Micro-grid static voltage stability analysis method and system

Abstract

The invention discloses a micro-grid static voltage stability analysis method and system. The method comprises the following steps: constructing a fitness function about a static voltage stability index; setting variables based on the microgrid model; iterating the micro-grid model by using a fox-monkey optimization algorithm to enable a fitness function to approach a critical value; and drawing a fitness curve and a voltage stability index curve based on an iteration process. The system comprises a function construction module, a variable setting module and an iterative convergence module. By using the method, the timeliness and the accuracy in the static voltage stability analysis of the micro-grid can be improved. The method can be widely applied to the field of power grid stability analysis.

Description

Technical Field

[0001] The present invention relates to the field of stability analysis, and in particular, to a method and system for analyzing the static voltage stability of a microgrid. Background Art

[0002] For the study of static voltage stability, stability indicators are generally divided into two categories: margin indicators and state indicators, both of which are used to measure the degree to which the system approaches voltage collapse. Currently, the research on state indicators is more comprehensive than that on margin indicators.

[0003] Margin indicators include: impedance modulus indicator: based on Thevenin equivalent, calculating the critical value of the node impedance modulus, but ignoring network dynamic coupling; load margin indicator: calculating the maximum load multiple through CPF, with clear physical meaning but large computational amount; the advantage of margin indicators is that they directly reflect the system's tolerance and are applicable to planning scenarios; their limitation is that they cannot provide information on the instability mechanism.

[0004] State indicators include: eigenvalue type (minimum singular value / modal analysis): reflecting the singularity degree of the Jacobian matrix, with high sensitivity but vulnerable to model errors; local voltage stability indicator (L indicator): based on the node voltage equation, quantifying the electrical distance between load nodes and generator nodes; voltage instability proximity indicator (VIPI): combining voltage amplitude and phase angle changes, with significant effect on identifying weak nodes. The advantage of state indicators is that they can be applied online, providing information on instability modes and critical nodes; their limitation is that the determination of thresholds depends on experience.

[0005] Existing methods for studying static voltage stability are traditional analysis methods, including eigenvalue analysis method, modal analysis method, sensitivity analysis method, continuation power flow method, collapse point analysis method, etc. The weights of the traditional artificial intelligence algorithms they apply to approach the local optimal value and the global optimal value in each iteration are fixed values, resulting in problems of slow convergence speed and low accuracy, thus affecting the timeliness and accuracy of the analysis. Summary of the Invention

[0006] In view of this, in order to solve the technical problem that the existing power grid stability analysis methods cannot simultaneously meet the analysis timeliness and accuracy required by the power grid scenario, on the one hand, the present invention proposes a method for analyzing the static voltage stability of a microgrid, and the method includes the following steps:

[0007] Construct a fitness function for the static voltage stability index;

[0008] Set variables based on the microgrid model;

[0009] Use the lemur optimization algorithm to iterate the microgrid model to make the fitness function approach the critical value;

[0010] Based on the iterative process, draw the fitness curve and the voltage stability index curve.

[0011] When the fitness curve gets closer and closer to the value of 0, it indicates that at least one point in the microgrid has a static voltage stability approaching the collapse point, and its voltage stability index approaches 1, which is reflected by the voltage stability index curve approaching 1.

[0012] In some embodiments, the step of using the lemur optimization algorithm to iterate the microgrid model to make the fitness function approach the critical value specifically includes:

[0013] The micro - power sources in the microgrid are set as PQ nodes for access, and the active power injected into each node in the microgrid is set as the solution a represents the number of solutions of the microgrid in each iteration, and b represents the node number in the microgrid.

[0014] Use the lemur optimization algorithm / improved lemur optimization algorithm to perform initialization operations on the solutions (the initialization processes of the two are the same), and randomly generate multiple initial solutions for the active power output of the microgrid Form a population P and calculate its fitness. This is the exploration stage;

[0015] In a loop, based on the population P, perform search and power flow calculations. Calculate the static voltage stability index and fitness based on the results such as voltage, current, active power, and reactive power obtained from the power flow calculation, and update the population P according to the population update formula in the lemur algorithm. This is the exploitation stage.

[0016] After multiple loops, when a certain node in the microgrid is approaching the voltage collapse point, the calculation terminates, and according to the iterative update process of the static voltage stability index and fitness, draw the fitness curve and the voltage stability index curve.

