CN117638991A - New energy power system frequency modulation parameter safety domain calculation and optimization method - Google Patents
New energy power system frequency modulation parameter safety domain calculation and optimization method Download PDFInfo
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Abstract
The invention discloses a new energy power system frequency modulation parameter safety domain calculation and optimization method, which belongs to the technical field of power system frequency control and comprises the following steps: s1, selecting a high-proportion new energy power system as a research object; s2, taking the difference of dynamic response of the power supply into consideration, and constructing a system active-frequency dynamic model by adopting a transfer function; s3, considering limiting links of all units in the system, and establishing a linearization mathematical model of a dynamic equation of the frequency modulation process of the system; s4, solving a two-dimensional frequency modulation parameter safety domain taking each frequency modulation parameter as a coordinate axis through identifying vertexes; and S5, deleting frequency modulation parameter points which do not meet the frequency stability requirement in the frequency modulation parameter safety domain by adopting a corner cutting method, and further optimizing the frequency modulation parameter safety domain. The frequency modulation parameter safety domain calculation and optimization method for the new energy power system realizes the frequency modulation parameter optimization setting based on the fault prediction set, and has field application value.
Description
Technical Field
The invention relates to the technical field of frequency control of power systems, in particular to a new energy power system frequency modulation parameter safety domain calculation and optimization method.
Background
The frequency modulation parameters in the system are important indexes for determining the frequency stability of the power system, and the frequency modulation parameters among stations cooperate to jointly ensure the frequency stability of the system. With the large-scale access of new energy, especially tens of millions of kilowatt-level new energy bases and deep-open-sea wind power, the system frequency faces a greater risk of instability. If the frequency modulation parameters of part of stations in the system are located outside the safety domain, the maximum deviation value of the disturbed frequency change rate and frequency is increased, and the high-frequency switching-off and low-frequency load shedding of the system are triggered, so that a blackout accident can be possibly caused.
Therefore, the safety range of the frequency modulation parameters of each station is critical, so that the method not only can provide frequency instability risk early warning for power grid dispatching operators, but also can be used as an important reference index for real-time control after disturbance.
The frequency modulation parameter safety domain of each station in the current system is formulated according to national standards. However, with the advance of the dual-carbon target, the installed proportion and the generated energy of the new energy are improved, the auxiliary service market has certain requirements on the spare capacity provided by each new energy station, and standards and benefits are regulated for the rapid frequency response service such as virtual inertia, primary frequency modulation and the like, so that the provision of additional frequency control by each new energy station is promoted. In the case of a high proportion of new energy or uneven distribution of inertia at the receiving end, the safety range of the current frequency modulation parameters may no longer be applicable. The safety range of the frequency modulation parameters of the system is not clear, and the frequency stability of the system is restricted.
Therefore, a new energy power system frequency modulation parameter safety domain calculation and optimization method is needed, so that the system frequency stability is ensured.
Disclosure of Invention
The invention aims to provide a new energy power system frequency modulation parameter safety domain calculation and optimization method, which solves the problem of optimizing and setting frequency modulation parameters of all stations of the system.
In order to achieve the above purpose, the invention provides a new energy power system frequency modulation parameter safety domain calculating and optimizing method, which comprises the following steps:
s1, selecting a high-proportion new energy power system as a research object, wherein the new energy unit participates in frequency modulation through virtual inertia response and primary frequency modulation control;
s2, taking the difference of dynamic response of the power supply into consideration, and constructing a system active-frequency dynamic model by adopting a transfer function;
s3, taking a synchronous unit and a limiting link of the new energy unit in the high-proportion new energy power system into consideration, and establishing a linearization mathematical model of a dynamic equation of the system frequency modulation process;
s4, solving a two-dimensional frequency modulation parameter safety domain taking each frequency modulation parameter as a coordinate axis through identifying vertexes;
and S5, deleting frequency modulation parameter points which do not meet the frequency stability requirement in the frequency modulation parameter safety domain by adopting a corner cutting method, and further optimizing the frequency modulation parameter safety domain.
Preferably, in step S1, the grid of the high-proportion new energy power system is an ac grid, and the power supply includes a synchronous power supply and a new energy unit.
Preferably, in step S2, after the power disturbance occurs in the high-proportion new energy power system, the frequency dynamic response process is represented by a rocking equation:
wherein f 0 Rated frequency for the system; Δf is the system frequency deviation; h g The inertia of the system synchronous machine is adopted; d is a damping coefficient; ΔP m The per unit value of the mechanical power variation of each frequency modulation unit; ΔP e The per unit value of the active mutation quantity of the load;
the transfer function of equation (1) is expressed as:
-(2H g s+D)Δf(s)＝ΔP m (s)-ΔP e (s) (2)
wherein Δf(s) is the frequency domain form of the per unit value of the system frequency deviation; ΔP m (s) is each frequency modulation unitA frequency domain version of the per unit value of the mechanical power variation; ΔP e (s) is a frequency domain version of the per unit value of the load active mutation quantity; s is the variation of the complex frequency domain;
the active power adjustment quantity of each frequency modulation unit is constrained by a dead zone link and an amplitude limiting link, and the dead zone link is ignored and only the influence of the amplitude limiting link on the frequency dynamic of the system is considered because the dead zone has small influence on the maximum deviation value of the frequency;
the method comprises the steps of performing equivalent aggregation on all synchronous machines in a high-proportion new energy power system to form equivalent synchronous units, wherein the turbine unit is regarded as a turbine unit with a reheating time constant of 0.5 times of a hydraulic hammer effect time constant and a high-pressure cylinder power proportion of-2;
For low-frequency disturbance, obtaining the mechanical power adjustment quantity of the equivalent synchronous unit, wherein the speed regulator limiting link of the equivalent synchronous unit is command limiting:
the mechanical power adjustment quantity of the equivalent synchronous unit under high-frequency disturbance is as follows:
wherein,the active limiting value is equivalent to that of the synchronous unit; />Is a low-frequency disturbanceThe active adjustment quantity of the lower equivalent synchronous unit after the amplitude limiting link; />The active adjustment quantity of the equivalent synchronous unit under high-frequency disturbance after the amplitude limiting link is adopted; k (K) g The gain of a speed regulator of the equivalent synchronous unit; />The active adjustment quantity is output by the equivalent synchronous unit through the prime motor under low-frequency disturbance; />The active adjustment quantity is output by the equivalent synchronous unit through the prime motor under high-frequency disturbance; f (F) H The high-pressure turbine coefficient is the equivalent synchronous machine; t (T) R The reheating time constant is equivalent to that of the synchronous unit;
according to the virtual inertia and the primary frequency modulation modeling, frequency support provided by each new energy unit is connected, and the equivalence of each new energy unit in the system is aggregated into an equivalence new energy unit;
for low-frequency disturbance, obtaining the mechanical power adjustment quantity of the equivalent new energy unit;
the mechanical power adjustment quantity of the equivalent synchronous unit under high-frequency disturbance is as follows:
wherein,adding active power adjustment quantity of a frequency control link for the equivalent new energy unit under low-frequency disturbance; Adding active power adjustment quantity of a frequency control link for the equivalent new energy unit under high-frequency disturbance; h ne An inertial time constant of virtual inertia response of the equivalent new energy unit; k (K) ne The gain coefficient is the gain coefficient of primary frequency modulation control of the equivalent new energy unit; t (T) ne The control time constant of the first-order inertia link of the inverter of the equivalent new energy unit is set; virtual inertial response of equivalent new energy unit and primary frequency modulation control together use standby power, wherein +.>Is the active limiting value of the equivalent new source unit, < ->The active adjustment quantity of the equivalent new energy unit under low-frequency disturbance after the limiting link is adopted; />The active adjustment quantity of the equivalent new energy unit under high-frequency disturbance after the limiting link is adopted.
