A Method and System for Quantitative Assessment of Power System Flexibility Based on Probabilistic Optimal Power Flow

Abstract

This invention belongs to the field of power system assessment technology and provides a method and system for quantitative assessment of power system flexibility based on probabilistic optimal power flow. The method includes: establishing a joint probability density function model including multiple types of renewable energy; constructing a flexibility index based on a joint probability density function model including the probability of insufficient flexibility, the expected flexibility margin, and the expected flexibility deficit; solving the flexibility index using a probabilistic optimal power flow model; and quantitatively assessing the power system based on the solved probability of insufficient flexibility, the expected flexibility margin, and the expected flexibility deficit. This invention uses a probabilistic optimal power flow model to assess and calculate the system, considering operating costs and aiming for optimal operating costs. Simultaneously, it treats margin as a bonus and deficit expectation and probability as deductions, thus achieving a correlation between deterministic and probabilistic indicators and enabling flexibility assessment of the system across multiple time scales.

Description

Technical Field

[0001] This invention belongs to the field of power system assessment technology, and in particular relates to a method and system for quantitative assessment of power system flexibility based on probabilistic optimal power flow. Background Technology

[0002] The integration of a high proportion of renewable energy into the power grid has become a development trend. The proportion of new energy power generation in the power system is gradually increasing. Its characteristics such as volatility, randomness, uncontrollability, and anti-peak shaving have brought new challenges to the construction of the power grid and increased the risk of flexible system operation. How to make full use of these resources has put forward new requirements for the flexibility of the power grid. However, so far, a relatively unified flexibility evaluation index and assessment method have not been formed.

[0003] In the current power system flexibility assessment, the assessment indicators are divided into deterministic indicators and probabilistic indicators. Deterministic indicators are mainly based on unit parameters, including the unit's upward and downward adjustment of flexibility capacity and the unit's ramp rate. Probabilistic indicators include the probability of insufficient flexibility and the expected deficit. The solution of probabilistic indicators is more complex and the calculation is more difficult.

[0004] The inventors discovered that in existing power system evaluations, the assessment of power systems using deterministic and probabilistic indicators only considers the capacity of generating units, neglecting their economic aspects and failing to link deterministic and probabilistic indicators. Summary of the Invention

[0005] To address the aforementioned problems, this invention proposes a method and system for quantitatively evaluating the flexibility of power systems based on probabilistic optimal power flow. When solving the problem using a probabilistic optimal power flow model, this invention aims to optimize operating costs and considers operating costs. At the same time, flexibility margin is regarded as a bonus item, while expected deficit and probability are regarded as deduction items. This achieves the correlation between deterministic and probabilistic indicators and enables flexibility evaluation of the system under multiple time scales.

[0006] To achieve the above objectives, the present invention is implemented through the following technical solution:

[0007] In a first aspect, the present invention provides a method for quantitatively evaluating the flexibility of a power system based on probabilistic optimal power flow, comprising:

[0008] Obtain historical data of the power system;

[0009] Based on the acquired historical data, a joint probability density function model including multiple types of renewable energy was established;

[0010] A flexibility index is constructed, which includes a joint probability density function model of inadequate flexibility probability, expected flexibility margin, and expected flexibility inadequacy. In the flexibility index, expected flexibility margin is regarded as a bonus item, and expected flexibility inadequacy and inadequate flexibility probability are regarded as deduction items.

[0011] A probabilistic optimal power flow model is used to solve for the insufficiency probability, flexibility margin expectation, and insufficiency expectation in the flexibility index; wherein, the objective function of the probabilistic optimal power flow model is cost optimization.

[0012] The power system is quantitatively evaluated based on the solved insufficiency probability, flexibility margin expectation, and flexibility insufficiency expectation.

[0013] Furthermore, historical data is divided into scenarios, and the kernel density estimation method is used to model the probability models of wind power, photovoltaic power, and load based on historical data under various scenarios. The joint probability function model of wind power, photovoltaic power, and load output is modeled using the copula function to obtain the joint probability density function model of time correlation. Combining Bayes' theorem, time series are generated by sampling based on the joint probability density function model.

[0014] Furthermore, wind power output was fitted using Weibull distribution, photovoltaic power output was fitted using Beta distribution, and load was modeled using normal distribution.

[0015] Furthermore, based on historical data and the operation and maintenance costs of various power plants and substations in the power system, a flexibility index is constructed that includes both upward and downward adjustments to the flexibility index.

[0016] Furthermore, the bonus item in the flexibility index is the expected flexibility margin, while the deduction items include the product of the expected insufficient flexibility and the probability of insufficient activity, the amount of load shedding, the amount of wind and solar curtailment, and the product of the economic penalty factor and cost.

[0017] Furthermore, the costs include the start-up and shutdown costs of each node power plant and hydropower station, operation and maintenance costs, renewable energy unit setup costs, pumped storage device activation costs, and energy storage device costs.

