Frequency dynamic characteristic analysis method for ultralow frequency oscillation of power system

Abstract

The invention discloses a frequency dynamic characteristic analysis method for ultralow frequency oscillation of a power system. The method comprises the following steps: constructing a frequency dynamic analysis model based on a rotor loop; analyzing the property of a distribution vector of the frequency dynamic analysis model; analyzing the property of the rotating speed response function matrix of the frequency dynamic analysis model; constructing a frequency low-dimensional dynamic practical analysis model under ultralow-frequency oscillation; and analyzing the ultralow frequency stability of the system containing the water turbine governor side stabilizer. According to the method, an analytical expression of a distribution vector is deduced on the basis of a rotor loop, a frequency dynamic analysis model is built according to the analytical expression, and the model can analyze the stability and the frequency regulation performance at the same time. The properties of two special matrixes in a frequency dynamic analysis model are analyzed and proved, the provided model is simplified in a special frequency band by combining the properties, a frequency low-dimensional dynamic practical analysis model is obtained, and meanwhile, a theoretical basis is provided for analyzing ultra-low frequency oscillation by adopting a unified frequency model in engineering.

Description

Technical Field

[0001] The present invention relates to the technical field of power grid safety, and in particular to a frequency dynamic characteristic analysis method for ultra-low frequency oscillation of a power system. Background Art

[0002] As the overall inertia of the power system decreases and the active output fluctuation increases, frequency stability and performance analysis face new challenges. Modern power systems have the basic characteristics of decentralized coordinated operation of multiple machines and multiple controllers. Their state space models are high-dimensional and have complex structures. When the polynomial model commonly used in control theory is used to describe them, there are also very complex mathematical relationships.

[0003] Compared with state space or polynomial models, the frequency domain model of the power system is much simpler and more compact, often containing only a few loops, so the research object of frequency domain analysis is much simpler, which shows that the frequency domain method is naturally suitable for dynamic analysis of large interconnected systems such as power systems. In addition, the frequency domain method can often constructively describe the analytical relationship between the stability and control performance indicators of the power system and the system parameters, making it easier to carry out control design.

[0004] Ultra-low frequency oscillations often occur in hydropower-dominated systems, and have been reported in power grids in hydropower-dominated areas such as Quebec, Columbia, Canada, and Yunnan, my country. Since ultra-low frequency oscillations are greatly affected by the speed governor parameters of hydropower units, common suppression methods usually start with shutting down some speed governors and optimizing the design of speed governor parameters, but these two methods either weaken the system frequency regulation capability or the oscillation suppression effect is not significant enough.

[0005] In response to the above problems, this paper proposes a constructive frequency dynamic analysis model from the frequency domain perspective, which can analyze the frequency stability and regulation performance at the same time, and combines the properties of special vectors and matrices in the model to give a simplified idea of ​​the model. This constructive analysis method can give a simple analytical relationship, which is convenient for practical application. The article focuses on the application of the simplified model in the field of ultra-low frequency oscillation. Summary of the invention

[0006] In view of the above-mentioned problems, the present invention is proposed.

[0007] Therefore, the present invention provides a frequency dynamic characteristic analysis method of ultra-low frequency oscillation of an electric power system, which can solve the problems mentioned in the background technology.

[0008] To solve the above technical problems, the present invention provides the following technical solutions: a method for analyzing the frequency dynamic characteristics of ultra-low frequency oscillations in an electric power system, comprising: constructing a frequency dynamic analysis model based on a rotor circuit; analyzing the properties of a distribution vector of the frequency dynamic analysis model; analyzing the properties of a speed response function matrix of the frequency dynamic analysis model; constructing a frequency low-dimensional dynamic practical analysis model under ultra-low frequency oscillations; and analyzing the ultra-low frequency stability of a stabilizer system containing a turbine governor side.

