Voltage stability margin calculation method considering control mode of photovoltaic power station

Abstract

The application discloses a voltage stability margin calculation method considering a control mode of a photovoltaic power station, and adds modeling consideration of a reactive power-voltage control mode of the photovoltaic power station in voltage stability margin calculation. In a continuous power flow calculation process, parameterized power flow equations are obtained by extending node voltage with the fastest voltage drop. Meanwhile, in a prediction link in the continuous power flow calculation process, a hybrid prediction method is adopted. In the case that voltage margin is large, nonlinear prediction is adopted to accelerate the calculation speed. In the case that voltage stability limit is approached, linear prediction is adopted. The voltage stability margin calculation method fully considers the influence of the control mode of the large-scale photovoltaic power station on voltage stability, and improves the calculation efficiency and the calculation precision.

Description

Technical Field

[0001] This invention relates to the field of power system stability technology, and in particular to a method for calculating voltage stability margin considering the control mode of a photovoltaic power plant. Background Technology

[0002] Power system voltage stability is defined as the system's ability to maintain or recover its voltage within acceptable limits without voltage collapse after being subjected to small or large disturbances. Depending on the type of disturbance, voltage stability can be divided into small-disturbance voltage stability and large-disturbance voltage stability. Small-disturbance voltage stability is also known as static voltage stability, while large-disturbance voltage stability includes transient voltage stability and medium- to long-term voltage stability. The voltage stability margin index refers to the distance between the current operating point and the voltage collapse point as the load or transmitted power gradually approaches the voltage collapse point according to a certain growth pattern. Compared to state indices, margin indices more intuitively represent the distance between the current operating point and the voltage collapse point; the margin index has a linear relationship with the distance between the current operating point and the voltage collapse point; and it can easily account for the impact of various factors during load power growth, such as load growth patterns and generator reactive power output limitations.

[0003] Domestic experts and scholars have conducted extensive research on voltage stability, with the following main research results. Zheng Xiaotian, Xia Chengjun, and others published "Static Voltage Stability Probability Analysis Based on Semi-Invariant and Maximum Entropy Principle" in the Acta Energiae Solaris Sinica (2022, (43): 126-132). This paper effectively considers the impact of the uncertainty of new energy output on the static voltage stability margin and proposes a static voltage stability probability analysis method based on the semi-invariant and maximum entropy principle. This method avoids the convolution operation in the random variable processing process and accelerates the speed of static voltage stability probability assessment. Yu Lin, Sun Huadong, and others published "Analysis of Short-Circuit Ratio Index and Calculation Method of Critical Short-Circuit Ratio for New Energy Grid-Connected Systems" in the Proceedings of the Chinese Society for Electrical Engineering (2022, (42): 919-928). This paper proposes two short-circuit ratio indices considering new energy access and a critical short-circuit ratio calculation method. Using the critical short-circuit ratio as a reference point and the short-circuit ratio index as a coordinate, the paper analyzes the voltage support strength of power systems with new energy access. Li Yuchen, Wang Guanzhong, et al., published "Intensity Analysis of Multi-Infeed DC Receiving-End Grid Considering Photovoltaic Reactive Power Compensation" in *Automation of Electric Power Systems* (2021, (45): 28-35). They analyzed the impact of photovoltaic power plant access on the static voltage stability margin of the receiving-end grid by calculating the generalized short-circuit ratio and its critical value. Based on the sensitivity of photovoltaic power plant access to the dominant eigenvalue of the Jacobian matrix of the AC network, they qualitatively analyzed the impact of different photovoltaic power plant control methods on static voltage stability. Na Guangyu, Wei Junhong, et al., published "Static Voltage Stability Probabilistic Assessment of Wind Power-Including Power Systems Based on Gram-Charlier Series" in *Power System Protection and Control* (2021, (49): 115-122). They considered the uncertainty of wind power output, derived the sensitivity of the load margin of each node to wind power injection, and used the semi-invariant method and Gram-Charlier method to obtain the load margin distribution of load nodes based on the wind power distribution, thereby conducting a static voltage stability probabilistic assessment. Cao Jie and Dang Yuan's paper, "A Fast Calculation Method for Static Voltage Stability Limit Points of Wind Power Access Systems," published in *Electrical Automation* (2020, (42): 12-16), uses a fast decomposition method instead of the conventional power flow calculation method, and obtains the static voltage stability limit points quickly through a quadratic curve fitting method. Wu Qianhong, Han Bei, et al.'s paper, "Online Prediction of Static Voltage Stability Based on Power Flow Jacobian Matrix and Convolutional Neural Network under Extremely High Photovoltaic Penetration," published in *Proceedings of the Chinese Society for Electrical Engineering* (2021, 41(12): 4058-4067), considers the impact of extremely high photovoltaic penetration on static voltage stability and proposes a convolutional neural network model with the power flow Jacobian matrix as input to predict bidirectional static voltage stability margin.Zheng Huankun, Zhao Liying, et al., published "Analysis of Voltage Stability Risk Assessment for AC / DC Hybrid Systems Considering Wind Power and Load Characteristics" in *Electrical Measurement & Instrumentation* (2021, 58(8): 110-117). This paper considers the impact of wind power on the static voltage stability of VSC-HVDC systems, combines probabilistic events with risk assessment, proposes a voltage risk index, accurately identifies the weak areas of the system, and analyzes the impact of different wind power output scenarios and different VSC control methods and parameters on the system's voltage stability risk. Most of the above literature focuses on the calculation methods for the corresponding voltage stability margin after the integration of new energy sources (wind power, photovoltaics, etc.), aiming to consider the impact of the uncertainty of new energy output on the voltage stability margin. However, most of these studies do not consider the reactive power-voltage control methods of new energy power plants during the assessment.