[0018] Furthermore, the probabilistic optimal power flow model includes power flow constraints, unit constraints, transmission line constraints, unit flexibility resource constraints, controllable load constraints, renewable energy constraints, and energy storage constraints.

[0019] Secondly, the present invention also provides a power system flexibility quantification evaluation system based on probabilistic optimal power flow, comprising:

[0020] The data acquisition module is configured to acquire historical data of the power system.

[0021] The joint probability density function model building module is configured to: build a joint probability density function model including multiple types of renewable energy based on the acquired historical data;

[0022] The flexibility index establishment module is configured to: construct a flexibility index that includes a joint probability density function model of the insufficiency probability, the flexibility margin expectation, and the flexibility insufficiency expectation; in the flexibility index, the flexibility margin expectation is regarded as a bonus item, and the flexibility insufficiency expectation and the flexibility insufficiency probability are regarded as deduction items.

[0023] The solution module is configured to use a probabilistic optimal power flow model to solve for the insufficiency probability, flexibility margin expectation, and insufficiency expectation in the flexibility index; wherein, the probabilistic optimal power flow model uses cost optimization as the objective function.

[0024] The evaluation module is configured to perform a quantitative evaluation of the power system based on the solved insufficiency probability, flexibility margin expectation, and insufficiency expectation.

[0025] Thirdly, the present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the power system flexibility quantification assessment method based on probabilistic optimal power flow described in the first aspect.

[0026] Fourthly, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the power system flexibility quantification assessment method based on probabilistic optimal power flow described in the first aspect.

[0027] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0028] This invention employs a probabilistic optimal power flow model to evaluate and calculate the system, taking into account the operating cost and aiming at the optimal operating cost. At the same time, it regards margin as a bonus and deficit expectation and probability as deductions, thus realizing the correlation between deterministic and probabilistic indicators and enabling flexibility assessment of the system under multiple time scales. Attached Figure Description

[0029] The accompanying drawings, which form part of this embodiment, are used to provide a further understanding of this embodiment. The illustrative embodiments and their descriptions are used to explain this embodiment and do not constitute an improper limitation of this embodiment.

[0030] Figure 1 This refers to the change in the initial cluster centers in Embodiment 1 of the present invention;

[0031] Figure 2This is a load fitting image from Embodiment 1 of the present invention;

[0032] Figure 3 This is a wind force fitting image from Embodiment 1 of the present invention;

[0033] Figure 4 This is a photovoltaic fitting image from Embodiment 1 of the present invention;

[0034] Figure 5 This illustrates the principle of the wind power, photovoltaic power, and load time sequence output generation method in Embodiment 1 of the present invention.

[0035] Figure 6 The wind power output curve is shown in Embodiment 1 of the present invention;

[0036] Figure 7 This is the photovoltaic power output curve of Embodiment 1 of the present invention;

[0037] Figure 8 This is the load output curve of Embodiment 1 of the present invention;

[0038] Figure 9 This is a flowchart of the flexibility evaluation method of Embodiment 1 of the present invention. Detailed Implementation

[0039] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0040] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0041] Example 1:

[0042] This embodiment provides a method for quantitatively evaluating the flexibility of a power system based on probabilistic optimal power flow, including:

[0043] Obtain historical data of the power system;

[0044] Based on the acquired historical data, a joint probability density function model including multiple types of renewable energy was established;

[0045] A flexibility index is constructed, which includes a joint probability density function model of inadequate flexibility probability, expected flexibility margin, and expected flexibility inadequacy. In the flexibility index, expected flexibility margin is regarded as a bonus item, and expected flexibility inadequacy and inadequate flexibility probability are regarded as deduction items.

[0046] A probabilistic optimal power flow model is used to solve for the insufficiency probability, flexibility margin expectation, and insufficiency expectation in the flexibility index; wherein, the objective function of the probabilistic optimal power flow model is cost optimization.

[0047] The power system is quantitatively evaluated based on the solved insufficiency probability, flexibility margin expectation, and flexibility insufficiency expectation.

