Method for suppressing low-frequency oscillation of photovoltaic grid-connected system by TCSC

Abstract

The invention provides a method for suppressing low-frequency oscillation of a photovoltaic grid-connected system through a TCSC, and the method comprises the steps: firstly constructing a potential energy function containing a photovoltaic power grid branch mode from the perspective of network mode energy, achieving the online identification of key links of the system according to online data, considering the scene of weaker system damping after photovoltaic grid connection, and employing the TCSC in combination with the mode energy, thereby achieving the low-frequency oscillation suppression of the photovoltaic grid-connected system. Therefore, oscillation on-line suppression with the purposes of improving the small interference stability of the system and rapidly calming the oscillation energy is realized.

Description

A method for suppressing low-frequency oscillations in a TCSC photovoltaic grid-connected system Technical Field

[0001] This application relates to the field of small-disturbance stability control technology for photovoltaic power systems, and is a method for suppressing low-frequency oscillations in photovoltaic grid-connected systems using TCSC. Background Technology

[0002] With the acceleration of the global energy transition, photovoltaic power generation, as an important component of clean and renewable energy, has seen its grid-connected scale continue to expand, providing strong support for energy structure optimization and the achievement of "dual carbon" goals. However, photovoltaic power sources have inherent characteristics of volatility, intermittency, and low inertia. After a large number of photovoltaic units are connected to the grid, they will significantly change the original power system's topology, parameter characteristics, and dynamic response patterns, leading to a weakening of system damping characteristics and making it highly susceptible to inducing low-frequency oscillations.

[0003] Low-frequency oscillations are a typical dynamic stability problem in power system operation. Their oscillation frequency is typically in the range of 0.1-2.5Hz. Once they occur, they can cause significant fluctuations in system voltage and frequency, and in severe cases, even trigger grid disconnection and large-scale blackouts, directly threatening the safe and stable operation of the power system. Currently, suppression technologies for low-frequency oscillations in photovoltaic grid-connected systems mainly include traditional power electronic device control and additional damping controller design. However, these technologies generally have the following drawbacks: First, they are mostly based on offline design using linearized system models, making it difficult to adapt to the time-varying characteristics of system parameters caused by photovoltaic output fluctuations, resulting in insufficient robustness of control. Second, they lack precise analysis of the energy distribution of system oscillations, making it impossible to locate key oscillation links, leading to weak targeting of control measures and low suppression efficiency. Third, the optimization of control parameters often relies on experience or simple algorithms, making it difficult to achieve the optimal balance between oscillation suppression effect and system operating economy.

[0004] Controllable series compensators (TCSCs), as an important member of flexible AC transmission systems (FACTS), possess advantages such as fast response speed, wide adjustment range, and continuous and smooth control of equivalent line reactance, demonstrating great potential in improving power system stability. However, existing technologies using TCSCs to suppress low-frequency oscillations have not fully incorporated network mode energy perspectives into their analysis and design, making it difficult to quickly and effectively quell oscillation energy at its source and failing to effectively solve the problem of low-frequency oscillation suppression in scenarios with weak system damping after photovoltaic grid connection. Therefore, developing a technical solution that can accurately locate key oscillation components, dynamically optimize TCSC control parameters, and efficiently suppress low-frequency oscillations in photovoltaic grid-connected systems has become a critical technical problem urgently needing to be solved in the current power system field.

[0005] Application content

[0006] The purpose of this application is to propose a method for suppressing low-frequency oscillations in a photovoltaic grid-connected system using TCSC. The method is characterized by starting from the perspective of network mode energy, identifying key components of the system online based on real-time measurement data, considering the scenario where the system damping is weak after photovoltaic grid connection, and using TCSC combined with mode energy to achieve online oscillation suppression with the aim of improving the stability of the system under small disturbances and quickly calming oscillation energy.

