Transient instability discrimination method based on power response curve

Abstract

The invention discloses a transient instability discrimination method based on a power response curve. The method specifically comprises the following steps: acquiring inherent information and electromagnetic power real-time measurement data of each generator of a target system; equivalently transforming the target system into a single-machine infinite bus system, and obtaining a power response curve of the single-machine infinite bus system; and judging the transient stability state of the target system according to whether the power response curve of the single-machine infinite bus system meets the transient instability main / supplementary criterion or not, and outputting a judgment result. According to the transient instability judgment method, the transient instability judgment process can be achieved only on the basis of the power response curve, good universality is achieved, and powerful technical support is provided for follow-up power grid safety and stability analysis and control.

Description

Technical Field

[0001] The present invention belongs to the field of power system analysis and control, and particularly relates to a transient instability discrimination method based on a power response curve. Background Art

[0002] With the gradual interconnection of cross-regional power grids and the access of large-scale intermittent energy sources, the operating characteristics of power grids have become more complex, and the possibility of system transient instability has increased. The long-term operation practice of power systems shows that large-scale power outages worldwide are mostly caused by system transient instability, and the lack of a fast and effective transient instability discrimination method is one of the important reasons for missing the best control opportunity and triggering large-scale power outages.

[0003] For transient instability discrimination methods, they can be divided into two categories: the transient instability discrimination method of "offline decision-making and real-time matching" and the transient instability discrimination method based on response information. Among them, the transient instability discrimination method of "offline decision-making and real-time matching" can obtain the transient stable states of the system's pre-fault set through numerical simulation based on a complete power grid topology structure and parameters. Therefore, the accuracy of such methods often depends on the accuracy of system modeling. However, with the expansion of the power grid scale and the access of power electronic devices such as new energy, it will become increasingly difficult to establish a power grid model that can accurately reflect the actual operating characteristics of the power grid.

[0004] With the wide deployment of the wide-area measurement system based on synchronous phasor measurement units in China's power grid, the method of quickly judging the transient stability of the system online based on response information has become a popular research means for power system security and stability assessment. Currently, the transient instability discrimination methods based on response information mainly include fixed phasor angle difference, transient energy function method, extended equal area criterion, response trajectory characteristics, etc. These methods effectively avoid the dependence on system models, parameters, and operating modes. However, the above methods all rely on the generator power angle and / or angular velocity information in the system, which faces two problems: one is that when directly measuring the generator power angle / angular velocity, a rotor position sensing device needs to be installed, but the sensor has errors such as electromagnetic interference and mechanical vibration, and when directly measuring the power angle, the initial value of the power angle also needs to be corrected when the unit is put into operation, which is difficult to apply in actual engineering; the other is that when indirectly measuring the generator power angle / angular velocity, it needs to be calculated through information such as the generator terminal voltage, which weakens the rapidity of the transient instability discrimination method due to this additional calculation link. In addition, when indirectly measuring the angular velocity, it is necessary to assume that the generator terminal electrical frequency is equal to the rotational speed, and when indirectly measuring the power angle, it is necessary to assume that the generator rotational speed remains unchanged, which makes it difficult to control the calculation errors when directly measuring the power angle / angular velocity during the transient process. Summary of the Invention

[0005] In view of the problem that existing transient instability discrimination methods all rely on the generator power angle / rotational speed to discriminate the transient stability of the system, the present invention provides a transient instability discrimination method based on the power response curve.

[0006] A transient instability discrimination method based on the power response curve of the present invention includes the following steps:

[0007] Step 1: Obtain the inherent information of the generators in the target system, and measure the electromagnetic power of each generator in the target system through the wide-area measurement system.

[0008] Among them, the target system refers to the power system that needs transient stability analysis, and the inherent information of the generator includes the number of generators in the target system, the inertia time constant of each generator, and the mechanical power of each generator.

[0009] Step 2: Based on the inherent information of the generator and the real-time measurement data of the generator electromagnetic power, equivalently transform the target system into a single-machine infinite-bus system, and obtain the power response curve of the single-machine infinite-bus system.

[0010] Step 3: Judge the transient stability of the target system according to the power response curve of the single-machine infinite-bus system. If the power response curve of the single-machine infinite-bus system does not satisfy the main criterion or supplementary criterion for transient instability, the target system is transiently stable; if it satisfies the main criterion or supplementary criterion for transient instability, the target system is transiently unstable, and the discrimination result is output.

[0011] Further, the process of measuring the electromagnetic power of each generator in the target system through the wide-area measurement system in Step 1 is specifically as follows:

[0012] Step 1.1: Denote the generator nodes in the target system as i, i = 1, 2, 3, …, v, where v is the number of generators.

