A method for optimizing power system frequency regulation under extreme weather conditions

Abstract

The present invention provides a method for optimizing power system frequency regulation under extreme weather conditions, comprising establishing a wind power model and a photovoltaic power model; constructing a typical extreme weather scenario using an improved fuzzy C-means clustering algorithm; establishing a frequency regulation optimization model with quasi-steady-state frequency deviation, system regulation time, and comprehensive cost of generator sets as objective functions; establishing constraint conditions; and solving the optimization model based on a multi-objective Lemur optimization algorithm. The present invention uses an improved fuzzy C-means clustering algorithm to construct a typical extreme weather scenario, evaluates sample membership using a comprehensive distance consisting of Euclidean distance and angle cosine distance, and improves the accuracy of scenario construction; comprehensively considers system frequency safety and economy, and achieves comprehensive optimization of multiple performance indicators; uses a multi-objective Lemur optimization algorithm for solution to prevent the algorithm from falling into a local optimum; improves the accuracy of system frequency stability assessment, and provides a more reliable guarantee for safe system operation under extreme weather conditions.

Description

Technical Field

[0001] The present invention relates to the technical field of power system optimization, and in particular to a method for optimizing power system frequency regulation under extreme weather conditions. Background Art

[0002] With the large-scale integration of renewable energy sources into the grid, the structure of the power system has undergone significant changes, reducing the overall system inertia and significantly weakening its ability to resist disturbances. At the same time, the intensification of global climate change has led to increasingly severe extreme weather events such as typhoons, heavy rains, and ice and snow disasters, exacerbating the risk of power system instability.

[0003] Currently, emergency response measures for extreme weather events in power system operations primarily target fossil fuel power generation and transmission and distribution networks. In extreme weather scenarios, the primary security risk for fossil fuel-based power systems is damage to the transmission and distribution network or a surge in load demand, leading to frequency fluctuations and power instability. Countermeasures include increasing system peak and frequency regulation reserves, incorporating dynamic frequency security constraints into economic dispatch decision-making frameworks, and employing multi-energy coordinated peak and frequency regulation during planned operations.

[0004] However, existing peak-shaving and frequency-regulation research focuses on dispatch models that comprehensively consider steady-state, transient, and quasi-steady-state frequency security constraints under small disturbances. Their applicability to extreme weather scenarios is still in its early stages of exploration. Compared to traditional power system optimization problems, the coupling mechanism of power system operation optimization considering extreme weather scenarios and frequency security is more complex, with the following two main research pain points:

[0005] 1) Regarding the coupling of multiple frequency modulation resources, how can we accurately quantify the inertia characteristics and frequency modulation performance of frequency modulation resources under extreme weather conditions? Furthermore, we can establish a system frequency response model that coordinates multiple frequency modulation resources by combining different frequency modulation strategies. Furthermore, we can seek to simplify the complex frequency modulation process to meet the needs of solving large-scale optimization problems.

[0006] 2) In terms of multi-time-scale optimization coupling, how to propose a multi-time-scale operation optimization model that can comprehensively cover the entire process of inertia support and frequency regulation, clarify the steady-state and transient operation requirements in different scenarios and stages, and achieve a balance between frequency safety and operational economy by optimizing the call of frequency regulation resources. Summary of the Invention

[0007] In response to the shortcomings of the existing technology, the present invention provides a method for optimizing power system frequency regulation under extreme weather conditions. The present invention solves the problems of reduced power system inertia and weakened frequency stability due to the access of a high proportion of renewable energy, as well as the risk of system instability exacerbated by extreme weather.

[0008] The technical solution of the present invention is: a method for optimizing power system frequency regulation under extreme weather conditions, comprising the following steps:

[0009] S1), establishing wind power model and photovoltaic power model;

[0010] S2), using the improved fuzzy C-means clustering algorithm to construct typical extreme weather scenarios;

[0011] S3) Establishing a frequency regulation optimization model with quasi-steady-state frequency deviation, system adjustment time and comprehensive cost of generator sets as objective functions;

[0012] S4), construct constraints;

[0013] S5) Solve the optimization model based on the multi-objective Lemur optimization algorithm.

[0014] Preferably, in step S1), the wind power model is expressed as:

[0015]

[0016] Where, P W is the output power of the fan; v is the actual wind speed of the fan; v in 、v out are the cut-in wind speed and cut-out wind speed of the fan respectively; v r is the rated wind speed of the fan; P S is the rated power of the fan.

[0017] Preferably, in step S1), the expression of the photovoltaic power model is:

[0018]

[0019] CF=η T η i n n n l ;

[0020] Where, P PV is the output power of the photovoltaic unit; CF is the conversion efficiency of the photovoltaic module to convert solar energy into electrical energy; G S is the solar radiation intensity; G is the sunshine intensity under standard conditions; P PVPeak is the total installed capacity of the photovoltaic system; η T ,η i 、n n 、n l They are temperature correction coefficient, photovoltaic module installation azimuth angle correction coefficient, photovoltaic system inverter efficiency, and photovoltaic system line correction coefficient.

[0021] Preferably, in step S2), the improved fuzzy C-means clustering algorithm constructs typical extreme weather scenarios by combining Euclidean distance and angle cosine distance.

[0022] Preferably, in step S2), an improved fuzzy C-means clustering algorithm is used to construct typical extreme weather scenarios, which specifically includes the following steps:

[0023] S21), Calculate the membership degree relative to the clustering center;

[0024] S22), Calculate the Euclidean distance from each sample point to the clustering center of each cluster set; [[ID=]

[0025] S23), Calculate the cosine of the angle distance and form a comprehensive distance with the Euclidean distance;

[0026] S24), Update the sample membership degree according to the comprehensive distance.

