ；
The small signal model of the power system is as follows:
wherein a=diag [ a ] GFM ,Α GFL ,A SG ]A state matrix complete for the system; small signal model of the power systemIncluding 28 state variables.
As a preferred technical solution, the method further includes:
and determining at least one of the influence of the new energy permeability change on the system stability, the influence of the network transformer permeability change on the system stability, the influence of the virtual moment of inertia change on the system stability and the influence of the virtual impedance change on the system stability according to the small signal model of the power system.
Compared with the prior art, the application has the following beneficial effects:
the method is suitable for an electric power system comprising a synchronous generator, a grid-connected converter and a follow-grid converter: the small signal modeling method for the electric power system of the heterogeneous power supply can model the electric power system simultaneously comprising the synchronous generator, the grid-structured converter and the grid-connected converter, and the obtained small signal model for the electric power system can better represent the dynamic characteristics of the electric power system comprising the synchronous generator, the grid-structured converter and the grid-connected converter, so that the method is beneficial to analyzing the influence of main relevant state variables and converter control parameters on the stability of the electric power system.
Drawings
FIG. 1 is a schematic flow chart of a small signal modeling method of an electric power system with heterogeneous power supply in an embodiment of the application;
FIG. 2 is a schematic diagram of a main circuit of a power system according to an embodiment of the present application;
FIG. 3 is an overall control block diagram of a grid-tied converter in accordance with an embodiment of the present application;
fig. 4 is an overall control block diagram of a grid-connected converter in an embodiment of the present application;
FIG. 5 shows the characteristic value lambda of the new energy permeability change in the embodiment of the present application 8,9 And lambda (lambda) 11,12 A change track schematic;
wherein FIG. 5 (a) is a characteristic value lambda 8,9 Is a schematic diagram of the change track of (a); FIG. 5 (b) is a characteristic value lambda 11,12 A change track schematic;
FIG. 6 shows lambda when the permeability of the new energy is changed in the embodiment of the application 15,16 Trace schematic of eigenvalues and participation factors;
wherein FIG. 6 (a) is a characteristic value lambda 15,16 Is a track schematic of (1); FIG. 6 (b) is lambda 15,16 Schematic trace of participation factors;
FIG. 7 shows a characteristic value lambda of the permeability change of a grid-structured converter according to an embodiment of the present application 8,9 Is a schematic diagram of the change track of (a);
FIG. 8 shows lambda as permeability of a networked converter varies in an embodiment of the application 15,16 Characteristic values and participation factor track schematic diagrams;
wherein FIG. 8 (a) is a characteristic value lambda 15,16 Is a track schematic of (1); FIG. 8 (b) is lambda 15,16 Schematic trace of participation factors;
FIG. 9 is a graph showing the characteristic value lambda of the virtual moment of inertia variation according to an embodiment of the present application 15,16 A change track schematic;
FIG. 10 shows the characteristic value lambda of the virtual impedance variation in the embodiment of the application 2,3 And lambda (lambda) 4,5 A trajectory schematic;
wherein FIG. 10 (a) is a characteristic value lambda 2,3 Is a track schematic of (1); FIG. 10 (b) is a characteristic value lambda 4,5 Is a track schematic of (1);
FIG. 11 is a schematic diagram of simulation results of system frequency in an embodiment of the present application;
FIG. 12 is a diagram of another simulation result of the system frequency according to an embodiment of the present application.
Detailed Description
The following description of the embodiments of the present application will be made clearly and fully with reference to the accompanying drawings, in which it is evident that the embodiments described are some, but not all embodiments of the application. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present application without making any inventive effort, shall fall within the scope of the present application.