Preferably, in step S3, the frequency modulation process dynamic equation is discretized by a forward difference method, and a bilinear term in the frequency modulation process dynamic equation is linearized by a mccomick envelope, so as to respectively construct a linear model of the frequency response of the high-proportion new energy power system after low-frequency disturbance and high-frequency disturbance;
(1) A linear model of the frequency response of the high-proportion new energy power system after low-frequency disturbance:
(1) high-proportion new energy power system frequency deviation:
wherein,the occurrence of the low-frequency disturbance is delta P L The frequency deviation of the n.n. -1 step of the system under the low frequency disturbance; d, d n For differential step length, H g The inertia time constant of the equivalent synchronous machine; p (P) L The total load of the new energy power system with high proportion is; />The active adjustment quantity of the nth-1 step length of the equivalent synchronous unit and the equivalent new energy unit under low-frequency disturbance is respectively calculated; f (f) 0 Rated frequency of a high-proportion new energy power system; s is S b The total capacity of the high-proportion new energy power system is obtained; />Is the rated capacity of the equivalent thermal power unit; />The rated capacity of the equivalent new energy unit; d is a system damping coefficient;
(2) active power adjustment quantity of equivalent synchronous unit:
wherein,the active adjustment quantity is output by the equivalent synchronous unit under low-frequency disturbance at the n-th and n-1 step length; />Respectively carrying out active adjustment quantity of the n-th and n-1 step length of the system after the equivalent synchronous machine set under low-frequency disturbance passes through the limiter link of the speed regulator; />The active limiting value and the rated capacity of the equivalent thermal power generating unit are respectively; k (K) g The gain of a speed regulator of the equivalent synchronous unit; t (T) R The reheating time constant is equivalent to that of the synchronous unit; f (F) H The high-pressure turbine coefficient is equal to the high-pressure turbine coefficient of the synchronous unit;
(3) active power adjustment quantity of equivalent new energy unit:
wherein,respectively obtaining the frequency deviation values of the nth and the n-1 step of the system after the equivalent new energy unit under the low-frequency disturbance passes through the first-order inertia link of the inverter; / >The active adjustment quantity after the first-order inertia link and the active adjustment quantity after the amplitude limiting link of the equivalent new energy unit under the low-frequency disturbance are respectively; />The active limiting value and the rated capacity of the equivalent new energy unit are respectively; h ne The inertial time constant is equivalent to the inertial time constant of the new energy unit; k (K) ne The speed regulator gain of the equivalent new energy unit; t (T) ne The time constant of the first-order inertia link of the inverter of the equivalent new energy unit;
(2) A linear model of the frequency response of the high-proportion new energy power system after high-frequency disturbance:
wherein,the occurrence of the high-frequency disturbance is delta P L System n under high frequency disturbance of (2) . 、n . -a frequency deviation of 1 step; />Respectively the active adjustment quantity of the nth-1 step length of the equivalent synchronous unit and the equivalent new energy unit under high-frequency disturbance; />Respectively the nth equivalent synchronous units under high-frequency disturbance . 、n . -an active adjustment amount output by 1 step; />Respectively, the nth system of the equivalent synchronous units under high-frequency disturbance after the speed regulator limiting link . 、n . -an active adjustment amount of 1 step; />Respectively, the system n is after the equivalent new energy units under the high-frequency disturbance pass through the first-order inertia link of the inverter . 、n . -a frequency offset value of 1 step; />The active adjustment quantity after the first-order inertia link and the active adjustment quantity after the limiting link of the equivalent new energy unit under the high-frequency disturbance are respectively;
(3) The initial state of the disturbed high-proportion new energy power system is as follows:
the disturbance comprises low-frequency disturbance and high-frequency disturbance, the high-proportion new energy power system normally operates before the disturbance occurs, the frequency of the high-proportion new energy power system is the rated frequency, the frequency deviation amount of the high-proportion new energy power system is 0 at the initial moment of the disturbance, the active adjustment amounts of the equivalent synchronous unit and the equivalent new energy unit are both 0, and the following constraint exists:
the equation (26) has a max/min operation function and bilinear terms, and the equation is solved by an equivalent processing method of the max/min operation function introduced in the limiting link and an McCormick envelope convex relaxation method introduced in the bilinear terms;
(1) equivalent synchronous unit and equivalent new energy unit amplitude limiting link in dynamic equation of frequency modulation process: the compact mathematical form of the equivalent synchronous unit and the equivalent new energy unit limiting link is expressed as y=min (x, a) or y=max (x, a), and the functional equivalent of the form as y=g (x) is expressed as:
wherein x and y are variables to be solved; g is the functional relation between the variables x and y;
for the amplitude limiting link of the equivalent synchronous unit, adding an objective function related to frequency deviationAnd the active adjustment quantity of the equivalent new energy unit after the first-order inertia link Then the constraint conditions comprising the min/max arithmetic function are equivalently transformed:
the governor clipping constraint is expressed equivalently in terms of a set of linear constraints:
(2) bilinear terms in the dynamic equation of the frequency modulation process: the bilinear term is the product term of two variables to be solved, and each bilinear term in the dynamic equation of the frequency modulation process is respectivelyWherein variables to be solved are respectively equal value new energy unit inertia time constant H ne Primary frequency modulation gain K of equivalent new energy unit ne System n under low frequency disturbance and high frequency disturbance . Frequency deviation of individual steps>Convex relaxation bilinear terms through the mccomick envelope; solving inertial time constant H of equivalent new energy unit ne Primary frequency modulation gain K of equivalent new energy unit ne The maximum and minimum values of (2) and (35) of the original objective function are eliminated, and the inertial time constant H of the equivalent new energy unit is respectively maximized and minimized under the original problem constraint formulas (11), (12), (14), (15), (16), (18), (20) to (22), (24) and (27) ne Primary frequency modulation gain K of equivalent new energy unit ne ；
Bilinear terms are linearized by the mccomick envelope:
wherein x is i 、x j The independent variable to be solved;independent variables x to be solved i Minimum and maximum values of (2); independent variables x to be solved j Minimum and maximum values of (2); y is a dependent variable to be solved; c ij Is a constant coefficient; omega ij ＝x i x j For two independent variables x to be solved i 、x j Is a product term of (2);
order the
For low frequency disturbances, the following linear constraints are added:
(29)
and the equivalent substitution of formula (16) to:
wherein,respectively equal value new energy unit inertia time constant H ne Minimum and maximum of (2);respectively equal value new energy unit primary frequency modulation gain K ne Minimum and maximum of (2); />The system frequency deviation value of the nth step under the low-frequency disturbance is equal to the inertia time constant H of the new energy unit ne Is a product of (2); />The system frequency deviation value of the nth step under low-frequency disturbance and the inertia time constant K of the equivalent new energy unit ne Is a product of (2); />The maximum deviation value limit value of the system frequency under low-frequency disturbance is set;
for high frequency disturbances, the following linear constraints are added: :
and the equivalent substitution of formula (22) to:
wherein,the system frequency deviation value of the nth step under high-frequency disturbance and the inertia time constant H of the equivalent new energy unit ne Is a product of (2); />The system frequency deviation value of the nth step under high-frequency disturbance and the inertia time constant K of the equivalent new energy unit ne Is a product of (2); />The maximum deviation value limit value of the system frequency under high-frequency disturbance is set;
in order to ensure the stable frequency of the high-proportion new energy power system, the maximum deviation value of the frequency of the high-proportion new energy power system is required to be not more than a required given value, namely:
Wherein,the system frequency deviation values of the nth step under the low-frequency disturbance and the high-frequency disturbance are respectively; the maximum deviation value limit value of the system frequency under the low-frequency disturbance and the high-frequency disturbance is respectively set.
Preferably, in step S4, because the dynamic equations of the frequency modulation process of the time domain discretization are all linear constraints, a frequency modulation parameter safety domain convex set is constructed; calculating a frequency modulation parameter safety domain through a PVE algorithm, firstly solving vertexes of the overall shape of the frequency modulation parameter safety domain, then expanding the existing vertex set, and calculating new vertexes beyond the current approximation value; the PVE algorithm objective function and constraints are as follows:
wherein α is a two-dimensional vector representing the direction of the identified vertex; h ne Virtual inertia time constant of the new energy unit with equivalent system; k (K) ne Primary frequency modulation gain coefficient of the system equivalent new energy unit;
the specific operation is as follows: firstly, enabling alpha to be the base of coordinate axes corresponding to two frequency modulation parameters respectively, further respectively obtaining frequency modulation parameter points corresponding to the maximum value and the minimum value of the two frequency modulation parameters, and further determining the basic shape of a frequency modulation parameter security domain; then, let alpha be the external normal vector of each side in the current security domain approximation, thereby solving the currentNew vertices outside the vertex set; let Deltah (i,k) The distance between the solved new vertex and the primary side of the safety domain approximation is calculated, wherein i is the number of circles around the safety domain approximation, and k is the number of the solved new vertex in one circle around the safety domain approximation; order D (i) ＝max{Δh (i,k) K is the maximum value of the distance between the new vertex and the primary side of the security domain approximation in one circle around the security domain approximation; if D (i) And not more than a pre-specified error margin epsilon, terminating the algorithm, and outputting the convex hull of the existing vertex as a frequency modulation parameter safety domain.
