A method for voltage regulation in distribution network sections considering the coupling of multidimensional meteorological factors

Abstract

This invention relates to the field of power system technology, specifically disclosing a distribution network interval voltage regulation method considering the coupling of multiple meteorological factors. The method includes: S1, introducing uncertainty into meteorological factors through an improved nonparametric kernel density estimation method involving the coupling of multiple meteorological elements, and estimating the meteorological factors using a joint probability density function to generate confidence intervals for the meteorological factors; S2, calculating the interval between photovoltaic power generation and load demand based on the confidence intervals of the meteorological factors using an affine algorithm based on forced boundary and spatial approximation; S3, constructing a distribution network interval voltage regulation optimization model with the objective of minimizing total voltage regulation costs, inputting the photovoltaic power generation interval and the load demand interval into the distribution network interval voltage regulation optimization model, and outputting an optimized voltage regulation scheme. The advantage of this invention is that it solves the uncertainty caused by the correlation between multiple meteorological factors, constructs a voltage regulation optimization model to obtain an accurate voltage regulation scheme, and effectively reduces voltage regulation costs.

Description

Technical Field

[0001] This invention relates to the field of power system technology, and in particular to a method for voltage regulation in distribution network sections that takes into account the coupling of multidimensional meteorological factors. Background Technology

[0002] In recent years, distributed renewable energy has experienced irreversible development due to its advantages in reducing electricity costs and promoting self-consumption. However, with the widespread adoption of these distributed renewable energy sources, active distribution networks (ADNs) face numerous technical challenges, with voltage overruns playing a dominant role. Voltage overruns are primarily caused by the intermittency / fluctuation and unschedulable nature of renewable energy, the increasing demand from nodes, and inappropriate power source location. Voltage overruns caused by these factors can result in significant economic losses, especially for voltage-sensitive users. In modern distribution networks with widespread renewable energy adoption, voltage regulation is one of the most pressing issues to be addressed.

[0003] Currently, methods for characterizing voltage regulation uncertainty can be broadly categorized into four types: scenario-based methods, probability-based methods, fuzzy logic methods, and interval value methods. Scenario-based methods set up multiple scenarios, such as AC loads or photovoltaic power generation with different penetration levels, to study changes in voltage regulation strategies. However, when processing large amounts of historical data, scenario-based methods inherently suffer from high computational costs and inaccuracies in rare or extreme scenarios. Probability-based methods can also be used, describing the uncertainty of load demand and renewable energy resources through typical probability variables or probability density functions, and deriving voltage regulation schemes based on this using probabilistic power flow models. However, these probability-based methods are usually based on certain probability distribution assumptions, which may deviate from actual results, further leading to inaccuracies. Uncertainty in fuzzy logic methods is represented by membership degrees and fuzzy membership functions. Existing technology, such as Power distribution network design considering the distributed generations and differential and dynamic pricing, uses fuzzy triangular membership functions to describe customer demand consumption and further proposes voltage control schemes. Existing technology, a new fuzzy adaptive particle swarm optimization for non-smootheconomic dispatch, utilizes fuzzification of control parameters to implement a price-based Volt / Var control strategy for ADN. While fuzzy logic methods are effective in the aforementioned prior art, they often involve subjective judgment and personal preferences, failing to provide scientific explanations. Interval-valued methods utilize interval parameters instead of traditional point parameters to handle uncertainty or variability. Existing technology, a transactive retail market mechanism for active distribution networks integrated with large-scale distributed energy resources, defines the uncertain output of distributed energy resources as intervals and proposes voltage regulation intervals for maximizing retailer profits. Existing technology, Estimating DLMP confidence intervals in distribution networks with AC power flow model and uncertain renewable generation, treats renewable energy volatility as polyhedral intervals and, considering node voltage constraints, provides distribution network voltage regulation intervals at different confidence levels.In summary, there are two major drawbacks: First, current methods for representing uncertainty (such as scenario-based, probability-based, and interval-based methods), especially for photovoltaic power generation output and AC load demand, are not precise enough and cannot directly rely on historical data. The correlation between multidimensional meteorological factors plays a key role in generating this uncertainty. Second, information on voltage regulation uncertainty remains limited. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a voltage regulation method for distribution network sections that takes into account the coupling of multi-dimensional meteorological factors.

[0005] The objective of this invention is achieved through the following technical solution: a voltage regulation method for distribution network sections considering the coupling of multidimensional meteorological factors, the method comprising:

[0006] S1. An improved nonparametric kernel density estimation method with coupling of multiple meteorological elements is introduced to introduce the uncertainty of meteorological factors, and the joint probability density function is used for estimation to generate the confidence interval of meteorological factors.

