CN114498734A - System frequency characteristic quantitative evaluation method considering frequency secondary falling - Google Patents

System frequency characteristic quantitative evaluation method considering frequency secondary falling Download PDF

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CN114498734A
CN114498734A CN202111676291.2A CN202111676291A CN114498734A CN 114498734 A CN114498734 A CN 114498734A CN 202111676291 A CN202111676291 A CN 202111676291A CN 114498734 A CN114498734 A CN 114498734A
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吴琛
辛焕海
张雯欣
黄伟
高晖胜
程旻
谢一工
张丹
曾丕江
黄润
刘旭斐
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Yunnan Power Grid Co Ltd
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Abstract

The invention relates to a system frequency characteristic quantitative evaluation method considering frequency secondary falling, and belongs to the technical field of power system frequency modulation. The method comprises the steps of firstly, considering power disturbance delta P in a multi-machine power system comprising power generation equipmentL(s) overall system frequency response characteristics and individual power plant power response Δ Pe(s) a relationship with the frequency-active transfer function g(s) of each power generation device; the overall frequency response characteristic of the system is expressed by frequency common-mode component delta omega(s); aiming at the frequency common-mode component, approximating the power response of each power generation device under disturbance by adopting a differential-proportion-first-order lag structure through an iterative algorithm, and obtaining a frequency modulation capability quantization parameter; by usingAnd calculating a frequency characteristic quantization index by using the obtained frequency modulation capability quantization parameter, and comparing the frequency characteristic quantization index with a frequency characteristic critical value allowed by a system to evaluate the frequency characteristic. The invention determines whether the lowest point of the system frequency and the average change rate of the system frequency meet the requirement of the system frequency modulation by evaluating the frequency characteristics, thereby realizing the frequency modulation.

Description

System frequency characteristic quantitative evaluation method considering frequency secondary falling
Technical Field
The invention belongs to the technical field of power system frequency modulation, relates to a power system frequency characteristic evaluation method, and particularly relates to a system frequency characteristic quantitative evaluation method considering frequency secondary falling.
Background
In recent years, the permeability of new energy such as wind and light in a power system is continuously improved, and the new energy generally runs in a maximum power tracking mode and does not participate in frequency modulation, so that the inertia of the system is reduced, the frequency modulation capability of the system is reduced, and the adverse effect is brought to the frequency stability of the system. Therefore, scholars at home and abroad propose a control strategy for actively participating in frequency modulation in new energy grid connection.
The wind turbine is generally connected to the grid through a converter, and the rotor speed is decoupled from the frequency of the power system. In order to support the frequency by utilizing the kinetic energy in the fan rotor, additional frequency modulation control is required. The fan based on the control can release the kinetic energy of the rotor in the process of supporting the frequency, and the rotating speed is reduced. When the rotor reaches the minimum rotational speed limit, it cannot continue to release kinetic energy to support the system frequency, but instead needs to absorb power from the grid to increase the rotational speed, which may result in a secondary drop in frequency. At present, the frequency modulation parameter of the fan is generally set based on the wind power self-adjustable frequency resource without considering the condition of frequency secondary drop. After the parameters are set, the fan can provide active support for the system as much as possible in the primary frequency drop process, and accordingly, more power needs to be absorbed in the secondary frequency drop process to recover the rotating speed of the rotor. This may cause the lowest point of the secondary fall to be lower than the primary fall, which is not favorable for the frequency stability of the system.
Therefore, in order to provide effective frequency support for the system and meet the actual frequency modulation requirements of the system, the whole frequency dynamic process including primary falling and secondary falling needs to be comprehensively considered. To do this, the whole frequency dynamics process needs to be resolved. Analyzing the frequency dynamics requires combining models of all the power generation equipment in the system, but considering detailed models of each equipment at the same time makes it difficult to resolve the frequency response due to the high number of model orders. Therefore, it is necessary to find a suitable transfer function structure to approximate the model of each power generation equipment to simplify the analysis and to effectively quantitatively evaluate the required frequency characteristics.
Disclosure of Invention
The invention aims to solve the defects of the prior art, effectively evaluate the frequency modulation effect of a wind turbine generator, and provide a system frequency characteristic quantitative evaluation method considering frequency secondary falling.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a system frequency characteristic quantitative evaluation method considering frequency quadratic dropping comprises the following steps:
step (1), in a multi-machine power system comprising power generation equipment, considering power disturbance delta PL(s) overall system frequency response characteristics and individual power plant power response Δ Pe(s) a relationship with the frequency-active transfer function g(s) of each power generation device; the overall frequency response characteristic of the system is expressed by frequency common-mode component delta omega(s);
step (2), aiming at a frequency common-mode component, approximating power response of each power generation device under disturbance by adopting a differential-proportion-first-order lag structure through an iterative algorithm, and obtaining four frequency modulation capability quantization parameters of effective inertia, an effective damping coefficient, an effective static difference modulation coefficient and a system difference modulation time constant;
step (3), calculating a frequency characteristic quantization index by using the frequency modulation capability quantization parameter obtained in the step (2);
and (4) comparing the frequency characteristic quantization index obtained in the step (3) with a frequency characteristic critical value allowed by a system, and evaluating the frequency characteristic.