[0004] Among existing patents, the invention patent "A Method for Calculating Voltage Stability Margin Considering Electro-Gas Coupling System Constraints" applied for by inventors Sun Hongbin, Guo Qinglai, et al. proposes a method for calculating voltage stability margin considering the coupling constraints of the power system and the natural gas system. This method effectively considers the safety and capacity constraints of the natural gas system and fully takes into account the actual application conditions in the application area, avoiding the overly optimistic voltage stability assessment results caused by traditional methods that only consider power system constraints. The invention patent "A Method for Calculating Power System Voltage Stability Margin Based on Ultra-Short-Term Wind Power Forecasting" applied for by inventors Cao Yinli, Yao Xu, et al., uses a power forecasting model to perform ultra-short-term wind power forecasts for the forecast date; utilizes the load forecast curve and wind power forecast values ​​for the forecast date to formulate a daily power generation plan; and based on the power generation plan, load forecast data, and the system operation grid structure, obtains the voltage stability margin using a continuous power flow method according to the ultra-short-term wind power forecast values ​​for a future period. The invention patent "A Method and System for Judging Transient Voltage Stability of Receiving-End System" applied for by Xiong Hongtao, Kong He, and other inventors divides the voltage curve into segments using difference equations, assigns corresponding weights to different voltage drop levels, and quantifies the accumulated drop amount through weighted integration, ultimately constructing an evaluation index and forming a complete transient voltage stability judgment method. The invention patent "An Online Prediction Method for Static Voltage Stability Margin Based on Convolutional Neural Network" applied for by Xiong Hongtao, Kong He, and other inventors proposes an online prediction method for static voltage stability margin based on a convolutional neural network model. First, a prediction model is obtained through offline training, and then the static voltage stability margin of the power system under photovoltaic access is predicted in real time. However, the reactive power-voltage control characteristics of the photovoltaic power station are not considered. The invention patent applied for by inventors Qi Jinshan, Liao Siyang, et al., entitled "A Probabilistic Prediction Method for Static Voltage Stability Margin of Power Grid Considering the Uncertainty of New Energy Generation," fully considers the randomness of new energy power generation and establishes wind power and photovoltaic scenario generation models based on prediction error models and Monte Carlo simulations. It uses deep learning methods to predict the static voltage stability margin of individual scenarios, balancing prediction accuracy and efficiency. It predicts probabilistic voltage stability margin using kernel density estimation, providing dispatchers with more reference information, but it does not consider the reactive power limitations of new energy power plants. The invention patent applied for by inventors Lin Wenli, Zhu Ling, et al., entitled "A Method and System for Improving Voltage Stability Margin of Power Systems with New Energy," based on load node voltage expressions, analyzes the key factors affecting voltage stability margin, establishes load node voltage stability margin indices, and, combined with real-time power grid operating conditions, obtains strategies to improve system voltage stability margin under new energy access.The invention patent applied for by Zhao Wei, Li Xiaojun, et al., entitled "A Method and Device for Determining the Critical Penetration Rate of New Energy Based on Voltage Stability Constraints," generates a set of regional sensitive faults according to the initial operating state of the system and identifies voltage-weak nodes; based on the static voltage stability margin requirements and the power fluctuation range of new energy, it determines the critical penetration rate of new energy to ensure static voltage stability; according to the transient voltage severity index, it determines the critical penetration rate of new energy under transient voltage stability; and finally, it obtains the critical penetration rate of new energy considering voltage stability constraints. However, this invention still mainly considers the uncertainty of power output from new energy power plants and does not incorporate the reactive power-voltage control characteristics of new energy power plants into the voltage stability margin assessment.

[0005] Therefore, for power systems with large-scale renewable energy plants connected to the grid, using an improved continuous power flow algorithm to calculate the voltage stability margin of the power system, based on the reactive power-voltage control of renewable energy plants, will make the calculation results closer to the actual grid with large-scale renewable energy integration and have better adaptability. Summary of the Invention

[0006] The purpose of this invention is to provide a method for calculating voltage stability margin considering the control mode of a photovoltaic power plant.

[0007] Therefore, the technical solution of the present invention is as follows:

[0008] This invention provides a method for calculating voltage stability margin considering the control mode of a photovoltaic power plant, comprising the following steps:

[0009] Step 1: Collect data from traditional generating units, grid structure, load-related data, and photovoltaic power plants;

[0010] Step 2: Update the access node type, voltage value, and reactive power input according to the photovoltaic power station control method;

[0011] Step 3: Set the load growth mode, the traditional generator output growth mode, and set the changes in active power, reactive power and voltage according to the control mode of the photovoltaic power station;

[0012] Step 4: Determine the dominant node, establish an extended power flow equation including voltage stability margin parameters with the dominant node voltage as a continuous variable, determine the prediction step size using the adaptive step size method, and use the hybrid prediction method to predict the parameterized power flow equation.

[0013] Step 5: Using the estimated value as the initial value, the Newton-Layer method is used to perform correction calculations on the extended power flow equations;

[0014] Step 6: Based on the power flow correction calculation results, obtain the state value at the next operating point and the set of nodes where structural transformation occurs. Determine whether the set of nodes where structural transformation occurs is empty. If yes, proceed to step 8; otherwise, proceed to step 7.

[0015] Step 7: For traditional generators and photovoltaic power plants in the node set of structural conversion, detect the degree of reactive power exceeding the limit in the PV node type. If there is, change the corresponding node type to PQ type, set its reactive power to its maximum allowable value, and go to step 4.

[0016] Step 8: Check if the voltage stability critical point has been reached. If so, end the process and obtain the voltage stability margin; otherwise, go to step 4 and repeat the above steps.

[0017] Furthermore, the extended power flow equations including voltage stability margin parameters are expressed as follows:

[0018] (1)

[0019] in, Inject power into the generator's ground state; This represents the ground-state power of the node load. The load growth method is composed of the load growth ratio factor of each node in the entire network; This is a generator dispatching method, composed of the load increment sharing ratio factor of each generator in the entire network; The load growth factor represents the overall load growth level of the entire network. This represents the load increment of each node in the entire network; Let be the system static state vector, where The node voltage phase angle vector. This represents the node voltage magnitude vector; Injecting power functions into the nodes of conventional power flow equations, The active power injection function for PV and PQ nodes, This is the reactive power injection function for the PQ node.