[0048] In this embodiment, the process is implemented in two parts. The first part involves solving the model for renewable energy sources such as wind and solar power. This includes: obtaining a mathematical model based on historical output data of renewable energy sources such as wind and solar power and loads, considering the spatiotemporal correlation of their output; establishing a power model based on the obtained historical output data of wind and solar power and loads, first using the k-means clustering algorithm (K-means) to perform scenario clustering analysis, obtaining the output of wind, solar, and loads under typical scenarios, and spatially dividing the output of wind, solar, and loads; constructing a probability model for wind and solar power output, using the kernel density estimation method to process the historical output data of wind and solar power under various typical scenarios, obtaining the probability density function of renewable energy output; based on the obtained kernel density estimation probability model, considering the temporal correlation, using the copula function to probabilistically model the output of wind, solar, and loads, solving the joint probability density function of wind, solar, and load outputs, and solving the T-value based on the fluctuation joint probability density function and Bayes' theorem. k Exert effort at all times, determine T k+1 Efforts are generated at all times, i.e., the conditional probability is solved. Based on the obtained conditional probability formula, sampling is performed to generate time series sequences until the operational requirements are met. The second part is the power system flexibility assessment and analysis based on probabilistic optimal power flow, including: considering that probabilistic indicators reflect the trend of power system flexibility changes, and deterministic indicators reflect the flexibility resource capacity of the current power system operation, considering the expected system flexibility margin, expected deficit, and probability of insufficiency, taking into account the economics of system operation, and considering the operating costs, the expected increase in input costs will improve system flexibility, combining probabilistic and deterministic indicators to determine a flexibility indicator that can reflect the trend of flexibility changes while assessing the current operating status; based on the current operating status of the new power system, the system's flexibility resources are calculated, including upward and downward adjustments of flexibility resources, the expected value of the expected cost acceptable to the manufacturer is determined, an economic penalty factor is set, a probabilistic optimal power flow (P-OPF) model is established, and the Monte Carlo simulation method is used to solve for the expected flexibility margin, expected deficit, and probability of deficit, and to perform index calculations.

[0049] The specific implementation steps of this embodiment are as follows:

[0050] S1. The K-means algorithm is used to divide the historical data into scenarios. Based on the historical data under various scenarios, the kernel density estimation method is used to model the probability models of wind power, photovoltaic and load. Using the Copula function and combined with Bayes' theorem, time series are generated by sampling according to the obtained probability formula.

[0051] S2. Based on the current operating status of the new power system, determine the expected value of the expected cost that the manufacturer can accept, set the economic penalty factor, analyze the P-OPF model, and use the Monte Carlo simulation method to solve for the expected flexibility margin, expected deficit, and probability of deficit, and conduct a flexibility assessment.

[0052] S1.1, the classification of wind power, solar power, and load scenarios includes:

[0053] S1.1.1. Divide typical operating scenarios and use the K-means algorithm to distinguish scenarios at each time step. First, select k points, μ1, μ2, ... μ k As cluster centers, the sample attributes mainly include wind power output and solar power output. Let the function arg j For sample X (i) To X (j) The distance is calculated using the following formula:

[0054]

[0055] Where d is the Minkowski distance; q is 2; i is the sample index i; j is the sample index j; x ik x is the value of the i-th attribute of the sample in the k-th class; jk is the j-th attribute value of the sample in the k-th class; k is the initial number of cluster centers.

[0056] Then for sample X (j) Perform clustering calculations and assign cluster centers μ according to equation (2). j Perform iterations:

[0057] c (j) =arg j min|x (i) -μ j | 2 (2)

[0058]

[0059] in, The features of cluster center j are sums; c is the number of cluster center j particles; (j) Let μ be the sum of the Ming-style distances to the cluster centers. j The calculated new cluster centers.

[0060] Perform iterative calculations until J (c,μ) Convergence means that each cluster center no longer moves;

[0061]

[0062] Among them, J (c,μ) The sum of Ming-style distances between the cluster centers of all samples; m is the number of samples; u c(i) Let i be the cluster center corresponding to sample i.

[0063] The relationship between J-value transformation and iteration number is shown in the graph below. Figure 1 As shown; the cluster centers were obtained after the above calculations; the clustering results are shown in Tables 1, 2, and 3:

[0064] Table 1 Clustering of Historical Load Data

[0065]

[0066]

[0067] Table 2 Clustering of Historical Wind Data

[0068]

[0069]

[0070] Table 3 Clustering of Historical Photovoltaic Data

[0071]

[0072]

[0073] S1.1.2. Construction of wind and solar power probability models: Based on the principles of wind and solar power generation, and according to historical data, the upper limits of local wind and solar power output are determined. Considering the principles of wind power generation and processing historical data, the wind power output can be fitted using a Weibull distribution (Weibull function).

[0074]

[0075] Where: x is the wind speed, m / s; λ is the proportional parameter; k is the shape parameter.

[0076] The mean is:

[0077]

[0078] The variance is:

[0079]

[0080] Where Γ is the gamma function.

[0081] The photovoltaic output can be fitted using a beta distribution:

[0082]

[0083] Where: P sun τ represents the photovoltaic output; α and β are shape parameters; τ represents solar radiation intensity; P represents the output of the photovoltaic system. max To maximize the contribution of photovoltaic theory.

[0084] For load modeling, if the load fluctuation values ​​follow a normal distribution, then a normal distribution can be used for modeling.

[0085]

[0086] Where, x l For load demand; σ l and μ l These are the mean and standard deviation, respectively.

[0087] Based on historical data, the above formulas were used to fit and process the data, resulting in probability density models for wind power, solar power, and load.