Further, it is preferable that the power generation facility includes a synchronous machine and a wind turbine.
Further, it is preferable that the specific method of step (1) is:
the multi-machine power system has n devices which can participate in frequency modulation power generation; gi(s) is the frequency-power transfer function i of the ith power generation equipment, belonging to {1, 2.. multidot.n }; delta Pei(s) is the active power generated by the ith power generation equipment; power disturbance of Δ PL(s)，ΔPL(s)＝-ΔPLS, s represents the laplace operator, Δ PL represents the perturbation magnitude;
system frequency common mode component delta omega(s) and power disturbance delta PL(s) the relationship is as follows:
Figure RE-GDA0003455990780000021
further, it is preferable that the specific method of the step (2) is:
the differential-proportional-first order lag structure expression is:
Figure RE-GDA0003455990780000022
in the formula, Ju，DuAnd KuExpressed as effective inertia, effective damping coefficient and effective static adjustment coefficient, T0Adjusting a time constant for the system;
approximate all equipment as differential-proportion-first-order lag structure parameters as a parameter optimization problem, and adopt the following iterative algorithm to obtain four frequency modulation capability quantization parameters of effective inertia, effective damping coefficient, effective static difference-adjusting coefficient and system difference-adjusting time constant:
2.1) setting initial values of inertia parameters, damping parameters, static difference adjustment parameters and difference adjustment time parameters of the differential-proportion-first-order lag structure of each power generation device so as to obtain the initial differential-proportion-first-order lag structure of each device
Figure RE-GDA0003455990780000023
And system initial differential-proportional-first order lag structure
Figure RE-GDA0003455990780000024
Figure RE-GDA0003455990780000025
Figure RE-GDA0003455990780000026
Wherein,
Figure RE-GDA0003455990780000027
and
Figure RE-GDA0003455990780000028
respectively representing initial values of inertia parameters, damping parameters and static difference-adjusting parameters of differential-proportion-first-order lag of each power generation device,
Figure RE-GDA0003455990780000029
expressed as the initial value of the system settling time parameter;
Figure RE-GDA00034559907800000210
respectively represents the initial inertia parameter, the damping parameter and the static adjustment parameter of the system, and meets the requirements
Figure RE-GDA00034559907800000211
SiExpressed as the rated capacity of each power generation equipment;
2.2) making an inner circulation variable r equal to 1; the external circulation variable j is 1;
2.3) at the time of the r iteration, obtaining a frequency track delta omega 'according to the following formula'(r-1)(s)；
Figure RE-GDA0003455990780000031
Wherein,
Figure RE-GDA0003455990780000032
the system differential-proportion-first-order lag structure of the generator at the r-1 iteration is represented; delta omega'(r-1)(s) representing a frequency locus corresponding to the frequency common-mode component of the (r-1) th iteration;
2.4) establishing the following parameter optimization problem:
Figure RE-GDA0003455990780000033
wherein, t0、tfRespectively an initial time and a terminal time, t, of a selected time period 00 is the disturbance initial moment; delta Pi(s) is the frequency-active power transfer function G of the individual power plantsi(s) calculated Power trajectory, Δ Pi'(s) is a differential-proportional-first-order lag structure of each power generation device
Figure RE-GDA0003455990780000034
A calculated power trajectory; power trace Δ Pi(s) obtaining delta P by inverse Ralstonian transformationi(t), Power Trace Δ P'i(s) obtaining delta P by inverse Ralstonian transformationi′(t)；
Solving the optimization problem by least square method to obtain parameters
Figure RE-GDA0003455990780000035
And
Figure RE-GDA0003455990780000036
2.5) making r be r +1, circularly carrying out the steps 2.2) to 2.4) until the parameters are converged, and recording the obtained equivalent parameters; the equivalent parameter is
Figure RE-GDA0003455990780000037
2.6) exiting the internal circulation to enter the external circulation to order
Figure RE-GDA0003455990780000038
2.7) making j equal to j +1, and circularly performing the steps 2.2) to 2.7) until an optimal value appears, so as to obtain the equivalent parameter of the unified structure
Figure RE-GDA0003455990780000039
Further, it is preferable that t isfIs set to 4tnadir，tnadirThe time when the frequency trace reaches the lowest point; the value range of delta T is-0.5.
