CN116191473B - Primary frequency modulation standby optimization method considering random-extreme disturbance - Google Patents

Primary frequency modulation standby optimization method considering random-extreme disturbance Download PDF

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CN116191473B
CN116191473B CN202310266944.2A CN202310266944A CN116191473B CN 116191473 B CN116191473 B CN 116191473B CN 202310266944 A CN202310266944 A CN 202310266944A CN 116191473 B CN116191473 B CN 116191473B
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CN116191473A (en
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王程
李瑶
毕天姝
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North China Electric Power University
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    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00Circuit arrangements for ac mains or ac distribution networks
    • H02J3/24Arrangements for preventing or reducing oscillations of power in networks
    • H02J3/241The oscillation concerning frequency
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00Circuit arrangements for ac mains or ac distribution networks
    • H02J3/002Flicker reduction, e.g. compensation of flicker introduced by non-linear load
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/381Dispersed generators
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/46Controlling of the sharing of output between the generators, converters, or transformers
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/46Controlling of the sharing of output between the generators, converters, or transformers
    • H02J3/466Scheduling the operation of the generators, e.g. connecting or disconnecting generators to meet a given demand
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/10Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2300/00Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/20The dispersed energy generation being of renewable origin
    • H02J2300/22The renewable source being solar energy
    • H02J2300/24The renewable source being solar energy of photovoltaic origin
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2300/00Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/20The dispersed energy generation being of renewable origin
    • H02J2300/28The renewable source being wind energy
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2300/00Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/40Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation wherein a plurality of decentralised, dispersed or local energy generation technologies are operated simultaneously
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02EREDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00Energy generation through renewable energy sources
    • Y02E10/50Photovoltaic [PV] energy
    • Y02E10/56Power conversion systems, e.g. maximum power point trackers

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Physics & Mathematics (AREA)
  • Nonlinear Science (AREA)
  • Supply And Distribution Of Alternating Current (AREA)
  • Feedback Control In General (AREA)

Abstract

The invention discloses a primary frequency modulation standby optimization method considering random-extreme disturbance, belonging to the technical field of new energy station power grid support. The method comprises the following steps: obtaining key frequency modulation parameters of a whole-network frequency modulation unit, describing external input disturbance, and constructing a random MM-SFR model; dividing a random MM-SFR model into a linear section and a saturation section for linearization, constructing a segmented single machine equivalent polymerization model, and converting the segmented single machine equivalent polymerization model into SDEs of the linear section and the saturation section; analyzing probability distribution characteristics of a dynamic mean value and a standard deviation of system frequency in a linear section and a saturated section; judging the section where the frequency extremum is located in the worst extreme scene, and constructing a frequency safety constraint; constructing an optimization model of the hyperplane coefficient; and constructing a primary frequency modulation standby optimization model considering system frequency safety constraint. The invention can effectively resist the adverse effect of uncertain disturbance of new energy on the system frequency stability.

Description

Primary frequency modulation standby optimization method considering random-extreme disturbance
Technical Field
The invention relates to the technical field of new energy station power grid support, in particular to a primary frequency modulation standby optimization method considering random-extreme disturbance.
Background
The energy power field is a main battlefield of 'carbon peak and carbon neutralization', and a power grid in China is converted into a new energy power system which takes a power electronic converter as an interface and complementally utilizes multiple energy sources from a traditional power system which takes a synchronous machine as a main body and coal as main primary energy.
With the continuous improvement of the installation ratio of new energy and the reduction of the proportion of the synchronous units, the kinetic energy of the rotor of the system is reduced, the characteristics of low inertia and weak support of the novel power system are gradually revealed, wind-solar power generation has random fluctuation, the problem of safety and stability of the system frequency is increasingly prominent, and the requirement on primary frequency modulation service is increased. The primary frequency modulation process of the system is mainly realized by a speed regulator system of a frequency modulation unit, and the mechanical power increment is distributed according to the primary frequency modulation standby capacity and the difference modulation coefficient of each unit to provide active support for the system frequency. With the access of large-scale new energy power and energy storage, the primary frequency modulation service of the system gradually shows the characteristics of frequency modulation resource diversification, frequency modulation characteristic differentiation and frequency modulation means activation. Therefore, how to reasonably arrange the primary standby capacity of the system frequency modulation unit and improve the frequency stability of the new energy power system becomes a current research hot spot.