Fig. 1 is a flowchart of a small signal modeling method for an electric power system including a heterogeneous power supply according to an embodiment of the present application. The present application provides method operational steps as described in the examples or flowcharts, but may include more or fewer operational steps based on conventional or non-inventive labor. The step sequence listed in the embodiments is only one small signal modeling method mode of the power system with heterogeneous power supply in the execution sequence of the steps, and does not represent the only execution sequence. The method should be implemented in software and/or hardware. Referring to fig. 1, the method may include:
step S100: respectively constructing a grid-structured converter small signal model, a follow-grid converter small signal model, a synchronous generator small signal model, a circuit and a filter small signal model;
step S200: and constructing a power system small signal model based on the grid-structured converter small signal model, the grid-following converter small signal model, the synchronous generator small signal model and the line and filter small signal model.
The structure of the power system according to this embodiment is shown in fig. 2, and overall control block diagrams of the grid-connected converter and the grid-connected converter are shown in fig. 3 and fig. 4, respectively, where the GFM converter is the grid-connected converter, and the GFL converter is the grid-connected converter, and the process of modeling the power system in fig. 2 to 4 is described below.
The small signal model of the network-structured converter comprises the following components: the power calculation sub-model, the VSG outer-loop control sub-model, the virtual impedance link sub-model and the inner-loop control link sub-model are described below as follows:
(1) The power calculation sub-model includes:
wherein omega c Is the filter cut-off frequency; p (P) e1 And Q e1 The output values of the electromagnetic power and the reactive power are respectively; u (u) o1 And i o1 The output voltage and the output current of the grid-formed converter are respectively; i od1 And U od1 Respectively outputting steady-state values of the current and the voltage in the d-axis component; i oq1 And U oq1 Steady state values of the output current and the output voltage in the q-axis component, respectively;
(2) The VSG outer loop control submodel includes:
wherein θ 1 Is the virtual internal potential phase angle; omega n And omega 1 Rated angular frequency and virtual rotor angular frequency respectively; j is virtual moment of inertia; d is a damping coefficient; k (K) f Is the active power-frequency droop coefficient; e, e d And e q The components of the instantaneous values in the d-axis and q-axis, respectively, obtained from the virtual internal potential phase angle and the effective value; k is an integral coefficient; k (K) v Is the reactive power-voltage sag factor;
(3) The virtual impedance link sub-model includes:
wherein u' od1 And u' oq1 The components of the output voltage of the virtual impedance link in the d axis and the q axis are respectively; r is (r) v And L v Is a virtual impedance;
(4) The inner loop control link sub-model includes:
voltage loop portion:
wherein χ is d And χ (x) q All are intermediate state variables introduced by the voltage inner loop; i' ld1 And i' lq1 The components of the output current value of the voltage inner loop in the d axis and the q axis are respectively; k (K) pv And K iv The proportional coefficient and the integral coefficient of the voltage ring are respectively;
current loop portion:
wherein, gamma d And gamma q All are intermediate state variables introduced by the current inner loop; u's' d1 And u' q1 The components of the output voltage value of the current inner loop in the d axis and the q axis are respectively; k (K) ii And K iv Is the proportional coefficient and the integral coefficient of the current loop.
The small signal model of the follow-net type converter comprises the following steps: the phase-locked loop sub-model, the power outer loop sub-model and the current inner loop sub-model are respectively described in detail below:
(1) The phase-locked loop sub-model includes:
wherein θ 2 Is the electrical angle of the converter; omega 2 The angular frequency of the converter; k (K) p,PLL And K i,PLL The phase-locked loop proportional link coefficient and the integral link coefficient are respectively; u (u) oq2 The voltage q-axis component is output by the following-net type converter;
(2) The power outer loop sub-model includes:
wherein x is 1 And x 2 Are all introduced intermediate state variables; p (P) e2 And Q e2 The actual value of the active power and the actual value of the reactive power are respectively; i.e dref And i qref D-axis and q-axis components of the power outer loop output current, respectively; k (K) pp And K ip The proportional coefficient and the integral coefficient of the active loop are respectively; k (K) pq And K iq The proportional coefficient and the integral coefficient of the reactive ring are respectively;
(3) The current inner loop sub-model includes:
wherein x is 3 And x 4 Are all intermediate state variables of the current inner loop; k (K) p1 And K i1 The proportional coefficient and the integral coefficient of the d axis of the current inner loop are respectively; k (K) p2 And K i2 The proportional coefficient and the integral coefficient of the q-axis of the current inner loop; u's' d2 And u' q2 The components of the current inner loop output value in the d axis and the q axis are respectively; u (u) o2 And i o2 The output voltage and the output current of the follow-net type converter are respectively.