[0007] The objective of this application is achieved through the following technical solution:

[0008] Step 1: Potential Energy Construction of Branch Mode Including Photovoltaic Grid

[0009] Under small perturbations, a photovoltaic system can be represented by the following linear state equation:

[0010]

[0011] In the formula, It is an n-dimensional state variable that includes the synchronous machine state variable and the photovoltaic state variable, Δx G =[Δδ i ,Δw i ] T Let Δx be the state variable of the synchronous machine. PV =[ΔU dci ,ΔI di ,ΔI qi ] T Let Δu be the state variable of the photovoltaic system, and let Δu = [Δu1, Δθ1, Δu2, Δθ2, ..., Δu] i ,Δθ i ] T ,Δu n , Δθ n Let A, B, C, and D be the node voltage amplitude increment and angle increment, respectively, and let A, B, C, and D be the coefficient matrix.

[0012] The general form of the solution to the state equation is:

[0013]

[0014] In the formula, ψ j φ j These are the left and right eigenvectors, λ. j (j=1,...,n) are the eigenvalues. x0 is the initial value of the state variable. In this system, it is written in matrix form as shown in equation (3):

[0015]

[0016] By transforming equation (1), we can obtain:

[0017] Δu(t)=-D -1 CΔx(t)=FΔx(t) (4)

[0018] In the formula, F = -D -1 C.

[0019] Then the voltage magnitude increment and voltage angle increment at node i can be expressed as:

[0020]

[0021] Where p represents the position of the state variable among all state variables, and q represents the number of small disturbance eigenvalues. Based on the above formula, key responses in the network are extracted, and the branch mode energy function is constructed:

[0022]

[0023] Based on the power expression of the branch between node i and node j in the system:

[0024]

[0025] Linearizing the line power yields the expression for the line power increment, which, after simplification, is shown in the following equation:

[0026] ΔP ij =k1Δu i +k2Δθ i +k3Δu j +k4Δθ j (9)

[0027] Where k1, k2, k3, and k4 are constants calculated from the admittance of branch ij and the initial value of the voltage angle difference between nodes i and j. Combined with the increment of the voltage angle difference between nodes i and j connected at both ends of the branch:

[0028]

[0029] Expand and simplify the active power increment and voltage angle increment of branch ij, and change the power increment coefficient from A1-A n This indicates that the reciprocal coefficient of the voltage angle increment is derived from B1-B. n express:

[0030]

[0031] When performing mode analysis on the system, it is necessary to identify the dominant oscillation mode and then further analyze it under the dominant oscillation mode. Considering the actual situation of the system, there are many cases where a single dominant oscillation mode with weak damping occurs. Therefore, we focus on the low-frequency oscillation phenomenon caused by a single dominant mode for energy analysis, ignoring the cross-correlation part of the branch mode energy. Then, the energy expression of the branch mode of the system is:

[0032]

[0033] Step 2: Locating the key oscillation element

[0034] Based on the branch mode energy expression of the photovoltaic grid-connected system, the transient energy of each branch is calculated by first measuring the active power and voltage angle increment of different branches.

[0035]

[0036] In the formula, V Pi-j Let be the transient state energy of branch ij. Let ω be the active power of branch ij in steady state. ij Let be the angular frequency difference between nodes i and j. Using the Prony analysis method, the transient energy calculated online is decomposed into a linear combination of multiple exponential terms. The oscillation mode corresponding to the oscillation frequency is identified, and the branch mode energy of the corresponding mode is obtained online based on the oscillation frequency, oscillation amplitude, and phase reconstruction. By comparing the mode energy amplitudes of different oscillation modes, the key oscillation components of the system are identified.

[0037] Step 3: Energy mode regulation based on TCSC

[0038] Find the equivalent reactance x of TCSC using the whale optimization algorithm. c The optimal solution minimizes the energy of the key oscillation mode. The parameter optimization model for TCSC is as follows:

[0039]

[0040] Constraints:

[0041]

[0042] In the formula, P ijmin The minimum transmission power of a branch in a critical oscillation stage; u i u j The voltage at both ends of the branch, θ ij The phase angle difference between the voltages at both ends of a branch; x ij Branch reactance; ΔV pminΔV ijmax The energy reduction of the minimum and maximum key oscillation points before and after regulation; ΔP ijmin ΔP ijmax The reduction in power of the minimum and maximum key oscillation links before and after regulation; x cmin x cmax This refers to the minimum and maximum equivalent reactance of the TCSC. Based on the optimization results, the equivalent reactance of the TCSC is adjusted to minimize the energy of the key oscillation mode, thereby effectively suppressing low-frequency oscillations in the photovoltaic grid-connected system.