Further, it is preferable that the specific method of step (3) is:
the approximate frequency-time domain analysis formula is:
Figure RE-GDA00034559907800000310
in the formula,
Figure RE-GDA0003455990780000041
wherein, Jus1、Dus1、1/Kus1Expressed as the effective coefficient of the unified structure of the system when the wind turbine generator participates in frequency modulation, Jus2、Dus2、1/Kus2The coefficient is expressed after the wind turbine generator quits frequency modulation; the effective coefficients of all the power generation equipment in the system are obtained in the step (2), and the effective coefficients J of the system are obtained by superposition (summation)us1、 Dus1、1/Kus1；Jus2、Dus2、1/Kus2The system effective coefficient is the system effective coefficient after the wind power equivalent coefficient is removed; omegad1、ωd2Respectively representing the damping oscillation frequency of the system frequency in the process of primary falling and secondary falling; sigma1、σ2Respectively representing the attenuation coefficients of the system frequency in the processes of primary falling and secondary falling; t is t1Indicating the time for the wind turbine generator to exit from frequency modulation; delta PL1Represents t1Disturbance of system input power at any moment;
the frequency characteristic index includes frequency change rate
Figure RE-GDA0003455990780000042
Frequency one-time falling lowest point delta omega1maxAnd frequency secondary fall minimum Δ ω2maxObtained using the following formula:
Figure RE-GDA0003455990780000043
Figure RE-GDA0003455990780000044
Figure RE-GDA0003455990780000045
in the formula,
Figure RE-GDA0003455990780000046
wherein, tp2maxThe moment of occurrence of the quadratic maximum frequency deviation; e is a natural constant, nt＝tp1max/tp1，tp1maxFor the occurrence of a maximum frequency deviation time tp1Represents the time 0t after the occurrence of the disturbancep1The time node used by the average change rate of the internal frequency.
Further, it is preferable that the specific method of step (4) is:
obtained according to step (3)The obtained frequency characteristic index is as follows: frequency one-time falling lowest point delta omega1maxFrequency secondary falling lowest point delta omega2maxAnd average rate of change of frequency
Figure RE-GDA0003455990780000051
Frequency characteristic evaluation is carried out on the three indexes; the method specifically comprises the following steps:
4.1) frequency feature nadir assessment:
when the obtained | Δ ω is calculated1max|、|Δω2maxAll of which are less than the system's allowable frequency minimum threshold | Δ ωmax_cWhen |, the lowest point of the system frequency meets the requirement of system frequency modulation, and enters 4.2); otherwise, the formula is not satisfied;
4.2) frequency rate of change assessment:
when calculated, the result is
Figure RE-GDA0003455990780000052
Less than the system's allowable threshold for the average rate of change of frequency
Figure RE-GDA0003455990780000053
And if so, the average change rate of the system frequency meets the requirement of the system frequency modulation, otherwise, the average change rate does not meet the requirement of the system frequency modulation.
In the invention, when initial values of inertia parameters, damping parameters, static difference adjustment parameters and difference adjustment time parameters of the differential-proportion-first-order lag structure of each power generation device are set, no specific limitation is provided, and the initial values can be set at will.
Compared with the prior art, the invention has the beneficial effects that:
the invention can approximately cover the frequency response of various power generation equipment in the power system in the process of frequency secondary falling by using a very simple structure of a differential-proportion-first-order lag structure, and has higher precision because the frequency track is considered in the process of obtaining parameters; based on an inertia-damping-integral first-order lag structure, the characteristics of a first frequency lowest point, a second frequency lowest point, an average change rate and the like can be well obtained, and the dynamic frequency characteristics involved in the frequency second falling process caused by frequency modulation of the wind turbine generator are effectively evaluated and considered; and by evaluating the frequency characteristics, whether the lowest point of the system frequency and the average change rate of the system frequency meet the frequency modulation requirement of the system is determined, so that the frequency modulation is realized.
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FIG. 1 is a schematic flow diagram of the process of the present invention.
Fig. 2 is a schematic diagram of a three-machine system in simulation verification according to an embodiment of the present invention.
FIG. 3 is a diagram of a steam turbine governor system model in simulation verification according to an embodiment of the present invention.
Fig. 4 is a control diagram of the wind turbine generator power in simulation verification according to the embodiment of the present invention.
FIG. 5 is a comparison graph of simulation trajectory and approximate trajectory of differential-proportional-first-order lag structure in simulation verification according to an embodiment of the present invention; wherein, (a) is a simulation track and differential-proportion-first-order lag structure approximate track comparison graph under the condition that the wind turbine generator does not participate in frequency modulation in simulation verification of the embodiment of the invention; (b) the simulation of the embodiment of the invention verifies the comparison graph of the simulation track and the approximate track of the differential-proportional-first-order lag structure under the condition that the wind generating set participates in frequency modulation.
FIG. 6 is an iterative flow diagram for solving an optimization problem.
Detailed Description
The present invention will be described in further detail with reference to examples.
It will be appreciated by those skilled in the art that the following examples are illustrative of the invention only and should not be taken as limiting the scope of the invention. The examples do not specify particular techniques or conditions, and are performed according to the techniques or conditions described in the literature in the art or according to the product specifications. The materials or equipment used are not indicated by manufacturers, and all are conventional products available by purchase.