[0007] S2. Using an affine algorithm based on forced boundary and spatial approximation, calculate the interval between photovoltaic power generation and load demand based on the confidence interval of meteorological factors.

[0008] S3. Construct a distribution network interval voltage regulation optimization model with the goal of minimizing total voltage regulation cost. Input the interval of photovoltaic power generation and load demand into the distribution network interval voltage regulation optimization model and output the optimized voltage regulation scheme.

[0009] Specifically, the steps of step S1 are as follows:

[0010] Define X i =[X i,1 ,X i,2, …,X i,m ] T The meteorological vector for the i-th sampling point is represented by m = 3, where m is the number of meteorological factors. The uncertainty of the meteorological factors is represented by a random vector x = [x1, x2, ..., x]. m ] T The joint probability density function is expressed as:

[0011]

[0012] In the formula, n is the number of sampling points; K[·] is the kernel function, used in conjunction with the Gaussian function; H=diag[H i,i ]∈R m×m The bandwidth matrix is ​​a key indicator that determines the accuracy of fitting the sample set.

[0013] The simplified formula is:

[0014]

[0015] In the formula, h j For the j-th th The bandwidth of each meteorological factor; M(x) is a polynomial, denoted as ∑ j ((x i -X i,j ) / h j ) 2 ;

[0016] To improve the smoothness and accuracy of the probability density function, Euclidean distance d is introduced. O (H) and maximum distance d M (H):

[0017]

[0018] In the formula, d i (H)=|f(x i )-f(X i )| represents the geometric distance of the i-th sampling point, based on d in equation (3). O (H) and d M (H), optimize bandwidth H:

[0019] minR(H)=min[d O (H Z )+d M (H Z (4)

[0020] In the formula, R(H) is the fitness function, and H Z This is represented as the optimal bandwidth, used to control the width of the kernel surrounding each meteorological sampling point; the fixed H of the meteorological sampling point is determined by the following formula. Z Does it produce undersmoothing in sparse local areas of observation, or oversmoothing in the opposite case?

[0021]

[0022] In the formula, λ is a constant coefficient; l is a certain sampling interval; L is the number of meteorological sampling points in sampling interval l; d l (H Z )=∑ i∈l d i (H Z ) represents the geometric distance of the sampling interval l; Let H represent the average geometric distance of the sampling interval l. If equation (5) holds, that is, if the sampling interval l has a local adaptive problem, then adjust H. Z for:

[0023]

[0024] In the formula, H l The adjusted bandwidth for the sampling interval l; d l (H z ) mid δ is the median of the geometric distance between sampling points within interval l; δ is the threshold of the kernel function;

[0025] According to formula (6), the final joint probability density function after bandwidth adjustment is expressed as:

[0026]

[0027] Based on formula (7), confidence intervals for meteorological factors are generated using rejection sampling and bootstrap methods.

[0028] Specifically, the photovoltaic power generation range P PV The calculation is as follows:

[0029]

[0030] In the formula, P STC Indicates the maximum power generation output under standard test conditions; G STC / G T Standard / actual illuminance; T τ / K represents the standard test temperature and efficiency coefficient; T C The temperature of the PV module is calculated using the following formula:

[0031]

[0032] In the formula, T a / D wt For temperature and wind speed;

[0033] Range of load demand for:

[0034]

[0035] In the formula, Rated power of the air conditioner; τ on / τ off This indicates the air conditioner's operating / stopping time within a unit operating cycle, at the actual temperature T compared to the set temperature T. set Calculations at 0.5℃ lower / higher:

[0036]

[0037] In the formula, the actual temperature T is determined through the heat exchange process, including the heat between the indoor air and the inner surface of the wall or window:

[0038]

[0039] In the formula, A out / A in / A wi This refers to the surface area of ​​the exterior / interior walls and the area of ​​the windows in the air-conditioned room; K wa / K wi T is the wall / window transfer factor. in / T out T represents the inner surface temperature of the inner / outer wall. a / f represents the outdoor temperature and its influence parameters; C represents the attribute parameter; Q represents the outdoor temperature and its influence parameters. AC For AC cooling capacity; ρ in and c in Where V is air density and heat capacity; T is room volume; τ is indoor air temperature; and τ is AC air conditioner maintenance time. Specifically, step S2 consists of the following steps:

[0040] Propose a mandatory boundary [x] = {x} l ,x u}, where x l / x u Indicates the upper / lower forced boundary, combining the forced boundary [x] and the affine interval. The affine interval can be represented as:

[0041]

[0042] In the formula, This represents the top / top operation;

[0043] To further reduce the conservatism of traditional affine algorithms, arbitrary affine binary operations are represented as:

[0044]

[0045] In the formula, x, y, z are values ​​in spatial geometric coordinates, A, B, C, D are four coefficients, and ε is the noise figure located in [-1, 1].