[0088] S1.2 Determination of joint probability density:

[0089] In this embodiment, a joint probability density model can be established using the Copula function, assuming variables [x1, x2, ..., x...]. n The joint distribution function is H(·), and the marginal distributions are F1, F2, ..., Fn. n Then there exists a Copula function C(·) that satisfies:

[0090] H(x1,x2,...,x n )=C(F1(x1),F2(x2),...,F n (x n (10)

[0091] If F1, F2, ..., F n If the sequence is continuous, then C(·) is uniquely determined, and H(x1,x2,...,x) is determined by equation (10). n ) is a marginal distribution F1, F2, ..., F n The n-ary joint distribution function.

[0092] Taking the partial derivatives of both sides of equation (10), we can obtain the joint probability density function of the random vectors:

[0093]

[0094] Where C(·) is the Copula probability density function; f i (x i ) is x i The probability density function.

[0095] Here, a binary Copula function is used, defined as follows: the domain of C(u,v) is [0,1]*[0,1]; C(u,v) has a zero base and is two-dimensionally increasing; for any u,v∈[0,1], it satisfies: C(u,1)=u, C(1,v)=v.

[0096] S1.2.1 Selection of Copula function:

[0097] In this embodiment, let (x) i ,y i (i = 1, 2, ..., n) are samples taken from the two-dimensional population (X, Y), that is, the wind power, photovoltaic and load output values ​​at two adjacent moments in a typical scenario.

[0098] Let C(u) i ,v i Let be the Copula joint distribution function. The squared Euclidean distance between the Copula joint distribution function and the empirical Copula function is:

[0099]

[0100] The Euclidean distance between the candidate Copula joint distribution function and the empirical Copula function is calculated according to formula (12). The smaller the Euclidean distance, the better the fitting effect.

[0101] In this embodiment, Kendall's coefficient and Spearman's rank correlation coefficient are used as correlation evaluation indicators. Kendall's coefficient and Spearman's rank correlation coefficient of the simulated data and the original data generated by Copula function sampling are calculated respectively. The closer the correlation coefficients are, the better the fitting effect of Copula function.

[0102] Kendall's correlation coefficient is defined as:

[0103] ρ τ =P[(V1-V2)(U1-U2)>0]-P[(V1-V2)(U1-U2)<0] (13)

[0104] The Spearman rank correlation coefficient is defined as:

[0105] ρ s=3{P[(V1-V2)(U1-U3)>0-(V1-V2)(U1-U3)<0]} (14)

[0106] The tail correlation coefficient is:

[0107] λ up =limP[U>G -1 (u)|V>F -1 (u)] (15)

[0108] λ lo =limP[U <G -1 (u)|V <F -1 (u)] (16)

[0109] Where (V1,U1), (V2,U2), and (V3,U3) are independent random vectors that follow the same distribution; P(·) is its probability density function; G -1 (u) represents the marginal distribution of sample U; F -1 (u) represents the marginal distribution of sample V.

[0110] The analysis results show that the normal Copula function has the best fitting effect.

[0111]

[0112] Where u is the distribution value of sample U; v is the distribution value of sample V; and ρ is the Pearson correlation coefficient.

[0113] S1.2.2 First, the historical data is normalized, and the probability density functions of wind and solar power output are fitted using Copula to obtain the joint probability density of output at adjacent times. Taking load and wind power output at times 0 and 1, and solar power output at times 10 and 11 as examples, as follows... Figure 2 , Figure 3 and Figure 4 As shown.

[0114] S1.3 According to Bayes' theorem:

[0115]

[0116] The probability density function of the power output at the next moment is obtained when the intermittent power output at the current moment is determined. Random sampling is then performed based on this probability density function to obtain the generated time series, as shown in the appendix. Figure 5 As shown.

[0117] S2.1 Flexible Resource Model Construction:

[0118] S2.1.1 Thermal power units: The flexibility resource capacity of thermal power units is related to their ramp-up capability and current operating status.

[0119] F G,+ =min{P G,max -P G,i ,Δt×R Ui} (19)

[0120] F G,- =min{P G,i -P G,min ,Δt×R Di} (20)

[0121] Among them, P G,max P G,min and P G,i These are the unit's maximum output limit, minimum output limit, and current output; F G,+ and F G,- The respective adjustments are upward and downward adjustment of flexibility resource capacity for thermal power units; R Ui ,R Di Δt represents the unit's upward and downward ramp rates; Δt represents the ramp duration.

[0122] S2.1.2 Hydropower units participate in the flexibility regulation within the system. Assuming that no water wastage occurs during the regulation process, the flexibility resource capacity is related to its climbing ability and water resource capacity. The flexibility resources it provides are as shown in equations (19) and (20).

[0123] S2.1.3 Energy storage devices. Energy storage devices are divided into chemical energy storage and physical energy storage. This paper does not consider the operation process of energy storage devices, but only the device capacity and power output.