[0017] In some embodiments, for the lemur optimization algorithm, the exploitation stage of its search process is improved as follows:

[0018] Introduce an iterative scaling factor and combine it with the Lévy flight algorithm to jointly generate the step size;

[0019] Combine the step - size adjustment assignment formula.

[0020] In some embodiments, for the lemur optimization algorithm, the risk rate is improved based on the dynamic adjustment method of the fitness standard deviation.

[0021] The present invention also proposes a microgrid static voltage stability analysis system, and the system includes:

[0022] A function construction module that constructs a fitness function regarding the static voltage stability index;

[0023] A variable setting module that sets variables based on a microgrid model;

[0024] An iterative convergence module that uses the lemur optimization algorithm to iterate on the microgrid model to approximate the fitness function to a critical value; based on the iterative process, plot the fitness curve and the voltage stability index curve.

[0025] Based on the above solution, the present invention provides a method and system for analyzing the static voltage stability of a microgrid. By using the lemur algorithm to analyze the static voltage stability index of the microgrid, compared with the prior art, it is more conducive to obtaining the global optimal solution, thereby accelerating the search speed and convergence accuracy. By introducing an iterative scaling factor and dynamic adjustment to improve the lemur algorithm, the search speed is further accelerated and the convergence accuracy is improved, which helps to improve the analysis efficiency and accuracy. Description of the Drawings

[0026] Figure 1 This is an equivalent model of two nodes in an embodiment of the present invention. The two nodes are equivalent to being connected by an impedance, and it is assumed that power and current flow from point i to point j.

[0027] Figure 2 This is the distribution diagram of the IEEE 33-node in an embodiment of the present invention.

[0028] Figure 3 This is the final generated L-index curve in an embodiment of the present invention.

[0029] Figure 4 This is the final generated fitness curve in an embodiment of the present invention. Detailed Embodiments

[0030] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work shall fall within the protection scope of the present application.

[0031] It should be noted that for the convenience of description, only the parts related to the relevant invention are shown in the drawings. Without conflict, the embodiments in the present application and the features in the embodiments can be combined with each other.

[0032] It should be understood that the "system", "device", "unit" and / or "module" used in the present application are a method for distinguishing different components, elements, parts, portions or assemblies at different levels. However, if other words can achieve the same purpose, they can be replaced by other expressions.

[0033] As shown in this application and the claims, unless the context clearly indicates otherwise, words such as "a", "an", "one", and / or "the" are not specifically singular and may also include the plural. Generally speaking, the terms "comprising" and "including" only indicate the inclusion of the clearly identified steps and elements, and these steps and elements do not constitute an exclusive list. The method or device may also include other steps or elements. An element defined by the statement "comprising one..." does not exclude the existence of another identical element in the process, method, commodity, or device that includes the element.

[0034] In the description of the embodiments of this application, "a plurality" means two or more than two. The following terms "first" and "second" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include one or more of such features.

[0035] In addition, flowcharts are used in this application to illustrate the operations performed by the system according to the embodiments of this application. It should be understood that the previous or subsequent operations do not necessarily need to be precisely executed in sequence. On the contrary, the steps can be processed in reverse order or simultaneously. At the same time, other operations can also be added to these processes, or one or several steps can be removed from these processes.

[0036] An optional embodiment of the microgrid static voltage stability analysis method proposed by the present invention. This method can be applied to computer devices. The analysis method proposed in this embodiment may include but is not limited to the following steps:

[0037] Step S1: Construct a fitness function based on the static voltage stability index;

[0038] Step S2: Set variables based on the microgrid model;

[0039] Step S3: With the goal of approximating the critical value of the fitness function, perform iterations on the microgrid model based on the lemur optimization algorithm, and draw the fitness curve and voltage stability index curve according to the iteration process.

[0040] In some feasible embodiments, step S1 specifically includes:

[0041] S1.1: Calculate the L ij index, where:

[0042]

[0043] where L represents the static voltage stability index, P j represents the active power flowing through node j, X ij represents the reactance value between node i and node j, Qj represents the reactive power flowing through node j, R ij represents the reactance value between node i and node j, U i is the amplitude of the input voltage.

[0044] As Figure 1 shown, in a microgrid with a total of N nodes, for any branch, the part between the two nodes can be equivalent to an impedance model, where U i is the amplitude of the input voltage, U j is the amplitude of the output voltage, δ i is the phase angle of the input voltage, δ j is the phase angle of the input voltage, R ij +jX ij is the equivalent resistance of the two nodes, S i =P i +jQ i is the complex power of the input, S j =P j +jQ j is the complex power of the output, I ij is the current value measured from i to j on the line.