[0027] Preferably, in step S21), the calculation formula for calculating the membership degree relative to the clustering center is:

[0028]

[0029] In the formula, u ik is the membership degree of the i-th sample to k cluster sets; c is the number of clusters; m is the fuzzy weighting parameter; d ik is the Euclidean distance from the i-th sample to the clustering center of k cluster sets; d ir is the Euclidean distance from the i-th sample to the clustering center of r cluster sets; is the central vector of the sample; x i is the i-th sample; n is the number of samples; V i is the i-th clustering center; L(c) is the adaptive factor;

[0030] The numerator part of the adaptive factor L(c) represents the inter-class distance, and the denominator part represents the intra-class distance. The convergence condition for determining the adaptive factor is: L(c)>L(c - 1) and L(c)<L(c + 1); to determine that the number of clusters c is the optimal number of clusters.

[0031] Preferably, in step S22), the Euclidean distance from each sample point to the clustering center of each cluster set is:

[0032]

[0033] In the formula, d ik is the Euclidean distance from the i-th sample to the clustering center of k cluster sets; x i is the i-th sample; V k is the k-th clustering center; x ij is the j-th data point of the i-th sample; V kj is the j-th data point of the k-th clustering center; s is the number of data points of the i-th sample.

[0034] As a preference, in step S23), the angle cosine distance The calculation formula is:

[0035]

[0036] Where x ij is the jth data point of the i-th sample; V kj is the jth data point of the kth cluster center; s is the number of data points of the i-th sample;

[0037] The comprehensive distance ρ ik The expression is:

[0038]

[0039] Where, ρ ik The comprehensive distance of the i-th sample to the k clusters; 1-σ is the weight of the Euclidean distance; β is the proportional coefficient; d ik is the Euclidean distance between the i-th sample and the cluster center of the k clusters; is the cosine distance of the angle between the i-th sample and the cluster centers of the k clusters.

[0040] Preferably, in step S24), the calculation formula for updating the sample membership according to the comprehensive distance is:

[0041]

[0042] Where u ik is the membership of the i-th sample to the k clusters; c is the number of clusters; m is the fuzzy weighting parameter; ρ ik The comprehensive distance between the i-th sample and the k clusters; ρ ir The comprehensive distance of the i-th sample to the r clusters.

[0043] Preferably, in step S3), the frequency modulation optimization model uses the quasi-steady-state frequency deviation as one of the objective functions f1, and its expression is:

[0044]

[0045] Where, f ss is the quasi-steady-state frequency deviation of the system; f0 is the initial frequency of the system; ΔP 0,t is the power impact on the system during period t; F g,i,t,PFR The primary frequency regulation reserve provided by adjustable unit i during period t; k D is the load adjustment coefficient; P d,t is the load power of the system in period t; N is the number of adjustable units.

[0046] Preferably, in step S3), the frequency modulation optimization model uses the system adjustment time as the second objective function f2, that is:

[0047]

[0048] Where, T reg It is the system adjustment time, including the total time of inertia response, primary frequency regulation and secondary frequency regulation.

[0049] Preferably, in step S3), the frequency regulation optimization model uses the comprehensive cost of the generator set as the third objective function f3, that is:

[0050]

[0051] Where T is the total number of dispatch periods; G is the set of generators in the power system; is the power generation cost coefficient of the i-th generator set in the power system; is the output plan of the i-th generator set in the power system during period t; is the startup cost of the i-th generator set in the power system; S i,t is the starting state of the i-th generator set in the power system during period t; S i,t =1 indicates the unit is started; C ESS is the daily investment cost of the energy storage device; C OM is the operation and maintenance cost of the energy storage device; C t,PFR is the primary frequency regulation reserve cost of the power system in period t; C t,SFR is the secondary frequency regulation reserve cost of the power system in period t.

[0052] Preferably, in step S4), the constraints include the frequency change rate RoCoF constraint taking into account the load inertia and the LFoT constraint taking into account the unit operating conditions, the frequency regulation standby constraint, the power balance constraint, the unit output constraint, the unit climbing constraint, and the energy storage constraint.

[0053] Preferably, in step S4), constructing a frequency change rate RoCoF constraint taking into account load inertia specifically includes the following steps:

[0054] S411) If the power impact on the power system during period t is ΔP 0,t , then the RoCoF of the power system after the disturbance is:

[0055]

[0056] Where, τ is the RoCoF of the power system; ρ is the inertia coefficient of the power system; f0 is the initial frequency of the system; P d,t is the load power of the system in period t;

[0057] S412), after taking into account the system inertia coefficient of the synchronous power supply and motor load, the RoCoF of the power system is:

[0058]

[0059] Where, η is the motor load ratio of the power system; H d is the uniform inertia time constant of the motor load; E g,i is the rotational kinetic energy of the i-th generator set in the power system; μ i,t is the operating status of unit i at time t;

[0060] S413) According to the security constraints, the RoCoF of the power system satisfies:

[0061] τ≤τ max ; (15)

[0062] Where, τ max is the maximum RoCoF allowed for the power system;

[0063] S413) Taking into account the load inertia, the RoCoF of the power system should meet the following unit rotational inertia requirements:

[0064]

[0065] Where, τ max is the maximum RoCoF allowed by the power system; η is the motor load ratio of the power system; H d is the uniform inertia time constant of the motor load; E g,i is the rotational kinetic energy of the i-th generator set in the power system; μ i,t is the operating status of unit i at time t; N is the number of generating units.