[0124] The flexibility resource capacity of an energy storage device is related to its current charge capacity and charging / discharging power. Energy storage devices operate in three states: charging, discharging, and neither charging nor discharging. Assuming constant charging / discharging power and neglecting self-discharge losses, the flexibility resource capacity is as follows:

[0125] During discharge, the up-and-down adjustment flexibility resource capacity of the energy storage device is:

[0126]

[0127] Among them, F storage,Ess,+ F storage,Ess,- These represent adjusting the capacity of flexible resources upwards and downwards during discharge. Q represents the maximum and minimum discharge power. s,t Let t be the electrical energy capacity within the device;

[0128] In energy storage mode, the uplink and downlink flexibility resource capacity of the energy storage device is:

[0129]

[0130] Among them, F charge,+ F charge,- The adjustments are respectively: increasing or decreasing the capacity of flexible resources under energy storage conditions; Q represents the maximum and minimum charging power. max η represents the maximum energy storage capacity; η represents the charging efficiency.

[0131] In non-charging and non-discharging states, the up-and-down flexibility resource capacity of the energy storage device is:

[0132]

[0133] Among them, F c,+ Increase flexibility resource capacity in non-charging / non-discharging states; F c,- Reduce the capacity of flexible resources in a non-charged / non-released state.

[0134] The energy storage device set in this paper is a pumped storage device, and the flexible resource capacity is shown in equations (21) to (23).

[0135] S2.1.4 Controllable load, the flexible resource capacity provided by the controllable load is:

[0136] F L,+ =min{P L,max,protocol -P L,i ,ΔP LU} (twenty four)

[0137] F L,- =min{P L,i -P L,min,protocol ,ΔP LD} (25)

[0138] Among them, F L,+ ,F L,- To adjust the capacity of flexible resources upwards or downwards; P L,i P represents the current load size. L,max,protocol P represents the maximum power of the contracted load. L,min,protocol The minimum load power stipulated in the agreement; ΔP LU ,ΔP LD Power limiting for upward and downward load changes.

[0139] Increase the total flexibility resource capacity by:

[0140] F + =∑F G,+ +F storage,Ess,+ / F charge,+ / F + +F L,+ (26)

[0141] The total flexibility resource capacity is reduced to:

[0142] F - =∑F G,+ +F storage,Ess,- / F charge,- / F - +F L,- (27)

[0143] Among them, F + To increase the total flexibility resources; F - To reduce the total amount of flexibility resources.

[0144] S2.2 Construction of Flexibility Indicators:

[0145] Deterministic indicators include basic unit parameters and operational flexibility margin indicators, while probabilistic indicators include the probability of insufficient flexibility, power system flexibility deficit, and power system flexibility measurement indicators.

[0146] The probability of insufficient flexibility in the commonly used power grid adjustment is:

[0147]

[0148] in, D represents the probability of insufficient flexibility in adjusting within time period T; F represents the flexibility requirement; + This is the sum of the increased flexibility capacity for all flexibility resources.

[0149] The probability of insufficient flexibility in the commonly used power grid downsizing is:

[0150]

[0151] in, D represents the probability of insufficient flexibility in adjusting within time period T; F represents the flexibility requirement; - This is the sum of the reduced flexibility capacity across all flexibility resources.

[0152] The expected grid flexibility margin is:

[0153]

[0154] ΔF flex,j =F j -D j (31)

[0155] Among them, E flex Let F be the expected internal flexibility margin under the j-hill event; j D j For the flexibility resources and requirements of the jth climbing event; ΔF flex,i For flexibility margin.

[0156] Insufficient grid flexibility expectations:

[0157]

[0158] ΔF lack,i ={|ΔF flex,i ||ΔF flex,i <0} (33)

[0159] Among them, E lack Let be the expected value of insufficient flexibility under climbing event j; n be the number of times flexibility resources are insufficient in climbing events; ΔF lack,i This represents the amount of power deficit during a single operation.

[0160] Based on historical data and the operation and maintenance costs of various power plants and substations in the power system, flexibility indicators are constructed:

[0161] The flexibility index is adjusted upwards as follows:

[0162]

[0163] The flexibility index has been lowered to:

[0164]

[0165]

[0166] Among them, C i,c,start C i,c,stop and C i,c,run These represent the start-up and shutdown costs and operation and maintenance costs of thermal power plants at each node, respectively, $; C i,w,start C i,w,stop and C i,w,run The costs for starting up and shutting down the hydropower plants at each node, and the operating and maintenance costs, are respectively $; C VRE Setting up costs for renewable energy units, $; C i,w,store and C i,store These represent the commissioning cost of the pumped-storage hydroelectric power system and the cost of the energy storage system, respectively, in dollars; ∑F represents the total available flexibility resources; EC sum and C sum Let $ and w represent the manufacturer's expected and actual production costs, respectively. + ,w - These represent the upward and downward adjustments to the economic penalty factors, respectively; λ i For load shedding and wind / solar curtailment penalty factors; P L,loss and P VRE,loss These are respectively the load shedding and the amount of wind and solar power curtailment; k i It is 0 or 1. It is 1 when the unit starts or stops, and 0 otherwise.