[0045] S1.2. Obtain the static voltage stability index (L-index), where:

[0046] L = max{L ij} (2)

[0047] This index is the maximum value of the L ij index for all branches in the microgrid. Under this index, when L ≤ 1, the microgrid reaches voltage static stability, and the smaller this value, the higher the stability; when L = 1, the microgrid reaches the critical value of voltage static stability; when L > 1, voltage static stability is not satisfied; the larger L is, the easier the voltage is to collapse.

[0048] S1.3. Construct the fitness function Fit, where:

[0049] Fit = (1 - L) 2 +dup (3)

[0050] The dup in the formula is the constructed penalty function, which is to meet the condition that the Fit function does not exceed 1 and satisfies the following formula:

[0051]

[0052] L q is the L ij index value of the q-th branch.

[0053] In some feasible embodiments, in step S3, the process of the lemur optimization algorithm includes:

[0054] For the LO algorithm, the main inspiration comes from two actions of lemurs: leap-up and dance-hup.

[0055] The behavior of lemurs can be divided into two cases:

[0056] When the distance between trees is within their jumping range, lemurs jump into the air and sit upright on a nearby branch, gripping the tree trunk tightly with their hands and feet. They can jump from one trunk to a 10-meter-high trunk within a few seconds.

[0057] When the distance between trees becomes too large, lemurs descend to the ground and, by standing upright and making horizontal jumps with their arms extended to one side and swinging up and down from chest to head height, ostensibly to maintain balance, they appear to be dancing.

[0058] During the search process based on a group of lemurs, it is divided into two stages: exploration and exploitation.

[0059] In the exploration stage, the dance-hup behavior is referred to, and the leap-up behavior is also beneficial for the LO algorithm to search the solution space. Each solution is regarded as a lemur individual, and each vector represents its individual coordinates, characterizing the position information of the lemur. It is adjusted in real time according to the fitness of the solution. There are two schemes for adjusting the position vector: jumping towards the optimal lemur within the entire range or dancing towards the nearest lemur. All the position solutions of each lemur individual constitute the lemur population, and its matrix is as follows:

[0060]

[0061] P represents the lemur population matrix, with a size of s×d, where s is the number of lemurs in the population and also the number of candidate solutions, and d is the number of decision variables.

[0062] The decision variable b in solution a is randomly generated by the following formula

[0063]

[0064] rand() ∈ [0, 1], ub b and lb b are the upper and lower limits of variable b.

[0065] In the exploitation stage, lemurs with lower fitness often change their decision variables, causing the fitness value of the entire group of lemurs to increase with each iteration. During each iteration, a global best lemur (gbl) and the best nearest lemur (bnl) for each lemur individual are selected based on the fitness value of the group.

[0066] For the decision variable b in solution a, when assigning values during each iteration, it follows the following formula:

[0067]

[0068] Among them, l(a, b) is the value of the decision variable b of the current lemur a, l(bnl, b) represents the value of the decision variable b of the nearest lemur bnl to the lemur a, l(gbl, b) represents the value of b of the globally optimal lemur, the free risk rate (FRR) represents the risk rate of the lemurs in the population, and rand ∈ [0, 1].

[0069] For the risk rate, the following formula is satisfied:

[0070]

[0071] Among them, High_Risk_Rate and Low_Risk_Rate are two fixed values respectively, which can limit the maximum and minimum values of FRR, MaxIter is the maximum number of iterations, and CurrIter is the current number of iterations.

[0072] Initialize the parameters of the LO algorithm. In formula (8), High_Risk_Rate and Low_Risk_Rate are set to 0.6 and 0.4 respectively, MaxIter is 150, build the IEEE33 - node model, generate a matrix about the active power output of each node's generator, the number of the lemur population is 100, the dimension of the active power output matrix is 100×33, ub j and lb j are set to 0MW and 6MW respectively, and the IEEE33 - node model is connected as Figure 2 .

[0073] In some feasible embodiments, step S3 specifically includes:

[0074] S3.1. At initialization, randomly generate a population matrix and calculate its fitness.

[0075] S3.2. Transfer to the core part of the LO algorithm, perform power flow calculation, then update the L index and fitness, and update the population according to formula (7).

