CN109659930B - VSG-IIDG-containing power system transient stability analysis method based on energy function - Google Patents

VSG-IIDG-containing power system transient stability analysis method based on energy function Download PDF

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CN109659930B
CN109659930B CN201811537169.5A CN201811537169A CN109659930B CN 109659930 B CN109659930 B CN 109659930B CN 201811537169 A CN201811537169 A CN 201811537169A CN 109659930 B CN109659930 B CN 109659930B
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CN109659930A (en
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卜京
殷明慧
周前
张宁宇
汪成根
刘建坤
焦永辉
龚睿
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Nanjing University of Science and Technology
Electric Power Research Institute of State Grid Jiangsu Electric Power Co Ltd
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Electric Power Research Institute of State Grid Jiangsu Electric Power Co Ltd
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • 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
    • 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
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]

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Abstract

The invention discloses a VSG-IIDG-containing power system transient stability analysis method based on an energy function, which is characterized in that a virtual power angle characteristic curve of an inverter is fitted under different working states, a unified model is presented between the output electromagnetic power of the inverter and a virtual power angle on the premise of not changing the virtual power angle characteristic, the inverter is enabled to output power according to the fitted virtual power angle characteristic curve, and finally a system energy function constructed according to the electromagnetic power calculated by fitting strictly meets the condition of Delaunaov and can be used for correctly judging whether the system is stable or not. The system energy function constructed by the method has negative qualitative property, can correctly judge the system stability, and has important significance for analyzing the transient stability of the system containing the VSG strategy inverter.

Description

VSG-IIDG-containing power system transient stability analysis method based on energy function
Technical Field
The invention relates to an inverter transient stability analysis technology, in particular to a VSG-IIDG-containing power system transient stability analysis method for an energy function.
Background
A Distributed Generation (DG) is mainly merged into a large power grid through a power electronic converter such as an inverter, the traditional inverter cannot provide necessary voltage support and frequency support for the power grid and can not provide a damping effect required by the system, the introduction of a Virtual Synchronous Generator (VSG) technology enables the problems to be well solved, however, the inverter generally has a current limiting control link, and when the inverter current reaches a saturation state under large interference, the inverter fades to be a current source, so that not only can the transient process of the inverter become more complex, but also the virtual power angle characteristic of the inverter can be changed, and further the energy function of the system is influenced.
Therefore, it is necessary to study the transient stability of the inverter under the VSG strategy.
Disclosure of Invention
The invention aims to provide an energy function-based VSG-IIDG-containing power system transient stability analysis method, which solves the problem that when inverter current is saturated under a VSG strategy, the system total energy function is suddenly changed and the Lyapunov condition is not met due to sudden change of system magnetic potential energy caused by change of virtual power angle characteristics.
The technical scheme for realizing the purpose of the invention is as follows: a VSG-IIDG-containing power system transient stability analysis method based on an energy function comprises the following steps:
step 1, modeling the virtual power angle characteristic of an inverter, and determining the virtual power angle characteristic curve of the inverter when a system respectively works in two working states of current unsaturated state and current saturated state;
step 2, fitting the virtual power angle characteristic curves of the inverter in two working states, replacing the virtual power angle characteristic curves in the two original states with the virtual power angle characteristic curves after fitting calculation, enabling the inverter to output power along the characteristic curves after fitting calculation on the premise of not changing the virtual power angle characteristic, and then solving an inverter power output equation corresponding to the fitting curves;
step 3, solving the magnetic potential energy of the system by using the fitted and calculated electromagnetic power equation of the inverter, and calculating the virtual rotor position potential energy, the virtual rotor kinetic energy, the load node potential energy and the loss potential energy to further solve the total energy of the system;
and 4, respectively calculating the system energy and the critical energy of the system when the system is subjected to fault removal by using the energy function equation after power fitting, comparing the system energy and the critical energy, and judging whether the system is stable after disturbance is applied.
Compared with the prior art, the invention has the remarkable advantages that: according to the method, the virtual power angle characteristics of the inverter in different working states in the transient process are fitted, so that the power output of the inverter has a uniform function equation, the constructed system energy function has negative nature, and the system stability can be correctly judged.