The following describes a synchronous generator small signal model:
the synchronous generator small signal model comprises:
wherein omega r Is the angular velocity deviation; h is an inertia constant; t (T) m And T e Mechanical torque and acceleration torque, respectively; k (K) D Is a damping torque coefficient; delta r Is the rotor angle; omega 0 Is the reference rotor angular velocity; psi phi type fd Is magnetic field winding flux linkage；R fd A rotor circuit resistance; l (L) adu Unsaturated mutual inductance of the stator and the rotor; e (E) fd Is the output voltage of the exciter; i.e fd Is the magnetic field winding current;
the small signal model of the synchronous generator can be obtained by the method:
wherein A is SG For a state matrix of a synchronous generator, the small-signal model has 3 state variables including Deltaomega r 、Δδ r And Deltapsi fd 。
The following describes a line and filter small signal model:
the line and filter small signal model includes:
wherein i is l1,2 Filtering inductance current for a grid-type follow-grid converter filter; l (L) f1,2 And C f1,2 The filter capacitor and the filter inductance are respectively a filter capacitor and a filter inductance of an output port LC filter of the grid-type and grid-type converter; r is (r) f1,2 Parasitic resistance of filtering inductance of the net-structured and net-connected converter; r is (r) c1,2 And L c1,2 The equivalent resistance and the equivalent inductance of the line from the grid-structured and grid-connected converter to the PCC are obtained; u (u) g Is the common connection point voltage.
Optionally, before step S200, the method for modeling a small signal of a power system including a heterogeneous power supply further includes:
converting the voltage of the converter connected with the PCC from a common rotation coordinate system to the respective coordinate system of the converter, specifically:
wherein delta is the phase angle difference; omega 1，2 The angular frequency of the grid-structured and grid-following type converter is set; omega com Angular frequency of the common rotation coordinate system;
the voltage at which the converter is connected into the PCC is u under the common rotation coordinate system gDQ Should be converted into u in the respective coordinate system of the converter gdq ：
The following describes a small signal model of the power system:
the power system small signal model comprises:
the small signal model of the network-structured converter is as follows:
wherein A is GFM A state matrix for the grid-formed converter;
the small signal model of the grid-built converter comprises 14 state variables including delta theta 1 、Δω 1 、ΔP e1 、ΔQ e1 、Δχ dq 、Δγ dq 、Δi ldq1 、Δu odq1 And Δi odq1 ；
The small signal model of the follow-net type converter is as follows:
wherein A is GFL A state matrix for the heel-net type converter;
the small signal model of the following net type converter comprises 11 state variables, wherein the state variables comprise delta omega 2 、Δx 1 、Δx 2 、Δx 3 、Δx 4 、Δi ldq2 、Δu odq2 And Δi odq2 ；
The small signal model of the power system is as follows:
wherein a=diag [ a ] GFM ,Α GFL ,A SG ]A state matrix complete for the system; the small signal model of the power system includes 28 state variables.
Optionally, the method for modeling the small signal of the power system with the heterogeneous power supply further comprises the following steps:
and determining at least one of the influence of the new energy permeability change on the system stability, the influence of the network transformer permeability change on the system stability, the influence of the virtual moment of inertia change on the system stability and the influence of the virtual impedance change on the system stability according to the small signal model of the power system.