At present, most of researches have little construction difference on primary frequency modulation model input disturbance, namely unit disturbance is modeled as determined step disturbance, however, as the access proportion of new energy is increased, the intensity of continuous random disturbance generated along with wind and light power generation is increased, and taking the actual measurement data of a Ulland-made wind and light storage station as an example, the maximum power fluctuation of the station minute level can be up to about 7% of the total capacity of the installation, and the influence of the uncertain disturbance of the new energy on the system frequency safety is not negligible. The input disturbance of the real system is actually a random process, a frequency response model under random excitation can be converted into a random differential equation set, and the frequency dynamic characteristic of the system is converted into a prediction error band under an uncertain disturbance scene from a determined response curve under a determined disturbance scene. If the primary frequency modulation standby tuning scheme taking the frequency safety constraint into consideration is constructed by the existing disturbance type, the situation that the system frequency in partial disturbance scenes does not meet the frequency minimum point requirement can be caused. In order to improve the frequency safety and robustness of the new energy power system, the influence of wind power uncertain disturbance needs to be considered, important frequency stability indexes are re-described, and the existing primary frequency modulation standby setting scheme is improved.
Disclosure of Invention
The invention aims to provide a primary frequency modulation standby optimization method under the condition of considering random-extreme disturbance, which is characterized by comprising the following steps of:
step 1: in a high-proportion new energy area alternating current power grid, dividing a set into a synchronous set, a wind turbine set and a photovoltaic set according to types, wherein the synchronous set adopts droop control to participate in system frequency modulation, and the new energy set adopts VSM control to participate in system frequency modulation; acquiring key frequency modulation parameters of a whole-network frequency modulation unit, describing external input disturbance, and constructing a random MM-SFR model considering a limiter link of a speed regulator;
step 2: the method comprises the steps of sequentially entering a limiting process by using a two-section linear function approximation unit speed regulator, linearizing a random MM-SFR model of a system into a linear section and a saturation section, constructing a sectionalized single machine equivalent polymerization model by polymerizing key frequency modulation parameters, and converting the sectionalized single machine equivalent polymerization model into SDEs of the linear section and the saturation section;
step 3: SDEs of a linear section and a saturation section are solved respectively, and probability distribution characteristics of a dynamic mean value and a standard deviation of system frequency under the linear section and the saturation section are analyzed;
step 4: considering the system frequency of the worst extreme scene under the wind-light uncertainty confidence coefficient c, judging the section where the frequency extremum under the worst extreme scene is located, and then analyzing the frequency extremum point moment and the extremum point under the worst extreme scene through derivative operation to construct a frequency safety constraint;
step 5: constructing an optimization model of the hyperplane coefficient, and solving by using a commercial solver GUROBI to realize hyperplane linear approximation of nonlinear frequency safety constraint;
step 6: and constructing a primary frequency modulation standby optimization model considering system frequency safety constraint, and solving by using a commercial solver GUROBI.
The random MM-SFR model in the step 1 is as follows:
w′(t)=σw(t)+μ
μ=ΔP L
wherein Δf is the frequency deviation of the system, H is the equivalent total inertia of the system, and ΔP m For the sum of the mechanical power increment of all the participating frequency modulation units, delta P L For unbalanced active power shortage, the load active mutation is generally adopted to express, D is equivalent damping coefficient, sigma i w i (t) is a random process, representing new energy from the ithRandom disturbance of nodes where units are located, w i (t) is standard Gaussian white noise, σ i The random disturbance intensity of the nodes is represented, and R is the total number of nodes accessed into a new energy unit; w '(t) is total disturbance input by the system, sigma w (t) represents equivalent random disturbance after random disturbance aggregation of each new energy node, w (t) is a standard Gaussian process, and sigma is standard deviation of total input disturbance w' (t); mu is the active mutation quantity delta P of the load side L
The formula for aggregating the key frequency modulation parameters in the step 2 is specifically as follows:
κ g =K mg K g
κ′ g =K mg R g
wherein for a linear segment lower equivalent aggregate power supply: k is the gain of the equivalent speed regulator, F H Is equivalent to the high-pressure turbine coefficient, T R Is equivalent reheat time constant; for the equivalent polymeric power supply under saturated section: r is R max For equivalent reserve capacity, F H ' is equivalent high pressure turbine coefficient, T R ' is equivalent reheat time constant, S g Rated capacity of g-th unit, K g Gain of speed regulator of g-th machine set, R g Reserve spare capacity for g-th unit, K mg Rated capacity duty ratio, κ of g-th machine set gg Kappa 'is an auxiliary variable for polymerization of chirp parameters' g /γ′ g Is an auxiliary variable for saturation segment frequency modulation parameter aggregation.
The SDE of the linear section in step 2 is:
dX(t)=A L X(t)dt+Kμdt+KσdB(t)
wherein: x (t) represents a system state variable matrix under a linear segment, A L K represents a coefficient matrix under a linear segment, and B (t) represents a wiener process matrix;
the SDE of the saturated section is:
dX(t)=A sat X(t)dt+(H+Kμ)dt+KσdB(t)
wherein: x (t) represents a system state variable matrix under a saturation segment, A sat K, H represents the coefficient matrix under the saturation segment and B (t) represents the wiener process matrix.