Drawings
Fig. 1 is a flowchart of an analysis of transient stability of an inverter under a VSG policy.
Fig. 2 is a graph of the inverter virtual power angle characteristic.
Fig. 3 is a comparison graph before and after virtual power angle curve fitting.
Fig. 4 is a system energy comparison graph before and after inverter power fitting calculation.
Fig. 5 is a comparison graph of stability criteria before and after inverter power fitting calculation.
Detailed Description
The method takes an inverter-infinite system as a research object, takes the inverter adopting a VSG strategy as a generator, and the rotor angle of the generator is called a virtual power angle; then fitting the virtual power angle characteristic curves in the two working states, so that the inverter outputs power according to the fitted power angle characteristic curves to obtain a fitting equation of the output power of the inverter; calculating the magnetic potential energy function of the system by using the equation, and solving the total energy function of the system; and finally, respectively calculating the energy and critical energy of the system during interference elimination by using the constructed energy function so as to judge whether the system is stable.
As shown in fig. 1, a method for analyzing transient stability of a power system including a VSG-IIDG based on an energy function includes the following steps:
step 1, modeling the virtual power angle characteristic of an inverter, and determining the virtual power angle characteristic curve of the inverter when a system is in two working states of current unsaturated and current saturated respectively;
step 2, fitting the virtual power angle characteristic curves of the inverter in two working states, replacing the virtual power angle characteristic curves in the two original states with the virtual power angle characteristic curves after fitting calculation, enabling the inverter to output power along the characteristic curves after fitting calculation on the premise of not changing the virtual power angle characteristic, and then solving an inverter power output equation corresponding to the fitting curves;
step 3, solving the magnetic potential energy of the system by using the fitted and calculated electromagnetic power equation of the inverter, and calculating the position potential energy of the virtual rotor, the kinetic energy of the virtual rotor, the potential energy of the load nodes and the depletion potential energy so as to solve the total energy of the system;
and 4, respectively calculating the system energy and the critical energy of the system when the system is subjected to fault removal by using the energy function equation after power fitting, comparing the system energy and the critical energy, and judging whether the system is stable after large disturbance is applied.
Further, in step 1, a power angle characteristic equation of the inverter under two conditions of current unsaturated and saturation is obtained by modeling the virtual power angle characteristic of the inverter;
when the current is not saturated, the power angle characteristic equation of the inverter is as follows:
Figure BDA0001907174930000031
where V is the inverter output voltage when the inverter current is not saturated, U is the voltage on the infinite power grid side, δ' is the inverter virtual power angle, and X∑Is the reactance, P, between the inverter and the infinite networkumIs the most current unsaturated stateHigh electromagnetic power, PEIs the inverter electromagnetic power;
when the current is saturated, the power angle characteristic equation of the inverter is as follows:
Figure BDA0001907174930000032
in the formula ImaxFor maximum limiting current of inverter, PsmThe maximum electromagnetic power in the current saturation state;
at the boundary point of current saturation and non-saturation, the system has a corresponding virtual work angle delta'mWhen the virtual power angle of the inverter is less than delta'mWhen the inverter works along the unsaturated virtual power angle characteristic curve; when the virtual power angle of the inverter is greater than delta'mWhen the inverter works along the saturated virtual power angle characteristic curve; therefore, considering the current clipping loop, the inverter electromagnetic power characteristic equation is:
Figure BDA0001907174930000033
further, in step 2, fitting a virtual power angle characteristic curve of the inverter in two operating states, that is: the working point of the system is switched between an unsaturated virtual power angle characteristic curve and a saturated virtual power angle characteristic curve in the swing process, the two power angle curves are fitted into a smooth characteristic curve under the condition that the original characteristics are not changed basically, the curve is used for replacing the original virtual power angle characteristic curve of the system, the power value is slightly changed only at the intersection point of the two curves, and the electromagnetic power of the system is basically unchanged before and after the fitting at other points.