[0043] Beneficial effects

[0044] Highly targeted oscillation suppression enhances system stability under small disturbances: This application, starting from the energy perspective of network mode, constructs energy functions for branch modes including photovoltaic power grids to accurately quantify the oscillation energy distribution of each branch. Combined with Prony analysis, it can quickly locate key oscillation links in the system, avoiding the drawbacks of blind regulation in traditional technologies. TCSC regulation based on key oscillation links can directly act on the region where oscillation energy is most concentrated, achieving targeted suppression of low-frequency oscillations and significantly improving system stability under small disturbances.

[0045] Adapting to the time-varying characteristics of the system and exhibiting excellent control robustness: This application achieves online identification of key system components based on real-time measurement data, dynamically tracking system parameter changes caused by factors such as photovoltaic output fluctuations and load variations, and updating branch mode energy calculation results and key oscillation location information in real time. Compared to traditional offline control schemes, the online adaptive characteristics of this application enable it to better adapt to the time-varying characteristics of the photovoltaic grid-connected system, maintaining good oscillation suppression under different operating conditions, and significantly improving control robustness.

[0046] Precise parameter optimization and high oscillation suppression efficiency: This application employs the whale optimization algorithm to find the optimal solution for the TCSC equivalent reactance, which minimizes the mode energy of key oscillations while satisfying system operating constraints. This optimization algorithm features fast convergence speed and high optimization accuracy, quickly determining the optimal control parameters. By adjusting the TCSC equivalent reactance, it directly weakens the oscillation energy of key components, achieving rapid suppression of low-frequency oscillations. Compared to traditional empirical parameter setting methods, the oscillation suppression efficiency is significantly improved.

[0047] The project boasts strong practicality and excellent system operation economy: The technologies employed in this application, such as measurement data acquisition, model energy calculation, Prony analysis, and whale optimization algorithm, are all mature and feasible. The required hardware equipment consists of commonly used existing power system components, eliminating the need for large-scale new hardware investment. This results in low implementation costs and strong feasibility. Furthermore, by precisely controlling the TCSC equivalent reactance, oscillations are effectively suppressed while optimizing branch power transmission efficiency, avoiding increased energy consumption due to over-control, thus balancing oscillation suppression effectiveness with system operation economy.

[0048] With wide applicability and high promotional value, this application focuses on typical scenarios where the system damping is weak after photovoltaic grid connection. Furthermore, its core logic of online identification and dynamic control can flexibly adapt to power systems with different photovoltaic grid-connected capacities and different grid topologies. Whether it's large-scale grid connection of centralized photovoltaic power plants or scattered access of distributed photovoltaic systems, this application can effectively suppress oscillations, making it applicable to a wide range of scenarios and possessing extremely high engineering promotion value. Attached Figure Description

[0049] To more clearly illustrate the technical solutions in this application or the prior art, the accompanying drawings involved in the embodiments or the prior art are briefly described below. Obviously, these drawings illustrate several embodiments of this application, and those skilled in the art can deduce other possible drawings based on these drawings without creative effort. The purpose of the drawings is limited to illustrating specific embodiments and does not limit the scope of this application.

[0050] Figure 1 is a flowchart of TCSC regulation;

[0051] Figure 2 is the wiring diagram of a photovoltaic unit connected to a 4-unit system;

[0052] Figure 3 shows the energy of each branch mode;

[0053] Figure 4 shows the branch active power before and after TCSC parameter optimization;

[0054] Figure 5 shows the branch mode energy before and after TCSC parameter optimization. Detailed Implementation

[0055] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the protection scope of this application.

[0056] The following specific examples illustrate the implementation of this invention. Those skilled in the art can understand the advantages and effects of this invention from the content presented in this specification. The invention will be further described in conjunction with the accompanying drawings, tables, and specific embodiments.

