A Construction Method for Quantifying Evaluation Index of Transient Voltage Support Capability

Abstract

The present invention relates to the technical field of power systems and discloses a method for constructing a quantitative evaluation index for transient voltage support capability. State variables x and output variables y are obtained through the mathematical models of each subsystem of the power system, and the attributes of each subsystem are calculated based on the state variables x and output variables y of each subsystem; based on the electrical network connection relationship according to the attributes of each subsystem, a quantitative evaluation index for power system stability is calculated to determine whether the power system can return to a stable state after being disturbed. When stability is satisfied, combined with the initial operating state of the power system, a quantitative evaluation index for security is calculated to judge the safety state of the transient process of the power system. The present invention decouples the stability analysis of subsystems in an interconnected system and analyzes the stability of the system through two algebraic inequalities. This method has a small amount of calculation and high calculation efficiency.

Description

Technical Field

[0001] The present invention relates to the technical field of power systems, and particularly to a method for constructing a quantitative evaluation index for transient voltage support capability. Background Art

[0002] Against the background of increasingly serious problems such as current energy shortage, environmental pollution and climate change, large-scale development and utilization of clean and renewable new energy sources such as wind energy and solar energy has become the consensus of countries around the world. The use of new energy plays a very important role in promoting the adjustment of China's energy structure and also becomes an important development direction for China's future power system.

[0003] However, since new energy power generation equipment is connected to the grid through a power electronic interface, its inherent characteristics of weak damping and low inertia will deteriorate the dynamic characteristics of the system and trigger voltage collapse of the power system, which seriously restricts the large-scale application of renewable energy in the power system. Therefore, there is an urgent need to develop a flexible and efficient transient voltage stability analysis method to accurately evaluate the transient voltage support capability of the power grid under the scenario of high proportion of new energy access and provide guidance for the safe and stable operation of the power system.

[0004] Existing transient voltage stability analysis methods for power systems mainly include time-domain simulation method and direct method.

[0005] Since the time-domain simulation method can consider complex system models and can obtain accurate stability analysis results, this method has been widely used. However, the time-domain simulation method has deficiencies such as large computational amount and difficulty in providing quantitative information on system stability margin, and is not suitable for the safe and stable analysis of the power grid under the scenario of new energy access.

[0006] The direct method has been applied in the safe and stable analysis of the power grid under the scenario of new energy access. By constructing a transient energy function, the transient voltage stability of the system is quantitatively analyzed. Due to the characteristics of strong nonlinearity and uncertainty of the power grid under the scenario of new energy access, it is challenging to construct a Lyapunov function or energy function and accurately describe the safe and stable boundary of the power grid, and it is difficult for the direct method to quantify the impact of external disturbances on the safe and stable operation of the power grid. Summary of the Invention

[0007] In view of the problems existing in the prior art, the present invention provides a method for constructing a quantitative evaluation index for transient voltage support capability.

[0008] The present invention is realized through the following technical solutions:

[0009] A method for constructing a quantitative evaluation index for transient voltage support capability includes the following steps:

[0010] Step 1, obtaining state variables x and output quantities y according to the mathematical models of each subsystem of the power system;

[0011] Step 2: Calculate the attributes of each subsystem based on the obtained state variables and output quantities.

[0012] Step 3: Based on the attributes of each subsystem and the electrical network connection relationship, calculate the quantitative evaluation index of power system stability, and determine whether the power system can return to the stable state after being disturbed. If the power system cannot return to the stable state after being disturbed, the power system is unstable; if the power system returns to the stable state after being disturbed, then execute Step 4.

[0013] Step 4: Combine the initial operating state of the power system, calculate the quantitative evaluation index of security, and determine whether the transient process of the power system meets the security and stability constraint conditions; if the transient process of the power system does not meet the security and stability constraint conditions, the power system operates in an unsafe state; otherwise, the power system operates in a safe state.