The function equation corresponding to the fitting curve is a 16-degree function about the virtual power angle delta', and the fitted electromagnetic power equation is as follows:
Pp(δ′)＝k16δ′16+...knδ′n+...k1δ′+k0(n＝1,2...16) (4)
in the formula (I), the compound is shown in the specification,knis Pp(δ') n-degree term coefficient.
Further, in the step 3, calculating the magnetic potential energy of the system by using an electromagnetic power equation corresponding to the fitted curve, and solving other energy of the system;
after the power fitting calculation, the calculation formula of the magnetic potential energy is as follows:
Figure BDA0001907174930000041
due to Pp(δ ') is a 16 th order function with respect to δ', obviously Pp(δ') can be integrated at any point, then the magnetic potential energy of the system calculated by the formula (5) becomes a continuous function and does not generate mutation due to current saturation;
the total energy of the system is then:
Figure BDA0001907174930000042
in the above formula, Ta.iIs the inertia time constant, omega, of the ith virtual rotornIs nominal angular frequency, ω'iIs the rotor angular frequency of the ith virtual synchronous generator delta'iRepresents a virtual power angle delta 'of the ith virtual synchronous generator'i.sTable i virtual power angle, P, of virtual synchronous generator in steady state0.iIs the output power of the inverter in steady state (corresponding to the mechanical power of the synchronous generator), λiDamping influence factor, k, for the ith virtual synchronous generatorPIs the droop control coefficient (corresponding to the damping coefficient of the synchronous generator), V, of the inverterk、Vrp、VDRespectively virtual rotor kinetic energy, virtual rotor position potential energy and loss potential energy generated due to damping of the system.
Further, in step 4, respectively substituting the parameters of the system during interference elimination and the parameters of the unstable balance point of the system into a formula (6), calculating the system energy and the critical energy of the system during interference elimination, and comparing the system energy and the critical energy to judge whether the system is stable; the method comprises the following specific steps:
solving the system energy and the critical energy of the system when the interference is removed, comparing the two energies and judging whether the system is stable; system energy V at interference ablationclIs calculated by dividing the parameters
Figure BDA0001907174930000051
(i.e., the system parameter at the time of interference removal) into equation (6), and the critical energy VcrIs calculated by dividing the parameters
Figure BDA0001907174930000052
(i.e., the unstable equilibrium point corresponding to the saturated virtual power angle curve) is substituted into equation (6). If Vcl＞VcrThe system is not stable; if Vcl≤VcrThe system will stabilize.
The invention discloses a VSG-IIDG-containing power system transient stability analysis method based on an energy function, which discusses the influence of a current saturation link on the energy function of a system aiming at the virtual power angle characteristics of an inverter under the two conditions of current unsaturation and current saturation under a VSG strategy, and provides a method for fitting and calculating the output power of the inverter under two running states, so that the energy function of the system conforms to the Lyapunov function after power fitting and calculation. And the system energy and critical energy of the system during the large interference removal are calculated according to the reconstructed energy function, and the stability of the system is accurately judged.
For an inverter adopting a VSG strategy, although the transient characteristic of the inverter is similar to that of a synchronous generator, due to the introduction of a current saturation link, a system has a virtual power angle characteristic different from that of the synchronous generator under large interference, so that an energy function of the system does not have negative characteristics, and misjudgment on whether the system is stable or not in a transient process is likely to be caused. For the problem, a method for performing fitting calculation on the output power of the inverter is provided, namely the inverter is fitted with a virtual power angle characteristic curve under different working states, on the premise that the virtual power angle characteristic is not changed basically, the output electromagnetic power of the inverter and the virtual power angle are represented by a unified model, the inverter is enabled to perform power output according to the fitted virtual power angle characteristic curve, and finally, a system energy function constructed according to the fitted calculated electromagnetic power strictly meets the Lyapunov condition and can be used for correctly judging whether the system is stable or not.
The present invention will be described in detail below with reference to examples and the accompanying drawings.
Examples
A VSG-IIDG-containing power system transient stability analysis method based on an energy function comprises the following steps:
firstly, modeling the virtual power angle characteristic of the inverter to obtain a power angle characteristic equation of the inverter under two conditions of current non-saturation and current saturation, wherein the expression is as follows:
Figure BDA0001907174930000061
wherein V is the inverter output voltage when the inverter current is not saturated, U is the voltage on the infinite power grid side, and X∑Is the reactance between the inverter and the infinite power network, ImaxThe maximum output current of the Norton equivalent current source is changed by the inverter after the current is saturated.