[0020] Furthermore, the method for setting the adaptive step size is as follows:

[0021] Given three power flow solutions, find a path through them. , and A conic section at three points And the maximum value of the curve can be easily obtained. ,in, Indicates the first The first trend solution The voltage amplitude of the nth node, the nth Each node is a weak point in voltage stability;

[0022] Determine step size Its representation method is as follows: ,in, It is a coefficient less than 1. The settings can achieve results in the flat region of the PV curve. Larger, steeper areas It is relatively small, enabling an automatic step-changing strategy.

[0023] Furthermore, the method of using hybrid prediction is as follows:

[0024] Before obtaining three power flow solutions, a linear prediction method is used;

[0025] After obtaining three power flow solutions, a quadratic interpolation prediction with step size control is used;

[0026] If the trend is explained , and Calculated Appear In cases where the prediction is not perfect, a linear prediction method is used; otherwise, a quadratic interpolation prediction with step size control is used.

[0027] Furthermore, quadratic interpolation is used to predict the next power flow solution. The method is as follows:

[0028]

[0029] Where n is greater than or equal to 3, , and Given three known power flow solutions, The step size.

[0030] Furthermore, the method for determining whether a node type conversion has occurred is as follows:

[0031] 1) If If a node's reactive power exceeds the upper limit, its reactive power handling will be fixed at the upper limit, and the node type will be converted. And it remains unchanged in subsequent continuous power flow calculations;

[0032] 2) If If a node's reactive power exceeds the lower limit, its reactive power output will be fixed at the lower limit in the current power flow calculation, and the node type will be changed. In the next step of power flow calculation, it is restored to Nodes participate in power flow calculations and reactive power limit checks.

[0033] Furthermore, the voltage stability critical point corresponds to the saddle node instability (SNB) and ultimate induced instability (LIB) in the power flow equation. The detection of the voltage stability critical point includes three aspects: saddle node instability detection (SNB), ultimate induced instability detection (LIB), and supplementary detection.

[0034] Furthermore, the specific details of the SNB saddle node instability detection are as follows:

[0035] When continuous power flow calculation occurs At that time, the SNB saddle node instability detection is initiated;

[0036] Restore the system state to the power flow solution. At this point, calculate the minimum eigenvalue of the power flow Jacobian matrix under this state, and determine the magnitude of the absolute value of the minimum eigenvalue;

[0037] If the absolute value of the minimum eigenvalue is sufficiently close to zero, it is determined that the SNB saddle node is unstable, and the continuous power flow calculation is terminated. If the absolute value of the minimum eigenvalue is greater than 0.01, the critical point may be the LIB point. To improve computational efficiency, the SNB detection is exited, and the continuous power flow calculation is terminated. If neither of the above two conditions is met, based on the principle that the eigenvalues ​​of the power flow Jacobian matrix undergo a continuous change before and after the SNB occurs, if the sign of the real part of the minimum eigenvalue is positive, it indicates that the power flow solution... If the critical point has not been reached, reduce the step size and continue the calculation. If the sign of the real part of the minimum eigenvalue is negative, it indicates that the power flow solution is not reached. The critical point has been reached; restore the system to power flow solution. If the number of SNB detections reaches the upper limit and no SNB is detected, the continuous power flow calculation is terminated.

[0038] Furthermore, the specific details of the LIB-induced instability detection are as follows:

[0039] When the voltage amplitude of the generator node that exceeds the upper limit of reactive power output appears in the continuous power flow calculation... In this case, search for trend solutions and Between The transformed nodes form a node set. Initiate LIB detection;

[0040] Determining the node set using the sensitivity method For the nodes to be detected, solve the system state when the node to be detected undergoes a transition; if it is found that a node exceeds the reactive power limit before the current node to be detected, restore the system state to the previous step, and re-detect that node as the node to be detected; otherwise, calculate... and Determine if a LIB has occurred; if not, proceed... Remove the detected nodes from the list, such as... If it is an empty set, then and No LIB occurred between them; such as If it is not an empty set, continue the detection process as described above until... Continue until an empty set is found or a LIB is detected.

[0041] Furthermore, the supplementary detection specifically includes the following:

[0042] When LIB detection was not initiated throughout the entire continuous power flow calculation, and no SNB saddle node instability was detected, the search system last occurred... The transformed nodes form a node set. Perform LIB testing.

[0043] Compared with existing technologies, this method for calculating the voltage stability margin of photovoltaic power plant control has the following advantages:

[0044] I. High practicality: A voltage stability margin calculation method considering the reactive power-voltage control mode of photovoltaic power plants has been established, and the traditional continuous power flow method has been improved. The invented method can be extended to large-scale power systems, which can fully consider the impact of the control mode of large-scale photovoltaic power plants on voltage stability.

[0045] Second, high efficiency; the voltage stability margin problem in continuous power flow calculation is essentially a large-scale, nonlinear problem, and traditional solution methods would be very time-consuming. In the continuous power flow calculation process, the parameterized power flow equation is obtained by expanding the voltage of the node with the fastest voltage drop, which can effectively reduce the number of calculation iterations. In the prediction stage of the continuous power flow calculation process, this invention adopts a hybrid prediction method: when the voltage margin is large, nonlinear prediction is used to speed up the calculation; when approaching the voltage stability limit, linear prediction is used to improve the calculation accuracy. The entire calculation process can greatly improve the solution efficiency. Attached Figure Description

[0046] Figure 1 A flowchart illustrating the voltage stability margin calculation method considering photovoltaic power plant control modes provided by this invention.

[0047] Figure 2 This is a schematic diagram of a photovoltaic power generation system.

[0048] Figure 3 This is a schematic diagram for solving continuous power flow.

[0049] Figure 4 A diagram showing the comparison of the prediction effects of various prediction methods.

[0050] Figure 5 This is a schematic diagram illustrating the induced instability. Detailed Implementation

[0051] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but the following embodiments are by no means intended to limit the present invention.