[0066] Preferably, in step S4), the LFoT constraint taking into account the unit operating conditions is:

[0067]

[0068] Where, F g,i,t,PFR is the primary frequency regulation reserve provided by the i-th adjustable unit in period t; M is the set of units participating in the primary frequency regulation; Δf m is the maximum frequency deviation of the power system.

[0069] Preferably, in step S4), when the system is disturbed, the primary frequency regulation response offsets part of the unbalanced power to achieve differential regulation, but the power system still has a power shortage. Considering that the system should have the ability to recover to the steady-state initial frequency after the primary frequency regulation is completed, the sum of the primary frequency regulation reserve and the secondary frequency regulation reserve of the unit should not be less than the power impact. Therefore, the frequency regulation reserve constraint is expressed as:

[0070]

[0071] Where, F g,i,t,SFR The secondary frequency regulation reserve provided for the i-th adjustable unit during period t.

[0072] Preferably, in step S4), the power balance constraint is:

[0073]

[0074] Where, is the output plan of the i-th generator set in the power system during period t; are the wind turbine output, photovoltaic unit output and load power consumption of the power system in period t respectively.

[0075] Preferably, in step S4), the unit output constraint is:

[0076]

[0077] Where U i,t is the startup state of the i-th generator set in the power system during period t, U i,t =1; are the minimum and maximum output of the i-th generator set respectively; Represents any generator set and any time.

[0078] Preferably, in step S4), the unit climbing constraint condition is:

[0079]

[0080] Where, are the up and down climbing rates of the i-th unit respectively; is the output plan of the i-th generator set in period t-1.

[0081] Preferably, in step S4), the energy storage constraint condition is:

[0082]

[0083]

[0084] Where C ESS 、C OM are the daily investment cost and operation and maintenance cost of the energy storage device respectively; C R is the daily cost conversion coefficient; n ESS is the amount of energy storage; α i is the unit capacity cost of the i-th energy storage; S n,i is the rated capacity of the i-th energy storage; β i is the unit power cost of the i-th energy storage; C γ is the annual operation and maintenance cost of the energy storage device; r is the discount rate; y is the service life of the energy storage system.

[0085] Preferably, in step S5), solving the optimization model based on the multi-objective lemur optimization algorithm specifically includes the following steps:

[0086] S51), set the initial parameters of the optimization algorithm, generate the initial population, and set the number of iterations iter = 0;

[0087] S52) Import the power data of wind power, photovoltaic power and load under extreme weather conditions, and set the upper and lower limits of dynamic frequency constraints and other system operation constraints according to system safety requirements;

[0088] S53) Randomly generate an initial population T, where each lemur individual x in the population i,j is a solution vector representing the coordinates of individual lemurs. Lemurs change their positions according to the fitness of the population. The population size is n, and there are d decision variables, corresponding to the output of various units in 24 time periods.

[0089]

[0090] x i,j =rand()×(ub j -lb j )+lb

[0091]

[0092] Where x i,j is the jth decision variable of the i-th population; lb j and ub j They represent the discrete lower limit and upper limit of the j-th decision variable respectively; rand() is a random number between 0 and 1;

[0093] S54) Introducing congestion distance D i ;Right now:

[0094]

[0095] Where, and are the objective function values ​​of adjacent solutions on target k respectively; are the maximum and minimum values ​​of target k, respectively, used for normalization; S is the number of targets;

[0096] S55) Calculate the free risk rate FRR of the lemur population. As the number of iterations increases, the free risk rate FRR gradually decreases to control the balance between exploration and exploitation, that is:

[0097]

[0098] Where, FRR base Free risk rate (FRR) high 、FRR low is the maximum and minimum value of the preset free risk rate; iter c This is the number of iterations; iter max is the maximum number of iterations; γ is the adjustment coefficient, which is used to control the impact of crowding distance on the free risk rate;

[0099] S56), using the position update strategy for optimization, the next position update strategy of the lemur individual is determined by one of the following two methods, namely local development and global exploration;

[0100]

[0101] Where x near,j and x global,j The neighboring optimal solution and global optimal solution for this round of iteration;

[0102] S57), check whether the updated position meets the constraint conditions, and make corrections if not;

[0103] S58), update the global optimal solution and output the optimal scheduling plan;

[0104] S59), performing non-dominated sorting on the updated population, and updating the Pareto optimal solution set;

[0105] S510), perform iterative update, if the maximum number of iterations has not been reached, return to step S54), otherwise continue to execute step S511);

[0106] S511) Outputting an optimal dispatching plan from the Pareto optimal solution set, including the output plan of each generator set, the charging and discharging plan of the energy storage system, and the allocation of primary frequency regulation reserve and secondary frequency regulation reserve.

[0107] The beneficial effects of the present invention are:

[0108] 1. This paper uses an improved fuzzy C-means clustering algorithm to construct typical extreme weather scenarios. The comprehensive distance consisting of Euclidean distance and angle cosine distance is used to evaluate sample membership. Compared with traditional clustering methods, it can more accurately identify extreme weather characteristics, improve the accuracy of scenario construction, and provide more reliable basic data for subsequent optimization.

[0109] 2. The present invention establishes a multi-objective optimization model with quasi-steady-state frequency deviation, system adjustment time, and comprehensive cost of generator sets as objective functions. This model comprehensively considers system frequency safety and economy, achieves comprehensive optimization of multiple performance indicators, and avoids the problem of overall system performance degradation caused by optimization of a single indicator.

[0110] 3. The present invention adopts the multi-objective Lemur optimization algorithm for solution. By introducing the crowding distance and free risk rate mechanism, the algorithm is prevented from falling into the local optimum in the early stage and the search range is expanded in the later stage to find the global optimal solution. Compared with the traditional multi-objective optimization algorithm, it has stronger global search ability and convergence performance.