The step 3 specifically comprises the following sub-steps:
step 31: the two-dimensional form of the ember formula is applied to 0, infinity x R 2 →R 2 C of (2) 2 Coordinate function g of map g 1 、g 2 In the following, g is specifically defined:
the method is applied to a system SDE under a linear segment to obtain:
substituting the above formula into the SDE of the frequency dynamic under the linear section, integrating the two sides of the equation, and solving the state variables of the system dynamic under the linear section as follows:
wherein X (0) is the initial value of a system state variable of a linear segment;
similarly, the state variables that solve for the system dynamics in the saturation region are as follows:
wherein X (0) is the initial value of a saturated section system state variable;
step 32: analyzing and quantifying the average value of frequency dynamic under the linear section:
the derivative of t on both ends of the above is obtained as follows:
wherein ,μΔf (t) is the mean value of the system frequency deviation,incremental for system mechanical powerIs the average value of (2);
step 33: analyzing and quantifying standard deviation of frequency dynamics under linear section:
wherein ,DX (t) is the variance of the system state variables;
the derivative of the two ends of the above with respect to t is obtained as follows:
wherein ,DΔf (t) is the variance of the system frequency deviation,cov (t) is the covariance of the system frequency deviation and the system mechanical power delta.
The step 4 specifically comprises the following substeps:
step 41: considering wind and light uncertainty confidence coefficient c, when the system frequency in the worst extreme scene reaches the lowest point, the valve opening of the unit speed regulator is in a saturation section, and the system frequency expression of the worst extreme scene in the saturation section is determined as follows:
Δf c,sat (t)=μ satΔf (t)-Φ -1 (c)σ satΔf (t)
wherein phi is a Gaussian cumulative distribution function, phi -1 (c) Indicating the quantiles of the gaussian distribution at confidence level c, deltaf c,sat (t) is the lower boundary frequency of the frequency envelope band, μ satΔf (t) is the mean value of the system frequency deviation of the saturation region, sigma satΔf (t) is the standard deviation mean of the saturated zone system frequency deviation;
step 42: carrying out first-order Taylor expansion on the standard deviation of the system frequency in the saturation region near the lowest point of the mean value of the system frequency, and realizing linearization treatment on the standard deviation of the saturation region:
σ satΔf (x)=σ′ satΔf (x n )(x-x n )+σ satΔf (x n )
=σ′ satΔf (x n )x-σ′ satΔf (x n )x nsatΔf (x n )
wherein ,t n represents the minimum point moment of the mean value of the system frequency, x n At t for variable x n Time corresponding value, sigma' satΔf (x n ) The standard deviation of the system frequency is x for the saturation section n Derivative of sigma satΔf (x n ) The standard deviation of the system frequency is x for the saturation section n Corresponding values at;
step 43: for delta under the following conditionsf c,sat (t) extremum:
Δfc,sat (t)=μ′ satΔf (t)-Φ -1 (c)σ′ satΔf (t)=0
wherein ,Δfc,sat (t) is the derivative of the lower boundary frequency of the frequency envelope band, μ' satΔf (t) is the derivative of the mean value of the system frequency deviation of the saturation segment, sigma' satΔf (t) is the derivative of the standard deviation of the system frequency in the saturation section;
solving the equation to obtain the frequency lowest point analysis expression under the worst extreme scene as follows:
Δf c,nadir =μ satΔf (t nadir )-Φ -1 (c)σ satΔf (t nadir )
wherein ,tnadir For the moment of the lowest frequency point, w 1 、w 2 Is an exponential coefficient, D is an equivalent damping coefficient, phi -1 (c) For Gaussian distribution quantiles at confidence c, σ' satΔf (x n ) The standard deviation of the system frequency is x for the saturation section n Derivative at R max For system aggregation, mu is the step disturbance quantity, k 1 、k 2 、C 1 、C 2 Are all coefficients;
step 44: constructing a system frequency security constraint:
Δf c,nadir ≤f min
wherein ,fmin Is the lowest standard for system frequency requirements.
The optimization model of the hyperplane coefficient in the step 5 is specifically as follows:
wherein v represents the number of hyperplanes in the set Ω, and w represents the number of hyperplanes in the set ψ; alpha 1,i2,i3,i Coefficients representing the ith hyperplane in the set Ω, β 1,j2,j3,j Coefficients representing the jth hyperplane within the set ψ;spare for equivalent synchrony unit at kth detection point,/->Is equivalent to the kth detection pointAnd f is a first group of hyperplane functions to be fitted, and g is a second group of hyperplane functions to be fitted.