[0009] As a preferred solution of the frequency dynamic characteristics analysis method of ultra-low frequency oscillation of the power system described in the present invention, the process of constructing the frequency dynamic analysis model includes the following steps:

[0010] Construct the transfer function matrix G related to the excitation system Q (s), the expression is as follows:

[0011] G Q (s) = -K2[K3 + sT d ′0+G EX (s)K6] -1

[0012] ·[G EX (s)K5+K4]

[0013] Assume that the active power change of the i-th load node is ΔP Li The disturbance vector ΔP of each generator node caused by this change d The following quantitative relationship exists:

[0014] ΔP d =ΔP Li d i

[0015] In the formula, the allocation vector d i The expression is as follows:

[0016]

[0017] Based on the above formula, the power disturbance ΔP occurring at any load node is obtained L Quantitative impact results on the frequency of each generator;

[0018] Define the speed response function matrix X(s):

[0019]

[0020] Obtain the speed vector of each generator Δω and the active power change ΔP of the i-th load node Li And the reference speed deviation input Δω ref The transfer function between:

[0021] Δω = X -1 (s)d i ΔP Li

[0022] Δω = X -1 (s)G M (s)e N Δω ref 。

[0023] As a preferred solution of the method for analyzing the frequency dynamic characteristics of ultra - low - frequency oscillations in the power system described in the present invention, wherein: the properties of the vector for analyzing the frequency dynamic analysis model include:

[0024] Split X(jω) as follows:

[0025] X(jω) = X0(jω) + X Δ (jω)

[0026]

[0027] X Δ (jω) = jωM + D + G M (jω)

[0028] wherein, X0(jω), X Δ (jω) are transition matrices in the derivation process; K1, K4, K5 satisfy that the row sum is 0, and it can be known from the fact that the right - multiplication of any matrix by a matrix with a row sum of 0 still satisfies that the row sum is 0 that G Q (jω) also satisfies that the combined row sum is 0, and X0(jω) also satisfies that the row sum is 0;

[0029] On the other hand, since G << B, K1 is a quasi - symmetric matrix, and G Q (jω) is a quasi - symmetric diagonally dominant matrix, and X0(jω) is a quasi - symmetric matrix; combined with the fact that X Δ (jω) is a diagonal matrix, it can be known that X(jω) is a quasi - symmetric matrix;

[0030] Denote the inertia sum M Σ = ΣM i , the damping sum D Σ = ΣD i , combined with the property that ||X0(jω)|| >> ||X Δ (jω)|| in the ultra - low - frequency band, we can obtain:

[0031]

[0032] As a preferred solution of the method for analyzing the frequency dynamic characteristics of ultra - low - frequency oscillations in the power system described in the present invention, wherein: constructing a low - dimensional dynamic practical analysis model of frequency under ultra - low - frequency oscillations, including,

[0033] Combined allocation vector d i and the disturbance response transfer function X -1 (jω) property, the frequency dynamic analysis model is simplified to obtain a frequency low-dimensional dynamic practical analysis model suitable for ultra-low frequency band analysis;

[0034] Because in the ultra-low frequency band, X -1 (s) If the matrix elements are almost all equal, then:

[0035]

[0036] According to the properties of the allocation vector, d i The sum of the elements is -1:

[0037] E N d i =-e N

[0038] but:

[0039]

[0040] As a preferred solution of the frequency dynamic characteristics analysis method of the ultra-low frequency oscillation of the power system described in the present invention, all elements of the column vector Δω are equal, indicating that when the active power of any load node in the system changes, the frequency deviation of each generator is consistent, and the form of the SISO system is obtained:

[0041]

[0042] Similarly, we can get:

[0043]

[0044] Build a low-dimensional dynamic practical analysis model for ultra-low frequency band analysis;

[0045] The open-loop transfer function L(s) of the system under the frequency low-dimensional dynamic practical analysis model is expressed as:

[0046]

[0047] Get the system frequency tracking transfer function T p (s):

[0048]

[0049] Where, T p (s) is the closed-loop transfer function of the system.