The following description is made on a method for determining the influence of the new energy permeability change on the system stability, the influence of the network-structured converter permeability change on the system stability, the influence of the virtual moment of inertia change on the system stability and the influence of the virtual impedance change on the system stability respectively:
(1) Influence of new energy permeability change on system stability
In order to study the influence of the change of the permeability of the new energy on the stability of the small signal of the system, the output power of the synchronous generator and the power set values of the two converters are changed, the permeability of the new energy is increased from 50% to 90%, and in the process, the permeability of the grid-built converter and the permeability of the grid-built converter are kept the same, and the system parameters in the initial state are shown in table 1. Eigenvalue lambda 8,9 And lambda (lambda) 11,12 As shown in fig. 5, the characteristic value lambda 15,16 The change trace of (2) and the participation factor trace thereof are shown in fig. 6. The curve with arrow in the characteristic value track graph is obtained by rough fitting of characteristic value distribution, and the arrow direction indicates that the permeability of the new energy is increased.
As the permeability of new energy increases, from lambda 8,9 Lambda of 11,12 The trace of the characteristic value is gradually increased in real part, the absolute value of the imaginary part is reduced, and the characteristic value is moved to the right in the complex planeMoving gradually closer to the imaginary axis but not across. Lambda (lambda) 15,16 Then when the new energy permeability increases to 80%, the imaginary axis is broken through to the right half plane of the complex plane, as shown in fig. 6 (b). This shows that as the permeability of the new energy increases, the stability of the small signal of the system gradually decreases, and when the synchronous generator accounts for 20% or less, the system is unstable.
Further, for lambda 15,16 Is analyzed at lambda 15,16 In the process of gradually moving right and crossing the virtual axis, the dominant state variable with larger participation factor is delta omega of the grid-structured converter 1 Delta omega of follow-net type converter 2 、Δi ldq2 、Δi odq2 The participation factor change trace is shown in fig. 6 (b). With the increase of the permeability of the two converters, the parameters of the outer ring control of the grid-structured converter, including the virtual moment of inertia J, the damping coefficient D and the active power-frequency droop coefficient K f Dominant state variable Δω 1 And phase-locked loop parameter K of the following-net type converter p,PLL 、K i,PLL Dominant state variable Δω 2 The participation coefficient of (2) gradually increases. This indicates that the system instability is mainly related to two reasons, on one hand, the frequency and inertia support provided by the grid-connected converter cannot compensate for the gap caused by the reduction of the synchronous generator, so that the system instability is caused, and on the other hand, the dynamic characteristics of the phase-locked loop related to the phase-locked loop of the grid-connected converter can weaken the stability margin of the system and cause instability under the condition that the overall frequency and inertia support of the system is reduced.
(2) Influence of permeability changes of a grid-built converter on system stability
The fixed synchronous generator accounts for 10%, the permeability of the grid-structured converter is changed to 50%, 60%, 70%, 80% and 90%, and the influence of the permeability of the grid-structured converter on the new energy permeability of the system and the stability of the small signals of the system is studied.
Selecting lambda 8,9 And lambda (lambda) 15,16 And analyzing the two groups of characteristic value tracks. Lambda (lambda) 8,9 The characteristic value trace is shown in FIG. 7, lambda 15,16 The characteristic value trace and the participation factor trace are shown in FIG. 8, along the arrow directionThe permeability of the grid-structured converter increases.
As can be seen from FIG. 7, lambda increases with increasing permeability of the networked converter 8,9 Always in the left half plane of complex plane, the real part gradually decreases, the eigenvalue moves leftwards and away from the imaginary axis, indicating that the stability of the system small signal is gradually enhanced. And lambda is 15,16 Then, differently, as can be seen from fig. 8 (a), when the permeability of the grid-structured converter increases from 60% to 70%, the eigenvalue moves from the right half plane of the complex plane to the left half plane across the imaginary axis, and the higher the grid-structured permeability, the more the eigenvalue moves to the left in the complex plane, indicating that the system changes from an unstable state to a stable state and tends to a more stable state.