The primary frequency modulation standby optimization model considering the system frequency safety constraint in the step 6 comprises the following steps:
objective function:
wherein T is the total time period number of scheduling, G is the total number of synchronous units, W is the total number of wind power units, and V is the total number of photovoltaic units;reserving cost for power generation cost and frequency modulation standby of various units respectively; p (P) i (t), { g, w, v } are respectively the power generated by each unit under the t scheduling period; />Positive/negative spare capacity reserved for each unit under the t scheduling period;
constraint conditions:
full network power balancing constraints:
wherein ,Pd (t) represents the load active demand of the t scheduling period, and D is the total system load;
line transmission power constraints:
wherein ,Pl (t) represents a line transmission power of a t-th scheduling period; coefficient pi n,l Is a power transfer factor; p (P) l min ,P l max Upper/lower limits of line transmission power, respectively;
synchronous machine power and climbing constraint:
wherein ,maximum/minimum active output of the synchronous machine set respectively; />The upward/downward climbing rate limit of the synchronous unit respectively; x is x g,t The starting mode of the synchronous machine set is adopted;
wind power active output constraint:
wherein ,predicting the power of the wind turbine; x is x w,t The starting mode of the wind turbine generator is adopted;
photovoltaic active power out-force constraint:
wherein ,predicting the power of the photovoltaic unit; x is x v,t The starting mode of the photovoltaic unit is adopted;
standby constraint of synchronous machine set:
standby constraint of wind turbine generator:
reserve restraint of photovoltaic unit:
the invention has the beneficial effects that:
the invention finely describes the second-level frequency dynamic characteristic of the system under the consideration of wind and light uncertainty, analyzes the improved frequency safety constraint under the consideration of the wind and light uncertainty confidence coefficient c, and the constructed primary frequency modulation standby setting model under the consideration of the wind and light uncertainty can effectively resist the adverse effect of the uncertain disturbance of new energy on the system frequency stability.
Drawings
FIG. 1 is a flow chart of a primary frequency modulation reserve optimization method under the consideration of random-extreme disturbance according to the present invention;
FIG. 2 is a graph of dynamic characteristics of mean and variance of frequency deviations of the system of the present invention;
FIG. 3 is a plot of primary frequency modulation positive standby tuning results for a 95% wind and solar uncertainty confidence of the present invention.
Detailed Description
The invention provides a primary frequency modulation standby optimization method under the consideration of random-extreme disturbance, and the invention is further described below with reference to the accompanying drawings and specific embodiments.
As shown in fig. 1, the implementation flow of the primary frequency modulation standby optimization method under the random-extreme disturbance is considered. The method comprises the following specific steps:
step 1: in a high-proportion new energy area alternating current power grid, dividing a set into a synchronous set, a wind turbine set and a photovoltaic set according to types, wherein the synchronous set adopts droop control to participate in system frequency modulation, and the new energy set adopts VSM control to participate in system frequency modulation; firstly, key frequency modulation parameters of a whole-network frequency modulation unit are obtained, wherein the key frequency modulation parameters comprise the total system inertia, a difference adjustment coefficient, a reheating time constant, a high-pressure turbine power fraction, a damping coefficient and a smoothing power of a wind turbine unit, a photovoltaic power generation unit and a synchronous power generation unit.
And then, the external input disturbance is described, and the construction of a random multi-machine frequency response model (storage MM-SFR) which takes into account the limiting link of the speed regulator is completed. The input disturbance w' (t) of the random multi-machine system frequency response model is modeled as a random process, and the specific formula is as follows:
w′(t)=σw(t)+μ (1)
μ=ΔP L (2)
wherein: sigma w (t) represents equivalent random disturbance after random disturbance aggregation of each new energy node, w (t) is a standard Gaussian process, sigma is disturbance intensity after aggregation, and the requirement is satisfiedSigma is the standard deviation of the total input disturbance w' (t); the average value mu of w' (t) is the active mutation quantity delta P at the load side L . Thus, the total disturbance w' (t) can be decomposed into load step disturbancesThe dynamic component mu and the wind-light random fluctuation component sigma w (t). w' (t) can more truly represent disturbance scenes existing in the high-proportion new energy regional power grid.
The frequency dynamic process of the system is characterized by a first-order rocking equation containing a random process, and the method is specifically expressed as follows:
wherein Δf is the frequency deviation of the system, H is the equivalent total inertia of the system, and ΔP m For the sum of the mechanical power increment of all the participating frequency modulation units, delta P L For unbalanced active power shortage, the load active mutation is generally adopted to express, D is equivalent damping coefficient, sigma i w i (t) is a random process, representing random disturbance from the node where the ith new energy unit is located, w i (t) is standard Gaussian white noise, σ i And the random disturbance intensity of the nodes is represented, and R is the total number of nodes accessed into the new energy unit. If the spatial distribution characteristic of the power grid frequency is not considered, the dynamic process of each unit participating in frequency modulation in the regional power grid for responding to unbalanced active power can be approximately described by a random multi-machine system frequency response model (storage MM-SFR), and meanwhile, in order to more accurately describe the real frequency dynamic characteristic of the system, the influence of a unit speed regulator limiting link on the frequency response process is considered.