[0057] This invention proposes a method for suppressing low-frequency oscillations in a photovoltaic grid-connected system from the perspective of network mode energy. Its feature is that it starts from the perspective of network mode energy, realizes online identification of key links of the system based on real-time measurement data, considers the scenario of weak system damping after photovoltaic grid connection, and uses TCSC combined with mode energy to achieve online oscillation suppression with the aim of improving the stability of the system under small disturbances and quickly calming oscillation energy.

[0058] Step 1: Potential Energy Construction of Branch Mode Including Photovoltaic Grid:

[0059] Under small perturbations, a photovoltaic system can be represented by the following linear state equation:

[0060]

[0061] In the formula, It is an n-dimensional state variable that includes the synchronous machine state variable and the photovoltaic state variable, Δx G =[Δδ i ,Δw i ] T Let Δx be the state variable of the synchronous machine. PV =[ΔU dci ,ΔI di ,ΔI qi ] T Let Δu be the state variable of the photovoltaic system, and let Δu = [Δu1, Δθ1, Δu2, Δθ2, ..., Δu] i ,Δθ i ] T ,Δu n , Δθ n Let A, B, C, and D be the node voltage amplitude increment and angle increment, respectively, and let A, B, C, and D be the coefficient matrix.

[0062] The general form of the solution to the state equation is:

[0063]

[0064] In the formula, ψ j φ j These are the left and right eigenvectors, λ. j (j=1,…,n) are the eigenvalues. x0 is the initial value of the state variable. In this system, it is written in matrix form as shown in equation (3):

[0065]

[0066] By transforming equation (1), we can obtain:

[0067] Δu(t)=-D -1 CΔx(t)=FΔx(t) (4)

[0068] In the formula, F = -D -1 C.

[0069] Then the voltage magnitude increment and voltage angle increment at node i can be expressed as:

[0070]

[0071] Where p represents the position of the state variable among all state variables, and q represents the number of small disturbance eigenvalues. Based on the above formula, key responses in the network are extracted, and the branch mode energy function is constructed:

[0072]

[0073] Based on the power expression of the branch between node i and node j in the system:

[0074]

[0075] Linearizing the line power yields the expression for the line power increment, which, after simplification, is shown in the following equation:

[0076] ΔP ij =k1Δu i +k2Δθ i +k3Δu j +k4Δθ j (9)

[0077] Where k1, k2, k3, and k4 are constants calculated from the admittance of branch ij and the initial value of the voltage angle difference between nodes i and j. Combined with the increment of the voltage angle difference between nodes i and j connected at both ends of the branch:

[0078]

[0079] Expand and simplify the active power increment and voltage angle increment of branch ij, and change the power increment coefficient from A1-A n This indicates that the reciprocal coefficient of the voltage angle increment is derived from B1-B. n express:

[0080]

[0081] When performing mode analysis on the system, it is necessary to identify the dominant oscillation mode and then further analyze it under the dominant oscillation mode. Considering the actual situation of the system, there are many cases where a single dominant oscillation mode with weak damping occurs. Therefore, we focus on the low-frequency oscillation phenomenon caused by a single dominant mode for energy analysis, ignoring the cross-correlation part of the branch mode energy. Then, the energy expression of the branch mode of the system is:

[0082]

[0083] Step 2: Locating the key oscillation element

[0084] Based on the branch mode energy expression of the photovoltaic grid-connected system, the transient energy of each branch is calculated by first measuring the active power and voltage angle increment of different branches.

[0085]

[0086] In the formula, V Pi-j Let be the transient state energy of branch ij. Let ω be the active power of branch ij in steady state. ij Let be the angular frequency difference between nodes i and j. Using the Prony analysis method, the transient energy calculated online is decomposed into a linear combination of multiple exponential terms. The oscillation mode corresponding to the oscillation frequency is identified, and the branch mode energy of the corresponding mode is obtained online based on the oscillation frequency, oscillation amplitude, and phase reconstruction. By comparing the mode energy amplitudes of different oscillation modes, the key oscillation components of the system are identified.