[0014] Preferably, in Step 1, each subsystem includes a generator, a distributed power source, a motor, a constant impedance load, and a constant power load; among them, the per-unit value of the terminal voltage is selected as the output for the generator and the distributed power source; the per-unit value of the terminal current is selected as the output for the motor, the constant impedance load, and the constant power load.

[0015] Preferably, in Step 2, the calculation formulas for the obtained state variables and output quantities are as follows:

[0016]

[0017] y = h(x, u);

[0018] where is, the input u ∈ U ∈ R m , the function f: D → R n , g: D → R n×m ; f and g are continuous with respect to x and satisfy the local Lipschitz condition; f(0, 0) = 0, h(0, 0) = 0, and D and U represent the local domains of the state variables and external inputs respectively.

[0019] Furthermore, calculating the attributes of each subsystem from the calculation formulas of the obtained state variables and output quantities includes the following steps:

[0020] For a nonlinear system with external inputs, there exists Then for any initial state and external input, if the following inequality holds:

[0021]

[0022] Among them, \(x(t)\) represents the variation of the system state variable over time, \(x_0\) represents the initial value of the system state variable, \(t\) represents time, the \(\gamma\) function represents the impact of the perturbation on the system, \(|\cdot|\) represents the Euclidean norm, \(\|\cdot\|\) represents the norm of a matrix, and the \(\beta\) function can quantify the dynamic process of the system state variable changing over time, \(\|u\|\) ∞ is the smallest \(a\) such that \(|u(t)|\leq a\) holds for all time \(t\); is a comparison function;

[0023] According to the integral-integral estimation, the definition formula is as follows:

[0024]

[0025]

[0026] Among them, \(\alpha\) is the gain function, \(\alpha_0\) is the initial value of the gain function, and \(s\) is the Laplace operator;

[0027] When calculating the corresponding local input range, initial value range, and gain functions \(\alpha\), \(\alpha_0\), \(\gamma\), each state variable, input, and output needs to refer to the corresponding equilibrium point, and the definition formula is as follows:

[0028]

[0029]

[0030]

[0031] Among them, \(u\) e , \(x\) e , \(y\) e are the equilibrium points of the subsystem input, state variable, and output respectively;

[0032] Given the input signal \(u\) and fixing the initial state \(x_0\) of the system, the output \(y\) is obtained;

[0033] Fix \(|x_0| = 0\), at this time \(\alpha_0(0)=0\), then the calculation formula for approximately estimating the input-output gain is as follows:

[0034]

[0035] Among them, is the integral energy of the subsystem output, is the integral energy of the subsystem input;

[0036] Changing the magnitude of the input or adopting different forms of input, calculating the input-output gain can obtain a series of \(\gamma\), and taking the maximum \(\gamma\) from them maxInput-output gain of the approximate subsystem; if the steady-state running interval type integral energy value of the system state variables and outputs exceeds the upper limit value, the power system becomes unstable; gradually reduce the input until the power system is stable, and estimate the range of the subsystem input signal.

[0037] Furthermore, determine γ max After that, change the initial value and input of the system within the specified range, and calculate the formula as follows:

[0038]

[0039] where γ max is the maximum value of the input-output gain.

[0040] Preferably, in step 3, based on the obtained LISS / LIOS properties of the subsystem, consider a dynamic system composed of n subsystems. The mathematical model expression of the i-th subsystem is as follows:

[0041]

[0042] y i = h i (x i , u i , ω i )

[0043] The mathematical model formed based on the electrical network connection relationship according to the properties of each subsystem is as follows:

[0044]

[0045]

[0046] 0 = g(y, u);

[0047] where x = [x1 … x n T ∈R N , N = n1 + … + n n , u = [u1 … u n T ∈R m , m = m1 + … + m n , y = [y1…y n T ∈R p , p = l1 + … + l n ; is the state variable of the i-th subsystem, and are the input and output of the subsystem respectively, and ω i is the external disturbance input received by the subsystem. ​​​