Thus, the construction of the random multi-machine system frequency response model taking the amplitude limiting link of the speed regulator into account is completed.
Step 2: firstly, two sections of linear functions are used for approximating the process that a unit speed regulator sequentially enters into amplitude limiting, so that the zoning linearization of the random MM-SFR model of the system is realized, namely, the system is dynamically divided into a linear zone and a saturated zone.
Next, the key frequency modulation parameters are aggregated, a sectional single machine equivalent aggregation model is constructed, and the key frequency modulation parameter aggregation formula of the sectional single machine aggregation equivalent model is specifically as follows:
wherein for a linear segment lower equivalent aggregate power supply: k is the gain of the equivalent speed regulator, F H Is equivalent to the high-pressure turbine coefficient, T R Equivalent reheat time constant; for the equivalent polymeric power supply under saturated section: r is R max For equivalent reserve capacity, F H ' is equivalent high pressure turbine coefficient, T R ' is equivalent reheat time constant, S g Rated capacity of g-th unit, K g Gain of speed regulator of g-th machine set, R g Reserve spare capacity for g-th unit, K mg Rated capacity duty ratio, κ of g-th machine set gg Auxiliary variation for aggregation of chirp parametersAmount, kappa' g /γ′ g Is an auxiliary variable for saturation segment frequency modulation parameter aggregation.
Next, considering the stochastic process w' (t) as an input disturbance, the linear segment single machine aggregation equivalent model is converted into a system of stochastic differential equations (stochastic differential equations, SDEs) in the time domain, as shown in the following formula:
since the standard gaussian white noise and the standard wiener process satisfy the following relation:
the SDE for converting the system random differential equation under the linear segment into the final matrix form is as follows:
dX(t)=A L X(t)dt+Kμdt+KσdB(t) (15)
wherein: x (t) represents a system state variable matrix under a linear segment, A L K represents the coefficient matrix under the linear segment, and B (t) represents the wiener process matrix.
According to the same steps, the final matrix form of the system SDE under the saturated section can be obtained as follows:
dX(t)=A sat X(t)dt+(H+Kμ)dt+KσdB(t) (16)
wherein: x (t) represents a system state variable matrix under a saturation segment, A sat K, H represents the coefficient matrix under the saturation segment and B (t) represents the wiener process matrix.
Step 3: firstly, solving SDEs in a linear section and a saturated section respectively, and applying a two-dimensional form of an Earthway formula to [0, ++) ×R 2 →R 2 C of (2) 2 Coordinate function g of map g 1 、g 2 In the following, g is specifically defined:
the application of the above to the system under linear segment SDE can be obtained:
the method comprises the steps of substituting the above method into the SDE of the frequency dynamic under the linear section, and integrating two sides of the equation to obtain the state variable of the system dynamic under the linear section, wherein the state variable is as follows:
wherein X (0) is the initial value of the system state variable of the linear segment.
Similarly, according to the same steps, the state variables of the system dynamics under the saturation section can be solved as follows:
wherein X (0) is the initial value of the system state variable of the saturated section.
Thus, the solution of the system dynamic segment SDE is completed.
Then, the probability distribution characteristic of the system frequency dynamic is analyzed in a segmentation way, and firstly, the average value of the frequency dynamic in the linear segment is analyzed and quantized:
deriving t from the two ends of the above equation, a differential equation set about the frequency mean can be obtained as follows:
wherein ,μΔf (t) is the mean value of the system frequency deviation,is the average value of the mechanical power increment of the system.
The time domain expression of the frequency dynamic mean value in the linear section can be obtained by solving the differential equation, and the time domain expression of the frequency dynamic mean value in the saturated section can be obtained according to the same steps.
Secondly, analyzing and quantifying standard deviation of frequency dynamics under a linear segment:
wherein ,DX And (t) is the variance of the system state variables.
The derivative equation set about the standard deviation of frequency can be obtained by deriving the t at the two ends of the above equation set as follows
wherein ,DΔf (t) is the variance of the system frequency deviation,cov (t) is the covariance of the system frequency deviation and the system mechanical power delta. Fig. 2 is a dynamic diagram of the mean and variance of the system frequency deviation.
The time domain expression of the frequency dynamic standard deviation in the linear section can be obtained by solving the differential equation, and the time domain expression of the frequency dynamic standard deviation in the saturated section can be obtained according to the same steps.
Step 4: according to the economic principle of primary frequency standby setting, when the system frequency under the worst extreme scene reaches the lowest point under the consideration of wind and light uncertainty confidence coefficient c, the valve opening of the unit speed regulator is necessarily in a saturated section, and the system frequency expression of the worst extreme scene under the saturated section is as follows:
Δf c,sat (t)=μ satΔf (t)-Φ -1 (c)σ satΔf (t) (25)
wherein phi is a Gaussian cumulative distribution function, phi -1 (c) Indicating the quantiles of the Gaussian distribution at confidence level c, Δf c,sat (t) is the lower boundary frequency of the frequency envelope band, μ satΔf (t) is the mean value of the system frequency deviation of the saturation section, sigma satΔf And (t) is the standard deviation mean of the system frequency deviation of the saturation section.