[0087] Step 3: Energy mode regulation based on TCSC

[0088] Find the equivalent reactance x of TCSC using the whale optimization algorithm. c The optimal solution minimizes the energy of the key oscillation mode. The parameter optimization model for TCSC is as follows:

[0089]

[0090] Constraints:

[0091]

[0092] In the formula, P ijmin The minimum transmission power of a branch in a critical oscillation stage; u i u j The voltage at both ends of the branch, θij The phase angle difference between the voltages at both ends of a branch; x ij Branch reactance; ΔV pmin ΔV ijmax The energy reduction of the minimum and maximum key oscillation points before and after regulation; ΔP ijmin ΔP ijmax The reduction in power of the minimum and maximum key oscillation links before and after regulation; x cmin x cmax This refers to the minimum and maximum equivalent reactance of the TCSC. Based on the optimization results, the equivalent reactance of the TCSC is adjusted to minimize the mode energy of the key oscillation element, thereby effectively suppressing low-frequency oscillations in the photovoltaic grid-connected system.

[0093] In the context of continuously increasing photovoltaic penetration, to improve the small-interference stability and anti-interference capability of photovoltaic grid-connected systems, this paper proposes the following specific TCSC configuration parameter determination process, the detailed flowchart of which is shown in Figure 1:

[0094] Step 1: Obtain the key oscillation components of the photovoltaic grid-connected system based on Prony decomposition;

[0095] Step 2: Set up TCSC control devices at key oscillation points;

[0096] Step 3: Determine the control target and constraints, and optimize the effective parameter xc of TCSC;

[0097] Step 4: Adjust the TCSC parameters based on the optimization results to minimize the mode energy of the key oscillation element;

[0098] Step 6: If the result meets the expected target, end the calculation; otherwise, repeat step 3.

[0099] Example:

[0100] In the 4-machine system, we studied how to obtain the minimum critical mode energy by adjusting the TCSC. The system wiring diagram is shown in Figure 2.

[0101] First, the transient energy is decomposed using Prony to obtain the mode energy of each branch. At this point, the branches with larger mode energies in the system are shown in Figure 3. The key oscillation element is branch 5-6.

[0102] After incorporating the TCSC into the critical oscillation branch 5-6, whale optimization calculations were performed on the parameters. When the parameter = 0.96451, the branch mode energy of branch 5-6 has a minimum value within the constraint range, which is 0.38512. The active power and branch mode energy curves of each branch are shown in Figures 4 and 5.

[0103] Figures 4a and 4b show the active power of branches 5-6 and 7-8 in the dominant path before and after parameter optimization, respectively; Figures 4c and 4d show the active power of branches 4-10 and 2-6 in the dominant path before and after parameter optimization, respectively; Figures 5a and 5b show the branch mode energy of branches 5-6 and 7-8 in the dominant path before and after parameter optimization, respectively; Figures 5c and 5d show the branch mode energy of branches 4-10 and 2-6 in the dominant path before and after parameter optimization, respectively. These are the branches containing PV1 and PV2, respectively. Observations show that after optimization, the oscillation amplitude of the active power and branch mode energy of each branch is generally reduced, the oscillation period is lengthened, and the oscillation frequency is reduced. Simulation results show that the optimized parameters have a significant effect on branches in both the dominant and non-dominant oscillation paths.

[0104] Those skilled in the art should understand that the above embodiments are merely illustrative of the content of this disclosure and do not limit its scope. The system capacity, voltage, line parameters, etc., shown may vary depending on the specific circumstances of the power electronic grid-connected generator set and its grid connection. Based on this disclosure, those skilled in the art can make other changes or adjustments, and these changes still fall within the scope of this disclosure.

Claims

1. A method for suppressing low-frequency oscillations in a photovoltaic grid-connected system using TCSC, characterized in that, The process includes the following steps: Step 1: Constructing the potential energy of the photovoltaic grid branch mode; Step 2: Locating the key oscillation link; Step 3: Energy mode regulation based on TCSC.