Preferably, in step S5, bilinear terms in a dynamic equation of a convex relaxation frequency modulation process by using a mccomick envelope method will cause the obtained frequency modulation parameter security domain to contain a frequency modulation parameter solution that does not meet the frequency stability requirement, and the frequency modulation parameter security domain is compressed by using a corner cut method, and then the frequency modulation parameter security domain is optimized by deleting parameter points in the frequency modulation parameter security domain that do not meet the system frequency stability requirement, which specifically comprises the following steps:
(1) Dividing each internal angle to be cut in frequency modulation parameter safety domain
Because the discretized frequency modulation process dynamic equations are all linear constraints, the solved frequency modulation parameter safety domain is a convex polygon;
arranging all vertexes of the frequency modulation parameter security domain along the anticlockwise direction to form a frequency modulation parameter security domain vertex set; sequentially selecting adjacent three vertexes in the vertex set to form an internal angle to be cut, wherein the internal angle of the safety domain of the ith frequency modulation parameter is an angle A i I=1, 2, … N; internal angle A i The corresponding 3 security domain vertexes are vertex V i,1 Vertex V i,2 And vertex V i,3 Wherein the inner angle A i Vertex V of (1) i,3 And inner angle A i+1 Vertex V of (1) i+1,1 The vertex of the security domain is the same frequency modulation parameter;
therefore, if the number of vertices of the security domain is odd, the first internal angle A is divided 1 Vertex V of (1) 1,1 I.e. the last internal angle A divided N Vertex V of (1) N,3 The method comprises the steps of carrying out a first treatment on the surface of the If the number of vertices of the security domain is even, the first interior angle A is divided 1 Vertex V of (1) 1,1 With the last internal angle A divided N Vertex V of (1) N,3 Adjacent;
(2) Solving cutting lines parallel to the bottom edges of all inner angles of the frequency modulation parameter security domain by a dichotomy
The frequency modulation parameter security domain is a continuous point set on a two-dimensional plane formed by inertia time constants of each synchronous unit and the new energy unit and primary frequency modulation gain, so that the frequency modulation parameter security domain is compressed from the boundary to the inside until each frequency modulation parameter point in the optimization result of the frequency modulation parameter security domain meets the requirement of system frequency stabilization;
(1) the first order of the cutting lines is the bottom edge of each inner angle, namely the inner angle A i Middle vertex V i,1 And vertex V i,3 Connecting the inner angle A i Middle vertex V i,1 And vertex V i,3 Each frequency modulation parameter point on the interconnecting line is respectively substituted into the system Simulink model for simulation verification, if the internal angle A i Middle vertex V i,1 And vertex V i,3 Each frequency modulation parameter point on the interconnecting line causes frequency instability, which indicates that each frequency modulation parameter point outside the cutting line does not meet the frequency stability requirement; thus, the interior angle A i The cutting line is the vertex V i,1 And vertex V i,3 The inter-connection line is used for cutting off the frequency modulation parameter safety domain part to be the whole frequency modulation parameter points of the inner angle;
(2) if the inner angle A i Middle vertex V i,1 And vertex V i,3 The frequency modulation parameter points on the interconnecting lines meet the frequency stability constraint, and the cutting line is made to be an over-peak V i,2 A straight line parallel to the bottom edge of the angle i, wherein the intersection of the cutting line and the frequency modulation parameter security domain is the vertex V i,2 The method comprises the steps of carrying out a first treatment on the surface of the Vertex V i,2 Substituting the frequency modulation parameter points into a system Simulink model for verification, and if the system frequency is stable, indicating that the frequency modulation parameter points corresponding to the inner angle boundaries meet the frequency stability requirement; therefore, the inner corner is free of cutting lines, i.e. no corner cutting operation is performed on the inner corner;
(3) if the inner angle A i Middle vertex V i,1 And vertex V i,3 The frequency modulation parameter points exist on the interconnecting lines to meet the frequency stability constraint, and the vertex V i,2 Substituting the frequency of the system into the Simulink model of the system to perform inspection so as to lead the system frequency to be unstable, and takingThe upper limit of cutting is the over-peak V i,2 A straight line parallel to the bottom edge of angle i; taking the lower limit of cutting as a straight line where the bottom edge of the angle i is positioned; the central lines of the upper cutting limit and the lower cutting limit are used as cutting lines, and the upper frequency modulation parameter points are substituted into a system Simulink model for inspection;
(4) If each frequency modulation parameter point on the current cutting line causes frequency instability, the frequency modulation parameter points outside the cutting line do not meet the frequency stability constraint, and meanwhile, the frequency modulation parameter points which do not meet the frequency stability constraint still exist inside the cutting line, namely, the cutting line still needs to move towards the inside of the frequency modulation parameter safety domain; thus, updating the current cut line to the upper cut limit in the next cycle;
if the frequency modulation parameter points on the current cutting line meet the frequency stability, the fact that the frequency modulation parameter points in the cutting line meet the frequency stability constraint is indicated, and the frequency modulation parameter points meeting the frequency stability constraint still exist outside the cutting line, namely the cutting line needs to move outside the frequency modulation parameter safety domain; thus, updating the current cut line to the lower cut limit in the next cycle;
gradually reducing the distance between the upper limit and the lower limit of cutting through the steps (1), (2), (3) and (4), and outputting a current result as a cutting line of the internal angle of the safety domain of the frequency modulation parameter if the distance between the upper limit and the lower limit of current cutting does not exceed the allowable error tolerance and each frequency modulation parameter point on the current cutting line does not meet the frequency stability constraint; traversing each interior angle divided by the security domain of the frequency modulation parameter in the step (2), and respectively recording cutting lines of each interior angle;
(3) Cutting off triangles surrounded by each inner angle of the frequency modulation parameter security domain and cutting lines of the inner angle;
for the internal angle A of the frequency modulation parameter safety domain i The two intersection points of the cutting line and the edge of the frequency modulation parameter security domain replace the vertex V in the vertex set i,2 Finishing the corner cutting operation;
(4) When the maximum deviation value of the frequency corresponding to the deleted frequency modulation parameter point meets the frequency stability requirement, completing the frequency modulation parameter safety domain optimization;
recording the frequency corresponding to the deleted frequency modulation parameter point around the frequency modulation parameter safety domainThe maximum deviation of the rate is recorded as Deltaf m,max Wherein m is the mth cycle around the frequency modulation parameter security domain; when Deltaf m,max When the frequency maximum deviation value limit value is not greater than the frequency maximum deviation value limit value, the algorithm is terminated, and a convex hull of the existing vertex set is output as an optimization result of the frequency modulation parameter security domain; if Δf m,max And when the algorithm termination standard is not met, the vertex sequence in the current vertex set of the frequency modulation parameter safety domain is adjusted, and the next outer loop is entered, so that the solving result of the frequency modulation parameter safety domain is further optimized.
It should be noted that the division order of the inner angles of the fm parameter security domain may cause that some fm parameter points that do not meet the frequency stability constraint cannot be deleted by the corner cut method, so that the algorithm cannot be terminated. Therefore, the internal angle order is updated in each external cycle, that is, the order of the vertices in the vertex set is adjusted, and the order of the remaining vertices is sequentially complemented after the first vertex in the vertex set is moved to the last vertex in the set.
Therefore, the invention adopts the method for calculating and optimizing the frequency modulation parameter safety domain of the new energy power system, and has the following technical effects:
(1) The method provided by the invention realizes the frequency modulation parameter safety domain calculation and optimization of each station in the system based on the improved frequency response model, so that when the station frequency modulation parameter points in the system are positioned in the safety domain, the system frequency stability is ensured.
(2) The frequency response model adopted by the invention considers the virtual inertia and sagging control of the new energy unit, considers nonlinear links such as clipping, first-order inertia time constant and the like of each unit, and more truly describes the frequency response process after disturbance.
(3) The invention provides an optimization algorithm of the frequency modulation parameter safety domain, the optimization result is visual and simple, and whether the system meets the frequency stability constraint can be judged by judging whether the frequency modulation parameter evaluation value is positioned in the frequency modulation parameter safety domain optimization result. Meanwhile, the safety and the robustness of the current system frequency modulation capacity can be quantitatively evaluated by measuring the distances from the frequency modulation parameter value to boundaries in different directions, so that correction, configuration or corresponding preventive control measures can be conveniently carried out by operating personnel and scheduling personnel.
The technical scheme of the invention is further described in detail through the drawings and the embodiments.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a high-proportion new energy power system frequency response model;
FIG. 3 is a schematic illustration of a PVE algorithm;
FIG. 4 is a flow chart of a security domain optimization algorithm for frequency modulation parameters;
FIG. 5 is a schematic diagram of dividing each interior angle to be cut in the FM parameter security domain;
FIG. 6 is a schematic diagram of solving a cut line by a dichotomy and performing a corner cut operation;
FIG. 7 is a solution of the security domain of the frequency modulation parameters of the three-machine system;
FIG. 8 shows the result of security domain optimization of the frequency modulation parameters of the three-machine system.
Detailed Description
The technical scheme of the invention is further described below through the attached drawings and the embodiments.
Unless defined otherwise, technical or scientific terms used herein should be given the ordinary meaning as understood by one of ordinary skill in the art to which this invention belongs.
Example 1
As shown in fig. 1, a flowchart of a new energy power system frequency modulation parameter safety domain calculation and optimization method includes the following steps:
s1, selecting a high-proportion new energy power system as a research object, wherein the new energy unit participates in frequency modulation through virtual inertia response and primary frequency modulation control.
As shown in fig. 2, the frequency response model of the high-ratio new energy power system is shown. The generator in the system comprises a synchronous unit and a new energy unit, wherein the new energy unit comprises wind power and photovoltaic. The high-proportion new energy power system grid is an alternating current power grid, the power supply comprises a synchronous power supply and a new energy unit, the new energy unit participates in frequency modulation through virtual inertia and primary frequency modulation control, and the load is a constant power load.