1) In a multi-machine power system including power generation equipment (e.g., synchronizers, wind turbines, etc.), power disturbances Δ P are consideredL(s) overall system frequency response characteristics (frequency common mode component) Δ ω(s) and power response Δ P of each power generation equipmente(s) a relationship with the frequency-active transfer function g(s) of each power generation device;
2) aiming at frequency common mode components, approximating power response under disturbance of each power generation device by adopting a differential-proportion-first-order lag structure (namely a uniform structure) through an iterative algorithm to obtain an approximate power track, and obtaining four parameters of effective inertia, an effective damping coefficient, an effective static difference adjustment coefficient and a system difference adjustment time constant;
3) establishing a frequency characteristic quantization index by using the frequency modulation capability quantization parameter;
4) obtaining a system frequency characteristic quantification result by utilizing a frequency characteristic index calculation formula, comparing the system frequency characteristic quantification result with a frequency characteristic critical value allowed by the system, and evaluating the frequency characteristic;
in the step 1), the multi-machine power system has n pieces of frequency modulation power generation equipment (if the dynamic response of equipment such as loads and the like is considered, the equipment is regarded as a special generator); establishing the overall frequency response characteristic (frequency common mode component) delta omega(s) and the power disturbance delta P of the systemL(s) the relationship is as follows:
Figure RE-GDA0003455990780000061
in the formula, Gi(s) is the frequency-power transfer function i of the ith power generation equipment, belonging to {1, 2.. multidot.n }; delta Pei(s) is the active power generated by the ith power generation equipment; the power disturbance (such as sudden load increase) is delta PL(s)，ΔPL(s)＝-ΔPLS, s denotes the Laplace operator, Δ PLRepresenting the magnitude of the disturbance;
in the step 2), the differential-proportional-first-order lag structure is as follows:
Figure RE-GDA0003455990780000062
in the formula, Ju，DuAnd KuExpressed as effective inertia, effective damping coefficient and effective static adjustment coefficient, T0Adjusting a time constant for the system;
approximate all equipment as differential-proportion-first-order lag structure parameters as a parameter optimization problem, and adopt the following iterative algorithm to obtain four frequency modulation capability quantization parameters of effective inertia, effective damping coefficient, effective static difference-adjusting coefficient and system difference-adjusting time constant:
2.1) setting inertia parameters, damping parameters, static difference adjustment parameters and initial values of difference adjustment time parameters of the differential-proportion-first-order lag structure of each power generation device, and calculating the initial differential-proportion-first-order lag structure of each device
Figure RE-GDA0003455990780000063
And system initial differential-proportional-first order lag structure
Figure RE-GDA0003455990780000064
Figure RE-GDA0003455990780000065
Figure RE-GDA0003455990780000066
Wherein,
Figure RE-GDA0003455990780000067
and
Figure RE-GDA0003455990780000068
respectively representing initial values of inertia parameters, damping parameters and static difference-adjusting parameters of differential-proportion-first-order lag of each power generation device,
Figure RE-GDA0003455990780000071
expressed as the initial value of the system settling time parameter;
Figure RE-GDA0003455990780000072
Figure RE-GDA0003455990780000073
respectively represents the initial inertia parameter, the damping parameter and the static adjustment parameter of the system, and meets the requirements
Figure RE-GDA0003455990780000074
SiExpressed as a per-unit value of the rated capacity of each power generation device;
2.2) making an inner circulation variable r equal to 1; the external circulation variable j is 1;
2.3) at the time of the r iteration, obtaining a frequency track delta omega 'according to the following formula'(r-1)(s)；
Figure RE-GDA0003455990780000075
Wherein,
Figure RE-GDA0003455990780000076
the system differential-proportion-first-order lag structure of the generator at the r-1 iteration is represented; delta omega'(r-1)(s) representing a frequency locus corresponding to the frequency common-mode component of the (r-1) th iteration;
2.4) establishing the following parameter optimization problem:
Figure RE-GDA0003455990780000077
wherein t is0、tfRespectively an initial time and a terminal time, t, of a selected time period 00 is the initial time of disturbance, tfIs generally selected to be 4tnadir，tnadirThe moment when the frequency trace reaches the lowest point; delta Pi(s) is the frequency-active power transfer function G of the individual power plantsi(s) calculated Power trajectory, Δ Pi'(s) is a differential-proportional-first-order lag structure of each power generation device
Figure RE-GDA0003455990780000078
A calculated power trajectory; power trace Δ Pi(s) obtaining delta P by inverse Ralstonian transformationi(t), Power Trace Δ P'i(s) obtaining delta P by inverse Ralstonian transformationi′(t)；
Solving the optimized objective function by a least square method to obtainParameter(s)
Figure RE-GDA0003455990780000079
And
Figure RE-GDA00034559907800000710
2.5) making r ═ r +1, circularly carrying out steps 2.2) to 2.4) until the parameters are converged, and recording the equivalent parameters
Figure RE-GDA00034559907800000711
2.6) exiting the internal circulation to enter the external circulation to order
Figure RE-GDA00034559907800000712
The value range of delta T is-0.5, (firstly, the optimal T is searched by using larger delta T0Interval of possible occurrence, search in optimum interval with smaller Δ T)
2.7) making j equal to j +1, and circularly performing the steps 2.2) to 2.7) until an optimal value appears, so as to obtain the equivalent parameter of the unified structure
Figure RE-GDA00034559907800000713
In the step 3), the approximate frequency trajectory under the step disturbance can be obtained according to the unified structure parameters solved by the iterative optimization:
Figure RE-GDA0003455990780000081
in the formula, Jus，DusAnd KusRespectively expressed as the effective inertia, effective damping coefficient and effective static difference coefficient of the system, T0The system settling time constant is obtained.