Carrying out first-order Taylor expansion on the standard deviation of the system frequency in the saturation section near the lowest point of the mean value of the system frequency, and realizing linearization treatment on the standard deviation of the saturation section:
wherein ,t n represents the minimum point moment of the mean value of the system frequency, x n At t for variable x n Time corresponding value, sigma' satΔf (x n ) The standard deviation of the system frequency is x for the saturation section n Derivative of sigma satΔf (x n ) The standard deviation of the system frequency is x for the saturation section n Corresponding values at that point.
At completion sigma satΔf After linearization of (t), for deltaf c,sat (t) extremum, the following condition should be satisfied:
Δfc,sat (t)=μ′ satΔf (t)-Φ -1 (c)σ′ satΔf (t)=0 (27)
wherein ,Δfc,sat (t) is the derivative of the lower boundary frequency of the frequency envelope band, μ' satΔf (t) is the derivative of the mean value of the system frequency deviation of the saturation segment, sigma' satΔf And (t) is the derivative of the standard deviation of the system frequency in the saturation section.
Solving the equation can obtain the analysis expression of the frequency lowest point under the worst extreme scene as follows:
wherein ,tnadir For the moment of the lowest frequency point, w 1 、w 2 Is an exponential coefficient, D is an equivalent damping coefficient, phi -1 (c) For Gaussian distribution quantiles at confidence c, σ' satΔf (x n ) The standard deviation of the system frequency is x for the saturation section n Derivative at R max For system aggregation, mu is the step disturbance quantity, k 1 、k 2 、C 1 、C 2 Are coefficients.
Finally, the system frequency security constraints are constructed as follows:
Δf c,nadir ≤f min (30)
wherein ,fmin Is the lowest standard for system frequency requirements. Fig. 3 is a plot of primary frequency modulation positive standby tuning results at 95% wind-solar uncertainty confidence.
Step 5: the optimization model of the hyperplane coefficients is constructed as follows:
wherein v represents the number of hyperplanes in the set Ω, and w represents the number of hyperplanes in the set ψ; alpha 1,i2,i3,i Coefficients representing the ith hyperplane in the set Ω, β 1,j2,j3,j Representation setCombining coefficients of the jth hyperplane within ψ;spare for equivalent synchrony unit at kth detection point,/->And f is a first group of hyperplane functions to be fitted, and g is a second group of hyperplane functions to be fitted.
The principle of hyperplane approximation is to find a group of optimal hyperplanes, so that the error sum of the maximum approximation value and the theoretical actual value of the hyperplanes at all monitoring points is minimum, and the optimal fitting effect is achieved.
And solving by using a commercial solver GUROBI to realize the hyperplane linear approximation of nonlinear frequency safety constraint.
Step 6: firstly, constructing an objective function of the primary frequency modulation standby optimization model considering the system frequency safety constraint, and taking the sum of the power generation cost and standby reserved cost of all units as the objective, wherein the objective function is specifically expressed as follows:
wherein T is the total time period number of scheduling, G is the total number of synchronous units, W is the total number of wind power units, and V is the total number of photovoltaic units;reserving cost for power generation cost and frequency modulation standby of various units respectively; p (P) i (t), { g, w, v } are respectively the power generated by each unit under the t scheduling period; />Positive/negative reserve capacities reserved for respective units at the t-th scheduling period. The secondary frequency modulation standby optimization setting model specifically comprises the following aboutThe beam, wherein in the present model, the power-on mode of all the units is considered to be known, is a constant value.
Next, a constraint condition of a primary frequency modulation standby optimization model considering the system frequency safety constraint is constructed, and the constraint condition is specifically as follows:
1) Full network power balancing constraints:
/>
wherein ,Pd (t) represents the load active demand of the t scheduling period, and D is the total number of system loads.
2) Line transmission power constraints:
wherein ,Pl (t) represents a line transmission power of a t-th scheduling period; coefficient pi n,l Is a power transfer factor; p (P) l min ,P l max The upper/lower limits of the line transmission power, respectively.
3) Synchronous machine power and climbing constraint:
wherein ,maximum/minimum active output of the synchronous machine set respectively; />The upward/downward climbing rate limit of the synchronous unit respectively; x is x g,t Is a starting mode of the synchronous machine set.
4) Wind power active output constraint:
wherein ,predicting the power of the wind turbine; x is x w,t The method is a starting mode of the wind turbine generator.
5) Photovoltaic active power out-force constraint:
wherein ,predicting the power of the photovoltaic unit; x is x v,t The method is a starting mode of the photovoltaic unit.