S2, taking the difference of dynamic response of the power supply into consideration, and constructing a system active-frequency dynamic model by adopting a transfer function;
after the high-proportion new energy power system generates power disturbance, the frequency dynamic response process is represented by a swinging equation:
wherein f 0 Rated frequency for the system; Δf is the system frequency deviation; h g The inertia of the system synchronous machine is adopted; d is a damping coefficient; ΔP m The per unit value of the mechanical power variation of each frequency modulation unit; ΔP e The per unit value of the active mutation quantity of the load;
the transfer function of equation (1) is expressed as:
-(2H g s+D)Δf(s)＝ΔP m (s)-ΔP e (s) (2)
wherein Δf(s) is the frequency domain form of the per unit value of the system frequency deviation; ΔP m (s) is a frequency domain form of per unit value of the mechanical power variation of each frequency modulation unit; ΔP e (s) is a frequency domain version of the per unit value of the load active mutation quantity; s is the variation of the complex frequency domain;
the active power adjustment quantity of each frequency modulation unit is constrained by a dead zone link and an amplitude limiting link, and the dead zone link is ignored and only the influence of the amplitude limiting link on the frequency dynamic of the system is considered because the dead zone has small influence on the maximum deviation value of the frequency;
the method comprises the steps of performing equivalent aggregation on all synchronous machines in a high-proportion new energy power system to form equivalent synchronous units, wherein the turbine unit is regarded as a turbine unit with a reheating time constant of 0.5 times of a hydraulic hammer effect time constant and a high-pressure cylinder power proportion of-2;
For low-frequency disturbance, obtaining the mechanical power adjustment quantity of the equivalent synchronous unit, wherein the speed regulator limiting link of the equivalent synchronous unit is command limiting:
the mechanical power adjustment quantity of the equivalent synchronous unit under high-frequency disturbance is as follows:
wherein,the active limiting value is equivalent to that of the synchronous unit; />The active adjustment quantity of the equivalent synchronous unit under low-frequency disturbance after the amplitude limiting link is adopted; />The active adjustment quantity of the equivalent synchronous unit under high-frequency disturbance after the amplitude limiting link is adopted; k (K) g The gain of a speed regulator of the equivalent synchronous unit; />The active adjustment quantity is output by the equivalent synchronous unit through the prime motor under low-frequency disturbance; />The active adjustment quantity is output by the equivalent synchronous unit through the prime motor under high-frequency disturbance; f (F) H The high-pressure turbine coefficient is the equivalent synchronous machine; t (T) R The reheating time constant is equivalent to that of the synchronous unit;
according to the virtual inertia and the primary frequency modulation modeling, frequency support provided by each new energy unit is connected, and the equivalence of each new energy unit in the system is aggregated into an equivalence new energy unit;
for low-frequency disturbance, obtaining the mechanical power adjustment quantity of the equivalent new energy unit;
/>
the mechanical power adjustment quantity of the equivalent synchronous unit under high-frequency disturbance is as follows:
wherein,adding active power adjustment quantity of a frequency control link for the equivalent new energy unit under low-frequency disturbance; Adding active power adjustment quantity of a frequency control link for the equivalent new energy unit under high-frequency disturbance; h ne An inertial time constant of virtual inertia response of the equivalent new energy unit; k (K) ne The gain coefficient is the gain coefficient of primary frequency modulation control of the equivalent new energy unit; t (T) ne The control time constant of the first-order inertia link of the inverter of the equivalent new energy unit is set; virtual inertial response of equivalent new energy unit and primary frequency modulation control together use standby power, wherein +.>Is the active power of the equivalent new source unitLimiting value, ->The active adjustment quantity of the equivalent new energy unit under low-frequency disturbance after the limiting link is adopted; />The active adjustment quantity of the equivalent new energy unit under high-frequency disturbance after the limiting link is adopted.
S3, taking a synchronous unit and a limiting link of the new energy unit in the high-proportion new energy power system into consideration, and establishing a linearization mathematical model of a dynamic equation of the system frequency modulation process;
discretizing a dynamic equation of the frequency modulation process by a forward difference method, and respectively constructing a linear model of the frequency response of the high-proportion new energy power system after low-frequency disturbance and high-frequency disturbance by using bilinear terms in the dynamic equation of the frequency modulation process by McCormick envelope linearization;
(1) A linear model of the frequency response of the high-proportion new energy power system after low-frequency disturbance:
(1) High-proportion new energy power system frequency deviation:
wherein,the occurrence of the low-frequency disturbance is delta P L The frequency deviation of the n.n. -1 step of the system under the low frequency disturbance; d, d n For differential step length, H g The inertia time constant of the equivalent synchronous machine; p (P) L The total load of the new energy power system with high proportion is; />The active adjustment quantity of the nth-1 step length of the equivalent synchronous unit and the equivalent new energy unit under low-frequency disturbance is respectively calculated; f (f) 0 Rated frequency of a high-proportion new energy power system; s is S b The total capacity of the high-proportion new energy power system is obtained; />Is the rated capacity of the equivalent thermal power unit; />The rated capacity of the equivalent new energy unit; d is a system damping coefficient;
(2) active power adjustment quantity of equivalent synchronous unit:
wherein,the active adjustment quantity is output by the equivalent synchronous unit under low-frequency disturbance at the n-th and n-1 step length; />Respectively carrying out active adjustment quantity of the n-th and n-1 step length of the system after the equivalent synchronous machine set under low-frequency disturbance passes through the limiter link of the speed regulator; />The active limiting value and the rated capacity of the equivalent thermal power generating unit are respectively; k (K) g The gain of a speed regulator of the equivalent synchronous unit; t (T) R The reheating time constant is equivalent to that of the synchronous unit; f (F) H The high-pressure turbine coefficient is equal to the high-pressure turbine coefficient of the synchronous unit;
(3) Active power adjustment quantity of equivalent new energy unit:
wherein,respectively obtaining the frequency deviation values of the nth and the n-1 step of the system after the equivalent new energy unit under the low-frequency disturbance passes through the first-order inertia link of the inverter; />The active adjustment quantity after the first-order inertia link and the active adjustment quantity after the amplitude limiting link of the equivalent new energy unit under the low-frequency disturbance are respectively; />The active limiting value and the rated capacity of the equivalent new energy unit are respectively; h ne The inertial time constant is equivalent to the inertial time constant of the new energy unit; k (K) ne The speed regulator gain of the equivalent new energy unit; t (T) ne The time constant of the first-order inertia link of the inverter of the equivalent new energy unit;
(2) A linear model of the frequency response of the high-proportion new energy power system after high-frequency disturbance:
wherein,the occurrence of the high-frequency disturbance is delta P L System n under high frequency disturbance of (2) . 、n . -a frequency deviation of 1 step; />Respectively the active adjustment quantity of the nth-1 step length of the equivalent synchronous unit and the equivalent new energy unit under high-frequency disturbance; />Respectively the nth equivalent synchronous units under high-frequency disturbance . 、n . -an active adjustment amount output by 1 step; />Respectively, the nth system of the equivalent synchronous units under high-frequency disturbance after the speed regulator limiting link . 、n . -an active adjustment amount of 1 step; / >Respectively, the system n is after the equivalent new energy units under the high-frequency disturbance pass through the first-order inertia link of the inverter . 、n . -a frequency offset value of 1 step; />The active adjustment quantity after the first-order inertia link and the active adjustment quantity after the limiting link of the equivalent new energy unit under the high-frequency disturbance are respectively;
(3) The initial state of the disturbed high-proportion new energy power system is as follows:
the disturbance comprises low-frequency disturbance and high-frequency disturbance, the high-proportion new energy power system normally operates before the disturbance occurs, the frequency of the high-proportion new energy power system is the rated frequency, the frequency deviation amount of the high-proportion new energy power system is 0 at the initial moment of the disturbance, the active adjustment amounts of the equivalent synchronous unit and the equivalent new energy unit are both 0, and the following constraint exists:
the equation (26) has a max/min operation function and bilinear terms, and the equation is solved by an equivalent processing method of the max/min operation function introduced in the limiting link and an McCormick envelope convex relaxation method introduced in the bilinear terms;
(1) equivalent synchronous unit and equivalent new energy unit amplitude limiting link in dynamic equation of frequency modulation process: the compact mathematical form of the equivalent synchronous unit and the equivalent new energy unit limiting link is expressed as y=min (x, a) or y=max (x, a), and the functional equivalent of the form as y=g (x) is expressed as:
Wherein x and y are variables to be solved; g is the functional relation between the variables x and y;
for equivalent synchronizationAn amplitude limiting link of the unit, adding an objective function related to frequency deviationAnd the active adjustment quantity of the equivalent new energy unit after the first-order inertia linkThen the constraint conditions comprising the min/max arithmetic function are equivalently transformed:
the governor clipping constraint is expressed equivalently in terms of a set of linear constraints:
(2) bilinear terms in the dynamic equation of the frequency modulation process: the bilinear term is the product term of two variables to be solved, and each bilinear term in the dynamic equation of the frequency modulation process is respectivelyWherein variables to be solved are respectively equal value new energy unit inertia time constant H ne Primary frequency modulation gain K of equivalent new energy unit ne And frequency deviation +.f. of nth step of system under low frequency disturbance and high frequency disturbance>Convex relaxation bilinear terms through the mccomick envelope; solving inertial time constant H of equivalent new energy unit ne Primary frequency modulation gain K of equivalent new energy unit ne The maximum and minimum values of (2) and (35) of the original objective function are eliminated, and the inertial time constant H of the equivalent new energy unit is respectively maximized and minimized under the original problem constraint formulas (11), (12), (14), (15), (16), (18), (20) to (22), (24) and (27) ne Primary frequency modulation gain K of equivalent new energy unit ne ；/>
Bilinear terms are linearized by the mccomick envelope:
wherein x is i 、x j The independent variable to be solved;independent variables x to be solved i Minimum and maximum values of (2); independent variables x to be solved j Minimum and maximum values of (2); y is a dependent variable to be solved; c ij Is a constant coefficient; omega ij ＝x i x j For two independent variables x to be solved i 、x j Is a product term of (2);
order the
For low frequency disturbances, the following linear constraints are added:
and the equivalent substitution of formula (16) to:
wherein,respectively equal value new energy unit inertia time constant H ne Minimum and maximum of (2);respectively equal value new energy unit primary frequency modulation gain K ne Minimum and maximum of (2); />The system frequency deviation value of the nth step under the low-frequency disturbance is equal to the inertia time constant H of the new energy unit ne Is a product of (2); />The system frequency deviation value of the nth step under low-frequency disturbance and the inertia time constant K of the equivalent new energy unit ne Is a product of (2); />The maximum deviation value limit value of the system frequency under low-frequency disturbance is set;
for high frequency disturbances, the following linear constraints are added: :
and the equivalent substitution of formula (22) to:
wherein,the system frequency deviation value of the nth step under high-frequency disturbance and the inertia time constant H of the equivalent new energy unit ne Is a product of (2); />The system frequency deviation value of the nth step under high-frequency disturbance and the inertia time constant K of the equivalent new energy unit ne Is a product of (2); />The maximum deviation value limit value of the system frequency under high-frequency disturbance is set;
in order to ensure the stable frequency of the high-proportion new energy power system, the maximum deviation value of the frequency of the high-proportion new energy power system is required to be not more than a required given value, namely:
wherein,the system frequency deviation values of the nth step under the low-frequency disturbance and the high-frequency disturbance are respectively; respectively under low-frequency disturbance and high-frequency disturbanceMaximum deviation value limit of the system frequency.