If the wind turbine generator unit exits frequency modulation after the system frequency modulation for a period of time, the unified structure parameters of the system and the input power disturbance of the system are changed. Definition Jus1、Dus1、1/Kus1The effective coefficient of the system is unified when the wind turbine generator participates in frequency modulation, Jus2、Dus2、1/Kus2Is t1Coefficient of the wind turbine generator after exiting frequency modulation at the moment; the effective coefficients of all the power generation equipment in the system obtained in the step 2) are superposed to form the effective coefficient J of the systemus1、Dus1、1/Kus1；Jus2、Dus2、1/Kus2The system effective coefficient is the system effective coefficient after the wind power equivalent coefficient is removed; delta PL1Is t1The disturbance magnitude of the system input power at the moment, and t0Magnitude of power disturbance Δ P at timeLThe rotating speed recovery strategy adopted when the wind turbine generator quits frequency modulation is related; if the wind turbine generator adopts a constant output electromagnetic power recovery rotating speed strategy, the wind turbine generator is at t1Variation Δ P of electromagnetic power output at a timew(t1)＝ΔPm(t1)-ΔPd，ΔPm(t1) For wind turbine at t1Change in mechanical power, Δ P, input at a timedTo define the power difference, satisfy Δ PL1＝ΔPL+ΔPd+ΔPm(t1)。
An approximate frequency time domain analytical formula considering that the wind turbine generator participates in frequency modulation and quits the frequency modulation can be obtained through a state space solution:
Figure RE-GDA0003455990780000082
in the formula,
Figure RE-GDA0003455990780000083
wherein, ω isd1、ωd2、σ1、σ2Respectively representing the damping oscillation frequency and the damping coefficient in the process of primary falling and secondary falling of the system frequency; t is t1Indicating the time for the wind turbine generator to exit from frequency modulation;
if a double-fed wind turbine generator is adopted, the wind turbine generator input mechanical power expression is as follows:
Figure RE-GDA0003455990780000091
in the formula, rho and R, v are respectively air density, wind wheel radius and undisturbed wind speed; cp(λ, β) is a wind energy utilization coefficient, and includes:
Figure RE-GDA0003455990780000092
wherein, lambda and beta are respectively the tip speed ratio and the pitch angle, omegarExpressed as wind turbine rotor speed; coefficient c1～c8Satisfies the following conditions:
c1＝0.5176、c2＝116、c3＝0.4、c4＝5、c5＝21、c6＝0.0068、c7＝0.08、c8＝0.035 。
the evaluated frequency characteristics include frequency rate of change
Figure RE-GDA0003455990780000093
Frequency dip minimum Δ ω1maxAnd frequency secondary fall minimum Δ ω2maxThe following formula can be used to approximate:
Figure RE-GDA0003455990780000094
Figure RE-GDA0003455990780000095
Figure RE-GDA0003455990780000096
in the formula,
Figure RE-GDA0003455990780000097
wherein, tp2maxAt the moment of the secondary maximum frequency deviation, the secondary frequency drop is caused because the wind turbine generator quits frequency modulation and absorbs the power difference caused by active power to the power grid; e is a natural constant parameter, nt＝tp1max/tp1Expressed as the number of segments, t, that segment from the time of occurrence of the disturbance to the time of maximum deviation of the frequency during the calculation of the rate of change of the frequencyp1maxFor the occurrence of a maximum frequency deviation time tp1Indicating that the time 0t after the disturbance occursp1The time node used by the average change rate of the internal frequency.
In the step 4), the obtained frequency characteristic index is the frequency one-time falling lowest point delta omega1maxFrequency secondary falling lowest point delta omega2maxAnd average rate of change of frequency
Figure RE-GDA0003455990780000098
And (3) evaluating the related frequency characteristics by using the indexes:
(1) performing frequency feature minimum point assessment:
when the obtained | Δ ω is calculated1max|、|Δω2maxAll of | is less than the system allowable frequency minimum threshold (maximum amplitude) | Δ ωmax_cAnd when the absolute value is greater than the absolute value, the lowest point of the system frequency meets the requirement of system frequency modulation.
(2) Frequency rate of change evaluation: when calculated, the result is
Figure RE-GDA0003455990780000101
Less than the system's allowable frequency average change rate threshold (maximum amplitude)
Figure RE-GDA0003455990780000102
And meanwhile, the average change rate of the system frequency meets the requirement of system frequency modulation.