[0052] The terminology used in one or more embodiments of this application is for the purpose of describing particular embodiments only and is not intended to limit the scope of one or more embodiments of this application. The singular forms “a,” “the,” and “the” used in one or more embodiments of this application and in the appended claims are also intended to include the plural forms, encompassing any or all possible combinations of one or more associated listed items.

[0053] This invention provides a method for calculating voltage stability margin considering the control mode of a photovoltaic power plant, such as... Figure 1 As shown, it includes the following steps:

[0054] Step 1: Collect data from traditional generating units, grid structure, load-related data, and photovoltaic power plants;

[0055] Step 2: Update the access node type, voltage value, and reactive power input according to the photovoltaic power station control method;

[0056] Step 3: Set the load growth mode, the traditional generator output growth mode, and set the changes in active power, reactive power and voltage according to the control mode of the photovoltaic power station;

[0057] Step 4: Determine the dominant node, establish an extended power flow equation including voltage stability margin parameters with the dominant node voltage as a continuous variable, determine the prediction step size using the adaptive step size method, and use the hybrid prediction method to predict the parameterized power flow equation.

[0058] Step 5: Using the estimated value as the initial value, the Newton-Layer method is used to perform correction calculations on the extended power flow equations;

[0059] Step 6: Based on the power flow correction calculation results, obtain the state value at the next operating point and the set of nodes where structural transformation occurs. Determine whether the set of nodes where structural transformation occurs is empty. If yes, proceed to step 8; otherwise, proceed to step 7.

[0060] Step 7: For traditional generators and photovoltaic power plants in the node set of structural conversion, detect the degree of reactive power exceeding the limit in the PV node type. If there is, change the corresponding node type to PQ type, set its reactive power to its maximum allowable value, and go to step 4.

[0061] Step 8: Check if the voltage has reached the critical point of stability. If yes, end the process; otherwise, go to step 4 and repeat the above steps.

[0062] Next, we will further explain the contents mentioned in the above steps:

[0063] 1. Introduction to Photovoltaic Systems and Their Control Methods

[0064] The photovoltaic power generation system described above utilizes the photovoltaic effect of solar cells to directly convert solar radiation energy into electrical energy. A typical photovoltaic power generation system is as follows: Figure 2 As shown, it mainly consists of solar panels, a DC / DC converter, a DC / AC grid-connected inverter, a step-up transformer, and control devices. The DC power generated by the photovoltaic cells is directly supplied to the local load or used as the DC power source for the inverter after passing through the DC / DC converter, achieving maximum power point tracking of the photovoltaic cells. Then, it is connected to the AC power grid through the DC / AC grid-connected inverter.

[0065] The DC / AC grid-connected inverter of a photovoltaic power generation system can operate in different reactive power-voltage control modes. The main control modes are as follows:

[0066] Constant power factor control

[0067] When power factor control mode is enabled, the inverter operates at a constant power factor. This type of solar photovoltaic system connects to PQ-type nodes, given the injected active and reactive power. The constraint of constant power factor control mode is that the power factor should always be the same as specified and must not exceed the inverter's rated capacity. Inverters typically operate at unity power factor, but they can be adjusted to maintain a lower ratio (provided the parameter values ​​remain within the model's operating range). In this mode, the inverter needs to operate within the range of -0.8 to 0.8. If the actual power output of the inverter changes, the reactive power output will be adjusted to maintain the target power factor.

[0068] Constant voltage control

[0069] This mode aims to control the reactive power output from the photovoltaic inverter as a function of voltage. In this mode, the inverter operates in variable power factor mode; since the actual injected power and bus voltage amplitude are specified, the nodes connected to the photovoltaic power station are treated as PV type. This mode enables generators to maintain the voltage distribution of the entire network within an acceptable range by injecting or absorbing reactive power.

[0070] Constant reactive power control

[0071] When this mode is enabled, the inverter provides constant reactive power support. This function should be embedded in the photovoltaic inverter and can be activated according to grid demand. It can fix the reactive power at a constant value based on the corresponding grid requirements, and the power factor may drop below 0.8 leading or lagging to retain a constant reactive power supply from the inverter. The choice of this value will affect the voltage stability of the photovoltaic grid connection. If the photovoltaic system capacity is fixed and a constant reactive power is required, the actual power output needs to be adjusted accordingly, which may affect the system's voltage stability differently depending on the reactive power setpoint.

[0072] 2. Power flow equations considering load growth

[0073] The extended power flow equations, which include voltage stability margin parameters, are expressed as follows:

[0074]

[0075] In the formula: Inject power into the generator's ground state; This represents the ground-state power of the node load. The load growth method is composed of the load growth ratio factor of each node in the entire network; This is a generator dispatching method, composed of the load increment sharing ratio factor of each generator in the entire network; The load growth factor represents the overall load growth level of the entire network. This represents the load increment of each node in the entire network; Let be the system static state vector, where The node voltage phase angle vector. This represents the node voltage magnitude vector; Inject power functions into the nodes of the conventional power flow equations; The active power injection function for PV and PQ nodes, This is the reactive power injection function for the PQ node.

[0076] In equation (1), the left side represents the total network node injection power determined by the steady-state characteristics of the power supply equipment, and the right side represents the total network node injection power determined by the network topology and network component parameters. and For formula The external parameters, given and , can be derived from the formula Determine the system state under the corresponding load conditions. To obtain different... The system state under a given value requires knowledge of the function. Specific form and They will be introduced separately below.