Further, for lambda 15,16 The dominant state variable of the participation matrix is the state variable delta omega generated by the power outer loop of the grid-type converter 1 、ΔP e1 、ΔQ e1 Phase-locked loop generated state variable delta omega of follow-net type converter 2 State variable Δx generated by power outer loop 1 The participation factor trace is shown in fig. 8 (b). Lambda after the permeability of the net-structured converter exceeds 60% 15,16 Δω in the dominant state variable of (2) 1 、ΔP e1 、ΔQ e1 Is increased by a factor of (a) and is increased to a larger extent, Δω 2 And Deltax 1 The participation factor of (2) is gradually reduced. The permeability of the grid-built converter is increased, the system stability enhancing process is mainly related to state variables generated by a power outer ring, and the control parameters of the grid-built converter outer ring comprise virtual moment of inertia J, damping coefficient D and active power-frequency droop coefficient K f Plays an important role. The outer ring control simulates the rotor characteristic of the synchronous generator, the permeability of the grid-structured converter is increased, and when the power reference value of the converter is actually increased, the frequency and inertia support for the system can be increased, so that the stability of the system can be improved.
(3) Influence of virtual moment of inertia variation on system stability
The permeability of the fixed-mesh converter is 80%, and the virtual moment of inertia J in the outer ring power control of the mesh converter is controlled from an initial value of 0.1kg/m 2 Up to 1kg/m 2 Wherein a pair of complex eigenvalues lambda 15,16 As shown in fig. 9, the virtual moment of inertia increases in the direction of the arrow. As can be seen from the figure, lambda is measured during the gradual increase of J 15,16 The real part of the signal is gradually increased, the absolute value of the imaginary part is gradually reduced, which indicates that the oscillation frequency corresponding to the characteristic value is reduced, the damping ratio is reduced, the stability of the small signal of the system is reduced, and after J is increased to a certain extent, lambda is increased 15,16 The system small signal is unstable after crossing the virtual axis and entering the right half plane of the complex plane. Therefore, although the value of J can be properly increased to enhance the frequency and inertia supporting capacity of the grid-structured converter, too large value of J can cause instability of a system small signal, so that the selection and optimization of the parameter J need to be considered in combination with the condition of the system.
(4) Influence of virtual impedance variation on system stability
The permeability of the fixed-network type transformer is 80%, the virtual impedance is gradually increased from the original set value to 50 times of the original set value, and two pairs of characteristic values lambda 2,3 And lambda (lambda) 4,5 As shown in fig. 10, the virtual impedance increases in the direction of the arrow. As the virtual impedance increases, λ 2,3 The real part gradually increases and the absolute value of the imaginary part decreases, indicating that the corresponding oscillation frequency decreases, and lambda is increased to a certain degree after the virtual impedance increases 2,3 And enters the right half plane of the complex plane across the imaginary axis. And lambda is 4,5 Different, always in the left half plane of the complex plane, the real part gradually decreases, and the absolute value of the imaginary part increases, indicating that the corresponding oscillation frequency increases. It follows that the change in virtual impedance is more complex to influence on the system characteristic value.
It can be appreciated that the present embodiment may utilize MATLAB/Simulink platform to build a circuit according to the electronic system structure in fig. 1 and the system parameters of table 1 as follows. In order to verify the influence of the change of the permeability of the new energy on the stability of the small signal of the system, the permeability of the new energy is increased from 79% to 80% in 0.2s, the simulation result of the system frequency is shown in fig. 11, the system frequency is in a stable state before 0.2s, the system frequency is kept at 50Hz, and the system is unstable after 0.2 s. Secondly, in order to verify the influence of the increase of the permeability of the GFM converter on the stability of a small signal of the system, the permeability of the GFM converter is increased from 69% to 70% at 0.2s, a simulation diagram of the system frequency is shown in fig. 12, the system frequency is in an oscillation state before 0.2s, and when the permeability of the GFM converter is increased again, the system frequency tends to 50Hz after small amplitude fluctuation, and the system reaches a stable state.
Table 1 electronic system parameters
While the application has been described with reference to certain preferred embodiments, it will be understood by those skilled in the art that various changes and substitutions of equivalents may be made and equivalents will be apparent to those skilled in the art without departing from the scope of the application. Therefore, the protection scope of the application is subject to the protection scope of the claims.