Examples of the applications
As shown in FIG. 1, the method of the invention is adopted to process, and the power generation equipment in a multi-machine power system comprises a synchronous machine, a wind turbine generator and the like. Combining the frequency-active transfer function matrix G(s) of each power generation device to obtain power disturbanceDynamic delta PL(s) is related to the overall frequency response of the system Δ ω(s). And then, each power generation device is converted into a differential-proportion-first-order lag structure by adopting an iterative algorithm, and four parameters of an approximate key track, effective inertia, effective damping, effective static adjustment and a system adjustment time constant are obtained. And finally, obtaining frequency characteristics by using the parameters and evaluating the frequency characteristics of the system.
The specific embodiment of the invention is as follows:
a three-machine power system is built in Matlab/Simulink software, as shown in FIG. 2. In the figure, the capacity of the synchronizers G1 and G2 at the nodes 1 and 2 are respectively 200MVA and 100MVA, and the prime movers adopt steam turbines. The capacity of the double-fed wind turbine generator WTG3 at the node 3 is 100 MVA. The nodes 4-6 are network nodes. The nodes 7-9 are load nodes, and the load is a constant power load. The network nodes and the load nodes are collectively referred to as constant power nodes. The line purity is expressed in table 1 when the capacity of G2 is used as a capacity reference value. In a steady state, the voltage of each node is converted into 1, and the phase angle difference of each line is converted into 0.
Table 1 example line reactance values in simulation verification
X14 0.05 X25 0.15 X36 0.05
X47 0.1 X48 0.1 X57 0.2
X59 0.2 X68 0.1 X69 0.1
Using the capacity of G2 as a capacity reference value, F is ═ F1,F2,F3]T＝[2,1,1]T。FiThe capacity ratio of each power generation device;
g1 frequency-active transfer function G1(s) is
G1(s)＝F1g1(s)
g1(s)＝J1s+D1+GTS(s)
Figure RE-GDA0003455990780000103
Wherein G isTS1(s) is the transfer function of the G1 governor-turbine system (simply referred to as the governor system), the model is shown in FIG. 3. The parameters per unit of the rated capacity are as follows: moment of inertia J 18; damping coefficient D 12; the rate of decrease R is 0.05; time constant T of speed regulatorG0.2 s; time constant T of steam inlet chamberCH0.3 s; time constant T of reheaterRH10 s; high pressure cylinder power ratio FHP＝0.3。
G2 frequency-active transfer function G2(s) is
G2(s)＝F2g2(s)
g2(s)＝J2s+D2+GTS2(s)
Figure RE-GDA0003455990780000111
Wherein GTS2(s) is the transfer function of the G2 governor system, the model being shown in FIG. 4. The parameters per unit of the rated capacity are as follows: moment of inertia J 28; damping coefficient D 22; rate of decrease R20.05; time constant T of speed regulatorG20.2 s; time constant T of steam inlet chamberCH20.3 s; time constant T of reheaterRH25 s; high pressure cylinder power ratio FHP2＝0.3。
The wind turbine generator set adopts a DFIG model as shown in figure 4, wherein V issqThe component of the q axis of the voltage at the stator side of the wind turbine generator is obtained; the PLL is a phase-locked loop; omegarefIs the rated value of the angular frequency of the power grid; omegagIs the grid angular frequency; omegarThe rotating speed of the rotor of the wind turbine generator set; kJAs a virtual coefficient of inertia, KDIs the sag factor; t is1Is a filtering link time constant; pMPPTThe active power reference value obtained by the MPPT curve; p isinAnd PdpAdditional active reference value components generated for virtual inertia and droop control respectively; prefIs the reference value of active power, P, of the wind turbineWTThe wind power generates electromagnetic power; delta PdAnd the difference value of the mechanical power and the electromagnetic power at the moment of exiting the frequency modulation.
Frequency-active transfer function G on electromechanical scale3(s) is
G3(s)＝F3g3(s)
Figure RE-GDA0003455990780000112
The values of the parameters are shown in table 2.
Table 2 parameter values of part of inverter variables in simulation verification of embodiment
Figure RE-GDA0003455990780000113
Figure RE-GDA0003455990780000121
By adopting the method of the invention, a relational expression of disturbance and frequency response is obtained:
Figure RE-GDA0003455990780000122
when a 50MW power disturbance occurs at node 8. As shown in fig. 6, for the frequency common mode component, the time range within 8s after disturbance is selected to convert each power generation device into a differential-proportional-first-order lag structure, so as to obtain an approximate frequency trajectory. The calculation results are shown in table 3, respectively.
TABLE 3 differential-proportional-first order lag structural parameters for each power plant
Uniform structure equivalent parameter G1 G2 WTG3
T
0 5 5 5
Jui 13.8820 6.7205 0.9368
Dui 11.5372 5.8186 15.9726
1/Kui 23.4344 16.6141 0.03710
According to the method of the invention, the frequency characteristics are obtained by using the effective parameters. According to calculation, the system frequency common mode lowest point of the wind turbine generator set under two working conditions of not participating in frequency modulation and participating in frequency modulation appears 2-4 s after disturbance, and n is taken when calculating the comprehensive inertiatI.e. the average rate of frequency change is calculated with a time of about several hundred milliseconds after the perturbation. The system requires a frequency minimum threshold of 0.8Hz and a frequency average change rate threshold of 0.9 Hz/s. The comparison and evaluation results of the calculated frequency average change rate and the frequency first and second lowest point frequency characteristics with the frequency characteristics obtained in the time domain simulation are shown in table 4.