[0013] Step 1.2: Based on the sampling start time, denote the electromagnetic power of the i-th generator measured at the k-th sampling step by the wide-area measurement system as P i (k), k = 1, 2, 3, …, where k represents the sampling serial number, indicating the sampling sequence number from the sampling start time to the current time.

[0014] Further, the process of equivalently transforming the target system into a single-machine infinite-bus system in Step 2 is specifically as follows:

[0015] Step 2.1: Based on the sampling start time, calculate the integral of the difference between the electromagnetic power and mechanical power of each generator in the target system with respect to time; sort the generators in ascending order of the integral value, and calculate the absolute difference between the integral values of adjacent generators; identify the generator pair corresponding to the largest absolute difference, and take the gap between this generator pair as the boundary to divide the generator group in the target system into a lagging group A and a leading group S.

[0016] Step 2.2: According to the lagging group A and the leading group S, calculate the angular frequency, power angle, inertia time constant, mechanical power, and electromagnetic power of the generator in the two-machine system through the following formula:

[0017]

[0018] In the formula, ω i (k), δ i (k), and M i respectively represent the angular frequency, power angle, and inertia time constant of generator i at the k-th sampling step; ω A (k), δ A (k), M A , P mA (k), P eA (k) respectively represent the equivalent angular frequency, equivalent power angle, equivalent inertia time constant, equivalent mechanical power, and equivalent electromagnetic power of the lagging group A at the k-th sampling step; ω S (k), δ S (k), M S , P mS (k), P eS (k) respectively represent the equivalent angular frequency, equivalent power angle, equivalent inertia time constant, equivalent mechanical power, and equivalent electromagnetic power of the leading group S at the k-th sampling step; P mi is the mechanical power of generator i in the target system.

[0019] Step 2.3: According to the two-machine system, calculate the angular frequency, power angle, inertia time constant, mechanical power, and electromagnetic power of the generator in the single-machine infinite-bus system through the following formula:

[0020]

[0021] In the formula, Δδ(k), Δω(k), M SA , P mSA (k), P eSA (k) are respectively the power angle, angular velocity, inertia time constant, mechanical power, and electromagnetic power of the generator in the single-machine infinite-bus system at the k-th sampling step.

[0022] Furthermore, the method for obtaining the power response curve of the single-machine infinite-bus system in Step 2 is as follows:

[0023] Taking the sampling start time as the reference, based on the electromagnetic power of each generator in the target system, calculate the electromagnetic power of the generator in the single-machine infinite-bus system at each sampling point in the interval from the sampling start time to the k-th sampling step, and generate the power response curve of the single-machine infinite-bus system through its discrete time-series data.

[0024] Furthermore, the main criterion for transient instability in step 3 is as follows:

[0025]

[0026] In the formula, P eSA (k - j), P eSA (k - 2j), P eSA (k - 3j) respectively represent the electromagnetic power of the single - machine infinite - bus system at the (k - j)th, (k - 2j)th, and (k - 3j)th sampling time steps; μ is a sufficiently small positive real number; j = 0, 1, 2, …, g, where g ≤ 10.

[0027] Furthermore, the supplementary criterion for transient instability in step 3 is as follows:

[0028]

[0029] In the formula, P eSA (k - n), P eSA (k - n - j), P eSA (k - n - j) respectively represent the electromagnetic power of the single - machine infinite - bus system at the (k - n)th, (k - n - j)th, and (k - n - j)th sampling time steps; n is a positive integer.

[0030] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0031] 1. The transient instability discrimination method proposed by the present invention can complete the discrimination of system transient instability only based on the power response curve by deeply exploring and establishing the correlation between system transient instability and the power response curve, which has good universality and provides strong technical support for subsequent power grid security and stability analysis and control.

[0032] 2. Compared with the prior art, by exploring the characteristics of system transient instability in severe instability scenarios, the present invention introduces a supplementary criterion for transient instability to identify severe instability scenarios, improving the reliability of the transient instability discrimination method. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a schematic flow chart of the transient instability discrimination method based on the power response curve of the present invention.

[0034] Figure 2 It is the CEPRI 36 - bus system. DETAILED DESCRIPTION OF THE INVENTION

[0035] The present invention will be further described in detail below with reference to the embodiments and the drawings.