S4, solving a two-dimensional frequency modulation parameter safety domain taking each frequency modulation parameter as a coordinate axis through identifying vertexes;
because the dynamic equations of the frequency modulation process of the time domain discretization are all linear constraints, a frequency modulation parameter safety domain convex set is constructed; calculating a frequency modulation parameter safety domain through a PVE algorithm, firstly solving vertexes of the overall shape of the frequency modulation parameter safety domain, then expanding the existing vertex set, and calculating new vertexes beyond the current approximation value; the PVE algorithm objective function and constraints are as follows:
wherein α is a two-dimensional vector representing the direction of the identified vertex; h ne Virtual inertia time constant of the new energy unit with equivalent system; k (K) ne Primary frequency modulation gain coefficient of the system equivalent new energy unit;
the specific operation is as follows: firstly, enabling alpha to be the base of coordinate axes corresponding to two frequency modulation parameters respectively, further respectively obtaining frequency modulation parameter points corresponding to the maximum value and the minimum value of the two frequency modulation parameters, and further determining the basic shape of a frequency modulation parameter security domain; then, alpha is respectively made to be the external normal vector of each side in the current safety domain approximation value, so that new vertexes outside the current vertex set are solved; let Deltah (i,k) The distance between the solved new vertex and the primary side of the safety domain approximation is calculated, wherein i is the number of circles around the safety domain approximation, and k is the number of the solved new vertex in one circle around the safety domain approximation; order D (i) ＝max{Δh (i,k) K is the maximum value of the distance between the new vertex and the primary side of the security domain approximation in one circle around the security domain approximation; if D (i) And not more than a pre-specified error margin epsilon, terminating the algorithm, and outputting the convex hull of the existing vertex as a frequency modulation parameter safety domain. FIG. 3 is a schematic illustration of a PVE algorithm, as shown in FIG. 3, whereinThe sexual time constant H and primary frequency modulation gain K are two frequency modulation parameters to be solved, and the frequency modulation parameter points are corresponding to the maximum value of K, the maximum value of H, the minimum value of K and the minimum value of H respectively. / >New vertices, Δh, are extended for the first week around the frequency modulation parameter safety domain approximation (1,1) 、Δh (1,2) 、Δh (1,3) 、Δh (1,4) Is thatDistance from the primary side of the security domain approximation, D (1) Is delta h (1,k) K is the maximum value in K.
And S5, deleting frequency modulation parameter points which do not meet the frequency stability requirement in the frequency modulation parameter safety domain by adopting a corner cutting method, and further optimizing the frequency modulation parameter safety domain.
Bilinear terms in the dynamic equation of the relaxation frequency modulation process are raised and relaxed by the McCormick envelope method, so that the obtained frequency modulation parameter safety domain contains frequency modulation parameter solutions which do not meet the frequency stability. Therefore, the frequency modulation parameter safety domain is considered to be compressed by adopting the corner cut method, and the frequency modulation parameter safety domain is optimized by deleting parameter points which do not meet the requirement of system frequency stability in the frequency modulation parameter safety domain. The basic idea of the algorithm is to solve a cutting line parallel to the bottom edge of an interior angle of a polygon formed by any adjacent three vertexes in a safety domain by a dichotomy, and cut off a triangle formed by the cutting line and the interior angle. FIG. 4 is a flowchart of the security domain optimization algorithm for frequency modulation parameters, comprising the following steps:
(1) Dividing each internal angle to be cut in the frequency modulation parameter safety domain. Because the discretized frequency modulation process dynamic equations are all linear constraints, the solved frequency modulation parameter safety domain is a convex polygon. Arranging frequency modulation parameters in a counter-clockwise direction And each vertex of the security domain forms a frequency modulation parameter security domain vertex set. Sequentially selecting adjacent three vertexes in the vertex set to form an internal angle to be cut, wherein the internal angle of the safety domain of the ith frequency modulation parameter is an angle A i I=1, 2, … N. Internal angle A i The corresponding 3 security domain vertexes are vertex V i,1 Vertex V i,2 And vertex V i,3 Wherein the inner angle A i Vertex V of (1) i,3 And inner angle A i+1 Vertex V of (1) i+1,1 The security domain vertices are the same frequency modulation parameters. Therefore, if the number of vertices of the security domain is even, the first interior angle A is divided 1 Vertex V of (1) 1,1 I.e. the last internal angle A divided N Vertex V of (1) N,3 . Otherwise, divide the first interior angle A 1 Vertex V of (1) 1,1 With the last internal angle A divided N Vertex V of (1) N,3 Adjacent. FIG. 5 shows a schematic diagram of dividing each interior angle to be cut in the FM parameter security domain, wherein the number of vertices in the FM parameter security domain is 8, and the 1 st interior angle A is divided 1 Vertex V of (1) 1,1 I.e. the 4 th internal angle A N Vertex V of (1) 4,3 。
(2) And solving a cutting line parallel to the bottom edge of each inner angle of the frequency modulation parameter security domain by a dichotomy. The frequency modulation parameter security domain is a continuous point set on a two-dimensional plane formed by a unit inertia time constant and a primary frequency modulation gain, so that the frequency modulation parameter security domain is compressed from the boundary to the inside until each frequency modulation parameter point in the optimization result of the frequency modulation parameter security domain meets the requirement of system frequency stability.
(1) The first order of the cutting lines is the bottom edge of each inner angle, namely the inner angle A i Middle vertex V i,1 And vertex V i,3 And (3) interconnecting wires, wherein each frequency modulation parameter point is substituted into a system Simulink model for simulation verification, and if each frequency modulation parameter point causes frequency instability, the condition that each frequency modulation parameter point outside the cutting line does not meet the frequency stability requirement is indicated. Thus, the interior angle A i The cutting line is the vertex V i,1 And vertex V i,3 And connecting wires, wherein the cut frequency modulation parameter safety domain part is the whole frequency modulation parameter points of the inner angle.
(2) If the inner angle A i Middle vertex V i,1 And vertex V i,3 The frequency modulation parameter points on the interconnecting lines meet the frequency stability constraint, and the cutting line is made to be an over-peak V i,2 A straight line parallel to the bottom edge of the angle i, wherein the intersection of the cutting line and the frequency modulation parameter security domain is the vertex V i,2 . Vertex V i,2 Substituting the frequency modulation parameter points into a system Simulink model for inspection, and if the system frequency is stable, indicating that the frequency modulation parameter points corresponding to the inner angle boundaries meet the frequency stability requirement. Therefore, the inner corner is free of cutting lines, i.e., no corner cutting operation is performed on the inner corner.
(3) If the inner angle A i Middle vertex V i,1 And vertex V i,3 The frequency modulation parameter points exist on the interconnecting lines to meet the frequency stability constraint, and the vertex V i,2 Substituting the cut upper limit into a system Simulink model to perform inspection so as to lead the system frequency to be unstable, and taking the cut upper limit as the over-vertex V i,2 A straight line parallel to the bottom edge of angle i; the lower limit of the cutting is taken as a straight line where the bottom edge of the angle i is located. And substituting the upper frequency modulation parameter points of the central lines of the cutting upper limit and the cutting lower limit into a system Simulink model for inspection.
(4) If each frequency modulation parameter point on the current cutting line causes frequency instability, the frequency modulation parameter points outside the cutting line are not satisfied with the frequency stability constraint, and meanwhile, the frequency modulation parameter points which are not satisfied with the frequency stability constraint still exist inside the cutting line, namely, the cutting line still needs to move towards the inside of the frequency modulation parameter safety domain. Thus, the current cut line is updated to the upper cut limit in the next cycle. Similarly, if the frequency modulation parameter points on the current cutting line meet the frequency stability, the fact that the frequency modulation parameter points in the cutting line meet the frequency stability constraint is indicated, and the frequency modulation parameter points meeting the frequency stability constraint still exist outside the cutting line, namely the cutting line needs to move outside the frequency modulation parameter safety domain. Thus, the current cut line is updated to the lower cut limit in the next cycle.