[0111] 4. Compared with the traditional method that only considers static constraints, the RoCoF constraint that takes into account load inertia and the LFoT constraint that takes into account unit operating conditions proposed in this invention more comprehensively reflect the dynamic frequency characteristics of the system, improve the accuracy of the system frequency stability assessment, and provide more reliable protection for the safe operation of the system in extreme weather conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0112] Figure 1 Schematic diagram of the process of the present invention;

[0113] Figure 2 This is a flow chart of the improved fuzzy C-means clustering algorithm of the present invention;

[0114] Figure 3 Flowchart of the multi-objective lemur optimization algorithm of the present invention;

[0115] Figure 4 Generate a typical extreme scene graph for clustering of an embodiment of the present invention;

[0116] Figure 5 This is a schematic diagram of the optimization scheduling results of an embodiment of the present invention. DETAILED DESCRIPTION

[0117] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings:

[0118] like Figure 1 As shown, this embodiment provides a method for optimizing power system frequency regulation under extreme weather conditions, comprising the following steps:

[0119] S1), establishing wind power model and photovoltaic power model;

[0120] The wind power model is expressed as follows:

[0121]

[0122] Where, P W is the output power of the fan; v is the actual wind speed of the fan; v in 、v out are the cut-in wind speed and cut-out wind speed of the fan respectively; v r is the rated wind speed of the fan; P S is the rated power of the fan.

[0123] Preferably, in step S1), the expression of the photovoltaic power model is:

[0124]

[0125] CF=η T η i n n n l ;

[0126] Where, P PV is the output power of the photovoltaic unit; CF is the conversion efficiency of the photovoltaic module to convert solar energy into electrical energy; G S is the solar radiation intensity (W / m 2 ); G is the sunshine intensity under standard conditions; P PVPeak is the total installed capacity of the photovoltaic system; η T ,η i 、n n 、n l They are respectively the temperature correction coefficient, the photovoltaic module installation azimuth angle correction coefficient, the photovoltaic system inverter efficiency, and the photovoltaic system line correction coefficient. In this embodiment, n l =0.95-0.98; n n =0.8-0.95.

[0127] S2) Use the improved fuzzy C-means clustering algorithm to construct typical extreme weather scenarios; Figure 2 As shown, the specific steps include:

[0128] S21) Calculate the membership degree relative to the cluster center; that is:

[0129]

[0130] Where u ik is the membership of the i-th sample to the k clusters; c is the number of clusters; m is the fuzzy weighting parameter, which is 2 in this embodiment; d ik is the Euclidean distance between the i-th sample and the cluster center of the k clusters; dir is the Euclidean distance from the i-th sample to the clustering centers of r clusters; is the central vector of the sample; x i is the i-th sample; n is the number of samples; V i is the i-th clustering center; L(c) is the adaptive factor;

[0131] The numerator part of the adaptive factor L(c) represents the inter-class distance, and the denominator part represents the intra-class distance. The convergence condition for determining the adaptive factor is: L(c) > L(c - 1) and L(c) < L(c + 1); to determine that the clustering number c is the optimal clustering number.

[0132] S22), calculate the Euclidean distance from each sample point to the clustering centers of each cluster; that is:

[0133]

[0134] In the formula, d ik is the Euclidean distance from the i-th sample to the clustering centers of k clusters; x i is the i-th sample; V k is the k-th clustering center; x ij is the j-th data point of the i-th sample; V kj is the j-th data point of the k-th clustering center; s is the number of data points of the i-th sample.

[0135] S23), calculate the cosine distance of the angle and form a comprehensive distance with the Euclidean distance; that is:

[0136] The cosine distance of the angle described above The calculation formula of is:

[0137]

[0138] In the formula, x ij is the j-th data point of the i-th sample; V kJ is the j-th data point of the k-th clustering center; s is the number of data points of the i-th sample;

[0139] The comprehensive distance ρ described above ik The expression of is:

[0140]

[0141] In the formula, ρ ik is the comprehensive distance from the i-th sample to k clusters; σ is the weight of the cosine distance of the angle; 1 - σ is the weight of the Euclidean distance; β is the proportionality coefficient, and β reduces the Euclidean distance by a certain multiple so that the cosine distance of the angle and the Euclidean distance are at the same order of magnitude; d ikis the Euclidean distance between the i-th sample and the cluster center of the k clusters; is the cosine distance of the angle between the i-th sample and the cluster centers of the k clusters.

[0142] S24) Update the sample membership according to the comprehensive distance, that is:

[0143]

[0144] Where u ik is the membership of the i-th sample to the k clusters; c is the number of clusters; m is the fuzzy weighting parameter; ρ ik The comprehensive distance between the i-th sample and the k clusters; ρ ir The comprehensive distance of the i-th sample to the r clusters.

[0145] S3) Establishing a frequency regulation optimization model with quasi-steady-state frequency deviation, system adjustment time and comprehensive cost of generator sets as objective functions;

[0146] The frequency modulation optimization model uses the quasi-steady-state frequency deviation as one of the objective functions f1. The quasi-steady-state frequency deviation is the frequency deviation after a frequency modulation process. Considering the power system's long-term low-frequency operation capability limitations, the expression for the quasi-steady-state frequency deviation of the power system is:

[0147]

[0148] Where, f ss is the quasi-steady-state frequency deviation of the system; f0 is the initial frequency of the system; ΔP 0,t is the power impact on the system during period t; F g,i,t,PFR The primary frequency regulation reserve provided by adjustable unit i during period t; k D is the load adjustment coefficient; P d,t is the load power of the system in period t; N is the number of adjustable units.