[0167] This indicator transforms a probabilistic problem into a deterministic one, and compared to traditional indicators, it considers the system's economic efficiency while reflecting the system's expected capacity.

[0168] S2.3 System Flexibility Assessment in New Power System Scenarios

[0169] In this embodiment, the novel power system scenario is a power plant in a northern region during summer, with time scales of 15 min, 30 min, and 1 h. A thousand simulations were performed using the Monte Carlo method, and the time series was generated as follows: Figure 1 The simulation results shown are wind and solar power output curves generated based on the joint probability density model. Figure 6 , Figure 7 and Figure 8 As shown.

[0170] The wind and solar power output forecast curves reflect the volatility, randomness, uncontrollability, and anti-peak-shaving characteristics of new energy output.

[0171] Under the condition of fixed system load and unit output, the system operation is analyzed using the P-OPF model, and the objective function is:

[0172]

[0173] Among them, F W,i, F S,j The wind and solar curtailment resources of each node, P L,z Let λ be the load shedding power of each node. i ,λ j ,λ z These are the weighting factors for wind curtailment, solar curtailment, and load shedding, respectively.

[0174] The constraints are as follows: power flow constraints:

[0175] At each node, the system power should meet the following requirements:

[0176] ∑P G,i +∑P storage -∑P L,i =0 (38)

[0177] Throughout the entire power system, satisfying

[0178] ∑P G,i +∑P storage -∑P L,i -∑ΔP L =0 (39)

[0179] Where, ΔP L For network loss in the system; P G,i P represents the power generation of node i; storageP represents the system's energy storage capacity. L,i P represents the load at node i; G For power generation capacity; ΔP L This is due to network loss.

[0180] Unit constraints, which should include the voltage P of each unit. Gi Active power Q G Reactive power V G and cost C sum,i constraint.

[0181] P Gmin <P G,i <P Gmax

[0182] Q Gmin G Gmax

[0183] V Gmin <V G <V Gmax

[0184]

[0185] Among them, c i2 c is the quadratic coefficient of economic cost; i1 c is the first-order coefficient of economic cost; c0 is the constant term of economic cost; k i A value of 0 or 1 determines whether the device starts or stops; C start For unit start-up costs; C stop Costs associated with unit shutdown.

[0186] Transmission line constraints, including the maximum allowable current constraint I for the transmission line. ij Emergency power transmission capacity P during line faults short Normal operation is based on the conveying capacity P. normal .

[0187] I ij ijmax (41)

[0188] P short <P shortmax (42)

[0189] P normal <P normalmax (43)

[0190] Conventional unit flexibility resources are constrained; flexibility is increased.

[0191] 0≤P G,flex,+ ≤P G,max -P​​​G,i (44)

[0192] 0≤P G,flex,+ ≤Δt×R Ui (45)

[0193] Where Δt is the time scale; R Ui This refers to the unit's ramp-up rate.

[0194] Reduce flexibility

[0195] 0≤P G,flex,- ≤P G,i -P G,min (46)

[0196] 0≤P G,flex,- ≤Δt×R Di (47)

[0197] Among them, R Di This refers to the unit's downhill gradient rate.

[0198] Controllable load constraints, the load constraints satisfied at the nodes are:

[0199] P L,min,protocol,i ≤P L,i ≤P L,max,protocol (48)

[0200] Renewable energy constraints, this paper focuses on wind and solar power, and the output must meet the following requirements:

[0201]

[0202]

[0203] Where ρ is air density; A is the cross-sectional area of ​​the fan; v is wind speed; v r To cut off the wind speed; P wind_r P represents the maximum wind power. sun_r τ is the maximum photovoltaic power; η is the solar radiation intensity; sun For efficiency; τ r This is the rated solar radiation intensity.

[0204] Energy storage constraints should include discharge state, charging state, and non-charge / non-discharge constraints.

[0205] The constraints under discharge conditions are:

[0206]

[0207]

[0208] Wherein, ΔT discharge time is; Q s,tThis represents the current capacity of the energy storage device.

[0209] The constraints during the charging state are:

[0210]

[0211]

[0212] Where ΔT is the charging time and η is the charging efficiency.

[0213] The non-charged and non-discharged operating state will transition to either a charging or discharging state when a ramp-up event occurs.

[0214] The optimal power flow solution is obtained using the in-point method based on the tracking center trajectory. For ease of discussion, the optimal power flow model is simplified to the following form:

[0215] minf(x)

[0216] stg(x)=0 (55)

[0217] a≤h(x)≤b (56)

[0218] Where f(x) is the objective function, corresponding to equation (37) above; g(x) is the equality constraint, corresponding to equations (38) and (39) above; and h(x) is the inequality constraint, corresponding to equations (40) to (54) above.

[0219] By setting slack variables that satisfy μ>0 and p>0, the inequality constraints are transformed into equality constraints:

[0220] h(x) + u = b (57)

[0221] h(x)-l=a (58)

[0222] Among them, u=[u1,u2,...u n ] T ; l = [l1, l2, ... l n ] T b and a are constraint boundary values.