[0077] Setting up a traditional generator output increase method:

[0078] Power generation growth vector It can be further broken down into:

[0079]

[0080] In formula (2): It is a constant vector composed of the active power output growth allocation factors of all PV nodes, i.e., the active power output growth mode of PV nodes; In the middle, the proportions between the remaining allocation factors are set according to the active power reserve ratio of each unit in the initial state, that is:

[0081]

[0082] In formula (3): Let be a constant vector composed of the active power output growth allocation factors of all PQ nodes, representing the active power output growth pattern of PQ nodes. The values ​​of each row's elements, if corresponding to non-generator nodes, are... If the corresponding PQ node is transformed from a PV node, then the value is determined by the formula. Decide; The reactive power output growth vector of all PV nodes is a variable to be determined in the power flow equations. This is the reactive power output growth vector for all PQ nodes; each element in its row, if corresponding to a non-generator node, takes the value... If the corresponding PQ node is transformed from a PV node, its reactive power output will have reached its limit and will no longer increase. ; The increase in active and reactive power output at the balancing node is a problem to be solved in the power flow equation.

[0083] Mode The mode of growth based on merit and output has been determined. The proportional relationship between the elements (or (direction angle), determine below The model.

[0084] For an N-node system, under the constraint of overall network active power balance, if the balancing machine does not participate in the allocation of power output increments, then:

[0085]

[0086] Or written in vector form:

[0087]

[0088] In the formula , ,Mode Japanese style The connection can be completely determined immediately. .

[0089] Configure the load growth method:

[0090] The commonly used load growth setting method is adopted, that is, the reactive power of the load increases together with the active power according to the power factor in the initial state:

[0091]

[0092] In the formula, For nodes The power factor angle of the load in its initial operating state.

[0093] Therefore, the active power load growth mode should be determined. The load growth method was thus determined. At this point, as long as the given... and This uniquely determines the system load and generator output. Solving the power flow equations... All required parameters are known.

[0094] 3. Calculate voltage stability margin using an improved continuous power flow method.

[0095] Continuous power flow mainly includes several models such as load-type, branch-type, and fault-type. The predictive-corrective continuous power flow method can be used to solve the problem. This method consists of four parts: a prediction process, a correction process, a parameterization strategy, and a step-size control method. The selection of the prediction method, parameterization strategy, and correction method is independent of each other, while the selection of the step-size control strategy usually depends on the selection of the other three.

[0096] The process of solving continuous power flow is as follows Figure 3 As shown, starting from the ground-state operating point A, a predicted solution B is obtained using a prediction method under a specified load growth mode. Then, under a fixed load, a power flow procedure is used to correct the predicted value, thereby obtaining the accurate operating point C. As the load continues to grow, if the newly predicted operating point D exceeds the maximum load, the correction under the fixed load will not converge. In this case, a correction under a fixed voltage is used to obtain the accurate operating point E. The introduced load parameters play a major role in avoiding singularities in the power flow Jacobian matrix.

[0097] The prediction stage uses the current point and several previous points to estimate the value of the next point on the solution trajectory, thus facilitating faster convergence in solving for the next point. In continuous power flow, the commonly used prediction methods are first-order differential methods (such as the tangent prediction method) and polynomial extrapolation methods (such as the bisection method). In terms of computational complexity, polynomial interpolation methods are less complex than first-order differential methods, but the former is more widely used. This is mainly because the calculation process usually requires checking whether a bifurcation point has been crossed, which is typically determined by calculating the first-order differential. The estimated values ​​of variables and parameters can be written as:

[0098]

[0099] In the formula, For the current point, This is an estimate for the next point. The gradient at the current point, The step size.

[0100] The calibration process is based on The operating point that actually satisfies the power flow equation is calculated from the initial point. The correction method employs Newton's method for solving nonlinear equations.

[0101] The parameterization strategy is the core of the entire continuous method. The efficiency and accuracy of the prediction step, as well as the convergence of the correction step, are closely related to the parameterization strategy. Parameterization refers to how to construct an equation that, together with the parameterized power flow equations, forms an (n+1)-dimensional system of equations with n+1 variables to be solved, in order to determine the next point of the curve. This one-dimensional supplementary equation can be written as:

[0102]

[0103] In the formula, The step size is a known quantity in the calculation.

[0104] Commonly used parameterization methods include local parameterization, arc length parameterization, quasi-arc length parameterization, and orthogonal parameterization.

[0105] Prediction and step size control play crucial roles in continuous power flow calculations. High-quality predictions enable rapid convergence of each power flow calculation step, while appropriate step size control methods allow the continuous power flow program to quickly reach the vicinity of the voltage stability critical point. Traditional linear predictions face a trade-off between prediction quality and computational efficiency, especially in regions with high PV curve curvature. Strong nonlinear characteristics mean that linear predictions can only guarantee sufficient prediction quality within small step sizes, but this increases the number of calculations and reduces computational efficiency. To address this issue, nonlinear prediction methods based on polynomial interpolation have achieved better prediction results, such as... Figure 4 As shown, improvements were made based on this, including the addition of an automatic variable step size function and the adoption of a hybrid prediction method.

[0106] The overall concept of the hybrid prediction method used in this invention can be summarized as follows:

[0107] 1) Before obtaining three power flow solutions, use a linear prediction method;

[0108] 2) After obtaining three power flow solutions, a quadratic interpolation prediction with step size control is used;

[0109] 3) If solved by current flow , and Calculated Appear If the situation indicates that a quadratic interpolation curve with opposite openings is obtained (caused by node type conversion), then the nonlinear prediction result is unreliable, and a linear prediction method should be used instead to deal with this special case.

[0110] It should be noted that quadratic interpolation is used to predict the next power flow solution. The method is as follows:

[0111]

[0112] Where n is greater than or equal to 3, , and Given three known power flow solutions, The step size.