2. The method for suppressing low-frequency oscillations in a photovoltaic grid-connected system according to claim 1, characterized in that... Step 1: Potential energy construction of the photovoltaic grid branch mode specifically includes: Under small disturbances, the photovoltaic system can be represented by the following linear state equation: In the formula, It is an n-dimensional state variable that includes the synchronous machine state variable and the photovoltaic state variable, Δx G =[Δδ i ,Δw i ] T Let Δx be the state variable of the synchronous machine. PV =[ΔU dci ,ΔI di ,ΔI qi ] T Let Δu be the state variable of the photovoltaic system, and let Δu = [Δu1, Δθ1, Δu2, Δθ2, ..., Δu] i ,Δθ i ] T ,Δu n , Δθ n Let A, B, C, and D be the node voltage magnitude increments and angle increments, respectively; let A, B, C, and D be the coefficient matrices; the general form of the solution to the state equation is: In the formula, ψ j φ j These are the left and right eigenvectors, λ. j (j=1,...,n) are the eigenvalues. x0 is the initial value of the state variable. In this system, it is written in matrix form as shown in equation (3): By transforming equation (1), we can obtain: Δu(t)=-D -1 CΔx(t)=FΔx(t) (4) where F=-D -1 C, then the voltage magnitude increment and voltage angle increment at node i can be expressed as: Where p represents the position of the state variable among all state variables, and q represents the number of small disturbance eigenvalues; based on the above formula, key responses in the network are extracted, and the branch mode energy function is constructed: Based on the power expression of the branch between node i and node j in the system: Linearizing the line power yields the expression for the line power increment, which, after simplification, is shown in the following equation: ΔP ij =k1Δu i +k2Δθ i +k3Δu j +k4Δθ j (9) Wherein, k1, k2, k3, and k4 are constants calculated from the admittance of branch ij and the initial value of the voltage angle difference between nodes i and j; combined with the voltage angle difference increment between nodes i and j connected at both ends of the branch: Expand and simplify the active power increment and voltage angle increment of branch ij, and change the power increment coefficient from A1-A n This indicates that the reciprocal coefficient of the voltage angle increment is derived from B1-B. n express: When performing mode analysis on the system, it is necessary to identify the dominant oscillation mode and then further analyze it under the dominant oscillation mode. Considering the actual situation of the system, there are many cases where a single dominant oscillation mode with weak damping occurs. Therefore, we focus on the low-frequency oscillation phenomenon caused by a single dominant mode for energy analysis, ignoring the cross-correlation part of the branch mode energy. Then, the energy expression of the branch mode of the system is:

3. The method for suppressing low-frequency oscillations in a photovoltaic grid-connected system according to claim 1, characterized in that... Step 2: Locating the key oscillation link specifically includes: based on the branch mode energy expression of the photovoltaic grid-connected system, firstly measuring the active power and voltage angle increment of different branches to calculate the transient energy of each branch. In the formula, V Pi-j Let be the transient state energy of branch ij. Let ω be the active power of branch ij in steady state. ij Let be the angular frequency difference between nodes i and j. Using the Prony analysis method, the transient energy calculated online is decomposed into a linear combination of multiple exponential terms. The oscillation mode corresponding to the oscillation frequency is identified, and the branch mode energy of the corresponding mode is obtained online based on the oscillation frequency, oscillation amplitude, and phase reconstruction. By comparing the mode energy amplitudes of different oscillation modes, the key oscillation components of the system are identified.

4. The method for suppressing low-frequency oscillations in a photovoltaic grid-connected system according to claim 1, characterized in that... Step 3, energy mode regulation based on TCSC, specifically includes: finding the equivalent reactance x of TCSC using the whale optimization algorithm. c The optimal solution minimizes the energy of the key oscillation mode. The parameter optimization model for TCSC is as follows: Constraints: In the formula, P ijmin The minimum transmission power of a branch in a critical oscillation stage; u i u j The voltage at both ends of the branch, θ ij The phase angle difference between the voltages at both ends of a branch; x ij Branch reactance; ΔV pmin ΔV ijmax The energy reduction of the minimum and maximum key oscillation points before and after regulation; ΔP ijmin ΔP ijmax The reduction in power of the minimum and maximum key oscillation links before and after regulation; x cmin x cmax Refers to the minimum and maximum equivalent reactance of TCSC.

5. The method for suppressing low-frequency oscillations in a photovoltaic grid-connected system according to claim 4, characterized in that, Adjust the equivalent reactance of TCSC based on the optimization results to minimize the energy of the key oscillation mode and effectively suppress low-frequency oscillations in the photovoltaic grid-connected system.

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