CN114021786A - System frequency lowest point prediction model construction method for random production simulation demand - Google Patents

System frequency lowest point prediction model construction method for random production simulation demand Download PDF

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CN114021786A
CN114021786A CN202111238972.0A CN202111238972A CN114021786A CN 114021786 A CN114021786 A CN 114021786A CN 202111238972 A CN202111238972 A CN 202111238972A CN 114021786 A CN114021786 A CN 114021786A
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李卫东
李梓锋
张娜
张明理
徐熙林
潘霄
李铁
高靖
杨博
赵琳
李芳�
满林坤
王义贺
王忠辉
李金起
刘禹彤
杨朔
刘凯
王宗元
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Dalian University of Technology
State Grid Corp of China SGCC
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Abstract

A system frequency lowest point prediction model construction method for random production simulation requirements is applied to a rapid frequency response standby planning problem. Firstly, based on a thermal power multi-machine aggregation method, parameter aggregation of multiple types of machine sets is realized through expansion of hydroelectric and gas machine sets, and a frequency response multi-resource system frequency dynamic process analysis model is established; representing the dynamic change process of the unit frequency by the characteristics of the unit speed regulator to realize the practical simplification and analysis of the model from a high order to a low order; and the frequency dynamic tracking from the default system steady state to the element initial state is completed by taking the system working condition as zero state input, so that the misjudgment of the stable situation is avoided and the system operation safety is better ensured. According to the method, through analytic simplification and consideration of the initial operation state of the element, the established model can give consideration to both calculation precision and calculation speed, and the method is suitable for the problem of rapid frequency response standby planning.

Description

System frequency lowest point prediction model construction method for random production simulation demand
Technical Field
The invention belongs to the field of power grid frequency stability control, and relates to a construction method of a system frequency lowest point prediction model for random production simulation requirements.
Background
The new energy grid-connected quantity of the power system is continuously improved under the double-carbon target, and the characteristics of high permeability and high power electronization are more remarkable. The system frequency response problem under the condition of high thermal power occupation ratio is not outstanding, but because the new energy unit does not have the inertia of the traditional unit, the whole high-proportion new energy system has the characteristics of low inertia and low frequency response capability, and the accident severity is upgraded suddenly. The traditional fixed coefficient standby reservation scheme is relatively lagged under a new frequency stabilization situation, the problem of 'double low' under a 'double high' power system is solved, the capability of improving the quick frequency response of the system is urgent, the demand of reasonably evaluating the quick frequency response standby under the new situation is urgently needed, and the dynamic characteristic of the system frequency is accurately grasped. The rapid frequency response is added for standby, the frequency modulation capability of the system can be accurately improved, a planning scheme is formulated according to the body and clothes, and the stable operation of the system can be ensured.
The current standby planning scheme is obtained, namely, a unit state and an unbalance load aggregate are obtained based on random production simulation, economic benefits are measured by making up the power shortage by standby capacity through system reliability analysis, and a fault data set which is hundreds of thousands of years is simply algebraic addition or subtraction on the calculated power shortage. The fast frequency response standby type is added, namely the static power shortage is concerned to be shifted to the dynamic process of the focusing frequency. Because the frequency drop situation in the system second level is most obvious, the rapid frequency response capability is considered in the planning scheme, and a frequency dynamic process must be included in the random production simulation system state so as to clarify the interception capability of the system resource capacity and the response speed to the power loss event. In the recovery process after the power system suffers power disturbance, the lowest point of the frequency directly reflects the severity of the accident and is also the basis of control decision in the actual engineering. Therefore, a system frequency dynamic process analysis should be added in the new random production simulation, and the lowest point in the frequency dynamic process after the system is disturbed is used as one of the bases for whether the planning scheme is feasible or not.
The existing models default to initial working condition rating, and the system frequency difference is default to zero as a main index of the operation working condition. However, in actual operation, the lowest point of the system frequency depends on the initial working condition of the system, if the initial value in the calculation process still adopts the rated frequency, and the obtained result is used as the system stability criterion, the situation of system safety and stability may be misjudged (for example, the system frequency instability may be caused by the occurrence of a fault with a small scale when the system frequency is already in low-order operation), and further the system operation safety is threatened. In addition, because the traditional analytic method can only represent the system frequency change state after disturbance, the method release with response delay cannot be described, and whether delay exists in the release process from the disturbance to the frequency response method or not can result in quite different frequency response results. Therefore, it is necessary to add the system initial state (under the nonstandard frequency) on the basis of the original zero state model to construct a full response model.
Disclosure of Invention
Aiming at the problems, the invention provides a system frequency lowest point prediction model facing to random production simulation requirements, which is applied to the problem of rapid frequency response standby planning, aims at the problems that the traditional frequency lowest point prediction model is rated by default in an initial working condition, is easy to cause misjudgment on the safety and stability situation of a system so as to threaten the operation safety of the system, and cannot be drawn by putting means with response delay.