[0113] The step size selection method is crucial for the efficiency of solving continuous power flow problems. A step size that is too small will result in too many calculation points, while a step size that is too large will cause slow convergence of the correction process, or even divergence, necessitating a reduction in the step size and recalculation. The parameters in the step size control strategy are largely determined by the specific system conditions. This invention employs an automatic variable step size control strategy, the specific control method of which is as follows:

[0114] Assume the first in the system The node is a voltage stability weak node, meaning it experiences the most severe voltage drop as the load increases. Given three power flow solutions, a power flow path can be derived through these three solutions. , and A conic section at three points And the maximum value of the curve can be easily obtained. ;in, Indicates the first The first trend solution Voltage amplitude at each node;

[0115] Considering the quasi-quadratic characteristics of the PV curve of the weak busbar, the quadratic curve It can simulate the shape of the PV curve to a certain extent, therefore the parameters in the current power flow solution With the conic section The difference between This can characterize the distance between the current power flow solution and the voltage stability critical point. However, simulating the PV curve using a quadratic curve introduces certain errors. Considering algorithm convergence, the estimated step size should not be too large. Therefore, in the actual algorithm... Not directly taken as Instead, it is multiplied by a coefficient h less than 1 and then assigned a value. :

[0116]

[0117] Obviously, the flat region of the PV curve is obtained Larger, steeper areas Because the step size is relatively small, this algorithm also has the function of automatically changing the step size.

[0118] During continuous power flow calculation, the problem of node power exceeding the limit may be encountered. At this time, the node type conversion mechanism should be activated to ensure that the continuous power flow can continue to operate in a realistic manner. The switching mechanism for nodes is given more consideration, while slack nodes are treated as "infinite power" nodes. This may cause the margin estimation to not reflect reality. Therefore, a switching mechanism for slack nodes is proposed, which changes the node type when the reactive power of a slack node exceeds the limit. Convert to Furthermore, in subsequent continuous power flow calculations, the power flow equations are supplemented with a one-dimensional reactive power equation corresponding to the equilibrium node. This node transformation method will be referred to as […]. .

[0119] In addition, under ground-state loading, some A node may experience reactive power exceeding the lower limit. If its reactive power output is consistently fixed at the lower limit, it becomes... If a generator node fails to demonstrate its original ability to dynamically regulate reactive power as the load increases, this is unrealistic. Therefore, for The issue of node reactive power exceeding limits is handled in the following ways:

[0120] ( )if If a node's reactive power exceeds the upper limit, its reactive power handling will be fixed at the upper limit, and the node type will be converted. And this method remains unchanged in subsequent continuous power flow calculations, and is simply referred to as... ;

[0121] ( )if If a node's reactive power exceeds the lower limit, its reactive power output will be fixed at the lower limit in the current power flow calculation, and the node type will be changed. In the next step of power flow calculation, it is restored to Nodes participate in power flow calculations and reactive power limit checks; this method is referred to as... .

[0122] The voltage stability critical point usually corresponds to the saddle node instability (SNB) and the limiting induced instability (LIB) in the power flow equation. The two have different characteristics and need to be distinguished.

[0123] At point SNB, the Jacobian matrix of the power flow equation is singular at the critical point, that is:

[0124]

[0125] In practice, it is possible Whether the minimum eigenvalue is sufficiently close to 0 is used as the criterion for SNB detection. The specific manifestation of the SNB detection method is as follows:

[0126] ( When continuous power flow calculations occur At that time, initiate SNB detection;

[0127] ( Restore the system state to the power flow solution. At this point, calculate the minimum eigenvalue of the tidal flow Jacobian matrix under this state. If the absolute value of the minimum eigenvalue is sufficiently close to zero, it is determined to be a SNB (Severe Inrush Point), and the continuous tidal flow calculation is terminated. If the absolute value of the minimum eigenvalue is quite large, the critical point may be a LIB (Limited Inrush Point). Typically, the minimum eigenvalue of the tidal flow Jacobian matrix at a LIB-type critical point is not zero. To improve computational efficiency, the SNB detection is exited, and the continuous tidal flow calculation is terminated. If neither of the above two conditions is met, based on the principle that the eigenvalues ​​of the tidal flow Jacobian matrix undergo a continuous change before and after an SNB occurs, if the sign of the real part of the minimum eigenvalue is positive, it indicates that the tidal flow solution... If the critical point has not been reached, reduce the step size and continue the calculation. If the sign of the real part of the minimum eigenvalue is negative, it indicates that the power flow solution is not reached. The critical point has been reached; restore the system to power flow solution. At that point, the step size is reduced and the calculation continues.

[0128] ( If the maximum number of SNB detections is reached and no SNB is detected, the continuous power flow calculation is terminated.

[0129] Limit-induced instability (LIB) is caused by the loss of dynamic reactive power regulation capability in some generators, such as... Figure 5 As shown, initially the generator node Able to maintain its terminal voltage, the power flow solution path follows the curve Proceeding forward, at point P, the reactive power output reaches its limit, transforming into node PQ, and the power flow solution path switches to a curve. Above. Since point P is on the curve. In the lower half, the power flow solution after point P is an unstable solution. Therefore, the voltage stability critical point is point P, not the maximum load limit point. The system experienced limit-induced instability (LIB) at point P.

[0130] The above analysis shows that two conditions must be met for point P to experience a LIB: firstly, point P must be on the curve... The lower half of the branch; in addition, if the generator terminal voltage can be maintained constant at point P, then the generator reactive power output should continue to increase as the load further increases; the ultimate induced instability LIB criterion can be summarized as:

[0131] ( )exist Under the conditions, there are ;

[0132] ( )exist Under the conditions, there are

[0133] In the LIB criterion for extreme induced instability and Two sensitivities can be achieved through Sensitivity analysis of the power flow equations at the transition point yielded the results. At the transition point, and Both conditions must be met simultaneously, therefore the occurrence can be... The node to be transformed becomes For nodes, add the corresponding reactive power equation to the power flow equations, and add a one-dimensional equation specifying its voltage amplitude to describe the system state at the transition point, as shown below:

[0134]

[0135] Mode The solution method is similar to that used in continuous power flow, employing Newton's method. Its iterative format is as follows:

[0136]

[0137] In the formula, .

[0138] and The solution method is as follows:

[0139] exist Under the condition that, assuming There are slight changes, for the formula Taking the derivative, we get:

[0140]

[0141] After sorting, we get:

[0142]

[0143] exist Under the condition that, assuming There are slight changes, for the formula Taking the derivative, we get:

[0144]

[0145] After sorting, we get:

[0146]

[0147] Due to the matrix Already in the style Therefore, obtaining the judgment quantity will not increase the amount of additional computation.