[0050] As a preferred solution of the frequency dynamic characteristics analysis method of ultra-low frequency oscillation of the power system described in the present invention, a water turbine prime mover-speed governor with GPSS is constructed, including:

[0051] Construct the transfer function of the turbine prime mover-speed governor model, including PID and GPSS parts;

[0052]

[0053] This method analyzes the impact of GPSS on ULF based on the vector margin method;

[0054] Further write out the contribution component ΔV of the stability of a single thermal power unit, hydropower unit PID speed regulator, and hydropower unit GPSS in the system s , ΔV PID , ΔV GPSS

[0055]

[0056] As a preferred solution of the frequency dynamic characteristic analysis method of ultra-low frequency oscillation of the power system described in the present invention, the contribution components of each link of each unit to the ultra-low frequency stability can be written in the form of a simple vector sum:

[0057] V L =1+L(jω o )

[0058] =1+∑ΔV s +∑ΔV PID +∑ΔV GPSS .

[0059] To further solve the above technical problems, the present invention provides the following technical solutions: a frequency dynamic characteristics analysis system for ultra-low frequency oscillation of an electric power system, comprising: a model introduction module for constructing a frequency dynamic analysis model based on a rotor circuit; a first characteristic analysis module for analyzing the properties of a distribution vector of the frequency dynamic analysis model; a second characteristic analysis module for analyzing the properties of a speed response function matrix of the frequency dynamic analysis model; a model construction module for constructing a frequency low-dimensional dynamic practical analysis model under ultra-low frequency oscillation; and a stability analysis module for analyzing the ultra-low frequency stability of a system containing a stabilizer on the turbine governor side.

[0060] A computer device comprises a memory and a processor, wherein the memory stores a computer program, and is characterized in that when the processor executes the computer program, the steps of the frequency dynamic characteristics analysis method of ultra-low frequency oscillation of an electric power system as described above are implemented.

[0061] A computer-readable storage medium having a computer program stored thereon, characterized in that when the computer program is executed by a processor, the steps of the frequency dynamic characteristics analysis method of ultra-low frequency oscillation of an electric power system as described above are implemented.

[0062] Beneficial effects of the present invention: The present invention derives an analytical expression of the distribution vector based on the rotor circuit, and builds a frequency dynamic analysis model based on this, which can analyze stability and frequency regulation performance at the same time. The properties of two special matrices in the frequency dynamic analysis model are analyzed and proved, and the proposed model is simplified in a special frequency band based on these properties to obtain a frequency low-dimensional dynamic practical analysis model, which also provides a theoretical basis for the use of a unified frequency model in engineering to analyze ultra-low frequency oscillations. Compared with existing methods, the method proposed by the present invention is simpler, has more rigorous mathematical theory, and has a broader application basis. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0064] Figure 1 It is a flow chart of the frequency dynamic characteristics analysis method of ultra-low frequency oscillation of the power system provided by the present invention;

[0065] Figure 2 It is the compact form Heffron-Phillips model of the rotor circuit provided by the present invention;

[0066] Figure 3 It is a power system frequency dynamic analysis model provided by the present invention;

[0067] Figure 4 It is a frequency low-dimensional dynamic practical analysis model suitable for ultra-low frequency oscillation provided by the present invention;

[0068] Figure 5 It is a turbine prime mover-speed governor model with GPSS provided by the present invention;

[0069] Figure 6 It is the contribution vector of different links to stability provided by the present invention. DETAILED DESCRIPTION

[0070] In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the drawings of the specification. Obviously, the described embodiments are part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in the art without creative work should fall within the scope of protection of the present invention.

[0071] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein, and those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0072] Example 1, reference Figure 1 to Figure 6 , which is an embodiment of the present invention, provides a method for analyzing the frequency dynamic characteristics of ultra-low frequency oscillations in a power system.

[0073] In the related art,

[0074] The present application provides a method for effectively solving the above-mentioned problems. Next, a method for analyzing the frequency dynamic characteristics of ultra-low frequency oscillation of the power system will be described in detail in combination with multiple embodiments.

[0075] Construct a frequency dynamic analysis model based on the rotor circuit, specifically:

[0076] Since the time scale of speed governor and load frequency control is 10 -1 ~10 3 ms, which means that when modeling, we only need to focus on the frequency range of electromechanical transients to achieve system order reduction. Therefore, we can consider building a frequency dynamic analysis model based on the conventional small disturbance stability analysis Heffron-Phillips model, and give the compact form of the rotor loop Heffron-Phillips model of the system as follows Figure 2 shown.