And gradually reducing the distance between the upper cutting limit and the lower cutting limit by the dichotomy, and outputting the current result as a cutting line of the internal angle of the frequency modulation parameter safety domain if the distance between the upper cutting limit and the lower cutting limit does not exceed the allowable error tolerance and each frequency modulation parameter point on the current cutting line does not meet the frequency stability constraint. Traversing the internal angles divided by the security domain of the frequency modulation parameter, and respectively recording cutting lines of the internal angles. As shown in fig. 6, the cutting line is solved by a dichotomy and a cutting angle operation is performed, the cutting upper limit and the cutting lower limit are gradually approximated, the cutting line is taken as a central line between the cutting upper limit and the cutting lower limit, and when the distance between the cutting upper limit and the cutting lower limit does not exceed the error tolerance and each frequency modulation parameter point on the cutting line does not meet the frequency stability constraint, the cutting angle operation is performed, and the solution which does not meet the frequency stability constraint is deleted.
(3) And cutting off the triangle surrounded by each inner angle of the frequency modulation parameter security domain and the cutting line thereof. For the internal angle A of the frequency modulation parameter safety domain i The two intersection points of the cutting line and the edge of the frequency modulation parameter security domain replace the vertex V in the vertex set i,2 And finishing the corner cutting operation.
(4) And when the maximum deviation value of the frequency corresponding to the deleted frequency modulation parameter point meets the frequency stability requirement, the frequency modulation parameter safety domain optimization is completed. Recording the maximum deviation value of the frequency corresponding to the deleted frequency modulation parameter point around the frequency modulation parameter safety domain, and recording as delta f m,max Where m is the mth cycle around the frequency modulation parameter security domain. When Deltaf m,max And when the frequency maximum deviation value limit value is not greater than the frequency maximum deviation value limit value, the algorithm is terminated, and the convex hull of the existing vertex set is output as an optimization result of the frequency modulation parameter security domain. If Δf m,max And when the algorithm termination standard is not met, the vertex sequence in the current vertex set of the frequency modulation parameter safety domain is adjusted, and the next outer loop is entered, so that the solving result of the frequency modulation parameter safety domain is further optimized.
It should be noted that the division order of the inner angles of the fm parameter security domain may cause that some fm parameter points that do not meet the frequency stability constraint cannot be deleted by the corner cut method, so that the algorithm cannot be terminated. Therefore, the internal angle order is updated in each external cycle, that is, the order of the vertices in the vertex set is adjusted, and the order of the remaining vertices is sequentially complemented after the first vertex in the vertex set is moved to the last vertex in the set.
The method according to the invention is illustrated by means of specific examples.
The embodiment of the invention comprises 3 generators, wherein G1 and G2 are synchronous generators, G3 is a new energy unit controlled by a virtual synchronous machine, and the additional frequency control mode is virtual inertia and primary frequency modulation. The parameters of the system are shown in table 1.
Table 1 generator parameters
Setting the active disturbance in the system as low-frequency disturbance with the size of 120MW; the maximum deviation value limit value of the frequency is 0.5Hz; the system damping coefficient is 0.05p.u.; the active load of the system is 900MW.
The frequency modulation parameter safety domain calculation and optimization method of the new energy power system comprises the following steps:
s110, selecting a high-proportion new energy power system as a research object, wherein the new energy unit participates in frequency modulation through virtual inertia response and primary frequency modulation control. For the three-machine system in the embodiment of the invention, the new energy capacity is 46.7 percent.
S120, taking the difference of dynamic response of the power supply into consideration, and constructing a system active-frequency dynamic model by adopting a transfer function.
S130, considering limiting links of all units in the system, and establishing a linearization mathematical model of a dynamic equation of the frequency modulation process of the system, wherein the discretization step length of the frequency dynamic equation is set to be 0.05.
And S140, solving a two-dimensional frequency modulation parameter safety domain taking each frequency modulation parameter as a coordinate axis by identifying the vertex. Fig. 7 shows the result of solving the frequency modulation parameter safety domain of the three-machine system according to the embodiment, when the virtual inertia time constant and the primary frequency modulation gain of the new energy unit G3 are smaller, the system does not meet the frequency stability requirement. Because the McCormick envelope method is adopted to convexly relax the bilinear term, the current frequency modulation parameter safety domain contains frequency modulation parameter solutions which do not meet the frequency stability.
S150, deleting frequency modulation parameter points which do not meet the frequency stability requirement in the frequency modulation parameter safety domain by adopting a chamfer method, and further optimizing the frequency modulation parameter safety domain. As shown in FIG. 8, the frequency modulation parameter safety domain optimization results of the three-machine system according to the embodiment are shown in the following figures, wherein the vertex coordinates of the frequency modulation parameter safety domain optimization results are [0,50 ]]、[29.312,50]、[0,11.288]、[0,16.667]The maximum deviation value of the frequency corresponding to each vertex of the frequency modulation parameter security domain optimization result is-0.4601 Hz, and the frequency stability constraint condition is met. When the virtual inertia time constant H of the new energy unit G3 ne Primary frequency modulation gain K ne When the frequency modulation parameter is positioned in the frequency modulation parameter safety domain optimization result, the system can ensure the frequency stability. Meanwhile, the safety and the robustness of the current system frequency modulation capacity can be quantitatively evaluated by measuring the distances from the frequency modulation parameter value of the new energy unit G3 to boundaries in different directions, so that the correction, configuration or corresponding preventive control measures can be conveniently carried out by operators and schedulers.
Therefore, the frequency modulation parameter safety domain calculation and optimization method for the new energy power system can solve the problem that the safety range of the frequency modulation parameters of the system is not clear, and realize the optimization setting of the frequency modulation parameters of each station of the system. The frequency modulation parameter safety domain optimization result is visual and simple in form, and whether the system meets the frequency stability constraint can be judged by judging whether the frequency modulation parameter evaluation value is located in the frequency modulation parameter safety domain optimization result. Meanwhile, the safety and the robustness of the current system frequency modulation capacity can be quantitatively evaluated by measuring the distances from the frequency modulation parameter value to boundaries in different directions, so that the correction, configuration or corresponding preventive control measures are conveniently carried out by operators and schedulers, and the system has field application value.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention and not for limiting it, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that: the technical scheme of the invention can be modified or replaced by the same, and the modified technical scheme cannot deviate from the spirit and scope of the technical scheme of the invention.
Claims (6)
1. The frequency modulation parameter safety domain calculation and optimization method for the new energy power system is characterized by comprising the following steps of:
s1, selecting a high-proportion new energy power system as a research object, wherein the new energy unit participates in frequency modulation through virtual inertia response and primary frequency modulation control;
s2, taking the difference of dynamic response of the power supply into consideration, and constructing a system active-frequency dynamic model by adopting a transfer function;
s3, taking a synchronous unit and a limiting link of the new energy unit in the high-proportion new energy power system into consideration, and establishing a linearization mathematical model of a dynamic equation of the system frequency modulation process;
s4, solving a two-dimensional frequency modulation parameter safety domain taking each frequency modulation parameter as a coordinate axis through identifying vertexes;
and S5, deleting frequency modulation parameter points which do not meet the frequency stability requirement in the frequency modulation parameter safety domain by adopting a corner cutting method, and further optimizing the frequency modulation parameter safety domain.
2. The method for calculating and optimizing the frequency modulation parameter safety domain of the new energy power system according to claim 1, wherein in step S1, the high-proportion new energy power system grid is an ac grid, and the power supply comprises a synchronous power supply and a new energy unit.