[0036] Existing transient instability discrimination methods all rely on generator power angle and / or angular velocity information, which face two problems: First, when directly measuring the generator power angle / angular velocity, a rotor position sensing device needs to be installed, but the sensor has errors such as electromagnetic interference and mechanical vibration, and when directly measuring the power angle, the initial power angle value also needs to be corrected during the commissioning of the unit, which is difficult to apply in actual engineering; Second, when indirectly measuring the generator power angle / angular velocity, it needs to be calculated through information such as the generator terminal voltage, and this additional calculation link weakens the rapidity of the transient instability discrimination method. In addition, when indirectly measuring the angular velocity, it is necessary to assume that the generator terminal electrical frequency is equal to the rotational speed, and when indirectly measuring the power angle, it is necessary to assume that the generator rotational speed remains unchanged, which makes it difficult to control the calculation error during the direct measurement of the power angle / angular velocity in the transient process. In response to this, the present invention provides a transient instability discrimination method based on the power response curve. By deeply exploring and establishing the correlation between system transient instability and the power response curve, this method can complete the discrimination of system transient instability only based on the power response curve, providing strong technical support for subsequent power grid safety and stability analysis and control.

[0037] The flow of a transient instability discrimination method based on the power response curve of the present invention is as Figure 1 shown, and specifically includes the following steps:

[0038] Step 1: Obtain the inherent information of the generators in the target system, and measure the electromagnetic power of each generator in the target system through the wide-area measurement system.

[0039] Among them, the target system refers to the power system that needs transient stability analysis. The inherent information of the generator includes the number of generators in the target system, the inertia time constant of each generator, and the mechanical power of each generator.

[0040] Step 2: Based on the inherent information of the generator and the real-time measurement data of the generator electromagnetic power, equivalently transform the target system into a single-machine infinite-bus system, and obtain the power response curve of the single-machine infinite-bus system.

[0041] Step 3: Judge the transient stability of the target system according to the power response curve of the single-machine infinite-bus system. If the power response curve of the single-machine infinite-bus system does not meet the main criterion or supplementary criterion for transient instability, the target system is transiently stable; if it meets the main criterion or supplementary criterion for transient instability, the target system is transiently unstable, and the discrimination result is output.

[0042] Compared with the drawbacks or limitations of existing transient instability discrimination methods, the transient instability discrimination method proposed by the present invention can complete the discrimination of system transient instability only based on the power response curve by deeply exploring and establishing the correlation between system transient instability and the power response curve, and introduces a supplementary criterion for transient instability to identify severe transient instability scenarios, improving the reliability of the transient instability discrimination method and providing strong technical support for subsequent power grid safety and stability analysis and control.

[0043] Further, the process of measuring the electromagnetic power of each generator in the target system by the wide area measurement system in step 1 is specifically as follows:

[0044] Step 1.1: Denote the generator nodes in the target system as i, where i = 1, 2, 3, …, v, and v is the number of generators.

[0045] Step 1.2: Based on the sampling start time, denote the electromagnetic power of the i-th generator measured by the wide area measurement system at the k-th sampling step as P i (k), where k = 1, 2, 3, …, and k represents the sampling sequence number, indicating the sampling sequence number from the sampling start time to the current time.

[0046] Further, the process of transforming the target system into a single-machine infinite-bus system in step 2 is specifically as follows:

[0047] Step 2.1: Based on the sampling start time, calculate the integral of the difference between the electromagnetic power and mechanical power of each generator in the target system with respect to time; sort the generators in ascending order of the integral value, and calculate the absolute difference between the integral values of adjacent generators; identify the generator pair corresponding to the largest absolute difference, and divide the generator group in the target system into a lagging group A and a leading group S with the gap between this generator pair as the boundary.

[0048] Step 2.2: According to the lagging group A and the leading group S, calculate the angular frequency, power angle, inertia time constant, mechanical power, and electromagnetic power of the generators in the two-machine system through the following formula:

[0049]

[0050] In the formula, ω i (k), δ i (k), and M i respectively represent the angular frequency, power angle, and inertia time constant of the i-th generator at the k-th sampling step; ω A (k), δ A (k), M A , P mA (k), P eA (k) respectively represent the equivalent angular frequency, equivalent power angle, equivalent inertia time constant, equivalent mechanical power, and equivalent electromagnetic power of the lagging group A at the k-th sampling step; ω S (k), δ S (k), M S , P mS (k), P eS(k) represent the equivalent angular frequency, equivalent power angle, equivalent inertia time constant, equivalent mechanical power, and equivalent electromagnetic power of the leading group S at the k-th sampling step; P mi is the mechanical power of generator i in the target system.