[0148] There may be more than one generator node between two power flow solutions in continuous power flow calculations. In this transition, the sensitivity method can be used to predict the order in which the reactive power of these nodes exceeds the upper limit, and then the nodes can be processed sequentially. Perform LIB checks at the transition point.

[0149] The power flow equations of a node can be expressed as:

[0150]

[0151] In the formula, for Nodes in power flow solution The reactive power output of the generator.

[0152] Pair Taking the derivative, we get:

[0153]

[0154] Due to the flow solution The point is not an SNB point; the Jacobian matrix is ​​invertible, as shown by the formula. The first equation yields:

[0155]

[0156] Mode Substitution The second equation yields:

[0157]

[0158] In the formula, The reactive power output of each generator is a factor affecting the load growth rate. Sensitivity.

[0159] In trend interpretation At this location, the reactive power reserve of the generator is:

[0160]

[0161] Dividing the reactive power margin of each generator by its sensitivity, and sorting the resulting values, yields the order in which each generator node exceeds its reactive power limit. The generator node corresponding to the minimum value is the one most likely to experience this first. The transformed node is used as the node to be detected for LIB judgment:

[0162]

[0163] In the formula, the function Return the generator node corresponding to the smallest element in the set. For the occurrence The set of nodes to be transformed.

[0164] Due to continuous power flow calculation Transition phenomena are very common, and detecting all transition points would undoubtedly lead to low computational efficiency. Continuing to increase the loading factor at the LIB point... It will appear The abnormal phenomenon is observed. Based on this phenomenon, the LIB detection method adopted is as follows:

[0165] When the voltage amplitude of the generator node that exceeds the upper limit of reactive power output appears in the continuous power flow calculation... In the case of current current flow solution It may be in the lower half of the PV curve, search and Between The transformed nodes form a node set. Initiate LIB detection;

[0166] Determining the node set using the sensitivity method The node to be detected in the solution formula Obtain the system state when the node to be detected undergoes a transition. If a node is found to have exceeded the reactive power limit before the current node to be detected, restore the system state to the previous step and re-detect that node as the node to be detected; otherwise, proceed according to the formula... Japanese style calculate and Determine if a LIB has occurred. If not, proceed... Remove the detected nodes from the list, such as... ,but and No LIB occurred between them; such as If so, continue testing according to the above steps until... Until LIB is detected.

[0167] It should be noted that generator nodes that exceed the reactive power limit when LIB occurs may not necessarily appear. Therefore, LIB detection will not be initiated due to the above reasons. To ensure the accuracy of the detection, this invention includes a supplementary detection: when LIB detection has not been initiated or SNB has not been detected throughout the entire continuous power flow calculation, the last occurrence of the search system... The transformed nodes form a node set. Then, LIB detection is performed.

[0168] The following examples verify the method:

[0169] This example applies the voltage stability margin calculation method considering photovoltaic power plant control modes to a region A in my country to meet the voltage stability margin verification requirements of the planned power grid in this region by 2025. According to the region's power grid plan, by 2025, the installed capacity of the 220kV and above network within the region is projected to be 444.45 million kilowatts, including 249.69 million kilowatts of thermal power, 24.09 million kilowatts of nuclear power, 16.46 million kilowatts of conventional hydropower, 28.61 million kilowatts of pumped storage, 50.28 million kilowatts of wind power, 75.42 million kilowatts of photovoltaic power, and 79.22 million kilowatts of UHVDC transmission from outside the region. The projected installed capacity of 220kV and above power sources in this region by 2025 is shown in Table 1.

[0170] By comparing the voltage stability margin of the power grid in Region A after N-2 faults before and after reactive power configuration in Table 2, it is found that without additional reactive power compensation, Region A's voltage stability margin does not meet the 5% requirement under severe N-2 faults. Adding reactive power compensation equipment can effectively improve the voltage stability margin of Region A after N-2 faults, ensuring it meets the 5% voltage stability margin requirement with sufficient margin.

[0171] By comparing the voltage stability margins of the regional A power grid after the N-2 fault in 2025 without considering the reactive power regulation capacity of wind and solar power and with considering the reactive power regulation capacity of wind and solar power in 2025, it can be seen that regardless of whether the reactive power regulation capacity of wind and solar power is considered, the voltage stability margin of the regional A power grid after the N-2 fault in 2025 meets the 5% margin requirement after the reactive power compensation device is configured. Considering the reactive power regulation capacity of wind and solar power can increase the voltage stability margin of the regional A power grid, but the increase is no more than 1%.

[0172] This embodiment demonstrates that the voltage stability margin calculation method considering photovoltaic power plant control mode provided by the present invention improves the calculation accuracy.

[0173] Table 1. Power Supply Capacity Composition of 220kV and Above Networks in Regional Power Grid A by 2025

[0174]

[0175] Table 2 Voltage stability margin of regional power grid A under severe fault N-2 before and after reactive power planning in 2025

[0176]

[0177] Table 3. Voltage stability margin of regional power grid A under severe fault N-2 in 2025 before and after considering the reactive power regulation capacity of wind, solar and energy storage

[0178]