[0149] In order to improve the rapidity of system response, it is necessary to minimize the time from the occurrence of a fault to the frequency recovery to a quasi-steady state. The frequency modulation optimization model uses the system adjustment time as the second objective function f2, that is:

[0150] f2=min(T reg ); (11)

[0151] Where, T reg It is the system adjustment time, including the total time of inertia response, primary frequency regulation and secondary frequency regulation.

[0152] The frequency regulation optimization model uses the comprehensive cost of the generator set as the third objective function f3, namely:

[0153]

[0154] Where T is the total number of dispatch periods; G is the set of generators in the power system; is the power generation cost coefficient of the i-th generator set in the power system; is the output plan of the i-th generator set in the power system during period t; is the startup cost of the i-th generator set in the power system; S i,t is the starting state of the i-th generator set in the power system during period t; S i,t =1 indicates the unit is started; C ESS is the daily investment cost of the energy storage device; C OM is the operation and maintenance cost of the energy storage device; C t,PFR is the primary frequency regulation reserve cost of the power system in period t; C t,SFR is the secondary frequency regulation reserve cost of the power system in period t.

[0155] S4), construct constraints;

[0156] In this embodiment, the constraints include the frequency change rate RoCoF constraint taking into account the load inertia and the LFoT constraint taking into account the unit operating conditions, the frequency regulation standby constraint, the power balance constraint, the unit output constraint, the unit climbing constraint, and the energy storage constraint.

[0157] In this embodiment, constructing a frequency change rate RoCoF constraint taking into account load inertia specifically includes the following steps:

[0158] S411) The frequency change rate RoCoF of the system is a technical indicator directly related to the inertia level of the power system. If the power impact received by the power system in period t is ΔP 0,t , then the RoCoF of the power system after the disturbance is:

[0159]

[0160] Where, τ is the RoCoF of the power system; ρ is the inertia coefficient of the power system; f0 is the initial frequency of the system; P d,t is the load power of the system in period t;

[0161] S412), after taking into account the system inertia coefficient of the synchronous power supply and motor load, the RoCoF of the power system is:

[0162]

[0163] Where, η is the motor load ratio of the power system; H d is the uniform inertia time constant of the motor load; E g,iis the rotational kinetic energy of the i-th generator set in the power system; μ i,t is the operating status of unit i at time t;

[0164] S413) According to the security constraints, the RoCoF of the power system satisfies:

[0165] τ≤τ max ; (15)

[0166] Where, τ max is the maximum RoCoF allowed for the power system;

[0167] S413) Taking into account the load inertia, the RoCoF of the power system should meet the following unit rotational inertia requirements:

[0168]

[0169] Where, τ max is the maximum RoCoF allowed by the power system; η is the motor load ratio of the power system; H d is the uniform inertia time constant of the motor load; E g,i is the rotational kinetic energy of the i-th generator set in the power system; μ i,t is the operating status of unit i at time t; N is the number of generating units.

[0170] In this embodiment, the primary frequency regulation capability of the unit is closely related to its own operating conditions. As the load decreases, the primary frequency regulation response performance of the unit also decreases. The primary frequency regulation capability of the unit accounts for approximately 6% to 10% of the rated capacity of the unit. The transient minimum frequency LFoT constraint considering the operating conditions of the unit is:

[0171]

[0172] Where, F g,i,t,PFR is the primary frequency regulation reserve provided by the i-th adjustable unit in period t; M is the set of units participating in the primary frequency regulation; Δf m is the maximum frequency deviation of the power system.

[0173] When the system is disturbed, the primary frequency regulation response offsets part of the unbalanced power and achieves differential regulation, but the system still has a power shortage. Considering that the system should have the ability to recover to the steady-state initial frequency after the primary frequency regulation is completed, the sum of the primary frequency regulation reserve and the secondary frequency regulation reserve of the unit should not be less than the power impact. Therefore, the frequency regulation reserve constraint is expressed as:

[0174]

[0175] Where, F g,i,t,SFRThe secondary frequency regulation reserve provided for the i-th adjustable unit during period t.

[0176] In this embodiment, the power balance constraint is:

[0177]

[0178] Where, is the output plan of the i-th generator set in the power system during period t; are the wind turbine output, photovoltaic unit output and load power consumption of the power system in period t respectively; Respectively represent the minimum and maximum output of the wind turbine; Respectively represent the minimum and maximum output of the photovoltaic unit; Respectively represent the minimum and maximum values ​​of load power;

[0179] In this embodiment, the unit output constraint is:

[0180]

[0181] Where U i,t is the startup state of the i-th generator set in the power system during period t, U i,t =1 means power on; are the minimum and maximum output of the i-th generator set respectively; Represents any generator set and any time.

[0182] In this embodiment, the unit climbing constraint condition is:

[0183]

[0184] Where, are the up and down climbing rates of the i-th unit respectively; is the output plan of the i-th generator set in period t-1.

[0185] In this embodiment, the energy storage constraint conditions are:

[0186]

[0187] Where C ESS 、C OM are the daily investment cost and operation and maintenance cost of the energy storage device respectively; C R is the daily cost conversion coefficient; n ESS is the amount of energy storage; α i is the unit capacity cost of the i-th energy storage; S n,i is the rated capacity of the i-th energy storage; β iis the unit power cost of the i-th energy storage; C γ is the annual operation and maintenance cost of the energy storage device; r is the discount rate; y is the service life of the energy storage system.