The technical scheme adopted by the invention is as follows:
a method for constructing a system frequency lowest point prediction model for random production simulation requirements comprises the following steps:
step 1: frequency response model parameter aggregation
The Aggregation System Frequency Response (ASFR) obtaining method based on weighted average can scientifically simplify different types of Multi-machine thermal power units into single machines, reduce the model order, expand the method from thermal power to Multi-Resource units such as water power and gas power, and provide ideas for the construction of an MR-SFR (Multi-Resource System Frequency Response) model on parameter aggregation.
Difference adjustment coefficient 1/R of multi-machine hydroelectric ASFR modelhCan be defined as:
Figure BDA0003318603130000021
wherein, 1/RhiFor the ith unit adjustment coefficient, KhiThe unit capacity of the ith unit accounts for the ratio, N is the total number of the on-line units, khiIs the equivalent gain parameter of the ith set.
Normalized gain (single-unit ratio) lambda of single-unit branchhiComprises the following steps:
Figure BDA0003318603130000022
wherein, the sum of the standardized gains of each unit accords with the following formula:
Figure BDA0003318603130000023
the model aggregation time constant may be defined as:
Figure BDA0003318603130000024
in the formula: y represents a set of model time constants, TwRepresenting the inertia time constant, T, of the hydroelectric generating setyRepresents the servomotor response time constant, TRSRepresenting the reset time of the governor, TRHRepresenting the transient droop time constant of the governor, YiRepresenting a certain type of time constant value in the ith unit set.
The polymerization process and method of the gas turbine set are the same as above.
Step 2: constructing a low-order frequency response model
The first-order inertia link describes that the SFR open-loop model of the gas turbine set constructed by the characteristics of the speed regulator has low order and high precision, the primary frequency modulation of the system is the process that the speed regulator of the gas turbine set senses the frequency difference of the system and then the valve acts to change the output power of the prime motor, and the open-loop processing of the frequency response model can be carried out on the basis of considering the characteristics of the speed regulator. The method is considered to be applied to thermal power generating units and hydroelectric generating units.
The method comprises the steps of fitting the characteristics of water, fire and gas units through speed regulators, solving fitting parameters based on a least square method, further realizing first-order inertia representation of unit performance, describing the energy storage unit participating in frequency modulation through a first-order inertia link to obtain an MR-SFR open loop structure represented by the characteristics of the speed regulators, connecting the speed regulators of various resource units in parallel, and representing a frequency response process (shown in figure 1) at the resource side of a system, wherein delta P is definedGiThe active power of each resource type unit is represented, and the complex frequency domain of the calculation mode is expressed as follows:
Figure BDA0003318603130000031
in the formula: kiFitting the power frequency static characteristic coefficient for the same type of resources; t isiFitting the response time constant for the same type of resources;Δf is the frequency offset of the whole system, and s is the complex frequency independent variable of the complex frequency domain expression.
The change rule of the system frequency after the power disturbance is generated conforms to the following formula:
Figure BDA0003318603130000032
in the formula (I), the compound is shown in the specification,
Figure BDA0003318603130000033
represents the analytical derivation of the system frequency f with respect to time t; Δ f (t) is a differentiated frequency approximation expression; h is an inertia time constant;ΔPLperturbing the load of the system; m isΔfThe initial attenuation slope of the frequency after the system is subjected to power disturbance is shown.
The formula (6) is brought into the formula (5) and inverse Laplace transformation is adopted to obtain the system output active power delta PGTime domain expression, where e is the natural index:
Figure BDA0003318603130000034
combining with the MR-SFR open loop structure characterized by the characteristic of the speed regulator, an SFR time domain expression of the system after suffering power disturbance can be obtained:
Figure BDA0003318603130000035
and step 3: constructing a full response model
The system components including the load side resources can be regarded as sufficiently large inductive elements, the energy charging and discharging are complicated to be a non-zero state response process, the dynamic process calculation after the SFR model simplification keeps high precision, if the initial state of the system elements is not considered when the system suffers power disturbance and the default system initial frequency deviation is zero, the actual frequency trajectory of the system can be greatly misjudged, a full-response SFR model considering the initial operation working condition is established, and the load side resource response process with time delay is accurately described.
Based on the output power equation of the generator set in the formula (5) in the step 1, obtaining by adopting Laplace inverse transformation:
Figure BDA0003318603130000041
if the initial state P of the system prime motor energy is taken into account in the process of converting the equation (9) from the time domain to the complex frequency domainGi(0-) New active power of each resource type unit can be obtainedΔPGiComplex frequency domain expression:
Figure BDA0003318603130000042
the term added by equation (10) compared to equation (5) is that the initial state is added based on the zero state response, and thus the power component is changed.