[0223] Introducing a perturbation factor, k>0, the objective function is rewritten as:

[0224]

[0225] Among them, l i For slack variables; u i is a slack variable; k is a constant.

[0226] The constraints are:

[0227] g(x) = 0

[0228] h(x) + u = b

[0229] h(x)-l=a

[0230] The problem is transformed into a problem with constraints containing equality, and then solved using the Lagrange multiplier method.

[0231] The Lagrange function is

[0232]

[0233] Where y = [y1, y2, ..., y n1 ], m = [m1, m2, ... m n2 ];s=[s1,s2,...s n3 All are Lagrange multipliers. The complementary gap and the corrected equations are obtained by applying the Lagrange method:

[0234]

[0235]

[0236]

[0237]

[0238]

[0239]

[0240]

[0241]

[0242]

[0243]

[0244] Where σ∈(0,1) is the central parameter; I is the identity matrix; r is the dimension of L; L -1 Let L be the inverse matrix of L; L is diag(l1,...,l) r M is diag(m1,m2,...,m) r ); Δm is m r The amount of correction; -(MΔl+LΔm); Let h(x) be the gradient transpose; Δl is l r The correction amount; L m for U⁻¹ is the inverse matrix of U; S is diag(s₁, s₂, ..., sₙ). r ); Δs is s r The amount of correction; It is -(SΔu+UΔs); Δu is u r The correction amount; L s H is a matrix variable; H' is a matrix variable; Let g(x) be the gradient of g(x); Δx be the correction factor for x; L x L is a matrix variable; Δy is the correction factor for y; y For matrix variables.

[0245] The problem is solved using Monte Carlo simulation, and the solution process is as follows: Figure 9 As shown.

[0246] Taking the 12-hour time period as an example, the results of the flexibility index calculation are shown in Table 4:

[0247] Table 4 Indicator Calculation

[0248]

[0249] Calculation results show that under this new power system scenario, the 12-hour up-adjustment flexibility is sufficient, while the down-adjustment flexibility is insufficient when the time scale is short. When the time scale is small, the wind and solar power output fluctuates greatly, the system's ability to absorb new energy sources is limited, and the phenomenon of wind and solar curtailment is prone to occur.

[0250] In this embodiment, the types of flexible resources existing in a power system with a high proportion of renewable energy are first identified, and their capacity is mathematically modeled. Mathematical models are then created for the system's wind, solar, and load models. Historical data is divided into scenarios using the K-means method, and parameter fitting is performed on the historical data for each scenario to obtain probability density functions. Copula functions are used to model the joint probability function of wind, solar, and load output, resulting in a time-dependent joint probability density distribution. Based on the joint probability density function, Bayes' theorem is used to solve for the probability density function of the output at the next time step when the output at the previous time step is determined. Based on this probability density function, sampling is performed to determine the time series sequence. A quantitative method for evaluating the flexibility of the new power system is determined, considering the expected system flexibility margin, expected deficit, and probability of insufficiency, taking into account the system's operational economy and operating costs. The expected increase in input costs will improve system flexibility. Margin is considered a bonus, while expected deficit and probability are considered deductions, resulting in a quantitative evaluation index for flexibility that can evaluate the system's flexibility across multiple time scales. Probabilistic optimal power flow is used to evaluate the system's flexibility, and Monte Carlo simulation is employed to solve the problem and perform system evaluation calculations.

[0251] Example 2:

[0252] This embodiment provides a power system flexibility quantification assessment system based on probabilistic optimal power flow, including:

[0253] The data acquisition module is configured to acquire historical data of the power system.

[0254] The joint probability density function model building module is configured to: build a joint probability density function model including multiple types of renewable energy based on the acquired historical data;

[0255] The flexibility index establishment module is configured to: construct a flexibility index that includes a joint probability density function model of the insufficiency probability, the flexibility margin expectation, and the flexibility insufficiency expectation; in the flexibility index, the flexibility margin expectation is regarded as a bonus item, and the flexibility insufficiency expectation and the flexibility insufficiency probability are regarded as deduction items.

[0256] The solution module is configured to use a probabilistic optimal power flow model to solve for the insufficiency probability, flexibility margin expectation, and insufficiency expectation in the flexibility index; wherein, the probabilistic optimal power flow model uses cost optimization as the objective function.

[0257] The evaluation module is configured to perform a quantitative evaluation of the power system based on the solved insufficiency probability, flexibility margin expectation, and insufficiency expectation.

[0258] The operating method of the system is the same as that of the power system flexibility quantification evaluation method based on probabilistic optimal power flow in Example 1, and will not be repeated here.

[0259] Example 3:

[0260] This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the power system flexibility quantification assessment method based on probabilistic optimal power flow described in Embodiment 1.

[0261] Example 4:

[0262] This embodiment provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps of the power system flexibility quantification assessment method based on probabilistic optimal power flow described in Embodiment 1.