6) Standby constraint of synchronous machine set:
7) Standby constraint of wind turbine generator:
8) Reserve restraint of photovoltaic unit:
therefore, the construction of the primary frequency modulation standby optimization model containing dynamic frequency security constraint is completed, and the model is solved through commercial software GUROBI, so that the daily scheduling arrangement and the frequency modulation standby reservation arrangement of each unit in the regional power grid can be obtained.
The invention finely describes the second-level frequency dynamic characteristic of the system under the consideration of wind and light uncertainty, analyzes the improved frequency safety constraint under the consideration of the wind and light uncertainty confidence coefficient c, and the constructed primary frequency modulation standby setting model under the consideration of the wind and light uncertainty can effectively resist the adverse effect of the uncertain disturbance of new energy on the system frequency stability.

Claims (3)

1. A primary frequency modulation standby optimization method considering random-extreme disturbance is characterized by comprising the following steps:
step 1: in a high-proportion new energy area alternating current power grid, dividing a set into a synchronous set, a wind turbine set and a photovoltaic set according to types, wherein the synchronous set adopts droop control to participate in system frequency modulation, and the new energy set adopts VSM control to participate in system frequency modulation; acquiring key frequency modulation parameters of a whole-network frequency modulation unit, describing external input disturbance, and constructing a random MM-SFR model considering a limiter link of a speed regulator;
the random MM-SFR model in the step 1 is as follows:
w′(t)=σw(t)+μ
μ=ΔP L
wherein Δf is the frequency deviation of the system, H is the equivalent total inertia of the system, and ΔP m For the sum of the mechanical power increment of all the participating frequency modulation units, delta P L For unbalanced active power shortage, the load active mutation is generally adopted to express, D is equivalent damping coefficient, sigma i w i (t) is a random process, representing random disturbance from the node where the ith new energy unit is located, w i (t) is standard Gaussian white noise, σ i The random disturbance intensity of the nodes is represented, and R is the total number of nodes accessed into a new energy unit; w '(t) is total disturbance input by the system, sigma w (t) represents equivalent random disturbance after random disturbance aggregation of each new energy node, w (t) is a standard Gaussian process, and sigma is standard deviation of total input disturbance w' (t); mu is the active mutation quantity delta P of the load side L
Step 2: the method comprises the steps of sequentially entering a limiting process by using a two-section linear function approximation unit speed regulator, linearizing a random MM-SFR model of a system into a linear section and a saturation section, constructing a sectionalized single machine equivalent polymerization model by polymerizing key frequency modulation parameters, and converting the sectionalized single machine equivalent polymerization model into SDEs of the linear section and the saturation section;
the SDE of the linear section in step 2 is:
dX L (t)=A L X L (t)dt+L L μdt+L L σdB(t)
wherein :XL (t) represents the system state variable matrix under the linear segment, A L 、L L Representing a coefficient matrix under the linear segment, and B (t) represents a wiener process matrix;
the SDE of the saturated section is:
dX sat (t)=A sat X sat (t)dt+(C+L sat μ)dt+L sat σdB(t)
wherein :Xsat (t) represents a system state variable matrix under the saturation segment, A sat 、C、L sat Representing a coefficient matrix under a saturation segment;
step 3: SDEs of a linear section and a saturation section are solved respectively, and probability distribution characteristics of a dynamic mean value and a standard deviation of system frequency under the linear section and the saturation section are analyzed;
the step 3 specifically comprises the following sub-steps:
step 31: the two-dimensional form of the ember formula is applied to 0, infinity x R 2 →R 2 C of (2) 2 Coordinate function g of map g 1 、g 2 In the following, g is specifically defined:
the method is applied to a system SDE under a linear segment to obtain:
substituting the above formula into the SDE of the frequency dynamic under the linear section, integrating the two sides of the equation, and solving the state variables of the system dynamic under the linear section as follows:
wherein ,XL (0) Initial values of system state variables of linear segments;
similarly, the state variables that solve for the system dynamics in the saturation region are as follows:
wherein ,Xsat (0) The initial value of the system state variable is the saturated section;
step 32: analyzing and quantifying the average value of frequency dynamic under the linear section:
the derivative of t on both ends of the above is obtained as follows:
wherein ,μΔf (t) is the mean value of the system frequency deviation,is the average value of the mechanical power increment of the system; f (F) H Equivalent high pressure turbine coefficients for the linear segment; k is the equivalent speed regulator gain;
step 33: analyzing and quantifying standard deviation of frequency dynamics under linear section:
wherein ,DX (t) is the variance of the system state variables;