The known rotor equation of motion is:
Figure BDA0003318603130000043
in the formula (I), the compound is shown in the specification,ΔPais the difference between the acceleration power, i.e. the mechanical power, and the load power; d is the system damping coefficient.
The analysis of the frequency components requires that Laplace inverse transformation is carried out on the formula (11) to obtain:
Figure BDA0003318603130000044
if the initial state of the kinetic energy of the rotor of the system is taken into account in the process of converting the equation (12) from the time domain to the complex frequency domain, the initial state is consideredΔf(0-) To obtain newΔf complex frequency domain expression:
Figure BDA0003318603130000045
one of the terms that equation (13) adds to equation (11) is that the initial state is added to the zero state response and thus the rotor description is changed.
According to the superposition theorem, the full response model is initialized by the power component and the frequency component (P)Gi(0-)、Δf(0-) Zero input response induced and externally excited by power and frequency components: (ΔPL、Δf) And (3) the two parts of the induced zero state response form, and a system full response open loop structure based on first-order inertia link description can be obtained by combining the MR-SFR open loop structure of the characteristic representation of the speed regulator obtained in the step 1.
The time domain analytic expression of the zero state response component in the full response model is described by the expressions (9) and (12), and the influence of the load damping on the system frequency is ignored in the process of the analytic calculation of the MR-SFR zero input response component because the influence of the load damping on the system frequency change before the frequency lowest point appears is small.
Taking into account only PGi(0-) A complex frequency domain expression can be obtained according to the full response process:
Figure BDA0003318603130000051
the initial state P of only considering the system prime motor energy can be obtained through Laplace inverse transformationGi(0-) The zero-input response time domain expression of (1):
Figure BDA0003318603130000052
when only taking into accountΔf(0-) According to the full response process, a complex frequency domain expression can be obtained:
Figure BDA0003318603130000053
the initial state of the kinetic energy of the rotor of the system can be considered only through Laplace inverse transformationΔf(0-) The zero-input response time domain expression of (c):
Figure BDA0003318603130000054
the zero-input time domain analytic expression considering the initial state of the system energy can be obtained by superposing the expression (15) and the expression (17):
Figure BDA0003318603130000055
the system full-response time domain analytic expression can be obtained by superposing the zero-state time domain analytic expression of the expression (8) and the expression (18):
Figure BDA0003318603130000056
and 4, step 4: calculating system frequency nadir
Single machine simplification of similar resources can be obtained through aggregation of system parameters in the step 1, on the basis, the model order is further reduced through fitting of a first-order inertia link in the step 2, in the step 3, the full response state of the system is considered on the basis of simplifying the model, so that the model is more consistent with the actual system operation condition, and the analytic model obtained through the 3 steps can provide a model basis for calculating the lowest point of the frequency in the step. The above processes are all based on solving the frequency downward exploration severity, so as to realize frequency dynamic analysis, wherein the lowest point of the frequency directly represents the threat degree to the system, and therefore, the established full response model needs to be further analyzed and solved.
Make the speed regulator of the ith unit fit parameters
Figure BDA0003318603130000057
I set of units full response component parameter
Figure BDA0003318603130000058
Let t be tminTime of flight
Figure BDA0003318603130000061
If the system frequency reaches the lowest point, equation (19) can be summarized as:
Figure BDA0003318603130000062
then there are:
Figure BDA0003318603130000063
when P in formula (21)Gi(0-)、Δf(0-) When all are 0, tminThe expression of (c) can be organized as:
Figure BDA0003318603130000064
the above equation is the time to reach the minimum frequency without considering the initial state. It can be seen that t is not considered in the initial stateminAnd power disturbanceΔPLIndependent of the characteristics of the system itself. But after considering the initial state, tminNot only with respect to the characteristics of the unit itself, but also with respect to power disturbancesΔPLAnd initial stateΔf(0-) And PGi(0-) And (4) correlating. Where δ (t) is the unit impulse function, so that the component is at t>When 0 takes the value zero, i.e. tminAndΔf(0-) Item independent, tminOnly with PGi(0-) And the characteristics of the unit.
Wherein Ci, Bi, tminThe MR-SFR full response models are all to-be-solved quantities, 2N +1 unknown quantities are counted, and therefore 2N +1 order equation sets are established for solving:
Figure BDA0003318603130000065
by integrating the two ends of equation (19), the method can be usedTo obtainΔf, full response model time domain expression:
Figure BDA0003318603130000066
substituting equation (6) into the above equation gives:
Figure BDA0003318603130000071
in the formula (25)Δf (t) perturbed by powerΔPLThe resulting frequency offset and an initial state characterizing the kinetic energy of the rotor of the systemΔf(0-) Two parts.