[0051] Step 2.3: According to the two-machine system, calculate the angular frequency, power angle, inertia time constant, mechanical power, and electromagnetic power of the generator in the single-machine infinite-bus system through the following formula:

[0052]

[0053] where Δδ(k), Δω(k), M SA , P mSA (k), P eSA (k) are the power angle, angular velocity, inertia time constant, mechanical power, and electromagnetic power of the generator in the single-machine infinite-bus system at the k-th sampling step, respectively.

[0054] Furthermore, the method for obtaining the power response curve of the single-machine infinite-bus system in Step 2 is as follows:

[0055] Taking the sampling start time as a reference, calculate the electromagnetic power of the generator in the single-machine infinite-bus system at each sampling point in the interval from the sampling start time to the k-th sampling step according to the electromagnetic power of each generator in the target system, and generate the power response curve of the single-machine infinite-bus system through its discrete time-series data.

[0056] Furthermore, the main criterion for transient instability in Step 3 is:

[0057]

[0058] where P eSA (k-j), P eSA (k-2j), P eSA (k-3j) represent the electromagnetic power of the single-machine infinite-bus system at the (k-j)-th, (k-2j)-th, and (k-3j)-th sampling steps, respectively; μ is a sufficiently small positive real number; j = 0, 1, 2, …, g, g ≤ 10.

[0059] Furthermore, the supplementary criterion for transient instability in Step 3 is:

[0060]

[0061] where P eSA (k-n), P eSA (k-n-j), P eSA (k-n-j) represent the electromagnetic power of the single-machine infinite-bus system at the (k-n)-th, (k-n-j)-th, and (k-n-j)-th sampling steps, respectively; n is a positive integer.

[0062] Embodiment:

[0063] The power system analysis comprehensive program PSASP is used to verify the feasibility of the transient instability discrimination method proposed by the present invention in the CEPRI 36 - bus system. The CEPRI 36 - bus system is as Figure 2 shown. All generators in the system adopt the classical second - order model, and the effects of governors, voltage regulators, and PSS are considered. The PSASP simulation step size is set to half a cycle (10 ms), and the electromagnetic power of each generator is output at each step, which is used as the real - time measurement data of the wide - area measurement system. In this embodiment, a three - phase grounding short - circuit fault is set at bus 24, and the fault is connected at 0 s. By setting different fault clearing times within the range of 10 - 60 ms, the transient stability of the system is judged by using the method described in the present invention. The specific process is as follows:

[0064] Step 1: Obtain the inherent parameters of each generator, and set different fault clearing times to 0.1 s, 0.3 s, 0.42 s, 0.45 s, 0.49 s, 0.53 s, and 0.57 s respectively, and obtain the power response curves of the generators in the system under different fault clearing times.

[0065] Step 2: According to the inherent parameters of each generator and the electromagnetic power change curves, divide the generator group into a leading group and a lagging group. Among them, the leading group includes Generator 1 and Generator 2, and the lagging group includes Generator 3, Generator 4, Generator 5, Generator 6, Generator 7, and Generator 8. According to the post - fault instability mode, the CEPRI 36 - bus system is equivalently transformed into a single - machine infinite - bus system, and the power response curve of the single - machine infinite - bus system is obtained.

[0066] Step 3: Determine whether the system is transiently stable by whether the power response curves of the single - machine infinite - bus system under different fault clearing times satisfy the transient instability main / supplementary criteria. Table 1 summarizes the determination results of the transient instability discrimination method proposed by the present invention.

[0067] Table 1 Determination results of the criteria under different fault clearing times

[0068] Fault clearing time Actual stability result Criterion judgment result 0.1 Stable Stable 0.3 Stable Stable 0.42 Unstable Unstable 0.45 Unstable Unstable 0.49 Unstable Unstable 0.53 Unstable Unstable 0.57 Unstable Unstable

[0069] It can be seen from Table 1 that, compared with the actual transient stable state of the system obtained by time - domain simulation, the transient stability discrimination method proposed by the present invention can correctly judge the transient stability of the system, providing a strong technical support for subsequent power grid security and stability analysis and control.