[0048] Preferably, in step 3, the conditions for judging whether the power system can return to a stable state after being disturbed are as follows:

[0049] A, when |x oi | ≤ v i , ||u i || ∞ ≤ τ i , ||ω i || ∞ ≤ ε i , each subsystem is LISS and LIOS, and has a linear asymptotic gain;

[0050] B, the function g(y, u) satisfies the implicit function theorem. In the application of the power system, this condition means that the power flow equation of the system has a solution; there exists z ij ≥ 0, d i ≥ 0, such that the following formula is satisfied

[0051] |u i (t)| ≤ ∑z ij (|y j (t)|) + d i

[0052] C, the small gain condition is satisfied, that is

[0053] ρ(G IOS ) < 1

[0054] where G IOS =Γ IOS Z, Γ IOS is an input / output gain matrix in the form of ; ρ represents the spectral radius of the matrix G IOS .

[0055] Furthermore, the following quantitative evaluation indexes reflecting the stable operation ability of the interconnected system are refined:

[0056] a = 1 - ρ(G LIOS );

[0057] where a is the defined quantitative evaluation index of stability.

[0058] Preferably, in step 4, the conditions for judging whether the transient process of the power system meets the security and stability constraint conditions are as follows:

[0059] (I d -G IOS ) -1 (β IOS ((|x o |) c , 0) + Γ IOS ·d) + d ≤ τ;

[0060] Where τ=[τ1 … τ n ] T , d=[d1 … d n ] T ,

[0061] Among them, τ i Enter the upper limit for the ith subsystem.

[0062] Preferably, the formula for calculating the safety quantitative evaluation index is as follows:

[0063]

[0064] Where b = Z(I d -G IOS ) -1 (β IOS ((|x o |) c ,0)+Γ IOS ·d)+d,b i and τ i are the i-th elements in b and τ respectively; when the safety and stability constraints are not satisfied, that is, Z·(I d -G IOS ) -1 β IOS ((|x o |) c ,0)>τ, the system operates in an unsafe state.

[0065] Compared with the prior art, the present invention has the following beneficial technical effects:

[0066] The present invention provides a method for constructing a quantitative evaluation index of transient voltage support capacity, which obtains state variables x and output y through mathematical models of each subsystem of the power system, and calculates the properties of each subsystem according to the state variables x and output y of each subsystem; calculates the quantitative evaluation index of power system stability based on the properties of each subsystem and the electrical network connection relationship, and judges whether the power system can return to a stable state after being disturbed; when the stability is satisfied, the quantitative evaluation index of safety is calculated in combination with the initial operation state of the power system, and the safety state of the transient process of the power system is judged. The present invention decouples the stability analysis of the subsystems in the interconnected system, and analyzes the stability of the system through two algebraic inequalities. The method has a small amount of calculation and high calculation efficiency.

[0067] Furthermore, the transient voltage stability analysis method proposed by the present invention can quantitatively evaluate the transient voltage stability of the power grid under the scenario of high proportion of new energy access, providing an effective way to measure the access scale of new energy; the proposed quantitative evaluation index of transient voltage support ability takes into account both system stability and security, and can comprehensively and accurately reflect the transient voltage stability level of the power grid under the scenario of high proportion of new energy access. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 is a flowchart of the method for constructing the quantitative evaluation index of transient voltage support ability in the present invention;

[0069] Figure 2 is a schematic diagram of the input state stability theory;

[0070] Figure 3 is a geographical wiring diagram of the power system in the embodiment;

[0071] Figure 4 is a schematic diagram of the dynamic change of the 750 kV bus voltage in area C under different new energy penetration rates during system faults. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0072] In order to enable those skilled in the art of the present technology to better understand the solution of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0073] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged under appropriate circumstances so that the embodiments of the present invention described herein can be implemented in an order different from those illustrated or described herein. In addition, the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device comprising a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0074] The present invention will be further described in detail below with reference to the accompanying drawings:

[0075] Refer to Figure 1 , in an embodiment of the present invention, a method for constructing a quantitative evaluation index of transient voltage support ability is provided, including the following steps:

[0076] Step 1: Obtain the state variables x and output variables y according to the mathematical models of the respective subsystems of the power system;

[0077] Specifically, the respective subsystems include generators, distributed power sources, motors, constant impedance loads, and constant power loads; among them, the per-unit value of the terminal voltage of the generators and distributed power sources is selected as the output; the per-unit value of the terminal current of the motors, constant impedance loads, and constant power loads is selected as the output.

[0078] Step 2: Calculate the attributes of the respective subsystems from the obtained state variables and output variables;

[0079] Specifically, the measurement in the form of input, output, and system state integration has a direct relationship with energy. Therefore, before introducing the LISS / LIOS simulation analysis method for the integral form of the subsystem integral energy, the integral energy definition is given, and its purpose is mainly in the following two aspects: 1) Facilitate the estimation of attributes such as the LISS stability domain and asymptotic gain of the subsystem. 2) Facilitate the judgment of whether the system state and output variables are within the safe operating range.

[0080] First, introduce the Input-to-state Stability (ISS) theory. Without loss of generality, consider a nonlinear system with external input:

[0081]

[0082] y = h(x, u);

[0083] where, is, the input u ∈ U ∈ R m , the function f: D → R n , g: D → R n×m ; f and g are continuous with respect to x and satisfy the local Lipschitz condition; f(0, 0) = 0, h(0, 0) = 0, and D and U represent the local domains of the state variables and external inputs respectively.

[0084] Calculate the attributes of the respective subsystems from the calculation formulas of the obtained state variables and output variables, including the following steps:

[0085] For a nonlinear system with external input, there exists Then for any initial state and external input, if the following inequality holds:

[0086]

[0087] Then the nonlinear system with external input is ISS;

[0088] Among them, \(x(t)\) represents the change of the system state variable over time…, \(x_0\) represents the initial value of the system state variable, \(t\) represents time, the \(\gamma\) function represents the impact of the perturbation on the system, \(|\cdot|\) represents the Euclidean norm, \(\|\cdot\|\) represents the norm of a matrix, and the \(\beta\) function can quantify the dynamic process of the change of the system state variable over time, \(\|u\|\) ∞ is the smallest \(a\) such that \(|u(t)|\leq a\) holds for all times \(t\); is a comparison function;

[0089] The definition of the comparison function is given below: A function \(\gamma:\mathbb{R}\) ≥0 \to\mathbb{R}\) ≥0 , if it satisfies continuity, strict monotonic increase, and \(\gamma(0)=0\), then it is called a function; further, if the \(\gamma\) function satisfies \(\gamma(s)\to\infty\) as \(s\to\infty\), then it is called a function; A function \(\beta:\mathbb{R}\) ≥0 \times\mathbb{R}\) ≥0 \to\mathbb{R}\) ≥0 , if it satisfies the continuity condition, and for any fixed \(t\geq0\), the function \(\beta(\cdot,t)\) is a function, \(\beta(s,t)\) is decreasing with respect to \(t\), and \(\beta(s,t)\to0\) as \(t\to\infty\), then \(\beta(s,t)\) is called a function.

[0090] The right - hand side of the ISS norm description expression consists of two terms. One is a function related to the initial value, which decays to 0 as time approaches infinity; the other is a function describing the final value. The \(\gamma\) in equation (2) is called the input - to - state gain. The function describes the attraction speed of the system state to its attractor, and the function describes the radius of this attractor.