Solving the equation set to obtain a result tminThe maximum frequency deviation of the system can be obtained by substituting formula (20)ΔfmaxAnd further calculating the famous frequency lowest point f of the system subjected to power disturbancemin。
fmin＝f0-fB·Δfmax (26)
Wherein f is0Representing the initial frequency before the system is disturbed, fBRepresenting the reference frequency of the system.
The impact time is considered to be 0 in the above equation, and for the description of the system load side response and continuous disturbance, the full response expression can be rewritten to be t from the first disturbance occurrence0The latter frequency response procedure:
Figure BDA0003318603130000072
and 5: based on the 4 steps, a system frequency lowest point prediction model facing random production simulation requirements is obtained. The frequency lowest point modeling and resolving process is shown in fig. 2, and can provide a frequency dynamic tracking means and an accident severity evaluation basis for a random production simulation process, better grasp the frequency response characteristics of the system, and provide a necessary analysis method for rapid frequency response backup planning.
The invention has the beneficial effects that: in the preparation of the rapid frequency response standby planning scheme, the random production simulation needs frequency stability analysis of mass operation modes and needs rapid analysis and calculation. Therefore, a system multi-resource full-response frequency lowest point prediction analysis model based on the superposition theorem is provided, and rapid analysis and analysis of a frequency dynamic process can be realized. The invention has the following characteristics: 1) the full response is considered. The initial state of system elements is taken into consideration, the misjudgment of the system frequency change track caused by the default system standard working condition is avoided, the defect that the traditional analytic method cannot take secondary power disturbance (support) into account is overcome, and the method has better adaptability. 2) The calculation speed is high. Because the order of the polymerization reduction model is irrelevant to the number of the units and the system capacity, the advantage of the polymerization reduction model in the aspect of solving speed is more prominent compared with the traditional simulation method along with the further expansion of the system scale. 3) The solving precision is high. Although multiple steps such as parameter aggregation and first-order inertia link fitting are carried out, the advantages of the system in the aspect of solving precision are shown by the calculation examples of the system under the conditions of power deficiency and load side response support.
Drawings
FIG. 1 is a schematic diagram of a system open loop based on a first-order inertial element description;
FIG. 2 is a flow chart of a full response MR-SFR modeling;
FIG. 3 is a simulation of the power system load loss for a year;
FIG. 4 shows the maximum frequency difference result of the simulation method;
FIG. 5 shows the maximum frequency difference result of the full response analysis;
fig. 6 is a comparison of error distributions.
Detailed Description
The invention will be further described with reference to the accompanying drawings and specific embodiments, but is not intended to be limited thereto.
A system frequency lowest point prediction model construction method facing random production simulation requirements comprises the following steps:
step 1: frequency response model parameter aggregation
The Aggregation System Frequency Response (ASFR) solving method based on weighted average can scientifically simplify different types of Multi-machine thermal power units into single machines, reduces the model order, expands the method from thermal power to Multi-Resource units such as water power and gas power, and can provide ideas for the construction of MR-SFR models on parameter aggregation.
Difference adjustment coefficient 1/R of multi-machine hydroelectric ASFR modelhCan be defined as:
Figure BDA0003318603130000081
wherein, 1/RhiFor the ith unit adjustment coefficient, KhiThe unit capacity of the ith unit accounts for the ratio, N is the total number of the on-line units, khiIs the equivalent gain parameter of the ith set.
Normalized gain (single-unit ratio) lambda of single-unit branchhiComprises the following steps:
Figure BDA0003318603130000082
wherein, the sum of the standardized gains of each unit accords with the following formula:
Figure BDA0003318603130000083
the model aggregation time constant may be defined as:
Figure BDA0003318603130000084
in the formula: y represents a set of model time constants, TwRepresenting the inertia time constant, T, of the hydroelectric generating setyRepresents the servomotor response time constant, TRSRepresenting the reset time of the governor, TRHRepresenting the transient droop time constant of the governor, YiRepresenting the ith unit setA certain type of time constant value. The polymerization process and method of the gas turbine set are the same.
Step 2: constructing a low-order frequency response model
The first-order inertia link describes that the SFR open-loop model of the gas turbine set constructed by the characteristics of the speed regulator has low order and high precision, the primary frequency modulation of the system is the process that the speed regulator of the gas turbine set senses the frequency difference of the system and then the valve acts to change the output power of the prime motor, and the open-loop processing of the frequency response model can be carried out on the basis of considering the characteristics of the speed regulator. The method is considered to be applied to thermal power generating units and hydroelectric generating units.