TABLE 4 evaluation of frequency dynamics and comparison results
Figure RE-GDA0003455990780000123
Figure RE-GDA0003455990780000131
According to the simulation result, the relative error between the theoretical frequency primary falling lowest point and the primary falling frequency lowest point in system simulation is within 3.5 percent, the relative error between the secondary falling frequency lowest point is within 1.5 percent, and the relative error of the frequency change rate is within 3 percent; the result shows that the established unified structure model and the system effective parameter calculation method can accurately analyze the overall frequency characteristic of the system in a long period of time and calculate the required frequency support dynamic frequency characteristic, and effectively evaluate the system frequency dynamic support effect after the wind turbine generator is connected to the grid.
The example of the invention proves the effectiveness of the approximate method of the overall frequency track of the multi-machine power system comprising the wind turbine generator and the like and the quantitative evaluation method of the system frequency characteristics, and the established parameters can evaluate the frequency characteristics such as the average change rate of the frequency, the primary and secondary minimum points and the like.
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (7)

1. A system frequency characteristic quantitative evaluation method considering frequency quadratic drop is characterized by comprising the following steps:
step (1), in a multi-machine power system comprising power generation equipment, considering power disturbance delta PL(s) overall system frequency response characteristics and individual power plant power response Δ Pe(s) a relationship with the frequency-active transfer function g(s) of each power generation device; the overall frequency response characteristic of the system is expressed by frequency common-mode component delta omega(s);
step (2), aiming at a frequency common-mode component, approximating power response of each power generation device under disturbance by adopting a differential-proportion-first-order lag structure through an iterative algorithm, and obtaining four frequency modulation capability quantization parameters of effective inertia, an effective damping coefficient, an effective static difference modulation coefficient and a system difference modulation time constant;
step (3), calculating a frequency characteristic quantization index by using the frequency modulation capability quantization parameter obtained in the step (2);
and (4) comparing the frequency characteristic quantization index obtained in the step (3) with a frequency characteristic critical value allowed by a system, and evaluating the frequency characteristic.
2. The system frequency characteristic quantitative evaluation method considering frequency secondary droop according to claim 1, wherein the power generation equipment comprises a synchronous machine and a wind turbine generator.
3. The system frequency characteristic quantitative evaluation method considering frequency quadratic dip according to claim 1, wherein the specific method in step (1) is as follows:
the multi-machine power system has n devices which can participate in frequency modulation power generation; gi(s) is the frequency-power transfer function i of the ith power generation equipment, which belongs to {1,2, …, n }; delta Pei(s) is the active power generated by the ith power generation equipment; power disturbance of Δ PL(s)，ΔPL(s)＝-ΔPLS, s denotes the Laplace operator, Δ PLRepresenting the magnitude of the disturbance;
system frequency common mode component delta omega(s) and power disturbance delta PL(s) the relationship is as follows:
Figure FDA0003451420510000011
4. the method for evaluating the frequency characteristics of the system considering the frequency secondary droop according to claim 3, wherein the specific method in the step (2) is as follows:
the differential-proportional-first order lag structure expression is:
Figure FDA0003451420510000012
in the formula, Ju，DuAnd KuRespectively expressed as effective inertia, effective damping coefficient and effective static difference coefficient, T0Adjusting a time constant for the system;
approximate all equipment as differential-proportion-first-order lag structure parameters as a parameter optimization problem, and adopt the following iterative algorithm to obtain four frequency modulation capability quantization parameters of effective inertia, effective damping coefficient, effective static difference-adjusting coefficient and system difference-adjusting time constant:
2.1) setting initial values of inertia parameters, damping parameters, static difference adjustment parameters and difference adjustment time parameters of the differential-proportion-first-order lag structure of each power generation device so as to obtain the initial differential-proportion-first-order lag structure of each device
Figure FDA0003451420510000021
And system initial differential-proportional-first order lag structure
Figure FDA0003451420510000022
Figure FDA0003451420510000023
Figure FDA0003451420510000024
Wherein,
Figure FDA0003451420510000025
and
Figure FDA0003451420510000026
respectively representing initial values of inertia parameters, damping parameters and static difference-adjusting parameters of differential-proportion-first-order lag of each power generation device,
Figure FDA0003451420510000027
expressed as the initial value of the system settling time parameter;
Figure FDA0003451420510000028
Figure FDA0003451420510000029
respectively represents the initial inertia parameter, the damping parameter and the static adjustment parameter of the system, and meets the requirements
Figure FDA00034514205100000210
SiExpressed as the rated capacity of each power generation equipment;