[0091] The geometric meaning of ISS is as Figure 2 shown. For a system with an initial value of \(x_0\), its state trajectory converges to the inside of a ball at a certain convergence speed. The radius of this ball is "proportional" to the infinity norm of the input \(\|u\|\) ∞ . In most practical engineering applications, most systems are only locally stable. The definition of the local input - to - state stability theory (Local Input - to - state Stability, LISS) is introduced below.

[0092] For traditional technologies, for any \(x_0\in\Omega\in\mathbb{R}\) n , \(u\in U\in\mathbb{R}\) m , if there exists a comparison function then for any initial state and external input, if the following inequality holds:

[0093]

[0094] Then the above non - linear system is LISS.

[0095] Where Ω and U represent the LISS domains of the initial state and the external input respectively.

[0096] And the present invention defines the formula according to the integral - integral estimation as follows:

[0097]

[0098]

[0099] Where α is the gain function, α0 is the initial value of the gain function, and s is the Laplace operator.

[0100] When calculating the corresponding local input range, initial value range, and gain functions α, α0, γ, each state variable, input, and output needs to use the corresponding equilibrium point as a reference, and the formula is defined as follows:

[0101]

[0102]

[0103]

[0104] Where u e , x e , y e are the equilibrium points of the subsystem input, state variable, and output respectively;

[0105] Given the input signal u and fixing the initial state x0 of the system, the output y is obtained;

[0106] Fixing |x0| = 0, at this time α0(0) = 0, then the calculation formula for approximately estimating the input - output gain is as follows:

[0107]

[0108] Where is the integral energy of the subsystem output, is the integral energy of the subsystem input.

[0109] Changing the magnitude of the input or using different forms of input, calculating the input - output gain can obtain a series of γ, and taking the maximum γ from them maxInput-output gain of the approximate subsystem; if the steady-state running interval type integral energy value of the system state variables and outputs exceeds the upper limit value, the power system becomes unstable; gradually reduce the input until the power system is stable, and estimate the range of the subsystem input signal.

[0110] Determine γ max After that, change the initial value and input of the system within the specified range, and the calculation formula is as follows:

[0111]

[0112] If the initial value is changed, different α0 functions can be obtained.

[0113] Among them, γ max is the maximum value of the input-output gain.

[0114] Step 3: Based on the electrical network connection relationship according to the attributes of each subsystem, calculate the power system stability quantitative evaluation index, and judge whether the power system can return to the stable state after being disturbed. When the power system cannot return to the stable state after being disturbed, the power system is unstable; when the power system returns to the stable state after being disturbed, execute Step 4;

[0115] Specifically, consider a dynamic system composed of n subsystems. The mathematical model expression of the i-th subsystem is as follows:

[0116]

[0117] y i =h i (x i , u i , ω i )

[0118] Among them, is the state variable of the i-th subsystem, and are the input and output of the subsystem respectively, and ω i is the external disturbance input received by the subsystem.

[0119] The system mathematical model formed by the interconnection of these subsystems is as follows:

[0120]

[0121]

[0122] 0 = g(y, u)

[0123] Among them, x = [x1 … x n T ∈R N , N = n1 + … + n​n , u = [u1 … u n T ∈ R m , m = m1 + … + m n , y = [y1 … y n T ∈ R p , p = l1 + … + l n .

[0124] Specifically, the conditions for judging whether the power system can return to a stable state after being disturbed are as follows:

[0125] A. When |x oi | ≤ v i , ||u i || ∞ ≤ τ i , ||ω i || ∞ ≤ ε i , each subsystem is LISS and LIOS and has a linear asymptotic gain;

[0126] B. The function g(y, u) satisfies the implicit function theorem. In the application of the power system, this condition means that the power flow equation of the system has a solution; there exists z ij ≥ 0, d i ≥ 0, such that the following formula is satisfied

[0127] |u i (t)| ≤ ∑z ij (|y j (t)|) + d i

[0128] C. The small gain condition is satisfied, that is

[0129] ρ(G IOS ) < 1

[0130] where G IOS = Γ IOS Z, Γ IOS is an input / output gain matrix in the form of ; ρ represents the spectral radius of the matrix G IOS .