[0076] S3.3. Generate a fitness curve and an L - index curve according to the iteration process.

[0077] In some feasible embodiments, for the lemur optimization algorithm in step S3, it is improved. The improved lemur optimization algorithm (Improved Lemurs Optimizer, ILO) is as follows:

[0078] The reference object, object behavior, and search stage of the algorithm are the same as those described in S2.1.1.

[0079] In the exploration stage, the process of the ILO algorithm is the same as that described for the LO algorithm.

[0080] In the exploitation stage, lemurs with lower fitness often change their decision variables, causing the fitness value of the entire lemur population to increase with each iteration. During each iteration, the global best lemur (gbl) and the best nearest lemur (bnl) for each individual lemur are selected based on the fitness value of the population.

[0081] For the decision variable b in solution a, the assignment during each iteration follows the following formula:

[0082]

[0083] where l(a,b) is the value of the decision variable b of the current lemur a, l(bnl,b) represents the value of the decision variable b of the nearest lemur bnl of lemur a, l(gbl,b) represents the value of b of the globally optimal lemur, the free risk rate (FRR) represents the risk rate of the lemurs in the population, and step represents the step size generated by the combined action of the Levy flight algorithm and the iteration scaling factor.

[0084] For the step size, it satisfies the following formula:

[0085]

[0086] In the formula, step_levy is the step size generated by the Levy flight algorithm, step_scale is the iteration scaling factor, itr is the current iteration number. Among other terms, u is a random variable that follows a normal distribution with variance σ, v is a random variable that follows a standard normal distribution, and β represents a shape variable related to σ and satisfies Equation (11):

[0087]

[0088] For the risk rate, a dynamic adjustment method based on the standard deviation of fitness is used, which satisfies the following formula:

[0089]

[0090] where High_Risk_Rate and Low_Risk_Rate are two fixed values that can limit the maximum and minimum values of FRR, fitness_std is the real-time fitness standard deviation, and initial_std is the initial standard deviation.

[0091] Initialize the parameters of the ILO algorithm. In Equation (12), set High_Risk_Rate and Low_Risk_Rate to 0.6 and 0.4 respectively, set MaxIter to 150, build the IEEE 33-node model, generate the matrix of the active power output of each node's generator, set the number of lemur populations to 100, the dimension of the active power output matrix to 100×33, ub j and lb j are set to 0 MW and 6 MW respectively. Set β in Equation (11) to 2.2. The IEEE 33-node model is connected as Figure 3 .

[0092] Generate the fitness curve, as Figure 3 ; generate the L-index curve, as Figure 4 . The obtained fitness curves and L-index curves of the LO algorithm and the ILO algorithm show the effectiveness of the LO algorithm and the ILO algorithm in static voltage stability analysis.

[0093] Compared with the prior art, the principles and advantages of this solution are as follows: 1. The structures of the LO algorithm and the ILO algorithm are simple. 2. The ideas of the LO algorithm and the ILO algorithm are novel. The leap-up behavior is used to approach the local optimal value each time, and the dance-up behavior is used to approach the global optimal value of the group each time. 3. In the traditional artificial intelligence algorithm, the weights of approaching the local optimal value and the global optimal value in each iteration are fixed values. However, in the LO algorithm and the ILO algorithm, the probability of each decision variable approaching the global optimal value increases with the increase of the number of iterations, which is more conducive to obtaining the global optimal solution finally. 4. The ILO algorithm changes the jump rate in the LO algorithm from linear decrease to adjusting the jump rate using the fitness variance, which can dynamically respond to the changes of the population; the ILO algorithm combines the decision variable generation process in the LO algorithm with the adaptive Levy algorithm and replaces the fixed perturbation factor to enhance the global search ability of the algorithm. Compared with the LO algorithm, the ILO algorithm can speed up the search speed and improve the convergence accuracy.

[0094] A microgrid static voltage stability analysis system includes:

[0095] A function construction module for executing step S1;

[0096] A variable setting module for executing step S2;

[0097] An iterative convergence module for executing step S3.

[0098] The content in the above method embodiments is applicable to the system embodiments. The functions specifically implemented by the system embodiments are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those in the above method embodiments.

[0099] A device for analyzing the static voltage stability of a microgrid:

[0100] At least one processor;

[0101] At least one memory for storing at least one program;

[0102] When the at least one program is executed by the at least one processor, the at least one processor implements a method for analyzing the static voltage stability of a microgrid as described above.