At the boundary point of current saturation and non-saturation, the system has a corresponding virtual power angle δ'mWhen the virtual power angle of the inverter is less than delta'mWhen the inverter works along the unsaturated virtual power angle characteristic curve; when the virtual power angle of the inverter is greater than delta'mAnd when the inverter works along the saturated virtual power angle characteristic curve.
Secondly, fitting the virtual power angle characteristic curves of the inverter in two working states, as shown in fig. 2: the curve OABCD is a virtual power angle characteristic curve under two different working states, the curve OAB is an unsaturated virtual power angle characteristic curve, the curve BCD is a saturated virtual power angle characteristic curve which is formed by combining two curves, the curve OABCD is fitted into a smooth characteristic curve under the condition that the original characteristics are not changed basically, the curve is used for replacing the original virtual power angle characteristic curve of the system, the electromagnetic power of the system at the point B only slightly changes, and the electromagnetic power of the system at other points is basically unchanged before and after fitting.
To ensure sufficient fitting accuracy, the function equation corresponding to the fitting curve can be a 16-degree function of the virtual work angle δ'. The fitted electromagnetic power equation is then:
Pp(δ′)＝k16δ′16+...knδ′n+...k1δ′+k0(n＝1,2...16) (8)
in the formula, knIs Pp(δ') n-degree term coefficient.
And thirdly, calculating the magnetic potential energy of the system by using the inverter output power equation obtained by fitting calculation. The formula is as follows:
Figure BDA0001907174930000071
due to Pp(δ ') can be integrated for any δ', so the magnetic potential energy of the system obtained by the formula (9) is a continuous function and cannot be suddenly changed due to the change of the virtual work angle curve. Then the total energy of the system will be a function of:
Figure BDA0001907174930000072
in the above formula, TaIs the inertia time constant of the virtual rotor, omeganAt a nominal angular frequency, P0Is the output power of the inverter in steady state (corresponding to the mechanical power of the synchronous generator), λ is the damping influence factor of the inverter, kPIs the droop control coefficient (corresponding to the damping coefficient of the synchronous generator), V, of the inverterk、Vrp、VDRespectively, the virtual rotor kinetic energy, the virtual rotor position potential energy and the loss potential energy generated by damping of the system.
And fourthly, solving the system energy and the critical energy of the system when the large interference is removed, comparing the system energy and the critical energy and judging whether the system is stable.
System energy V during large interference removalclIs calculated by dividing the parameters
Figure BDA0001907174930000073
(i.e. δ'c、ω′cVirtual power angle and rotor angular acceleration at large disturbance removal) is substituted for formula (10), and critical energy VcrIs calculated by using the parameters
Figure BDA0001907174930000074
(δ′uI.e., the unstable equilibrium angle corresponding to the saturated virtual power angle curve) is substituted into equation (10). If Vcl＞VcrThe system is not stable; if Vcl≤VcrThe system will stabilize.
According to the virtual power angle transient energy function analysis method, fitting calculation of inverter power basically does not change an original virtual power angle characteristic curve, but fits an original piecewise curve into a smooth and continuous virtual power angle characteristic curve, and magnetic potential energy and total energy of a system are calculated according to a power equation obtained through fitting calculation, as shown in fig. 3. It can be seen from fig. 4 that the energy function distribution of the system is obviously different before and after the fitting of the output power of the inverter, the magnetic potential energy and the total energy of the system are suddenly changed before the fitting calculation, and the energy distribution diagram of the system obtained after the fitting calculation is strictly monotonically decreased, so that the system meets the lyapunov condition. According to fig. 5, a misjudgment of the system stability may occur before the power fitting calculation is performed, and whether the system is stable or not may be accurately judged after the power fitting calculation.
Therefore, the power output equation of the inverter under two working conditions of current unsaturation and current saturation is fitted into one equation, and the method has important significance for analyzing the transient stability of the system by using an energy function method.