[0188] S5), solve the optimization model based on the multi-objective lemur optimization algorithm, such as Figure 3 As shown, the specific steps include:

[0189] S51), set the initial parameters of the optimization algorithm, generate the initial population, and set the number of iterations iter = 0;

[0190] S52) Import the power data of wind power, photovoltaic power and load under extreme weather conditions, and set the upper and lower limits of dynamic frequency constraints and other system operation constraints according to system safety requirements;

[0191] S53) Randomly generate an initial population T, where each lemur individual x in the population i,j is a solution vector representing the coordinates of individual lemurs. Lemurs change their positions according to the fitness of the population. The population size is n, and there are d decision variables, corresponding to the output of various units in 24 time periods.

[0192]

[0193] x i,j =rand()×(ub j -lb j )+lb

[0194]

[0195] Where x i,j is the jth decision variable of the i-th population; lb j and ub j They represent the discrete lower limit and upper limit of the j-th decision variable respectively; rand() is a random number between 0 and 1;

[0196] S54) In order to maintain the diversity of the Pareto frontier, the crowding distance D is introduced i ; When the crowding distance is high, the lemur individual x i,j A large distance from neighboring solutions indicates that the individual is in a sparse area. These solutions help maintain the diversity of the Pareto front and prevent the concentration of solutions in certain areas. On the contrary, when the crowding distance is low, the solution may be a high-quality solution, but due to its dense distribution, its contribution to diversity is low; that is:

[0197]

[0198] Where, and are the objective function values ​​of adjacent solutions on target k respectively; are the maximum and minimum values ​​of target k, respectively, used for normalization; S is the number of targets;

[0199] S55) Calculate the free risk rate FRR of the lemur population. As the number of iterations increases, the free risk rate FRR gradually decreases to control the balance between exploration and exploitation, that is:

[0200]

[0201] Where, FRR base Free risk rate (FRR) high 、FRR low is the maximum and minimum value of the preset free risk rate; iter c This is the number of iterations; iter max is the maximum number of iterations; θ is the adjustment coefficient, which is used to control the impact of crowding distance on the free risk rate;

[0202] S56), using the position update strategy for optimization, the next position update strategy of the lemur individual is determined by one of the following two methods, namely local development and global exploration;

[0203]

[0204] Where x near,j and x global,j The neighboring optimal solution and global optimal solution for this round of iteration;

[0205] S57), check whether the updated position meets the constraint conditions, and make corrections if not;

[0206] S58), update the global optimal solution and output the optimal scheduling plan;

[0207] S59), performing non-dominated sorting on the updated population, and updating the Pareto optimal solution set;

[0208] S510), perform iterative update, if the maximum number of iterations has not been reached, return to step S54), otherwise continue to execute step S511);

[0209] S511) Outputting an optimal dispatching plan from the Pareto optimal solution set, including the output plan of each generator set, the charging and discharging plan of the energy storage system, and the allocation of primary frequency regulation reserve and secondary frequency regulation reserve.

[0210] Example 2

[0211] This example uses an IEEE-33 node distribution system to verify the feasibility of this method: two thermal power units are located at nodes 1 and 6, with capacities of 3500 and 1000 kW; two wind turbines are located at nodes 25 and 33, with capacities of 960 and 1000 kW; two photovoltaic units are located at nodes 18 and 30, with capacities of 1000 and 600 kW; and two energy storage units are located at nodes 16 and 22, with capacities of 1000 kW and 800 kW.

[0212] This embodiment uses the fuzzy C-means clustering algorithm to generate typical extreme weather scenarios as shown in the attached figure. Figure 4 shown.

[0213] This example sets four comparison scenarios to analyze the feasibility and superiority of the method:

[0214] Scenario 1: Optimized scheduling that ignores dynamic frequency constraints and does not consider the system frequency regulation backup part.

[0215] Scenario 2: Optimal dispatch with dynamic frequency constraints but without the frequency regulation effects of wind power and photovoltaics.

[0216] Scenario 3: Optimal scheduling of integrated dynamic frequency constraints and wind-solar-thermal-storage combined peak-shaving and frequency regulation (based on the multi-objective Lemur algorithm solution of Example 1).

[0217] Scenario 4: Optimal scheduling of integrated dynamic frequency constraints and wind-solar-thermal-storage combined peak-shaving and frequency regulation (based on traditional multi-objective particle swarm algorithm solution).

[0218] According to the four comparison scenarios, the operation results and economic performance comparisons obtained after solving the optimization algorithm are shown in Tables 1 and 2.

[0219] Table 1 Comparison of running results in different scenarios

[0220]

[0221] Table 2 Comparison of economic efficiency under different scenarios

[0222]

[0223] Scenario 1, which targets purely economic dispatch and does not consider dynamic frequency constraints, has a comprehensive operating cost of 101,073 yuan, making it the most economical of the four scenarios. However, under extreme weather conditions, load fluctuations and reduced renewable energy output lead to an imbalance in system power supply and demand. The minimum frequency dropped to 48.63 Hz, and the quasi-steady-state frequency was 49.35 Hz, indicating a severe underfrequency operation state, making frequency security difficult to guarantee.

[0224] Scenario 2 incorporates dynamic frequency constraints in the optimization model, improving system frequency stability through the frequency regulation of thermal power units and energy storage units. The minimum frequency reaches 49.2Hz, and the quasi-steady-state frequency is 49.76Hz, meeting frequency safety standards. However, due to the underutilization of the frequency regulation capabilities of wind power and photovoltaic power, relying solely on thermal power and energy storage units for frequency regulation, while the renewable energy absorption rate has improved, the problem of wind and solar power curtailment remains significant.