[0131] Specifically, the following quantitative evaluation indexes reflecting the stable operation ability of the interconnected system are refined:

[0132] a = 1 - ρ(G LIOS );

[0133] where a is the defined quantitative evaluation index of stability.

[0134] ​​Step 4: Calculate the safety quantification evaluation index in combination with the initial operating state of the power system, and determine whether the transient process of the power system meets the security and stability constraint conditions; when the transient process of the power system does not meet the security and stability constraint conditions, the power system operates in an unsafe state; otherwise, the power system operates in a safe state.

[0135] Specifically, the method for determining whether the transient process of the power system meets the security and stability constraint conditions is as follows:

[0136] (I d -G IOS ) -1 (β IOS ((|x o |) c , 0)+Γ IOS ·d)+d ≤ τ;

[0137] where τ = [τ1 … τ n T , d = [d1 … d n T ,

[0138] where τ i is the input upper limit of the i-th subsystem.

[0139] Specifically, the formula for calculating the safety quantification evaluation index is as follows:

[0140]

[0141] where b = Z(I d -G IOS ) -1 (β IOS ((|x o |) c , 0)+Γ IOS ·d)+d, b i and τ i are the i-th elements of b and τ respectively; when the security and stability constraint conditions are not met, that is, when Z·(I d -G IOS ) -1 ·β IOS ((|x o |) c , 0) > τ, the system operates in an unsafe state.

[0142] The above stability and safety quantification evaluation indexes can fully reflect the safe and stable operation level of the power system, quantify and evaluate the transient support ability of the system under the scenario of high proportion of new energy access, and provide a theoretical basis and evaluation standard for analyzing the impact of new energy access on the transient voltage stability of the power system.​​

[0143] The embodiments of the present invention will be further described below through an example. The following is only an example of the embodiments of the present invention, and the embodiments of the present invention are not limited thereto.

[0144] The typical 750 kV power grid structure in a certain area is as Figure 3 shown. The total installed capacity of traditional power sources is 11.75 million kilowatts, the total installed capacity of wind power is 9.85 million kilowatts, the total installed capacity of photovoltaic power is 12.92 million kilowatts, and the load level is 31.3 million kilowatts. Among them, the installed capacity of new energy attributed to each bus at 750 kV is as follows: the installed capacity of wind power in the 750 kV power supply area of Region D is 6.36 million kilowatts, and the installed capacity of photovoltaic power is 2.59 million kilowatts; the installed capacity of wind power in the 750 kV power supply area of Region A is 1.25 million kilowatts, and the installed capacity of photovoltaic power is 1.27 million kilowatts; the installed capacity of wind power in the 750 kV power supply area of Region C is 0.27 million kilowatts, and the installed capacity of photovoltaic power is 0.75 million kilowatts; the installed capacity of wind power in the 750 kV power supply area of Region F is 1.15 million kilowatts, and the installed capacity of photovoltaic power is 1.21 million kilowatts; the installed capacity of wind power in the 750 kV power supply area of Region J is 0.21 million kilowatts, and the installed capacity of photovoltaic power is 1.32 million kilowatts. The installed capacity of photovoltaic power in the 750 kV power supply area of Region I is 0.71 million kilowatts; the installed capacity of wind power in the 750 kV power supply area of Region H is 0.21 million kilowatts, and the installed capacity of photovoltaic power is 1.08 million kilowatts; the installed capacity of wind power in the 750 kV power supply area of Region G is 0.33 million kilowatts, and the installed capacity of photovoltaic power is 0.15 million kilowatts. At this time, the new energy penetration rate of the power grid in a certain area is 35%.