[0070] The specific embodiments described above further elaborate on the purpose, technical solutions, and beneficial effects of the present invention. It should be understood that the above description is only for the specific embodiments of the present invention and is not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A transient instability discrimination method based on a power response curve, characterized in that, It includes the following steps: Step 1: Obtain the inherent information of the generators in the target system, and measure the electromagnetic power of each generator in the target system through a wide-area measurement system; The target system refers to the power system that requires transient stability analysis. The inherent information of the generator includes the number of generators in the target system, the inertia time constant of each generator, and the mechanical power of each generator; Step 2: Based on the inherent information of the generator and the real-time measurement data of the generator electromagnetic power, equivalently transform the target system into a single-machine infinite-bus system, and obtain the power response curve of the single-machine infinite-bus system; Step 3: Judge the transient stability of the target system according to the power response curve of the single-machine infinite-bus system. If the power response curve of the single-machine infinite-bus system does not meet the main criterion or supplementary criterion for transient instability, the target system is transiently stable; If it meets the main criterion or supplementary criterion for transient instability, the target system is transiently unstable, and the discrimination result is output.

2. The transient instability discrimination method based on a power response curve according to claim 1, wherein The process of measuring the electromagnetic power of each generator in the target system through the wide-area measurement system in Step 1 is specifically as follows: Step 1.1: Denote the generator nodes in the target system as i, where i = 1, 2, 3, …, v, and v is the number of generators; Step 1.2: Taking the sampling start time as a reference, denote the electromagnetic power of the \(i\)-th generator measured by the wide area measurement system at the \(k\)-th sampling step as \(P^{(k)}\), where \(k = 1, 2, 3,\cdots\), and \(k\) represents the sampling sequence number, indicating the sampling sequence number from the sampling start time to the current time. i (k), \(k = 1, 2, 3,\cdots\), where \(k\) represents the sampling sequence number, indicating the sampling sequence number from the sampling start time to the current time.

3. The transient instability discrimination method based on the power response curve according to claim 1, characterized in that The process of equivalently transforming the target system into a single-machine infinite-bus system in Step 2 is specifically as follows: Step 2.1: Based on the sampling start time, calculate the integral of the difference between the electromagnetic power and mechanical power of each generator in the target system over time; sort the generators in ascending order of the integral value, and calculate the absolute difference between the integral values of adjacent generators; identify the generator pair corresponding to the largest absolute difference, and divide the generator group in the target system into a lagging group A and a leading group S with the gap of this generator pair as the boundary; Step 2.2: According to the lagging group A and the leading group S, calculate the angular frequency, power angle, inertia time constant, mechanical power, and electromagnetic power of the generators in the two-machine system through the following formula: where ω i (k), δ i (k), and M i represent the angular frequency, power angle, and inertia time constant of generator i at the k-th sampling step, respectively; ω A (k), δ A (k), M A , P mA (k), P eA (k) represent the equivalent angular frequency, equivalent power angle, equivalent inertia time constant, equivalent mechanical power, and equivalent electromagnetic power of lagging group A at the k-th sampling step, respectively; ω S (k), δ S (k), M S , P mS (k), P eS (k) represent the equivalent angular frequency, equivalent power angle, equivalent inertia time constant, equivalent mechanical power, and equivalent electromagnetic power of leading group S at the k-th sampling step, respectively; P mi is the mechanical power of generator i in the target system; Step 2.3: According to the two-machine system, calculate the angular frequency, power angle, inertia time constant, mechanical power, and electromagnetic power of the generator in the single-machine infinite-bus system through the following formula: where Δδ(k), Δω(k), M SA , P mSA (k), P eSA (k) are the power angle, angular velocity, inertia time constant, mechanical power, and electromagnetic power of the generator in the single-machine infinite-bus system at the k-th sampling step, respectively.

4. A transient instability discrimination method based on a power response curve according to claim 1, characterized in that The method for obtaining the power response curve of the single-machine infinite-bus system in Step 2 is as follows: Based on the sampling start time, calculate the electromagnetic power of the generator in the single-machine infinite-bus system at each sampling point in the interval from the sampling start time to the kth sampling step according to the electromagnetic power of each generator in the target system, and generate the power response curve of the single-machine infinite-bus system through its discrete time series data.

5. A transient instability discrimination method based on a power response curve according to claim 1, characterized in that The main criterion for transient instability in Step 3 is: where P eSA (k - j), P eSA (k - 2j), P eSA (k - 3j) respectively represent the electromagnetic power of the single - machine infinite - bus system at the (k - j) - th, (k - 2j) - th, and (k - 3j) - th sampling - step moments; μ is a sufficiently small positive real number; j = 0, 1, 2, …, g, where g ≤ 10.

6. The transient instability discrimination method based on a power response curve according to claim 1, wherein The supplementary criterion for transient instability in Step 3 is: Where, P eSA (k - n), P eSA (k - n - j), P eSA (k - n - j) represent the electromagnetic powers of the single - machine infinite - bus system at the (k - n)th, (k - n - j)th, and (k - n - j)th sampling step moments respectively; n is a positive integer.

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