Claims (1)

1. A VSG-IIDG-containing power system transient stability analysis method based on an energy function is characterized by comprising the following steps:
step 1, modeling the virtual power angle characteristic of an inverter, and determining the virtual power angle characteristic curve of the inverter when a system respectively works in two working states of current unsaturated state and current saturated state; the method comprises the following specific steps:
obtaining a power angle characteristic equation of the inverter under two conditions of current non-saturation and current saturation by modeling the virtual power angle characteristic of the inverter;
when the current is not saturated, the power angle characteristic equation of the inverter is as follows:
Figure FDA0003602225990000011
where V is the inverter output voltage when the inverter current is not saturated, U is the voltage on the infinite power grid side, delta is the inverter virtual power angle, and X is∑Is the reactance, P, between the inverter and the infinite networkumMaximum electromagnetic power in the current non-saturated state, PEIs the inverter electromagnetic power;
when the current is saturated, the power angle characteristic equation of the inverter is as follows:
Figure FDA0003602225990000012
in the formula ImaxFor maximum limiting current of inverter, PsmThe maximum electromagnetic power in the current saturation state;
at the boundary point of current saturation and non-saturation, the system has a corresponding virtual work angle delta'mWhen the virtual power angle of the inverter is less than delta'mWhen the inverter works along the unsaturated virtual power angle characteristic curve; when the virtual power angle of the inverter is greater than delta'mWhen the inverter works along the saturated virtual power angle characteristic curve; therefore, when the current clipping link is considered, the electromagnetic power characteristic equation of the inverter is as follows:
Figure FDA0003602225990000013
step 2, fitting the virtual power angle characteristic curves of the inverter in two working states, replacing the virtual power angle curves in the two original states with the virtual power angle characteristic curves subjected to fitting calculation, enabling the inverter to carry out power output along the characteristic curves subjected to fitting calculation on the premise of not changing the virtual power angle characteristics, and then solving an inverter power output equation corresponding to the fitting curves;
and (3) enabling a function equation corresponding to the fitting curve to be a 16-order function related to the virtual power angle delta', wherein the fitted electromagnetic power equation is as follows:
Pp(δ′)＝k16δ′16+...knδ′n+...k1δ′+k0 (4)
in the formula, knIs Pp(δ') n-degree coefficient, n being 1,2.. 16;
step 3, solving the magnetic potential energy of the system by using the fitted and calculated electromagnetic power equation of the inverter, and calculating the position potential energy of the virtual rotor, the kinetic energy of the virtual rotor, the potential energy of the load node and the consumption potential energy to further solve the total energy of the system;
after the power fitting calculation, the calculation formula of the magnetic potential energy is as follows:
Figure FDA0003602225990000021
due to Pp(δ ') is a 16 th order function with respect to δ', Pp(delta') can be integrated at any point, the magnetic potential energy of the system calculated by the formula (5) becomes a continuous function and cannot be suddenly changed due to current saturation; the total energy of the system is formulated as:
Figure FDA0003602225990000022
in the above formula, Ta.iIs the inertia time constant, omega, of the ith virtual rotornIs nominal angular frequency, ω'iIs the rotor angular frequency, delta 'of the ith virtual synchronous generator'iRepresents a virtual power angle delta 'of the ith virtual synchronous generator'i.sTable i virtual power angle, P, of virtual synchronous generator in steady state0.iIs the output power of the inverter in steady state, lambdaiDamping influence factor, k, for the ith virtual synchronous generatorPIs a droop control coefficient, V, of the inverterk、Vrp、VDRespectively the virtual rotor kinetic energy, the virtual rotor position potential energy and the loss potential energy generated by damping of the system;
step 4, respectively calculating system energy and system critical energy when the system is subjected to fault removal by using an energy function equation after power fitting, comparing the system energy and the system critical energy, and judging whether the system is stable after disturbance is applied; the method comprises the following specific steps:
and (3) respectively substituting the parameters of the system during interference elimination and the parameters of the unstable balance point of the system into an equation (6), calculating the system energy and the critical energy of the system during interference elimination, and comparing the system energy and the critical energy to judge whether the system is stable.
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