The method comprises the steps of fitting the characteristics of water, fire and gas turbine units through speed regulators, solving fitting parameters based on a least square method, further realizing first-order inertia representation of the unit performance, describing the energy storage unit participating in frequency modulation by adopting a first-order inertia link to obtain an MR-SFR open loop structure represented by the characteristics of the speed regulators, wherein delta P is shown in figure 1GiThe active power of each resource type unit is represented, and the complex frequency domain of the calculation mode is expressed as follows:
Figure BDA0003318603130000091
in the formula: kiFitting the power frequency static characteristic coefficient for the same type of resources; t isiFitting the response time constant for the same type of resources;Δf is the frequency offset of the whole system, and s is the complex frequency independent variable of the complex frequency domain expression.
The change rule of the system frequency after the power disturbance is generated conforms to the following formula:
Figure BDA0003318603130000092
in the formula (I), the compound is shown in the specification,
Figure BDA0003318603130000093
represents the analytical derivation of the system frequency f with respect to time t; Δ f (t) is a differentiated frequency approximation expression; h is inertiaA time constant of sex;ΔPLperturbing the load of the system; m isΔfThe initial attenuation slope of the frequency after the system is subjected to power disturbance is shown.
Substituting the formula (6) into the formula (5) and obtaining the system output active power delta P by adopting Laplace inverse transformationGTime domain expression, where e is the natural index:
Figure BDA0003318603130000094
combining with the MR-SFR open loop structure characterized by the characteristic of the speed regulator, an SFR time domain expression of the system after suffering power disturbance can be obtained:
Figure BDA0003318603130000095
and step 3: constructing a full response model
The system components including the load side resources can be regarded as sufficiently large inductive elements, the energy charging and discharging are complicated to be a non-zero state response process, the dynamic process calculation after the SFR model simplification keeps high precision, if the initial state of the system elements is not considered when the system suffers power disturbance and the default system initial frequency deviation is zero, the actual frequency trajectory of the system can be greatly misjudged, a full-response SFR model considering the initial operation working condition is established, and the load side resource response process with time delay is accurately described.
Based on the output power equation of the generator set in the formula (5) in the step 1, obtaining by adopting Laplace inverse transformation:
Figure BDA0003318603130000101
if the initial state P of the system prime motor energy is taken into account in the process of converting the equation (9) from the time domain to the complex frequency domainGi(0-) And then the new active power of each resource type unit is obtainedΔPGiComplex frequency domain expression:
Figure BDA0003318603130000102
the term added by equation (10) compared to equation (5) is that the initial state is added based on the zero state response, and thus the power component is changed.
The known rotor equation of motion is:
Figure BDA0003318603130000103
in the formula (I), the compound is shown in the specification,ΔPais the difference between the acceleration power, i.e. the mechanical power, and the load power; d is the system damping coefficient.
The analysis of the frequency components requires that Laplace inverse transformation is carried out on the formula (11) to obtain:
Figure BDA0003318603130000104
if the initial state of the kinetic energy of the rotor of the system is taken into account in the process of converting the equation (12) from the time domain to the complex frequency domain, the initial state is consideredΔf(0-) To obtain newΔf complex frequency domain expression:
Figure BDA0003318603130000105
one of the terms that equation (13) adds to equation (11) is that the initial state is added to the zero state response and thus the rotor description is changed.
According to the superposition theorem, the full response model is initialized by the power component and the frequency component (P)Gi(0-)、Δf(0-) Zero input response induced and externally excited by power and frequency components: (ΔPL、Δf) The induced zero state response is formed by two parts, and the MR-SFR open loop structure of the characteristic representation of the speed regulator obtained in the step 1 is combined to obtain the speed regulatorTo a system full response open loop structure based on first-order inertia link description.
The time domain analytic expression of the zero state response component in the full response model is described by the expressions (9) and (12), and the influence of the load damping on the system frequency is ignored in the process of the analytic calculation of the MR-SFR zero input response component because the influence of the load damping on the system frequency change before the frequency lowest point appears is small.
Taking into account only PGi(0-) A complex frequency domain expression can be obtained according to the full response process:
Figure BDA0003318603130000111
the initial state P of only considering the system prime motor energy can be obtained through Laplace inverse transformationGi(0-) The zero-input response time domain expression of (1):
Figure BDA0003318603130000112
when only taking into accountΔf(0-) According to the full response process, a complex frequency domain expression can be obtained:
Figure BDA0003318603130000113
the initial state of the kinetic energy of the rotor of the system can be considered only through Laplace inverse transformationΔf(0-) The zero-input response time domain expression of (c):
Figure BDA0003318603130000114
the zero-input time domain analytic expression considering the initial state of the system energy can be obtained by superposing the expression (15) and the expression (17):
Figure BDA0003318603130000115
the system full-response time domain analytic expression can be obtained by superposing the zero-state time domain analytic expression of the expression (8) and the expression (18):
Figure BDA0003318603130000116
and 4, step 4: calculating system frequency nadir
The aggregation of system parameters in the step 1 is based on the fitting of the first-order inertia link in the step 2 and the construction of the full response model in the step 3, so that the dynamic frequency analysis is realized, wherein the lowest point of the frequency directly represents the threat degree to the system, and the established full response model needs to be further analyzed and solved.