[0225] Scenario 3 introduces dynamic frequency constraints into the optimization model and fully utilizes the combined peak and frequency regulation capabilities of wind power, photovoltaic power, thermal power and energy storage systems. Figure 5 The optimized dispatch results for Scenario 3 were presented, including the daily load curve and the power generation plan for each unit. The Lemur optimization algorithm, which achieves multi-energy collaborative optimization, significantly improved system frequency stability, reaching a minimum frequency of 49.2 Hz and a quasi-steady-state frequency of 49.94 Hz. These performances outperform Scenario 1 and Scenario 2, meeting frequency safety requirements.

[0226] With the frequency regulation capabilities of wind and photovoltaic power fully utilized, the renewable energy absorption rate increased to 96.7%, significantly reducing wind and solar curtailment. Joint frequency regulation reduced system frequency regulation and standby costs. Wind, solar, and thermal power storage units coordinated frequency regulation, partially replacing the frequency regulation and standby capacity of thermal power units, reducing overall operating costs to 109,448 yuan, closer to the economic level of pure economic dispatch than Scenario 2. Scenario 3 also performed better in terms of frequency security and renewable energy absorption capacity, achieving a good balance between economy, security, and renewable energy utilization, making it the best overall dispatch strategy among all scenarios.

[0227] As shown in Table 2, Scenario 3 reduces total dispatch costs by 4.29% and 2.99% compared to Scenario 2 and Scenario 4, respectively, indicating that the Lemur algorithm outperforms the multi-objective particle swarm optimization algorithm in terms of economic efficiency. The above analysis demonstrates that this method can optimize the allocation of generation and backup resources while ensuring frequency security, improving the economic efficiency and safety of the system.

[0228] The above embodiments and descriptions are only for explaining the principles and best embodiments of the present invention. Without departing from the spirit and scope of the present invention, the present invention may be subject to various changes and improvements, which shall fall within the scope of the invention to be protected.

Claims

1. A method for optimizing power system frequency regulation under extreme weather conditions, characterized in that: It includes the following steps: S1). Establish a wind power model and a photovoltaic power model; S2). Construct typical extreme weather scenarios by using an improved fuzzy C-means clustering algorithm; S3). Establish a frequency modulation optimization model with the quasi-steady-state frequency deviation, the system regulation time, and the comprehensive cost of the generator sets as the objective functions; In the said frequency modulation optimization model, the quasi-steady-state frequency deviation is used as one of the objective functions f1, and its expression is: Where, f ss is the quasi-steady-state frequency deviation of the system; f0 is the initial frequency of the system; ΔP 0,t is the power impact on the system during period t; F g,i,t,PFR The primary frequency regulation reserve provided by adjustable unit i during period t; k D is the load adjustment coefficient; P d,t is the load power of the system in period t; N is the number of adjustable units; In the said frequency modulation optimization model, the system regulation time is used as the second objective function f2, that is: f2=min(T reg ); (11) Where, T reg The system adjustment time includes the total time of inertia response, primary frequency regulation and secondary frequency regulation; In the said frequency modulation optimization model, the comprehensive cost of the generator sets is used as the third objective function f3, that is: Where T is the total number of dispatch periods; G is the set of generators in the power system; is the power generation cost coefficient of the i-th generator set in the power system; is the output plan of the i-th generator set in the power system during period t; is the startup cost of the i-th generator set in the power system; S i,t is the starting state of the i-th generator set in the power system during period t; S i,t =1 indicates the unit is started; C ESS is the daily investment cost of the energy storage device; C OM is the operation and maintenance cost of the energy storage device; C t,PFR is the primary frequency regulation reserve cost of the power system in period t; C t,SFR is the secondary frequency regulation reserve cost of the power system in period t; S4). Construct constraint conditions; S5). Solve the optimization model based on the multi-objective lemur optimization algorithm; specifically, it includes the following steps: S51). Set the initial parameters of the optimization algorithm, generate an initial population, and set the iteration number iter = 0; S52). Import the power data of wind power, photovoltaic power, and load under extreme weather, and set the upper and lower limits of the dynamic frequency constraint and other system operation constraints according to the system safety requirements; S53) Randomly generate an initial population T, where each lemur individual x in the population i,j is a solution vector representing the coordinates of individual lemurs. Lemurs change their positions according to the fitness of the population. The population size is n, and there are d decision variables, corresponding to the output of various units in 24 time periods. x i,j =rand()×(ub j -lb j )+lb Where x i,j is the jth decision variable of the i-th population; lb j and ub j They represent the discrete lower limit and upper limit of the j-th decision variable respectively; rand() is a random number between 0 and 1; S54) Introducing congestion distance D i ;Right now: Where, and are the objective function values ​​of adjacent solutions on target k respectively; are the maximum and minimum values ​​of target k, respectively, used for normalization; S is the number of targets; S55). Calculate the free risk rate FRR of the lemur population. As the iteration number increases, the free risk rate FRR gradually decreases to control the balance between exploration and development, that is: Where, FRR base Free risk rate (FRR) high 、FRR low is the maximum and minimum value of the preset free risk rate; iter c This is the number of iterations; iter max is the maximum number of iterations; θ is the adjustment coefficient, which is used to control the impact of crowding distance on the free risk rate; S56). Use the position update strategy for optimization. The next position update strategy of the lemur individual is determined by one of the following two methods, namely local development and global exploration; Where x near,j and x global,j The neighboring optimal solution and global optimal solution for this round of iteration; S57). Check whether the updated position satisfies the constraint conditions. If not, make corrections; S58). Update the global optimal solution and output the optimal scheduling plan; S59). Perform non-dominated sorting on the updated population and update the Pareto optimal solution set; S510). Perform iterative update. If the maximum iteration number is not reached, return to step S54). Otherwise, continue to execute step S511); S511). Output the optimal scheduling plan from the Pareto optimal solution set, including the output plans of each generator set, the charge and discharge plans of the energy storage system, and the allocation of primary frequency modulation reserve and secondary frequency modulation reserve.