Claims

1. A method for calculating voltage stability margin considering the control mode of a photovoltaic power station, characterized in that, Includes the following steps: Step 1: Collect data from traditional generating units, grid structure, load-related data, and photovoltaic power plants; Step 2: Update the access node type, voltage value, and reactive power input according to the photovoltaic power station control method; Step 3: Set the load growth mode, the traditional generator output growth mode, and set the changes in active power, reactive power and voltage according to the control mode of the photovoltaic power station; Step 4: Determine the dominant node, establish an extended power flow equation including voltage stability margin parameters with the dominant node voltage as a continuous variable, determine the prediction step size using the adaptive step size method, and use the hybrid prediction method to predict the parameterized power flow equation. Step 5: Using the estimated value as the initial value, the Newton-Layer method is used to perform correction calculations on the extended power flow equations; Step 6: Based on the power flow correction calculation results, obtain the state value at the next operating point and the set of nodes where structural transformation occurs. Determine whether the set of nodes where structural transformation occurs is empty. If yes, proceed to step 8; otherwise, proceed to step 7. Step 7: For traditional generators and photovoltaic power plants in the node set of structural conversion, detect the degree of reactive power exceeding the limit in the PV node type. If there is, change the corresponding node type to PQ type, set its reactive power to its maximum allowable value, and go to step 4. Step 8: Check if the voltage stability critical point has been reached. If yes, end the process and obtain the voltage stability margin; otherwise, go to step 4 and repeat the above steps. The extended power flow equations, which include voltage stability margin parameters, are expressed as follows: （1） in, Inject power into the generator's ground state; This represents the ground-state power of the node load. The load growth method is composed of the load growth ratio factor of each node in the entire network; This is a generator dispatching method, composed of the load increment sharing ratio factor of each generator in the entire network; The load growth factor represents the overall load growth level of the entire network. This represents the load increment of each node in the entire network; Let be the system static state vector, where The node voltage phase angle vector. This represents the node voltage magnitude vector; Injecting power functions into the nodes of conventional power flow equations, The active power injection function for PV and PQ nodes, This is the reactive power injection function for the PQ node.

2. The voltage stability margin calculation method considering photovoltaic power plant control mode according to claim 1, characterized in that, The method for setting the adaptive step size is as follows: Given three power flow solutions, find a path through them. , and A conic section at three points And the maximum value of the curve can be easily obtained. ,in, Indicates the first The first trend solution The voltage amplitude of the nth node, the nth Each node is a weak point in voltage stability; Determine step size Its representation method is as follows: ,in, It is a coefficient less than 1. The settings can achieve results in the flat region of the PV curve. Larger, steeper areas were obtained It is relatively small, enabling an automatic step-changing strategy.

3. The voltage stability margin calculation method considering the control mode of a photovoltaic power station according to claim 2, characterized in that, The method of using hybrid prediction is as follows: Before obtaining three power flow solutions, a linear prediction method is used; After obtaining three power flow solutions, a quadratic interpolation prediction with step size control is used; If the trend is explained , and Calculated Appear In cases where the prediction is not perfect, a linear prediction method is used; otherwise, a quadratic interpolation prediction with step size control is used.

4. The voltage stability margin calculation method considering the control mode of a photovoltaic power station according to claim 3, characterized in that, Using quadratic interpolation to predict the next power flow solution The method is as follows: Where n is greater than or equal to 3, , and Given three known power flow solutions, The step size.

5. The voltage stability margin calculation method considering the control mode of a photovoltaic power station according to claim 4, characterized in that, The method for determining whether a node type conversion has occurred is as follows: 1) If If a node's reactive power exceeds the upper limit, its reactive power handling will be fixed at the upper limit, and the node type will be converted. And it remains unchanged in subsequent continuous power flow calculations; 2) If If a node's reactive power exceeds the lower limit, its reactive power output will be fixed at the lower limit in the current power flow calculation, and the node type will be changed. In the next step of power flow calculation, it is restored to Nodes participate in power flow calculations and reactive power limit checks.

6. The voltage stability margin calculation method considering the control mode of a photovoltaic power station according to claim 5, characterized in that, The voltage stability critical point corresponds to the saddle node instability (SNB) and limit-induced instability (LIB) in the power flow equation. The detection of the voltage stability critical point includes three aspects: saddle node instability detection (SNB), limit-induced instability detection (LIB), and supplementary detection.

7. The voltage stability margin calculation method considering the control mode of a photovoltaic power station according to claim 6, characterized in that, The specific details of the SNB saddle node instability detection are as follows: When continuous power flow calculation occurs At that time, the SNB saddle node instability detection is initiated; Restore the system state to the power flow solution. At this point, calculate the minimum eigenvalue of the power flow Jacobian matrix under this state, and determine the magnitude of the absolute value of the minimum eigenvalue; If the absolute value of the minimum eigenvalue is sufficiently close to zero, it is determined that the SNB saddle node is unstable, and the continuous power flow calculation is terminated. If the absolute value of the minimum eigenvalue is greater than 0.01, the critical point may be the LIB point. To improve computational efficiency, the SNB detection is exited, and the continuous power flow calculation is terminated. If neither of the above two conditions is met, based on the principle that the eigenvalues ​​of the power flow Jacobian matrix undergo a continuous change before and after the SNB occurs, if the sign of the real part of the minimum eigenvalue is positive, it indicates that the power flow solution... If the critical point has not been reached, reduce the step size and continue the calculation. If the sign of the real part of the minimum eigenvalue is negative, it indicates that the power flow solution is not reached. The critical point has been reached; restore the system to power flow solution. If the number of SNB detections reaches the upper limit and no SNB is detected, the continuous power flow calculation is terminated.

8. The voltage stability margin calculation method considering the control mode of a photovoltaic power station according to claim 7, characterized in that, The specific details of the LIB-induced instability detection are as follows: When the voltage amplitude of the generator node that exceeds the upper limit of reactive power output appears in the continuous power flow calculation... In this case, search for trend solutions and Between The transformed nodes form a node set. Initiate LIB detection; Determining the node set using the sensitivity method For the node to be detected, solve the system state when the node to be detected undergoes a transition; If a node is found to have exceeded the reactive power limit before the currently detected node, the system state is restored to the previous step, and that node is re-detected as the new detected node; otherwise, the calculation is performed. and Determine if a LIB occurs; if not, proceed. Remove the detected nodes from the list, such as... If it is an empty set, then and No LIB occurred between them; such as If it is not an empty set, continue the detection process as described above until... Continue until an empty set is found or a LIB is detected.

9. The voltage stability margin calculation method considering the control mode of a photovoltaic power station according to claim 8, characterized in that, The supplementary testing specifically includes the following: When LIB detection was not initiated throughout the entire continuous power flow calculation, and no SNB saddle node instability was detected, the search system last occurred... The transformed nodes form a node set. Perform LIB testing.

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