3. The method for calculating and optimizing the frequency modulation parameter safety domain of the new energy power system according to claim 2, wherein in step S2, after the power disturbance occurs in the high-proportion new energy power system, the frequency dynamic response process is represented by a rocking equation:
Wherein f 0 Rated frequency for the system; Δf is the system frequency deviation; h g The inertia of the system synchronous machine is adopted; d is a damping coefficient; ΔP m The per unit value of the mechanical power variation of each frequency modulation unit; ΔP e The per unit value of the active mutation quantity of the load;
the transfer function of equation (1) is expressed as:
-(2H g s+D)Δf(s)＝ΔP m (s)-ΔP e (s) (2)
wherein Δf(s) is the frequency domain form of the per unit value of the system frequency deviation; ΔP m (s) is a frequency domain form of per unit value of the mechanical power variation of each frequency modulation unit; ΔP e (s) is a frequency domain version of the per unit value of the load active mutation quantity; s is the variation of the complex frequency domain;
the active power adjustment quantity of each frequency modulation unit is constrained by a dead zone link and an amplitude limiting link, and the dead zone link is ignored and only the influence of the amplitude limiting link on the frequency dynamic of the system is considered because the dead zone has small influence on the maximum deviation value of the frequency;
the method comprises the steps of performing equivalent aggregation on all synchronous machines in a high-proportion new energy power system to form equivalent synchronous units, wherein the turbine unit is regarded as a turbine unit with a reheating time constant of 0.5 times of a hydraulic hammer effect time constant and a high-pressure cylinder power proportion of-2;
for low-frequency disturbance, obtaining the mechanical power adjustment quantity of the equivalent synchronous unit, wherein the speed regulator limiting link of the equivalent synchronous unit is command limiting:
The mechanical power adjustment quantity of the equivalent synchronous unit under high-frequency disturbance is as follows:
wherein,the active limiting value is equivalent to that of the synchronous unit; />The active adjustment quantity of the equivalent synchronous unit under low-frequency disturbance after the amplitude limiting link is adopted; />The active adjustment quantity of the equivalent synchronous unit under high-frequency disturbance after the amplitude limiting link is adopted; k (K) g The gain of a speed regulator of the equivalent synchronous unit; ΔP g - The active adjustment quantity is output by the equivalent synchronous unit through the prime motor under low-frequency disturbance;the active adjustment quantity is output by the equivalent synchronous unit through the prime motor under high-frequency disturbance; f (F) H The high-pressure turbine coefficient is the equivalent synchronous machine; t (T) R The reheating time constant is equivalent to that of the synchronous unit;
according to the virtual inertia and the primary frequency modulation modeling, frequency support provided by each new energy unit is connected, and the equivalence of each new energy unit in the system is aggregated into an equivalence new energy unit;
for low-frequency disturbance, obtaining the mechanical power adjustment quantity of the equivalent new energy unit;
the mechanical power adjustment quantity of the equivalent synchronous unit under high-frequency disturbance is as follows:
wherein,adding active power adjustment quantity of a frequency control link for the equivalent new energy unit under low-frequency disturbance; />Adding active power adjustment quantity of a frequency control link for the equivalent new energy unit under high-frequency disturbance; h ne An inertial time constant of virtual inertia response of the equivalent new energy unit; k (K) ne The gain coefficient is the gain coefficient of primary frequency modulation control of the equivalent new energy unit; t (T) ne The control time constant of the first-order inertia link of the inverter of the equivalent new energy unit is set; virtual inertial response of equivalent new energy unit and primary frequency modulation control together use standby power, wherein +.>Is the active limiting value of the equivalent new source unit, < ->The active adjustment quantity of the equivalent new energy unit under low-frequency disturbance after the limiting link is adopted; />The active adjustment quantity of the equivalent new energy unit under high-frequency disturbance after the limiting link is adopted.
4. The method for calculating and optimizing the frequency modulation parameter safety domain of the new energy power system according to claim 3, wherein in the step S3, a dynamic equation of a frequency modulation process is discretized by a forward difference method, and a bilinear term in the dynamic equation of the frequency modulation process is linearized by an envelope of McCormick to respectively construct a linear model of frequency response of the new energy power system with high proportion after low-frequency disturbance and high-frequency disturbance;
(1) A linear model of the frequency response of the high-proportion new energy power system after low-frequency disturbance:
(1) high-proportion new energy power system frequency deviation:
wherein,the occurrence of the low-frequency disturbance is delta P L The frequency deviation of the n.n. -1 step of the system under the low frequency disturbance; d, d n For differential step length, H g The inertia time constant of the equivalent synchronous machine; p (P) L The total load of the new energy power system with high proportion is; />The active adjustment quantity of the nth-1 step length of the equivalent synchronous unit and the equivalent new energy unit under low-frequency disturbance is respectively calculated; f (f) 0 Rated frequency of a high-proportion new energy power system; s is S b The total capacity of the high-proportion new energy power system is obtained;is the rated capacity of the equivalent thermal power unit; />The rated capacity of the equivalent new energy unit; d is a system damping coefficient;
(2) active power adjustment quantity of equivalent synchronous unit:
wherein,the active adjustment quantity is output by the equivalent synchronous unit at the nth step and the n-1 th step under the low-frequency disturbance; />Respectively the active adjustment amounts of the nth step length and the n-1 th step length of the system after the equivalent synchronous machine set under low-frequency disturbance passes through the limiter link of the speed regulator; />The active limiting value and the rated capacity of the equivalent thermal power generating unit are respectively; k (K) g The gain of a speed regulator of the equivalent synchronous unit; t (T) R The reheating time constant is equivalent to that of the synchronous unit; f (F) H The high-pressure turbine coefficient is equal to the high-pressure turbine coefficient of the synchronous unit;
(3) active power adjustment quantity of equivalent new energy unit:
wherein,respectively obtaining frequency deviation values of the nth step and the n-1 th step of the system after the equivalent new energy unit under low-frequency disturbance passes through the first-order inertia link of the inverter; / >The active adjustment quantity after the first-order inertia link and the active adjustment quantity after the amplitude limiting link of the equivalent new energy unit under the low-frequency disturbance are respectively; />The active limiting value and the rated capacity of the equivalent new energy unit are respectively; h ne The inertial time constant is equivalent to the inertial time constant of the new energy unit; k (K) ne The speed regulator gain of the equivalent new energy unit; t (T) ne The time constant of the first-order inertia link of the inverter of the equivalent new energy unit;
(2) A linear model of the frequency response of the high-proportion new energy power system after high-frequency disturbance:
wherein,the occurrence of the high-frequency disturbance is delta P L The frequency deviation of the nth step length and the n-1 step length of the system under the high-frequency disturbance; />Respectively the active adjustment quantity of the nth-1 step length of the equivalent synchronous unit and the equivalent new energy unit under high-frequency disturbance; />Respectively the active adjustment amounts output by the equivalent synchronous units under the high-frequency disturbance at the n-1 th step length; />Respectively the active adjustment amounts of the nth step length and the n-1 th step length of the system after the equivalent synchronous machine set under high-frequency disturbance passes through the limiter link of the speed regulator; />Respectively obtaining frequency deviation values of the nth step and the n-1 th step of the system after the equivalent new energy unit under high-frequency disturbance passes through the first-order inertia link of the inverter; />The active adjustment quantity after the first-order inertia link and the active adjustment quantity after the limiting link of the equivalent new energy unit under the high-frequency disturbance are respectively;
(3) The initial state of the disturbed high-proportion new energy power system is as follows:
the disturbance comprises low-frequency disturbance and high-frequency disturbance, the high-proportion new energy power system normally operates before the disturbance occurs, the frequency of the high-proportion new energy power system is the rated frequency, the frequency deviation amount of the high-proportion new energy power system is 0 at the initial moment of the disturbance, the active adjustment amounts of the equivalent synchronous unit and the equivalent new energy unit are both 0, and the following constraint exists:
the equation (26) has a max/min operation function and bilinear terms, and the equation is solved by an equivalent processing method of the max/min operation function introduced in the limiting link and an McCormick envelope convex relaxation method introduced in the bilinear terms;
(1) equivalent synchronous unit and equivalent new energy unit amplitude limiting link in dynamic equation of frequency modulation process: the compact mathematical form of the equivalent synchronous unit and the equivalent new energy unit limiting link is expressed as y=min (x, a) or y=max (x, a), and the functional equivalent of the form as y=g (x) is expressed as:
wherein x and y are variables to be solved; g is the functional relation between the variables x and y;
for the amplitude limiting link of the equivalent synchronous unit, adding an objective function related to frequency deviationAnd the active adjustment quantity of the equivalent new energy unit after the first-order inertia link Then the constraint conditions comprising the min/max arithmetic function are equivalently transformed:
the governor clipping constraint is expressed equivalently in terms of a set of linear constraints:
(2) bilinear terms in the dynamic equation of the frequency modulation process: the bilinear term is the product term of two variables to be solved, and each bilinear term in the dynamic equation of the frequency modulation process is respectivelyWherein variables to be solved are respectively equal value new energy unit inertia time constant H ne Primary frequency modulation gain K of equivalent new energy unit ne And the frequency deviation of the nth step of the system under low-frequency disturbance and high-frequency disturbance +.>Convex relaxation bilinear terms through the mccomick envelope; solving inertial time constant H of equivalent new energy unit ne Primary frequency modulation gain K of equivalent new energy unit ne The maximum and minimum values of (2) and (35) of the original objective function are eliminated, and the inertial time constant H of the equivalent new energy unit is respectively maximized and minimized under the original problem constraint formulas (11), (12), (14), (15), (16), (18), (20) to (22), (24) and (27) ne Primary frequency modulation gain K of equivalent new energy unit ne ；
Bilinear terms are linearized by the mccomick envelope:
wherein x is i 、x j The independent variable to be solved;independent variables x to be solved i Minimum and maximum values of (2); /> Independent variables x to be solved j Minimum and maximum values of (2); y is a dependent variable to be solved; c ij Is a constant coefficient; omega ij ＝x i x j For two independent variables x to be solved i 、x j Is a product term of (2);
order the
For low frequency disturbances, the following linear constraints are added:
and the equivalent substitution of formula (16) to:
wherein,respectively equal value new energy unit inertia time constant H ne Minimum and maximum of (2); />Respectively equal value new energy unit primary frequency modulation gain K ne Minimum and maximum of (2); />The system frequency deviation value of the nth step under the low-frequency disturbance is equal to the inertia time constant H of the new energy unit ne Is a product of (2); />The system frequency deviation value of the nth step under low-frequency disturbance and the inertia time constant K of the equivalent new energy unit ne Is a product of (2); />The maximum deviation value limit value of the system frequency under low-frequency disturbance is set;
for high frequency disturbances, the following linear constraints are added: :
and the equivalent substitution of formula (22) to:
wherein,the system frequency deviation value of the nth step under high-frequency disturbance and the inertia time constant H of the equivalent new energy unit ne Is a product of (2); />The system frequency deviation value of the nth step under high-frequency disturbance and the inertia time constant K of the equivalent new energy unit ne Is a product of (2); />The maximum deviation value limit value of the system frequency under high-frequency disturbance is set;
in order to ensure the stable frequency of the high-proportion new energy power system, the maximum deviation value of the frequency of the high-proportion new energy power system is required to be not more than a required given value, namely:
Wherein,the system frequency deviation values of the nth step under the low-frequency disturbance and the high-frequency disturbance are respectively; /> The maximum deviation value limit value of the system frequency under the low-frequency disturbance and the high-frequency disturbance is respectively set.