[0263] The above description is merely a preferred embodiment of this practice and is not intended to limit the scope of this practice. Various modifications and variations can be made to this practice by those skilled in the art. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of this practice should be included within the protection scope of this practice.

Claims

1. A method for quantitatively evaluating the flexibility of a power system based on probabilistic optimal power flow, characterized in that, include: Obtain historical data of the power system; Based on the acquired historical data, a joint probability density function model including multiple types of renewable energy was established; A flexibility index is constructed, which includes a joint probability density function model of the insufficiency probability, the flexibility margin expectation, and the flexibility insufficiency expectation. In the flexibility index, the flexibility margin expectation is regarded as a bonus item, and the flexibility insufficiency expectation and the flexibility insufficiency probability are regarded as deduction items. Based on historical data and according to the operation and maintenance costs of various power plants and substations in the power system, a flexibility index is constructed, which includes both upward and downward adjustment of the flexibility index. A probabilistic optimal power flow model is employed to solve for the insufficiency probability, expected flexibility margin, and expected insufficiency in the flexibility indices. This model includes power flow constraints, generator constraints, transmission line constraints, generator flexibility resource constraints, controllable load constraints, renewable energy constraints, and energy storage constraints. The objective function of this model is cost optimization. Under the condition of determined system load and generator output, the system operation is analyzed using a P-OPF model, with the following objective function: in, The actual production cost that the manufacturer can accept. These represent the wind and solar curtailment resources at each node. For the load shedding power of each node, These are the weighting factors for wind curtailment, solar curtailment, and load shedding, respectively. The power system is quantitatively evaluated based on the solved insufficiency probability, flexibility margin expectation, and flexibility insufficiency expectation.

2. The power system flexibility quantitative assessment method based on probabilistic optimal power flow as described in claim 1, characterized in that, Historical data is divided into scenarios, and the kernel density estimation method is used to model the probability models of wind power, photovoltaic power, and load based on historical data under various scenarios. The joint probability function model of wind power, photovoltaic power, and load output is modeled using the connection function to obtain the joint probability density function model of time correlation. Combining Bayes' theorem, time series are generated by sampling according to the joint probability density function model.

3. The power system flexibility quantitative assessment method based on probabilistic optimal power flow as described in claim 2, characterized in that, Wind power output was fitted using Weibull distribution, photovoltaic power output was fitted using Beta distribution, and load was modeled using normal distribution.

4. The power system flexibility quantitative assessment method based on probabilistic optimal power flow as described in claim 1, characterized in that, The bonus item in the flexibility index is the expected flexibility margin, while the deduction items include the product of the expected insufficient flexibility and the probability of insufficient activity, the amount of load shedding, the amount of wind and solar curtailment, and the product of the economic penalty factor and cost.

5. The power system flexibility quantitative evaluation method based on probabilistic optimal power flow as described in claim 4, characterized in that, Costs include start-up and shutdown costs of thermal power plants and hydropower stations at each node, operation and maintenance costs, renewable energy unit setup costs, pumped storage unit activation costs, and energy storage device costs.

6. A power system flexibility quantification evaluation system based on probabilistic optimal power flow, characterized in that, include: The data acquisition module is configured to acquire historical data of the power system. The joint probability density function model building module is configured to: build a joint probability density function model including multiple types of renewable energy based on the acquired historical data; The flexibility index establishment module is configured to: construct a flexibility index that includes a joint probability density function model of the insufficiency probability, the flexibility margin expectation, and the flexibility insufficiency expectation; in the flexibility index, the flexibility margin expectation is regarded as a bonus item, and the flexibility insufficiency expectation and the flexibility insufficiency probability are regarded as deduction items; based on historical data and according to the operation and maintenance costs of various power plants and substations in the power system, a flexibility index that includes both upward and downward adjustment of the flexibility index is constructed. The solution module is configured to: employ a probabilistic optimal power flow model to solve for the insufficiency probability, flexibility margin expectation, and insufficiency expectation in the flexibility indices; the probabilistic optimal power flow model includes power flow constraints, unit constraints, transmission line constraints, unit flexibility resource constraints, controllable load constraints, renewable energy constraints, and energy storage constraints; wherein, the objective function of the probabilistic optimal power flow model is cost optimization; under the condition of determined system load and unit output, the system operation analysis is performed using the P-OPF model, and the operational objective function is... in, The actual production cost that the manufacturer can accept. These represent the wind and solar curtailment resources at each node. For the load shedding power of each node, These are the weighting factors for wind curtailment, solar curtailment, and load shedding, respectively. The evaluation module is configured to perform a quantitative evaluation of the power system based on the solved insufficiency probability, flexibility margin expectation, and insufficiency expectation.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by the processor, the program implements the steps of the power system flexibility quantification assessment method based on probabilistic optimal power flow as described in any one of claims 1-5.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the power system flexibility quantification assessment method based on probabilistic optimal power flow as described in any one of claims 1-5.

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