[0077] Figure 2 And in formula (1): G Q (s) is the transfer function matrix related to the excitation system, expressed as follows:

[0078]

[0079] Where: M is the diagonal matrix of the generator rotor motion inertia constant; D is the diagonal matrix of the rotor motion damping coefficient; ΔP m is the mechanical power column vector of the prime mover output; ΔP e1 and ΔP e2 is the component column vector of the generator electromagnetic power; ΔPd is the power disturbance column vector of each generator by the system; Δω is the angular frequency column vector of each generator; matrix K1~K6 is the coefficient matrix of the system linearization model; G M (s) is the diagonal matrix of the transfer function of the speed governor-prime mover system; G EX (s) is the diagonal matrix of the excitation system transfer function; ω0 is the system synchronous angular velocity; T′ d0 is the diagonal matrix containing the transient time constants of the d-axis of each generator; I is the unit matrix; s is the Laplace operator.

[0080] from Figure 2 The given block diagram can easily obtain the speed Δω of each generator and the power disturbance column vector ΔP d However, this alone is not enough to analyze the frequency dynamics. In engineering, more attention is paid to the power disturbance ΔP occurring at the load node. L The impact on the generator speed. For this purpose, the concept of distribution vector is introduced.

[0081] Assume that the active power change of the i-th load node is ΔP Li The disturbance vector ΔP of each generator node caused by this change d The following quantitative relationship exists:

[0082] ΔP d =ΔP Li d i (2)

[0083] where d is defined i is the distribution vector, which is a constant vector and is only related to the system flow.

[0084] Next, we derive the distribution vector d according to the system's power flow equation and node equation. i expression.

[0085] The power flow equation of the power system is shown below

[0086]

[0087] The full array H, N′, J, and L′ are the partial derivative coefficient matrices of the system linearized power flow equation for active power ΔP and reactive power ΔQ with respect to power angle Δθ and voltage ΔV, respectively.

[0088] Assume that all nodes are sorted according to generator and non-generator nodes, the generator nodes are labeled SG, the non-generator nodes are labeled b, and the single node with power disturbance is L. Then ΔP SG , ΔP b , ΔP LRepresent the active power of the generator node, non-generator node, and single node with power disturbance respectively; similarly, Δθ SG , Δθ b , Δθ L They represent the power angles of the generator node, non-generator node, and single node with power disturbance. SG , H SG,b 、h SG,L Represents ΔP SG For Δθ SG , Δθ b , Δθ L The partial derivative coefficient matrix of b,SG , H b 、h b,L Represents ΔP b For Δθ SG , Δθ b , Δθ L The partial derivative coefficient matrix of ; H b Represents ΔP L For Δθ SG , Δθ b , Δθ L The partial derivative coefficient matrix of .

[0089] Then the active power flow equation after PQ decomposition can be written as

[0090]

[0091] Normally, all non-generator nodes are considered as PQ nodes, satisfying ΔP b =0, we can get

[0092]

[0093] Eliminate PQ nodes and Δθ L Available

[0094]

[0095] Thus, the decoupling of the power components is achieved, which includes two components. The first component represents the influence of the electromechanical oscillation link and the excitation link, and the second component represents the influence of the disturbance in the power grid. Therefore, the distribution vector d i The expression is as follows

[0096]

[0097] Based on the above formula, the power disturbance ΔP occurring at any load node can be obtained L Quantitative impact results on the frequency of each generator.

[0098] Figure 2 In the model shown, the load disturbance ΔP is considered Li and reference speed deviation Δω ref Afterwards, we can get Figure 3 Frequency dynamic analysis model. Among them, e N is an N-dimensional vector whose elements are all 1, Δω ref is the column vector of the speed deviation reference value, Δω er is the column vector of speed deviation.

[0099] based on Figure 3 , we can obtain the speed vector Δω of each generator and the active power change ΔP of the i-th load node Li And the reference speed deviation input Δω ref The transfer function between:

[0100]

[0101] Define the speed response function matrix X(s):

[0102]

[0103] Then formula (8) can be written as:

[0104] Δω=X -1 (s)d i ΔP Li (11)

[0105] Formula (9) can be written as:

[0106] Δω=X -1 (s)G M (s)e N Δω ref (12)

[0107] The properties of the analysis frequency dynamic analysis model allocation vector in step 2) are specifically:

[0108] According to Theorem 1, for any block matrix with a column sum of 0

[0109]

[0110] satisfy

[0111] sum(a-AB -1 b)+cc T B -1 b=0 (14)

[0112] in, sum(·) means to find the sum of all elements in a matrix or vector.