[0145] Study the influence of different new energy penetration rates on the voltage dynamic process when a short-circuit fault occurs in the system. A three-phase short-circuit fault occurs on the 750 kV bus of Shanyuheng. Based on the proposed method for estimating the LIOS attributes of subsystems and the idea of analyzing the stability of interconnected systems, the transient voltage stability of a simplified power system in a certain area is analyzed. Specifically, the new energy penetration rates are set to 30%, 50%, and 70% respectively, and it is judged whether the small gain condition: ρ(G LIOS ) < 1 and the security and stability constraint condition: Z·(I d -G IOS ) -1 ·β IOS ((|x o |) c , 0) < τ are satisfied after a three-phase short-circuit fault occurs. If the small gain condition is not satisfied, the system becomes unstable; if the small gain condition is satisfied, calculate the stability quantitative evaluation index: 1 - ρ(G LIOS ). The larger this index is, the greater the stability margin of the system and the better the stability. If the security and stability constraint condition is not satisfied, the system operates in an unsafe state; if the security and stability constraint condition is satisfied, calculate the security quantitative evaluation index The larger this index is, the greater the safe operating margin of the system and the better the security. The calculation results are shown in Table 1.

[0146]

[0147] Table 1 System Quantitative Evaluation Indexes under Different New Energy Penetration Rates

[0148] The results show that: when a short - circuit fault occurs in the system, with the increase of new energy penetration rate, the small - gain condition and the security and stability constraint conditions are always satisfied, but the system stability quantitative evaluation index and the security quantitative evaluation index gradually decrease, and the stability margin and the security margin of the system continuously decrease. The time - domain simulation verifies the analysis results, and the dynamic change of the 750 kV bus voltage in Area C is as Figure 4 shown.

[0149] In summary, the present invention provides a method for constructing a quantitative evaluation index of transient voltage support ability. The state variable x and the output variable y are obtained through the mathematical models of each subsystem of the power system, and the attributes of each subsystem are calculated according to the state variable x and the output variable y of each subsystem; based on the electrical network connection relationship according to the attributes of each subsystem, the power system stability quantitative evaluation index is calculated to judge whether the power system can return to a stable state after being disturbed. When the stability is satisfied, combined with the initial operating state of the power system, the security quantitative evaluation index is calculated to judge the safety state of the transient process of the power system. The present invention decouples the stability analysis of the subsystems in the interconnected system and analyzes the stability of the system through two algebraic inequalities. This method has a small amount of calculation and high calculation efficiency.

[0150] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications or equivalent replacements can still be made to the specific embodiments of the present invention, and any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered by the protection scope of the claims of the present invention.

Claims

1. A method for constructing a quantitative evaluation index of transient voltage support ability, characterized in that It includes the following steps: Step 1: Obtain the state variables x and output variables y according to the mathematical models of the various subsystems of the power system; Step 2: Calculate the attributes of the various subsystems through the obtained state variables and output variables; Among them, calculating the attributes of the various subsystems according to the calculation formulas of the obtained state variables and output variables includes the following steps: For a non-linear system with external inputs, there exist and , then for any initial state and external input, if the following inequality holds: Among them, is the input represents the change of the system state variable over time, represents the initial value of the system state variable, represents time, The function represents the influence of the perturbation on the system, |∙| represents the Euclidean norm, and ‖∙‖ represents the matrix norm, The function can quantify the dynamic process of the change of the system state variable over time, is such that for all times is the smallest 𝑎 for which it holds; and are comparison functions; According to the integral-integral estimation, the formula is defined as follows: ； Among them, is the gain function, is the initial value of the gain function, and s is the Laplace operator; Calculate the corresponding local input range, initial value range, and gain function , , When calculating, each state variable, input, and output needs to use the corresponding equilibrium point as a reference, and the defined formula is as follows: ； ； ； wherein, , , are the equilibrium points of the subsystem input, state variable, and output, respectively; Given the input signal , fix the initial state of the system , and obtain the output ; Fixed At this time The calculation formula for approximately estimating the input-output gain is as follows: ； Among them, is the integral energy output of the subsystem, is the integral energy input of the subsystem; By changing the size of the input or using different forms of input, a series of can be obtained when calculating the input-output gain, and the maximum is taken as the input-output gain of the approximate subsystem; if the integral energy value of the steady-state operating interval of the system state variables and output exceeds the upper limit value, the power system will become unstable; gradually reduce the input until the power system is stable, and estimate the range of the input signal of the subsystem; Step 3: Based on the electrical network connection relationship according to the attributes of the various subsystems, calculate the quantitative evaluation index of the power system stability, and judge whether the power system can return to the stable state after being disturbed. When the power system cannot return to the stable state after being disturbed, the power system is unstable; when the power system returns to the stable state after being disturbed, then execute Step 4; Step 4: Combine the initial operating state of the power system, calculate the quantitative evaluation index of security, and judge whether the transient process of the power system meets the security and stability constraint conditions; when the transient process of the power system does not meet the security and stability constraint conditions, the power system operates in an unsafe state; otherwise, the power system operates in a safe state.