5. The method for calculating and optimizing the frequency modulation parameter safety domain of the new energy power system according to claim 4, wherein in the step S4, since the dynamic equations of the frequency modulation process of the time domain discretization are all linear constraints, a convex set of the frequency modulation parameter safety domain is constructed; calculating a frequency modulation parameter safety domain through a PVE algorithm, firstly solving vertexes of the overall shape of the frequency modulation parameter safety domain, then expanding the existing vertex set, and calculating new vertexes beyond the current approximation value; the PVE algorithm objective function and constraints are as follows:
wherein α is a two-dimensional vector representing the direction of the identified vertex; h ne Virtual inertia time constant of the new energy unit with equivalent system; k (K) ne Primary frequency modulation gain coefficient of the system equivalent new energy unit;
the specific operation is as follows: firstly, enabling alpha to be the base of coordinate axes corresponding to two frequency modulation parameters respectively, further respectively obtaining frequency modulation parameter points corresponding to the maximum value and the minimum value of the two frequency modulation parameters, and further determining the basic shape of a frequency modulation parameter security domain; then, alpha is respectively made to be the external normal vector of each side in the current safety domain approximation value, so that new vertexes outside the current vertex set are solved; let Deltah (i,k) The distance between the solved new vertex and the primary side of the safety domain approximation is calculated, wherein i is the number of circles around the safety domain approximation, and k is the number of the solved new vertex in one circle around the safety domain approximation; order D (i) ＝max{Δh (i,k) K is the maximum value of the distance between the new vertex and the primary side of the security domain approximation in one circle around the security domain approximation; if D (i) And not more than a pre-specified error margin epsilon, terminating the algorithm, and outputting the convex hull of the existing vertex as a frequency modulation parameter safety domain.
6. The method for calculating and optimizing the frequency modulation parameter safety domain of the new energy power system according to claim 5, wherein in step S5, bilinear terms in dynamic equations of the convex relaxation frequency modulation process by the mccomick envelope method cause the solved frequency modulation parameter safety domain to contain frequency modulation parameter solutions which do not meet the frequency stability, the frequency modulation parameter safety domain is compressed by adopting a corner cut method, and the frequency modulation parameter safety domain is optimized by deleting parameter points which do not meet the system frequency stability requirement in the frequency modulation parameter safety domain, which comprises the following specific operations:
(1) Dividing each internal angle to be cut in frequency modulation parameter safety domain
Because the discretized frequency modulation process dynamic equations are all linear constraints, the solved frequency modulation parameter safety domain is a convex polygon;
Arranging all vertexes of the frequency modulation parameter security domain along the anticlockwise direction to form a frequency modulation parameter security domain vertex set; sequentially selecting adjacent three vertexes in the vertex set to form an internal angle to be cut, wherein the internal angle of the safety domain of the ith frequency modulation parameter is an angle A i I=1, 2, … N; internal angle A i The corresponding 3 security domain vertexes are vertex V i,1 Vertex V i,2 And vertex V i,3 Wherein the inner angle A i Vertex V of (1) i,3 And inner angle A i+1 Vertex V of (1) i+1,1 The vertex of the security domain is the same frequency modulation parameter;
therefore, if the number of vertices of the security domain is odd, the first internal angle A is divided 1 Vertex V of (1) 1,1 I.e. the last internal angle A divided N Vertex V of (1) N,3 The method comprises the steps of carrying out a first treatment on the surface of the If the number of vertices of the security domain is even, the first interior angle A is divided 1 Vertex V of (1) 1,1 With the last internal angle A divided N Vertex V of (1) N,3 Adjacent;
(2) Solving cutting lines parallel to the bottom edges of all inner angles of the frequency modulation parameter security domain by a dichotomy
The frequency modulation parameter security domain is a continuous point set on a two-dimensional plane formed by inertia time constants of each synchronous unit and the new energy unit and primary frequency modulation gain, so that the frequency modulation parameter security domain is compressed from the boundary to the inside until each frequency modulation parameter point in the optimization result of the frequency modulation parameter security domain meets the requirement of system frequency stabilization;
(1) The first order of the cutting lines is the bottom edge of each inner angle, namely the inner angle A i Middle vertex V i,1 And vertex V i,3 Connecting the inner angle A i Middle vertex V i,1 And vertex V i,3 Each frequency modulation parameter point on the interconnecting line is respectively substituted into the system Simulink model for simulation verification, if the internal angle A i Middle vertex V i,1 And vertex V i,3 Each frequency modulation parameter point on the interconnecting line causes frequency instability, which indicates that each frequency modulation parameter point outside the cutting line does not meet the frequency stability requirement; thus, the interior angle A i The cutting line is the vertex V i,1 And vertex V i,3 The inter-connection line is used for cutting off the frequency modulation parameter safety domain part to be the whole frequency modulation parameter points of the inner angle;
(2) if the inner angle A i Middle vertex V i,1 And vertex V i,3 The frequency modulation parameter points on the interconnecting lines meet the frequency stability constraint, and the cutting line is made to be an over-peak V i,2 A straight line parallel to the bottom edge of the angle i, wherein the intersection of the cutting line and the frequency modulation parameter security domain is the vertex V i,2 The method comprises the steps of carrying out a first treatment on the surface of the Vertex V i,2 Substituting the frequency modulation parameter points into a system Simulink model for verification, and if the system frequency is stable, indicating that the frequency modulation parameter points corresponding to the inner angle boundaries meet the frequency stability requirement; therefore, the inner corner is free of cutting lines, i.e. no corner cutting operation is performed on the inner corner;
(3) if the inner angle A i Middle vertex V i,1 And vertex V i,3 The frequency modulation parameter points exist on the interconnecting lines to meet the frequency stability constraint, and the vertex V i,2 Substituting the cut upper limit into a system Simulink model to perform inspection so as to lead the system frequency to be unstable, and taking the cut upper limit as the over-vertex V i,2 A straight line parallel to the bottom edge of angle i; taking the lower limit of cutting as a straight line where the bottom edge of the angle i is positioned; the central lines of the upper cutting limit and the lower cutting limit are used as cutting lines, and the upper frequency modulation parameter points are substituted into a system Simulink model for inspection;
(4) if each frequency modulation parameter point on the current cutting line causes frequency instability, the frequency modulation parameter points outside the cutting line do not meet the frequency stability constraint, and meanwhile, the frequency modulation parameter points which do not meet the frequency stability constraint still exist inside the cutting line, namely, the cutting line still needs to move towards the inside of the frequency modulation parameter safety domain; thus, updating the current cut line to the upper cut limit in the next cycle;
if the frequency modulation parameter points on the current cutting line meet the frequency stability, the fact that the frequency modulation parameter points in the cutting line meet the frequency stability constraint is indicated, and the frequency modulation parameter points meeting the frequency stability constraint still exist outside the cutting line, namely the cutting line needs to move outside the frequency modulation parameter safety domain; thus, updating the current cut line to the lower cut limit in the next cycle;
gradually reducing the distance between the upper limit and the lower limit of cutting through the steps (1), (2), (3) and (4), and outputting a current result as a cutting line of the internal angle of the safety domain of the frequency modulation parameter if the distance between the upper limit and the lower limit of current cutting does not exceed the allowable error tolerance and each frequency modulation parameter point on the current cutting line does not meet the frequency stability constraint; traversing each interior angle divided by the security domain of the frequency modulation parameter in the step (2), and respectively recording cutting lines of each interior angle;
(3) Cutting off triangles surrounded by each inner angle of the frequency modulation parameter security domain and cutting lines of the inner angle;
for the internal angle A of the frequency modulation parameter safety domain i The two intersection points of the cutting line and the edge of the frequency modulation parameter security domain replace the vertex V in the vertex set i,2 Finishing the corner cutting operation;
(4) When the maximum deviation value of the frequency corresponding to the deleted frequency modulation parameter point meets the frequency stability requirement, completing the frequency modulation parameter safety domain optimization;
recording the maximum deviation value of the frequency corresponding to the deleted frequency modulation parameter point around the frequency modulation parameter safety domain, and recording as delta f m,max Wherein m is the mth cycle around the frequency modulation parameter security domain; when Deltaf m,max When the frequency maximum deviation value limit value is not greater than the frequency maximum deviation value limit value, the algorithm is terminated, and a convex hull of the existing vertex set is output as an optimization result of the frequency modulation parameter security domain; if Δf m,max The algorithm termination standard is not met, the vertex sequence in the current vertex set of the frequency modulation parameter safety domain is adjusted, and the next outer loop is entered, so that the frequency modulation parameter safety domain is further optimizedAnd (5) solving the result.
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