Claims (10)
1. The utility model provides a small signal modeling method of electric power system that contains heterogeneous power, electric power system includes synchronous generator, network structure converter and with net converter, its characterized in that, small signal modeling method includes:
respectively constructing a grid-structured converter small signal model, a follow-grid converter small signal model, a synchronous generator small signal model, a circuit and a filter small signal model;
and constructing a power system small signal model based on the grid-structured converter small signal model, the grid-following converter small signal model, the synchronous generator small signal model and the line and filter small signal model.
2. The method for modeling a small signal of an electric power system with heterogeneous power supply according to claim 1, wherein the network-structured converter small signal model comprises: a power computation sub-model, a VSG outer loop control sub-model, a virtual impedance link sub-model, and an inner loop control link sub-model.
3. The method for modeling a small signal of an electric power system including a heterogeneous power supply according to claim 2, wherein the power calculation sub-model includes:
wherein omega c Is the filter cut-off frequency; p (P) e1 And Q e1 The output values of the electromagnetic power and the reactive power are respectively; u (u) o1 And i o1 The output voltage and the output current of the grid-formed converter are respectively; i od1 And U od1 Respectively outputting steady-state values of the current and the voltage in the d-axis component; i oq1 And U oq1 Steady state values of the output current and the output voltage in the q-axis component, respectively;
the VSG outer loop control submodel includes:
wherein θ 1 Is the virtual internal potential phase angle; omega n And omega 1 Rated angular frequency and virtual rotor angular frequency respectively; j is virtual moment of inertia; d is a damping coefficient; k (K) f Is the active power-frequency droop coefficient; e, e d And e q Respectively by virtual internal potential phase angle sumThe instantaneous values obtained by the effective values are components of d axis and q axis; k is an integral coefficient; k (K) v Is the reactive power-voltage sag factor;
the virtual impedance link submodel comprises:
wherein u is o ′ d1 And u o ′ q1 The components of the output voltage of the virtual impedance link in the d axis and the q axis are respectively; r is (r) v And L v Is a virtual impedance;
the inner ring control link sub-model comprises:
voltage loop portion:
wherein χ is d And χ (x) q All are intermediate state variables introduced by the voltage inner loop; i.e l ′ d1 And i l ′ q1 The components of the output current value of the voltage inner loop in the d axis and the q axis are respectively; k (K) pv And K iv The proportional coefficient and the integral coefficient of the voltage ring are respectively;
current loop portion:
wherein, gamma d And gamma q Are all in currentIntermediate state variables introduced by the ring; u (u) d ′ 1 And u q ′ 1 The components of the output voltage value of the current inner loop in the d axis and the q axis are respectively; k (K) ii And K iv Is the proportional coefficient and the integral coefficient of the current loop.
4. The method for modeling a small signal of an electric power system with heterogeneous power supply according to claim 1, wherein the small signal model of the heel-net type converter comprises: a phase-locked loop sub-model, a power outer loop sub-model, and a current inner loop sub-model.
5. The method for modeling a small signal of an electric power system including a heterogeneous power supply according to claim 4, wherein the phase-locked loop sub-model comprises:
wherein θ 2 Is the electrical angle of the converter; omega 2 The angular frequency of the converter; k (K) p,PLL And K i,PLL The phase-locked loop proportional link coefficient and the integral link coefficient are respectively; u (u) oq2 The voltage q-axis component is output by the following-net type converter;
the power outer loop sub-model includes:
wherein x is 1 And x 2 Are all introduced intermediate state variables; p (P) e2 And Q e2 The actual value of the active power and the actual value of the reactive power are respectively; i.e dref And i qref D-axis and q-axis components of the power outer loop output current, respectively; k (K) pp And K ip The proportional coefficient and the integral coefficient of the active loop are respectively; k (K) pq And K iq The proportional coefficient and the integral coefficient of the reactive ring are respectively;
the current inner loop sub-model includes:
wherein x is 3 And x 4 Are all intermediate state variables of the current inner loop; k (K) p1 And K i1 The proportional coefficient and the integral coefficient of the d axis of the current inner loop are respectively; k (K) p2 And K i2 The proportional coefficient and the integral coefficient of the q-axis of the current inner loop; u (u) d ′ 2 And u q ′ 2 The components of the current inner loop output value in the d axis and the q axis are respectively; u (u) o2 And i o2 The output voltage and the output current of the follow-net type converter are respectively.