[0113] The element expression of the H matrix in Equation (4) is as follows:

[0114]

[0115] Among them, G and B are the conductance and susceptance parameters in the system. It can be seen from the above formula that the H matrix is a Laplacian matrix, and the row sum is 0. And because G << B, the off-diagonal elements satisfy

[0116] H ij ≈ -V i0 V j0 B ij cosθ ij0 = H ji (16)

[0117] It can be known that the H matrix is quasi-symmetric and the column sum is also 0.

[0118] Let the right sub-block of H be H r :

[0119]

[0120] Obviously, the column sum of H r is also 0. Combining Theorem 1, it can be known that

[0121]

[0122] Therefore, the distribution vector d i satisfies the column stochastic property, that is, the sum of the vector elements is -1.

[0123] Analyze the properties of the rotational speed response function matrix of the frequency dynamic analysis model, specifically:[[]]

[0124] When s = jω, all elements in the inverse matrix of the rotational speed response function matrix have approximately equal properties at low frequencies (when ω is small). For the ultra-low frequency band with f < 0.1 Hz, this property is more obvious.

[0125] According to Theorem 2, when the matrix satisfies:[[]]

[0126] 1) X = X0 + X Δ and is a quasi-symmetric matrix;

[0127] 2) X0 is a rank N - 1 symmetric matrix with row sum 0;

[0128] 3) ||X0|| >> ||X Δ ||

[0129] When,[[]] all elements are approximately all equal, and the element value is equal to 1 / sum(X), that is

[0130]

[0131] where E N represents an N-order square matrix with all elements being 1.

[0132] Decompose X(jω) as follows

[0133]

[0134] where X0(jω), X Δ (jω) are transitional matrices in the derivation process.

[0135] Research shows that K1, K4, and K5 satisfy the condition that the row sum is 0. And since the right multiplication of any matrix by a matrix with a row sum of 0 still satisfies the condition that the row sum is 0, it can be known that G Q (jω) also satisfies the condition that the combined row sum is 0. Substituting the above properties into (20), it can be known that X0(jω) also satisfies the condition that the row sum is 0.

[0136] On the other hand, since G << B, K1 is a quasi-symmetric matrix, and G Q (jω) is a quasi-symmetric diagonally dominant matrix, and X0(jω) is a quasi-symmetric matrix. Combining with the fact that X Δ (jω) is a diagonal matrix, it can be known that X(jω) is a quasi-symmetric matrix.

[0137] Denote the inertia sum M Σ = ΣM i , and the damping sum D Σ = ΣD i . Combining with the property that ||X0(jω)|| >> ||X Δ (jω)|| in the ultra-low frequency band, we can obtain

[0138]

[0139] Construct a low-dimensional dynamic practical analysis model for frequency under ultra-low frequency oscillation, specifically:

[0140] Combining the distribution vector d i and the properties of the perturbation response transfer function X -1 (jω), simplify the Figure 3 given frequency dynamic analysis model, and derive a low-dimensional dynamic practical analysis model for frequency applicable to ultra-low frequency band analysis.

[0141] The above steps give the frequency change conditions of each unit in the system when the active power of a single load node changes. Since in the ultra-low frequency band, the matrix elements of X -1 (s) are almost all equal, expand equation (11) according to (21)

[0142]

[0143] According to the properties of the allocation vector derived in 2.2, d i The sum of the elements is -1, so

[0144] E N d i =-e N (twenty three)

[0145] but

[0146]

[0147] It is not difficult to see from the above formula that all elements of the column vector Δω are equal, which means that when the active power of any load node in the system changes, the frequency deviation of each generator is consistent. Therefore, consider writing (24) in the form of a SISO system:

[0148]

[0149] Similarly, substituting (21) into (12) yields

[0150]

[0151] Based on the above formula, a low-dimensional dynamic practical analysis model suitable for ultra-low frequency band analysis is rebuilt as follows: Figure 4 .