the derivative of the two ends of the above with respect to t is obtained as follows:
wherein ,DΔf (t) is the variance of the system frequency deviation,cov (t) is the covariance of the system frequency deviation and the system mechanical power increment;
step 4: considering the system frequency of the worst extreme scene under the wind-light uncertainty confidence coefficient c, judging the section where the frequency extremum under the worst extreme scene is located, and then analyzing the frequency extremum point moment and the extremum point under the worst extreme scene through derivative operation to construct a frequency safety constraint;
the step 4 specifically comprises the following substeps:
step 41: considering wind and light uncertainty confidence coefficient c, when the system frequency in the worst extreme scene reaches the lowest point, the valve opening of the unit speed regulator is in a saturation section, and the system frequency expression of the worst extreme scene in the saturation section is determined as follows:
Δf c,sat (t)=μ satΔf (t)-Φ -1 (c)σ satΔf (t)
wherein phi is a Gaussian cumulative distribution function, phi -1 (c) Indicating the quantiles of the gaussian distribution at confidence level c, deltaf c,sat (t) is the lower boundary frequency of the frequency envelope band, μ satΔf (t) is the mean value of the system frequency deviation of the saturation region, sigma satΔf (t) is the standard deviation mean of the saturated zone system frequency deviation;
step 42: carrying out first-order Taylor expansion on the standard deviation of the system frequency in the saturation region near the lowest point of the mean value of the system frequency, and realizing linearization treatment on the standard deviation of the saturation region:
σ satΔf (x)=σ′ satΔf (x n )(x-x n )+σ satΔf (x n )
=σ′ satΔf (x n )x-σ′ satΔf (x n )x n
satΔf (x n )
wherein ,t n represents the minimum point moment of the mean value of the system frequency, x n At t for variable x n Time corresponding value, sigma' satΔf (x n ) The standard deviation of the system frequency is x for the saturation section n Derivative of sigma satΔf (x n ) The standard deviation of the system frequency is x for the saturation section n Corresponding values at;
step 43: for delta under the following conditionsf c,sat (t) extremum:
Δfc,sat (t)=μ′ satΔf (t)-Φ -1 (c)σ′ satΔf (t)=0
wherein ,Δfc,sat (t) is the derivative of the lower boundary frequency of the frequency envelope band, μ' satΔf (t) is the derivative of the mean value of the system frequency deviation of the saturation segment, sigma' satΔf (t) is the derivative of the standard deviation of the system frequency in the saturation section;
solving the equation to obtain the frequency lowest point analysis expression under the worst extreme scene as follows:
Δf c,nadir =μ satΔf (t nadir )-Φ -1 (c)σ satΔf (t nadir )
wherein ,tnadir For the moment of the lowest frequency point, w 1 、w 2 Is an exponential coefficient, sigma' satΔf (x n ) The standard deviation of the system frequency is x for the saturation section n Derivative of k 1 、k 2 、C 1 、C 2 Are all coefficients; r is R max Is equivalent spare capacity;
step 44: constructing a system frequency security constraint:
Δf c,nadir ≥f min
wherein ,fmin Is the lowest standard of system frequency requirements;
step 5: constructing an optimization model of the hyperplane coefficient, and solving by using a commercial solver GUROBI to realize hyperplane linear approximation of nonlinear frequency safety constraint;
step 6: and constructing a primary frequency modulation standby optimization model considering system frequency safety constraint, and solving by using a commercial solver GUROBI.
2. The primary frequency modulation standby optimization method considering random-extreme disturbance according to claim 1, wherein the formula for aggregating key frequency modulation parameters in step 2 is specifically as follows:
κ g =K mg K g
κ′ g =K mg R g
wherein for a linear segment lower equivalent aggregate power supply: k is the gain of the equivalent speed regulator, F H Equivalent high pressure turbine coefficient for linear segment, T R An equivalent reheat time constant for the linear segment; for the equivalent polymeric power supply under saturated section: r is R max For equivalent reserve capacity, F H ' is the equivalent high-pressure turbine coefficient of the saturation section, T R ' is the saturated section equivalent reheat time constant; s is S g Rated capacity of g-th unit, K g Gain of speed regulator of g-th machine set, R g Reserve spare capacity for g-th unit, K mg Rated capacity duty ratio, κ of g-th machine set g 、γ g Kappa 'is an auxiliary variable for polymerization of chirp parameters' g 、γ′ g Is an auxiliary variable for saturation segment frequency modulation parameter aggregation.
3. The optimization method for primary frequency modulation backup under consideration of random-extreme disturbance according to claim 1, wherein the optimization model of the hyperplane coefficients in step 5 is specifically as follows:
wherein v represents the number of hyperplanes in the set Ω, and w represents the number of hyperplanes in the set ψ; alpha 1,h2,h3,h Coefficients representing the h hyperplane in the set Ω, β 1,j2,j3,j Coefficients representing the jth hyperplane within the set ψ;spare for equivalent synchrony unit at kth detection point,/->F is a first group of hyperplane functions to be fitted, and l is a second group of hyperplane functions to be fitted.
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