2. The method for constructing a transient voltage support ability quantification evaluation index according to claim 1, characterized in that In Step 1, the various subsystems include generators, distributed power sources, motors, constant impedance loads, and constant power loads; among them, the per-unit value of the terminal voltage of the generator and the distributed power source is selected as the output; the per-unit value of the terminal current of the motor, the constant impedance load, and the constant power load is selected as the output.

3. The method for constructing a transient voltage support ability quantification evaluation index according to claim 1, characterized in that In Step 2, the calculation formulas of the obtained state variables and output variables are as follows: ； wherein, is the input , the function , ; and with respect to is continuous and satisfies the local Lipschitz condition; , , and respectively represent the local domains of the state variables and the external inputs.

4. A method for constructing a quantitative evaluation index for transient voltage support ability according to claim 1, characterized in that Determine After that, within the specified range, change the initial values and inputs of the system, and calculate as follows: ； Among them, is the maximum input-output gain.

5. A method for constructing a quantization evaluation index for transient voltage support ability according to claim 1, characterized in that Step 3, based on the obtained subsystem LISS / LIOS attributes, consider the dynamic system composed of subsystems. The mathematical model expression of the th subsystem is as follows: The mathematical model formed based on the electrical network connection relationship according to the attributes of the various subsystems is as follows: ； ； ； Among them, , , , , , ; is the state variable of the th subsystem, and are the input and output of the subsystem respectively, is the external disturbance input received by the subsystem.

6. A method for constructing a quantitative evaluation index of transient voltage support ability according to claim 1, characterized in that In Step 3, the conditions for judging whether the power system can return to the stable state after being disturbed are as follows: A, when each subsystem is both LISS and LIOS and has a linear asymptotic gain; B, function satisfies the implicit function theorem. In the application of power systems, this condition indicates that the power flow equations of the system have solutions; there exists such that the following equation is satisfied C. The small gain condition is satisfied, that is <1 Among them, , is in the form of input / output gain matrix; represents the matrix spectral radius.

7. A method for constructing a quantization evaluation index for transient voltage support ability according to claim 6, characterized in that Refine the quantitative evaluation index reflecting the stable operation ability of the interconnected system as follows: ； Among them, is the defined stability quantification evaluation index.

8. A method for constructing a quantization evaluation index of transient voltage support ability according to claim 1, characterized in that In Step 4, the method for judging whether the transient process of the power system meets the security and stability constraint conditions is as follows: ； Among them, , , ; Among them, is the input upper limit of the 9. The method for constructing a transient voltage support ability quantization evaluation index according to claim 1, characterized in that The formula for calculating the quantitative evaluation index of security is as follows: ； Among them, and are respectively and the th elements in; when the security and stability constraint conditions are not satisfied, that is the system operates in an unsafe state.

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