[0152] The advantage of the above model over the model proposed in Section 2 is that it converts the MIMO system into a SISO system, which greatly simplifies the complexity of the analysis, and the model can simultaneously analyze the stability and frequency tracking performance of the ultra-low frequency band system.

[0153] based on Figure 4 The open-loop transfer function L(s) of the system under the frequency low-dimensional dynamic practical analysis model can be obtained

[0154]

[0155] When the system is stable, define V L is the vector closest to the Nyquist curve L(jω) on the complex plane from the point (-1,0). The vector modulus |V L | is the stability margin of the system. The frequency corresponding to the point closest to (-1,0) on the Nyquist curve L(jω) is the frequency of the ultra-low frequency oscillation ω o .

[0156] Since there is a conflict between the stability and frequency tracking performance of the hydropower system speed regulator, it is also necessary to pay attention to the frequency tracking performance indicators of the frequency low-dimensional dynamic practical analysis model.

[0157] The system frequency tracking transfer function T is given by equation (26): p (s)

[0158]

[0159] T p (s) is essentially the closed-loop transfer function of the system.

[0160] Closed loop transfer function T p The point where the amplitude-frequency characteristic curve crosses 0.707 (corresponding to -3dB after taking the logarithm) from top to bottom is called the bandwidth ω of the system. B .

[0161] T p (jω B )|=0.707 (29)

[0162] Bandwidth can usually directly reflect the performance of the system, so it can be used as a frequency domain tracking performance indicator of the system. It corresponds to the time domain performance indicators required in engineering: for a second-order system, its rise time t r and the closed-loop transfer function bandwidth ω B Approximately inversely proportional

[0163] t r ω B ≈1.8(30)

[0164] ω B The larger the t r The smaller the rise time, the better the system tracking performance. r0 After that, the target bandwidth ω can be determined accordingly B0 However, due to ω B There is no analytical expression for the relationship between the speed regulator parameters, and it is not convenient to form an optimization model that is easy to solve by directly using it as the objective function.

[0165] Analyze the ultra-low frequency stability of the stabilizer system on the turbine governor side, specifically:

[0166] The parallel PID speed regulator is a commonly used speed regulator in large turbines. Based on this, the turbine prime mover-speed regulator with GPSS shown below is built.

[0167] Figure 5 In the prime mover-speed governor part K P is the proportionality coefficient, K I is the integration coefficient, K D is the differential coefficient, b p is the permanent droop coefficient, T G is the servo system time constant, T Wis the water hammer time constant; GPSS part K GP is the GPSS gain, T a1 , T b1 , T a2 , T b2 is the GPSS lead-lag time constant.

[0168] The transfer function of the turbine prime mover-speed governor model is shown in formula (31), which can be divided into two parts: PID and GPSS.

[0169]

[0170] This method analyzes the impact of GPSS on ultra-low frequency based on the vector margin method.

[0171] Further write out the contribution component ΔV of the stability of a single thermal power unit, hydropower unit PID speed regulator, and hydropower unit GPSS in the system s , ΔV PID , ΔV GPSS

[0172]

[0173] Among them G Ms (s) represents the prime mover-speed governor transfer function of the thermal power unit.

[0174] From (27), we can see that the contribution of each link of each unit to the ultra-low frequency stability can be expressed in the form of a simple vector sum.

[0175]

[0176] L(jω o ) is used as the origin to draw the contribution vectors of the typical parameters of thermal power units, hydropower units PID speed regulators, and hydropower units GPSS to stability at 0.05Hz, corresponding to Figure 6 Medium ΔV s , ΔV PID , ΔV GPSS As can be seen from the figure, the turbine PID speed governor link will deteriorate the stability of ultra-low frequency oscillation, while the thermal power unit will not have a negative effect on the stability of ultra-low frequency oscillation. More importantly, installing GPSS on the turbine speed governor side will provide positive damping for ultra-low frequency oscillation, compensate for the lag phase angle of the PID speed governor, and thus enhance the stability of the system under ultra-low frequency oscillation.