2. The method for optimizing power system frequency regulation under extreme weather conditions according to claim 1, characterized in that: In step S2), the said improved fuzzy C-means clustering algorithm constructs typical extreme weather scenarios by comprehensively considering the Euclidean distance and the cosine distance of the angle; specifically, it includes the following steps: S21). Calculate the membership degree relative to the clustering center; S22). Calculate the Euclidean distance from each sample point to the clustering center of each cluster set; S23). Calculate the cosine distance of the angle and form a comprehensive distance with the Euclidean distance; S24). Update the sample membership degree according to the comprehensive distance.

3. The method for optimizing power system frequency regulation under extreme weather conditions according to claim 2, characterized in that: In step S21), the calculation formula for calculating the membership degree relative to the clustering center is: Where u ik is the membership of the i-th sample to the k clusters; c is the number of clusters; m is the fuzzy weighting parameter; d ik is the Euclidean distance between the i-th sample and the cluster center of the k clusters; d ir is the Euclidean distance between the i-th sample and the cluster center of the r clusters; is the center vector of the sample; x i is the i-th sample; n is the number of samples; V i is the i-th cluster center; L(c) is the adaptive factor; The numerator part of the adaptive factor L(c) represents the inter-class distance, and the denominator part represents the intra-class distance. The convergence condition for determining the adaptive factor is: L(c)>L(c - 1) and L(c)<L(c + 1); to determine that the clustering number c is the optimal clustering number.

4. The method for optimizing power system frequency regulation under extreme weather conditions according to claim 2, characterized in that: In step S22), the Euclidean distance from each sample point to the clustering center of each cluster set is: Where, d ik is the Euclidean distance between the i-th sample and the cluster center of the k clusters; x i is the i-th sample; V k is the kth cluster center; x ij is the jth data point of the i-th sample; V kj is the jth data point of the kth cluster center; s is the number of data points of the ith sample.

5. The method for optimizing power system frequency regulation under extreme weather conditions according to claim 2, characterized in that: In step S23), the angle cosine distance The calculation formula is: Where x ij is the jth data point of the i-th sample; V kj is the jth data point of the kth cluster center; s is the number of data points of the i-th sample; The comprehensive distance ρ ik The expression is: Where, ρ ik The comprehensive distance of the i-th sample to the k clusters; σ is the weight of the angle cosine distance; 1-σ is the weight of the Euclidean distance; β is the proportional coefficient; d ik is the Euclidean distance between the i-th sample and the cluster center of the k clusters; is the cosine distance of the angle between the i-th sample and the cluster centers of the k clusters.

6. The method for optimizing power system frequency regulation under extreme weather conditions according to claim 2, characterized in that: In step S24), the calculation formula for updating the sample membership degree according to the comprehensive distance is: Where u ik is the membership of the i-th sample to the k clusters; c is the number of clusters; m is the fuzzy weighting parameter; ρ ik The comprehensive distance between the i-th sample and the k clusters; ρ ir The comprehensive distance of the i-th sample to the r clusters.

7. The method for optimizing power system frequency regulation under extreme weather conditions according to claim 1, characterized in that: In step S4), the constraints include the frequency change rate RoCoF constraint taking into account the load inertia and the LFoT constraint taking into account the unit operating conditions, the frequency regulation standby constraint, the power balance constraint, the unit output constraint, the unit climbing constraint, and the energy storage constraint.

8. The method for optimizing power system frequency regulation under extreme weather conditions according to claim 7, characterized in that: In step S4), a frequency change rate RoCoF constraint taking into account load inertia is constructed. Taking into account load inertia, the power system RoCoF should meet the following unit rotational inertia requirements: Where, τ max is the maximum RoCoF allowed for the power system; η is the motor load ratio of the power system; H d is the uniform inertia time constant of the motor load; E g,i is the rotational kinetic energy of the i-th generator set in the power system; μ i,t is the operating state of unit i at time t, where starting is 1 and stopping is 0; N is the number of generating units; f0 is the initial frequency of the power system; ΔP 0,t is the power impact on the system during period t; P d,t is the load power of the system in period t; The LFoT constraints considering the unit operating conditions are: Where, F g,i,t,PFR is the primary frequency regulation reserve provided by the i-th adjustable unit in period t; M is the set of units participating in the primary frequency regulation; Δf m is the maximum frequency deviation of the power system; The frequency regulation reserve constraint is expressed as: Where, F g,i,t,SFR Secondary frequency regulation reserve provided for the i-th adjustable unit during period t; The power balance constraint is: Where, is the output plan of the i-th generator set in the power system during period t; are the wind turbine output, photovoltaic unit output and load power consumption of the power system in period t respectively; The unit output constraint is: Where U i,t is the startup state of the i-th generator set in the power system during period t, U i,t =1; are the minimum and maximum output of the i-th generator set respectively; Represents any generator set and any time; The unit climbing constraint conditions are: Where, are the up and down climbing rates of the i-th unit respectively; is the output plan of the i-th generator set in period t-1; The energy storage constraints are: Where C ESS 、C OM are the daily investment cost and operation and maintenance cost of the energy storage device respectively; C R is the daily cost conversion coefficient; n ESS is the amount of energy storage; α i is the unit capacity cost of the i-th energy storage; S n,l is the rated capacity of the i-th energy storage; β i is the unit power cost of the i-th energy storage; C γ is the annual operation and maintenance cost of the energy storage device; r is the discount rate; y is the service life of the energy storage system.

Images