[0103] The content in the above method embodiments is applicable to the device embodiments. The functions specifically implemented by the device embodiments are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those in the above method embodiments.

[0104] A storage medium storing instructions executable by a processor, where the instructions executable by the processor are used to implement a method for analyzing the static voltage stability of a microgrid as described above when executed by the processor.

[0105] The content in the above method embodiments is applicable to the storage medium embodiments. The functions specifically implemented by the storage medium embodiments are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those in the above method embodiments.

[0106] The above is a specific description of the preferred embodiments of the present invention, but the present invention is not limited to the described embodiments. Those skilled in the art can make various equivalent deformations or substitutions without departing from the spirit of the present invention, and these equivalent deformations or substitutions are all included within the scope defined by the claims of this application.

Claims

1. A method for analyzing the static voltage stability of a microgrid, characterized in that, It includes the following steps: Construct a fitness function based on static voltage stability indices; Set variables based on the microgrid model; Aim at approximating the critical value with the fitness function, and iterate the microgrid model based on the lemur optimization algorithm to generate a fitness curve and a voltage stability index curve.

2. The method for analyzing the static voltage stability of a microgrid according to claim 1, characterized in that, The static voltage stability index is expressed as follows: Among them, L represents the static voltage stability index, P j represents the active power flowing through node j, X ij represents the reactance value between node i and node j, Q j represents the reactive power flowing through node j, R ij represents the reactance value between node i and node j, U i is the input terminal voltage amplitude.

3. The method for analyzing the static voltage stability of a microgrid according to claim 2, characterized in that, The fitness function is expressed as follows: Fit=(1-L) 2 +dup Among them, L q is the L ij index value of the q-th branch.

4. The method for analyzing the static voltage stability of a microgrid according to claim 1, wherein The step of aiming at approximating the critical value with the fitness function, and iterating the microgrid model based on the lemur optimization algorithm to generate a fitness curve and a voltage stability index curve specifically includes: Based on the microgrid model, set the active power injected into each node in the microgrid as the solution; Initialize the solution based on the lemur optimization algorithm, randomly generate a population and calculate its fitness; In a loop, search and perform power flow calculations based on the population, calculate the static voltage stability index and fitness using the relevant parameters obtained from the power flow calculations, and update the population according to the population update formula in the lemur algorithm; After multiple loops, when a certain node in the microgrid approaches the voltage collapse point, the calculation terminates, and based on the iterative update process of the static voltage stability index and fitness, plot the fitness curve and the voltage stability index curve.

5. The method for analyzing the static voltage stability of a microgrid according to claim 4, wherein For the decision variable b in solution a, the assignment formula is expressed as follows: Where, l(bnl, b) represents the value of the decision variable b of the lemur bnl closest to solution a, l(gbl, b) represents the value of b of the globally optimal lemur, and FRR represents the risk rate of the lemurs in the population.

6. The method for analyzing the static voltage stability of a microgrid according to claim 4, wherein Introduce an iterative scaling factor. For the decision variable b in solution a, the assignment formula is expressed as follows: step_levy is the step size generated by the Levy flight algorithm, step_scale is the iterative scaling factor, itr is the current iteration number, u is a random variable that follows a normal distribution with variance σ; v is a random variable that follows a standard normal distribution; β represents a shape variable related to σ.

7. The method for analyzing the static voltage stability of a microgrid according to claim 6, characterized in that Set the risk rate of the lemurs in the population based on a dynamic adjustment method of fitness standard deviation, which is expressed as follows: Where, High_Risk_Rate and Low_Risk_Rate are two preset fixed values, fitness_std is the real-time fitness standard deviation, and initial_std is the initial standard deviation.

8. A method and system for analyzing the static voltage stability of a microgrid, characterized in that, It includes: A function construction module for constructing a fitness function based on static voltage stability indices; A variable setting module for setting variables based on the microgrid model; An iterative convergence module for aiming at approximating the critical value with the fitness function, and using the lemur optimization algorithm to iterate the microgrid model to generate a fitness curve and a voltage stability index curve.

9. A device for analyzing the static voltage stability of a microgrid, characterized in that, It includes: At least one processor; At least one memory for storing at least one program; When the at least one program is executed by the at least one processor, the at least one processor implements a method for analyzing the static voltage stability of a microgrid as described in any one of claims 1 - 7.

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