[0177] In summary, the present invention derives the analytical expression of the distribution vector based on the rotor loop, and builds a frequency dynamic analysis model based on this, which can analyze the stability and frequency regulation performance at the same time. The properties of two special matrices in the frequency dynamic analysis model are analyzed and proved. Combining these properties, the proposed model is simplified in a special frequency band to obtain a frequency low-dimensional dynamic practical analysis model. At the same time, it also provides a theoretical basis for the use of a unified frequency model in engineering to analyze ultra-low frequency oscillations. Compared with existing methods, the method proposed in the present invention is simpler, the mathematical theory is more rigorous, and the application basis is broader.

[0178] Embodiment 2 is an embodiment of the present invention, which provides a frequency dynamic characteristic analysis system for ultra-low frequency oscillation of an electric power system, including: a model introduction module, used to construct a frequency dynamic analysis model based on a rotor circuit; a first characteristic analysis module, used to analyze the properties of the frequency dynamic analysis model allocation vector; a second characteristic analysis module, used to analyze the properties of the speed response function matrix of the frequency dynamic analysis model; a model construction module, used to construct a frequency low-dimensional dynamic practical analysis model under ultra-low frequency oscillation; a stability analysis module, used to analyze the ultra-low frequency stability of a system containing a stabilizer on the turbine governor side.

[0179] Embodiment 3 is an embodiment of the present invention, which is different from the previous embodiment in that: if the function is implemented in the form of a software function unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk and other media that can store program codes.

[0180] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as an ordered list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by an instruction execution system, device or apparatus (such as a computer-based system, a system including a processor, or other system that can fetch instructions from an instruction execution system, device or apparatus and execute instructions), or in conjunction with such instruction execution systems, devices or apparatuses. For the purposes of this specification, "computer-readable medium" can be any device that can contain, store, communicate, propagate or transmit a program for use by an instruction execution system, device or apparatus, or in conjunction with such instruction execution systems, devices or apparatuses.

[0181] More specific examples of computer-readable media (a non-exhaustive list) include the following: an electrical connection with one or more wires (electronic device), a portable computer disk case (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disk read-only memory (CDROM). In addition, the computer-readable medium may even be a paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, deciphering or, if necessary, processing in another suitable manner, and then stored in a computer memory.

[0182] It should be understood that the various parts of the present invention can be implemented by hardware, software, firmware or a combination thereof. In the above-mentioned embodiments, a plurality of steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, it can be implemented by any one of the following technologies known in the art or their combination: a discrete logic circuit having a logic gate circuit for implementing a logic function for a data signal, a dedicated integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0183] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A frequency dynamic characteristics analysis method for ultra-low frequency oscillation of a power system, characterized in that: include: Construct a frequency dynamic analysis model based on the rotor circuit; Analyzing properties of the frequency dynamic analysis model allocation vector; Analyze the properties of the speed response function matrix of the frequency dynamic analysis model; Construct a practical analysis model of low-dimensional dynamic frequency under ultra-low frequency oscillation; Analyze the ultra-low frequency stability of the turbine governor-side stabilizer system.

2. The method for analyzing the frequency dynamic characteristics of ultra-low frequency oscillation in a power system according to claim 1, characterized in that: The process of constructing the frequency dynamic analysis model includes the following steps: Construct the transfer function matrix G related to the excitation system Q (s), the expression is as follows: G Q (s)=-K2[K3+sT d ′0+G EX (s)K6] -1 ·[G EX (s)K5+K4] Assume that the active power change of the i-th load node is ΔP Li The disturbance vector ΔP of each generator node caused by this change d The following quantitative relationship exists: ΔP d =ΔP Li d i In the formula, the allocation vector d i The expression is as follows: Based on the above formula, the power disturbance ΔP occurring at any load node is obtained L Quantitative impact results on the frequency of each generator; Define the speed response function matrix X(s): Obtain the speed vector of each generator Δω and the active power change ΔP of the i-th load node Li And the reference speed deviation input Δω ref The transfer function between: Give=X -1 (s)d i ΔP Li Give=X -1 (s)G M (s)e N Give ref 。 3. The method for analyzing the frequency dynamic characteristics of ultra-low frequency oscillation in a power system according to claim 2, characterized in that: The analyzing the properties of the frequency dynamic analysis model allocation vector includes: Split X(jω) as follows: X(jω)=X0(jω)+X Δ (jω) X Δ (jω)=jωM+D+G M (jω) Among them, X0(jω), X Δ (jω) is the transition matrix in the derivation process; K1, K4, K5 satisfy the row sum of 0, and any matrix with a row sum of 0 multiplied by any matrix on the right still satisfies the row sum of 0. It can be known that G Q (jω) also satisfies the combined row sum to be 0, and X0(jω) also satisfies the row sum to be 0; On the other hand, since G << B, K1 is a quasi-symmetric matrix, and G Q (jω) is a quasi-symmetric diagonally dominant matrix, and X0(jω) is a quasi-symmetric matrix; combining with X Δ (jω) being a diagonal matrix, it can be seen that X(jω) is a quasi-symmetric matrix; Remember the inertia and M Σ =ΣM i , damping and D Σ =ΣD i , combined with ultra-low frequency band ||X0(jω)||>>||X Δ (jω)||This property can be obtained:

4. The method for analyzing the frequency dynamic characteristics of ultra-low frequency oscillation in a power system according to claim 3, characterized in that: Construct a practical analysis model of low-dimensional dynamic frequency under ultra-low frequency oscillation, including: Combined allocation vector d i and the disturbance response transfer function X -1 (jω) property, the frequency dynamic analysis model is simplified to obtain a frequency low-dimensional dynamic practical analysis model suitable for ultra-low frequency band analysis; Because in the ultra-low frequency band, X -1 (s) If the matrix elements are almost all equal, then: According to the properties of the allocation vector, d i The sum of the elements is -1: AND N d i =-and N but:

5. The method for analyzing the frequency dynamic characteristics of ultra-low frequency oscillation in a power system according to claim 4, characterized in that: All elements of the column vector Δω are equal, indicating that when the active power of any load node in the system changes, the frequency deviation of each generator is consistent, and the form of the SISO system is obtained: Similarly, we can get: Build a low-dimensional dynamic practical analysis model for ultra-low frequency band analysis; The open-loop transfer function L(s) of the system under the frequency low-dimensional dynamic practical analysis model is expressed as: Get the system frequency tracking transfer function T p (s): Where, T p (s) is the closed-loop transfer function of the system.

6. The method for analyzing the frequency dynamic characteristics of ultra-low frequency oscillation in a power system according to claim 5, characterized in that: Build a water turbine prime mover-speed governor with GPSS, including: Construct the transfer function of the turbine prime mover-speed governor model, including PID and GPSS parts; This method analyzes the impact of GPSS on ULF based on the vector margin method; Further write out the contribution component ΔV of the stability of a single thermal power unit, hydropower unit PID speed regulator, and hydropower unit GPSS in the system s , ΔV PID , ΔV GPSS ΔV PID =(jω o M Σ +D Σ ) -1 G PID (jω o )。 7. The method for analyzing frequency dynamic characteristics of ultra-low frequency oscillation in a power system according to claim 6, characterized in that: The contribution of each link of each unit to the ultra-low frequency stability can be expressed in the form of a simple vector sum: V L =1+L(jω o )=1+∑ΔV s +∑ΔV PID +SDV GPSS 。 8. A system using the frequency dynamic characteristics analysis method of ultra-low frequency oscillation in a power system as claimed in any one of claims 1 to 7, characterized in that: include: Model introduction module, used to build frequency dynamic analysis model based on rotor circuit; A first characteristic analysis module, used for analyzing the properties of the frequency dynamic analysis model allocation vector; The second characteristic analysis module is used to analyze the properties of the speed response function matrix of the frequency dynamic analysis model; Model building module, used to build a practical analysis model of low-dimensional dynamic frequency under ultra-low frequency oscillation; The stability analysis module is used to analyze the ultra-low frequency stability of the stabilizer system including the turbine governor side.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method for analyzing frequency dynamic characteristics of ultra-low frequency oscillation of a power system according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for analyzing frequency dynamic characteristics of ultra-low frequency oscillation of a power system according to any one of claims 1 to 7 are implemented.

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