2.2) making an inner circulation variable r equal to 1; the external circulation variable j is 1;
2.3) at the time of the r iteration, obtaining a frequency track delta omega 'according to the following formula'(r-1)(s)；
Figure FDA00034514205100000211
Wherein,
Figure FDA00034514205100000212
the system differential-proportion-first-order lag structure of the generator at the r-1 iteration is represented; delta omega'(r-1)(s) representing a frequency locus corresponding to the frequency common-mode component of the (r-1) th iteration;
2.4) establishing the following parameter optimization problem:
Figure FDA00034514205100000213
wherein, t0、tfRespectively an initial time and a terminal time, t, of a selected time period00 is the disturbance initial moment; delta Pi(s) is the frequency-active power transfer function G of the individual power plantsi(s) calculated Power trajectory, Δ Pi'(s) is a differential-proportional-first-order lag structure of each power generation device
Figure FDA0003451420510000031
A calculated power trajectory; power trace Δ Pi(s) obtaining delta P by inverse Ralstonian transformationi(t), Power Trace Δ P'i(s) obtaining delta P by inverse Ralstonian transformationi′(t)；
Solving the optimization problem by least square method to obtain parameters
Figure FDA0003451420510000032
And
Figure FDA0003451420510000033
2.5) making r be r +1, circularly carrying out the steps 2.2) to 2.4) until the parameters are converged, and recording the obtained equivalent parameters; the equivalent parameter is
Figure FDA0003451420510000034
2.6) exiting the internal circulation to enter the external circulation to order
Figure FDA0003451420510000035
2.7) making j equal to j +1, and circularly performing the steps 2.2) -2.7) until an optimal value appears, so as to obtain the equivalent parameter of the unified structure
Figure FDA0003451420510000036
The unified structure is a differential-proportion-first-order lag structure.
5. The method of claim 4, wherein t is the frequency characteristic of the systemfIs set to 4tnadir，tnadirThe moment when the frequency trace reaches the lowest point; the value range of delta T is-0.5.
6. The method for evaluating the frequency characteristics of the system considering the frequency secondary droop according to claim 4, wherein the specific method in the step (3) is as follows:
the approximate frequency-time domain analysis formula is:
Figure FDA0003451420510000037
in the formula,
Figure FDA0003451420510000038
wherein, Jus1、Dus1、1/Kus1Expressed as the effective coefficient of the unified structure of the system when the wind turbine generator participates in frequency modulation, Jus2、Dus2、1/Kus2The coefficient is expressed after the wind turbine generator quits frequency modulation; omegad1、ωd2Respectively representing the damping oscillation frequency of the system frequency in the process of primary falling and secondary falling; sigma1、σ2Respectively representing the attenuation coefficients of the system frequency in the processes of primary falling and secondary falling; t is t1Indicating the time for the wind turbine generator to exit from frequency modulation; delta PL1Represents t1Disturbance of system input power at the moment;
the frequency characteristic index includes frequency change rate
Figure FDA0003451420510000041
Frequency one-time falling lowest point delta omega1maxAnd frequency secondary fall minimum Δ ω2maxObtained using the following formula:
Figure FDA0003451420510000042
Figure FDA0003451420510000043
Figure FDA0003451420510000044
in the formula,
Figure FDA0003451420510000045
wherein, tp2maxThe moment of occurrence of the quadratic maximum frequency deviation; e is a natural constant, nt＝tp1max/tp1，tp1maxFor the occurrence of a maximum frequency deviation time tp1Indicating that the time 0t after the disturbance occursp1The time node used by the average change rate of the internal frequency.
7. The method for quantitatively evaluating the frequency characteristics of the system in consideration of the frequency quadratic dip according to claim 6, wherein the specific method in the step (4) is as follows:
according to the obtained frequency characteristic index obtained in the step (3): frequency one-time falling lowest point delta omega1maxFrequency secondary falling lowest point delta omega2maxAnd average rate of change of frequency
Figure FDA0003451420510000046
Frequency characteristic evaluation is carried out on the three indexes; the method specifically comprises the following steps:
4.1) frequency feature nadir assessment:
when the obtained | Δ ω is calculated1max|、|Δω2maxAll of which are less than the system's allowable frequency minimum threshold | Δ ωmax_cWhen |, the lowest point of the system frequency meets the requirement of system frequency modulation, and enters 4.2); otherwise, the formula is not satisfied;
4.2) frequency rate of change assessment:
when calculated, the result is
Figure FDA0003451420510000051
Less than the system's allowable threshold for the average rate of change of frequency
Figure FDA0003451420510000052
And if so, the average change rate of the system frequency meets the requirement of the system frequency modulation, otherwise, the average change rate does not meet the requirement of the system frequency modulation.
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Publication number Priority date Publication date Assignee Title
CN117293860A (en) * 2023-09-28 2023-12-26 暨南大学 Frequency safety index evaluation method, system and storage medium of power system

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117293860A (en) * 2023-09-28 2023-12-26 暨南大学 Frequency safety index evaluation method, system and storage medium of power system
CN117293860B (en) * 2023-09-28 2024-04-23 暨南大学 Frequency safety index evaluation method, system and storage medium of power system

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