Make the speed regulator of the ith unit fit parameters
Figure BDA0003318603130000117
I set of units full response component parameter
Figure BDA0003318603130000118
Let t be tminTime of flight
Figure BDA0003318603130000119
If the system frequency reaches the lowest point, equation (19) can be summarized as:
Figure BDA00033186031300001110
then there is
Figure BDA00033186031300001111
When P in formula (21)Gi(0-)、Δf(0-) When all are 0, tminThe expression of (c) can be organized as:
Figure BDA0003318603130000121
the above equation is the time to reach the minimum frequency without considering the initial state. It can be seen that t is not considered in the initial stateminAnd power disturbanceΔPLIndependent of the characteristics of the system itself. But after considering the initial state, tminNot only with respect to the characteristics of the unit itself, but also with respect to power disturbancesΔPLAnd initial stateΔf(0-) And PGi(0-) And (4) correlating. Where δ (t) is the unit impulse function, so that the component is at t>When 0 takes the value zero, i.e. tminAndΔf(0-) Item independent, tminOnly with PGi(0-) And the characteristics of the unit.
Wherein Ci, Bi, tminThe MR-SFR full response models are all to-be-solved quantities, 2N +1 unknown quantities are counted, and therefore 2N +1 order equation sets are established for solving:
Figure BDA0003318603130000122
by integrating the two ends of equation (19), we can getΔf, full response model time domain expression:
Figure BDA0003318603130000123
substituting equation (6) into the above equation gives:
Figure BDA0003318603130000124
in the formula (25)Δf (t) perturbed by powerΔPLThe resulting frequency offset and an initial state characterizing the kinetic energy of the rotor of the systemΔf(0-) Two parts.
Solving the equation set to obtain a result tminThe maximum frequency deviation of the system can be obtained by substituting formula (20)ΔfmaxAnd further calculating the famous frequency lowest point f of the system subjected to power disturbancemin。
fmin＝f0-fB·Δfmax(26)
Wherein f is0Representing the initial frequency before the system is disturbed, fBRepresenting the reference frequency of the system.
The impact time is considered to be 0 in the above equation, and for the description of the system load side response and continuous disturbance, the full response expression can be rewritten to be t from the first disturbance occurrence0The latter frequency response procedure:
Figure BDA0003318603130000131
and 5: based on the 4 steps, a system frequency lowest point prediction model facing random production simulation requirements is obtained. The frequency lowest point modeling and resolving process is shown in fig. 2, and can provide a frequency dynamic tracking means and an accident severity evaluation basis for a random production simulation process, better grasp the frequency response characteristics of the system, and provide a necessary analysis method for rapid frequency response backup planning.
In the specific embodiment, the frequency lowest point of the full-response MR-SFR solved by the annual random production simulation process is simulated and analyzed as an object to compare the solving speed. After the fault of the system random production simulation occurs, the load side resource with response delay of 1s and the size of 50% of the system load loss amount is set for power support, and the frequency response support effect under the spare capacity is analyzed. Considering the power shortage caused by the unit fault, setting the simulation time to be one year, setting the time interval to be 1h, and setting the time interval to be 8736h all year round, and according to the annual load loss simulation curve of the power system shown in the figure 3, combining the full-response MR-SFR model to complete the frequency lowest point prediction of the multi-resource system facing the random production simulation demand.
FIGS. 4 and 5 correspond to the best simulation and analysis of the full response MR-SFR under the full annual load loss condition of FIG. 3, respectivelyAccording to the large frequency difference comparison result, the frequency difference reference values are all 50Hz, and the distribution and the value of the whole lowest point are relatively consistent. For clearer comparison, the absolute error and the relative error distribution of the two in FIG. 6 were calculated, and the maximum absolute error was-5.6935 x 10-4Hz, the relative error rate taking the simulation method as a reference value is 0.058 percent, which corresponds to a 3257 th sampling point, and the system power shortage of 365.9MW is corresponded to at the moment; the 5814 th sampling point corresponds to a small-probability extreme event that the annual maximum power loss of the system is 865.6MW, and the absolute error of the lowest point of the system frequency is-2.9105 x 10-4The relative error rate of Hz is 0.012%; the maximum predicted relative error rate of the 3239 th sampling point corresponding to the lowest point of the system frequency is 0.089%, and the absolute error is-6.29 x 10-7Hz, the corresponding system power shortage is 263.5kW at the moment, and the frequency lowest point prediction error is relatively large under the condition that the system has small power disturbance. The average absolute error value of the prediction of the lowest point of the overall frequency of the load loss situation at 8736 time intervals in the whole year is-5.9263 x 10-5Hz, the average relative error is 0.014%. In terms of solving speed, in the CPU: under the AMD Ryzen 33200G, the main frequency is 3.60GHz and the memory is 16.00GB, MATLAB R2018b is applied to process 543 load loss points simulated all the year round, the time consumed by a full response analysis method is 258.97s, the time consumed by an original simulation method is 2017.43s, and the speed is increased by 7.79 times.