6. The method for modeling a small signal of an electric power system with heterogeneous power supply according to claim 1, wherein the synchronous generator small signal model comprises:
wherein omega r Is the angular velocity deviation; h is an inertia constant; t (T) m And T e Mechanical torque and acceleration torque, respectively; k (K) D Is a damping torque coefficient; delta r Is the rotor angle; omega 0 Is the reference rotor angular velocity; psi phi type fd Is magnetic field winding flux linkage; r is R fd A rotor circuit resistance; l (L) adu Unsaturated mutual inductance of the stator and the rotor; e (E) fd Is the output voltage of the exciter; i.e fd Is the magnetic field winding current;
the small signal model of the synchronous generator can be obtained by the method:
wherein A is SG For a state matrix of a synchronous generator, the small-signal model has 3 state variablesIncluding Deltaomega r 、Δδ r And Deltapsi fd 。
7. The method for modeling small signals of a power system with heterogeneous power supply according to claim 1, wherein the circuit and filter small signal model comprises:
wherein i is l1,2 Filtering inductance current for a grid-type follow-grid converter filter; l (L) f1,2 And C f1,2 The filter capacitor and the filter inductance are respectively a filter capacitor and a filter inductance of an output port LC filter of the grid-type and grid-type converter; r is (r) f1,2 Parasitic resistance of filtering inductance of the net-structured and net-connected converter; r is (r) c1,2 And L c1,2 The equivalent resistance and the equivalent inductance of the line from the grid-structured and grid-connected converter to the PCC are obtained; u (u) g Is the common connection point voltage.
8. The method of modeling a small signal of a power system including a heterogeneous power supply of claim 1, wherein prior to said constructing a small signal model of a power system based on said grid-connected converter small signal model, said synchronous generator small signal model, and said line and filter small signal model, said method further comprises:
converting the voltage of the converter connected with the PCC from a common rotation coordinate system to the respective coordinate system of the converter, specifically:
wherein delta is the phase angle difference; omega 1，2 The angular frequency of the grid-structured and grid-following type converter is set; omega com Angular frequency of the common rotation coordinate system;
common rotation of the voltage at the point where the converter is connected to the PCCU in the coordinate system gDQ Should be converted into u in the respective coordinate system of the converter gdq ：
9. The method for modeling a small signal of a power system including a heterogeneous power supply according to claim 1, wherein the small signal model of the power system includes:
the small signal model of the network-structured converter is as follows:
wherein A is GFM A state matrix for the grid-formed converter;
the small signal model of the grid-built converter comprises 14 state variables including delta theta 1 、Δω 1 、ΔP e1 、ΔQ e1 、Δχ dq 、Δγ dq 、Δi ldq1 、Δu odq1 And Δi odq1 ；
The small signal model of the follow-net type converter is as follows:
wherein A is GFL A state matrix for the heel-net type converter;
the small signal model of the following net type converter comprises 11 state variables, wherein the state variables comprise delta omega 2 、Δx 1 、Δx 2 、Δx 3 、Δx 4 、Δi ldq2 、Δu odq2 And Δi odq2 ；
The small signal model of the power system is as follows:
wherein a=diag [ a ] GFM ,Α GFL ,A SG ]A state matrix complete for the system; the small signal model of the power system includes 28 state variables.
10. The method of modeling a small signal in an electrical power system including a heterogeneous power source of claim 1, further comprising:
and determining at least one of the influence of the new energy permeability change on the system stability, the influence of the network transformer permeability change on the system stability, the influence of the virtual moment of inertia change on the system stability and the influence of the virtual impedance change on the system stability according to the small signal model of the power system.
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