The preferred method of the present invention is described above. It is to be understood that this invention is not limited to the particular embodiments described above, and that equipment and structures not described in detail are to be understood as being practiced in a manner common to the art; those skilled in the art can make many possible variations and modifications to the disclosed methods and techniques, or modify the equivalents thereof, without departing from the spirit and scope of the invention. Therefore, any simple modification, equivalent change and modification of the above method according to the technical spirit of the present invention will still fall within the protection scope of the technical method of the present invention, unless the technical essence of the present invention departs from the content of the technical method of the present invention.

Claims (1)

1. A system frequency lowest point prediction model building method for random production simulation requirements is characterized by comprising the following steps:
step 1: frequency response model parameter aggregation
Adopting a polymerization system frequency response solving method based on 'weighted average' to construct a multi-resource system frequency response model;
difference adjustment coefficient 1/R of multi-machine hydroelectric ASFR modelhIs defined as:
Figure FDA0003318603120000011
wherein, 1/RhiFor the ith unit adjustment coefficient, KhiThe unit capacity of the ith unit accounts for the ratio, N is the total number of the on-line units, khiEquivalent gain parameters of the ith unit;
normalized gain lambda of a single branchhiComprises the following steps:
Figure FDA0003318603120000012
wherein, the sum of the standardized gains of each unit accords with the following formula:
Figure FDA0003318603120000013
the model polymerization time constant is defined as:
Figure FDA0003318603120000014
in the formula: y represents a set of model time constants, TwRepresenting the inertia time constant, T, of the hydroelectric generating setyRepresents the servomotor response time constant, TRSRepresenting the reset time of the governor, TRHRepresenting speed regulationTransient droop time constant of the device, YiRepresenting a certain time constant value in the ith unit set;
the polymerization process and method of the gas turbine set are the same as described above;
step 2: constructing a low-order frequency response model
The method comprises the steps of fitting the characteristics of water, fire and gas turbine units through speed regulators, solving fitting parameters based on a least square method, realizing first-order inertia representation of unit performance, representing that energy storage units participate in frequency modulation by adopting a first-order inertia link, and obtaining an MR-SFR open loop structure represented by the characteristics of the speed regulators, wherein delta PGiThe active power of each resource type unit is represented, and the complex frequency domain of the calculation mode is expressed as follows:
Figure FDA0003318603120000015
in the formula: kiFitting the power frequency static characteristic coefficient for the same type of resources; t isiFitting the response time constant for the same type of resources; Δ f is the frequency offset of the whole system, and s is the complex frequency independent variable of the complex frequency domain expression;
the change rule of the system frequency after the power disturbance is generated conforms to the following formula:
Figure FDA0003318603120000021
wherein, Δ f (t) is a frequency approximate expression after differentiation; h is an inertia time constant; delta PLPerturbing the load of the system; m isΔfThe initial attenuation slope of the frequency after the system is subjected to power disturbance;
substituting the formula (6) into the formula (5) and obtaining the system output active power delta P by adopting Laplace inverse transformationGTime domain expression, where e is the natural index:
Figure FDA0003318603120000022
combining with the MR-SFR open loop structure characterized by the characteristic of the speed regulator, an SFR time domain expression of the system after suffering power disturbance can be obtained:
Figure FDA0003318603120000023
and step 3: constructing a full response model
Based on the output power equation of the generator set in the formula (5) in the step 1, obtaining by adopting Laplace inverse transformation:
Figure FDA0003318603120000024
if the initial state P of the system prime motor energy is taken into account in the process of converting the equation (9) from the time domain to the complex frequency domainGi(0-) Obtaining the new active power delta P of each resource type unitGiComplex frequency domain expression:
Figure FDA0003318603120000025
the equation of motion of the rotor is:
Figure FDA0003318603120000026
in the formula,. DELTA.PaIs the difference between the acceleration power, i.e. the mechanical power, and the load power; d is a system damping coefficient;
analyzing the frequency components requires performing inverse Laplace transform on equation (11) to obtain:
Figure FDA0003318603120000027
considering the initial state of the kinetic energy of the rotor of the system in the transformation process from the time domain to the complex frequency domain for the formula (12)Filter delta f (0)-) And obtaining a new delta f complex frequency domain expression:
Figure FDA0003318603120000028
according to the superposition theorem, the full response model is initialized by the power component and the frequency component (P)Gi(0-)、Δf(0-) Zero input response and external excitation (Δ P) by power and frequency componentsLDelta f) and zero state response, and the system full response open loop structure based on first-order inertia link description can be obtained by combining the MR-SFR open loop structure of the characteristic representation of the speed regulator obtained in the step 1;
describing a time domain analytic expression of a zero state response component in a full response model through expressions (9) and (12), and neglecting the influence of load damping on system frequency in the process of solving the analytic solution of the MR-SFR zero input response component;
taking into account only PGi(0-) A complex frequency domain expression can be obtained according to the full response process:
Figure FDA0003318603120000031
the initial state P of only considering the system prime motor energy can be obtained through Laplace inverse transformationGi(0-) The zero-input response time domain expression of (1):
Figure FDA0003318603120000032
when only Δ f (0) is taken into account-) According to the full response process, a complex frequency domain expression can be obtained:
Figure FDA0003318603120000033
by inverse Laplace transformOnly the initial state delta f (0) of the kinetic energy of the rotor of the system is considered-) The zero-input response time domain expression of (c):
Figure FDA0003318603120000034
and (5) obtaining a zero-input time domain analytical expression considering the initial state of the system energy by superposing the expression (15) and the expression (17):
Figure FDA0003318603120000035
and (3) superposing the zero-state time domain analysis of the formula (8) and the formula (18) to obtain a system full-response time domain analysis formula:
Figure FDA0003318603120000036
and 4, step 4: calculating system frequency nadir
Make the speed regulator of the ith unit fit parameters
Figure FDA0003318603120000037
I set of units full response component parameter
Figure FDA0003318603120000038
Let t be tminTime of flight
Figure FDA0003318603120000039
When the system frequency reaches the lowest point, equation (19) is:
Figure FDA00033186031200000310
then there are:
Figure FDA00033186031200000311
when P in formula (21)Gi(0-)、Δf(0-) When all are 0, tminThe expression of (a) is:
Figure FDA0003318603120000041
the above equation is the time to reach the minimum frequency without considering the initial state; where δ (t) is the unit impulse function, so that the component is at t>When 0 takes the value zero, i.e. tminAnd Δ f (0)-) Item independent, tminOnly with PGi(0-) The characteristics of the unit are related; wherein Ci, Bi, tminAll the quantities are to-be-solved, and 2N +1 order equation sets are established for solving:
Figure FDA0003318603120000042
integrating two ends of equation (19) to obtain a full response model time domain expression of Δ f:
Figure FDA0003318603120000043
substituting equation (6) into the above equation gives:
Figure FDA0003318603120000044
solving the equation set to obtain a result tminSubstituting formula (20) to obtain the maximum frequency deviation delta f of the systemmaxThe famous value f of the lowest frequency point after the computing system is subjected to power disturbancemin；
fmin＝f0-fB·Δfmax (26)
Wherein f is0Indicating the initial frequency of the system before it is subjected to interference,fBrepresenting the reference frequency of the system;
the impact time is considered to be 0 in the above equation, and for the description of the system load side response and continuous disturbance, the full response expression can be rewritten to be t from the first disturbance occurrence0The latter frequency response procedure:
Figure FDA0003318603120000051
and 5: based on the 4 steps, a system frequency lowest point prediction model facing to the random production simulation requirement is obtained, a frequency dynamic tracking means and an accident severity evaluation basis can be provided facing to the random production simulation process, and the system frequency response characteristic can be grasped.
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114583746A (en) * 2022-02-15 2022-06-03 四川大学 Universal modeling method for predicting lowest frequency point of new energy accessed to power grid
CN116961033A (en) * 2023-09-18 2023-10-27 昆明理工大学 Wind and water through direct current delivery system frequency characteristic analysis method considering generalized load

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114583746A (en) * 2022-02-15 2022-06-03 四川大学 Universal modeling method for predicting lowest frequency point of new energy accessed to power grid
CN114583746B (en) * 2022-02-15 2022-11-25 四川大学 Universal modeling method for predicting lowest frequency point of new energy accessed to power grid
CN116961033A (en) * 2023-09-18 2023-10-27 昆明理工大学 Wind and water through direct current delivery system frequency characteristic analysis method considering generalized load
CN116961033B (en) * 2023-09-18 2023-11-28 昆明理工大学 Wind and water through direct current delivery system frequency characteristic analysis method considering generalized load

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