[0046] Geometrically, formula (14) can be interpreted as two parallel planes in the (x,y,z) space lying in a given domain U. xy In the case of tightly surrounding the surface of z, as shown in the following equation:

[0047]

[0048] In the formula, A and B are the partial derivatives at the central value;

[0049]

[0050] The solution to formula (15) is expressed as:

[0051]

[0052] In the formula, d(x,y) is the distance function. To provide a clear perspective on the spatial approximation techniques in equations (16) and (17), let's take multiplication as an example, where the values ​​of A and B are:

[0053]

[0054] According to equation (18), the specific distance function d(x,y) is calculated as follows:

[0055]

[0056] Specifically, the voltage regulation optimization model for the distribution network section is as follows:

[0057]

[0058] Eq.(24)-(25),(27),(30)-(31),(33)-(37) (39h)

[0059] In the formula, For pressure regulation costs; C OLTC For OLTC voltage regulation costs; C CB For voltage regulation fees of CB circuit breakers; The cost of voltage regulation for photovoltaic systems; For the voltage regulation cost of ES; σ P and σ Q The active / reactive power calculation coefficient; The active power of TS; The reactive power of TS; The active / reactive output factor of node i; To represent the reduction in active power of PV at node i at time t; This refers to the charging / discharging power of the ES. The active power of the air conditioning load at time t is the value of node i. Let be the maximum power output of PV at node i at time t; The optimal power flow loss at time t; This represents the reactive power of PV at node i at time t; Let be the reactive power of CB at node i at time t; for The optimal power flow reactive power loss at time t; The voltage difference at node i before and after voltage regulation; Let be the capacitance of CB at time t at node j; Let be the reactive power of PV at node i at time t; Voltage sensitivity factor injected into the active / reactive power of a node; ΔV1,t This represents the root node voltage during the k-th tap operation of the OLTC. d represents the highest number of taps on an OLTC tap changer; k,t For binary variables; λ i and V err These are the voltage offset coefficient and the maximum voltage offset, respectively; α c,0 / α c,1 / α c,2 These are the polygon approximation coefficients; Power of bus l; BSF lp,l-i / BSF lq,l-i Sensitivity factor for branch power flow when active / reactive power is injected into a node.

[0060] Specifically, the OLTC voltage regulation cost C OLTC for:

[0061] C OLTC =θ OLTC ∑ t δ t (twenty three)

[0062] In the formula, θ OLTC δ represents the unit price of the switching action. t The change in OLTC tap position between adjacent time points:

[0063] tap t+1 -tap t ≤δ t ,tap t -tap t+1 ≤δ t (twenty four)

[0064] In the formula, tap t Let t be the change in tap position of the OLTC tap changer at time t. t With v ro,t The correlation between them is expressed by the following formula:

[0065]

[0066] In the formula, k is the tap position index, and d k,t This is a binary variable representing the on / off state of tap position k at time t; tap up This is the maximum tap position for the OLTC; V uni ΔV is the initial node voltage at the root node. uni This indicates the voltage adjustment range within a one-click step.

[0067] Specifically, the voltage regulation cost C of the CB circuit breaker CB for:

[0068] C CB =C C ∑ i ∑ k λ i,k,t (26)

[0069] In the formula, C C The unit cost of the capacitor switch; i / k is the number of nodes / capacitors, λ i,k,t Calculated by the following formula:

[0070]

[0071] In the formula, c i,k,t For k th The state binary variable represents the i-th... th The state of the k-th capacitor in each CB at time t; a i,k,t =c i,k,t ·c i,k,t+1 It is an auxiliary variable.

[0072] Specifically, the voltage regulation cost of the photovoltaic system. for:

[0073]

[0074] In the formula, α PV for The ratio of total photovoltaic investment cost; ρ P The average active power price; Let tanθ represent the reactive power of the i-th PV at time t; tanθ is... and The ratio; This represents the revenue / cost per unit of active power in a given PV unit. PV active / reactive power loss coefficient; This represents the reduction in active power of the i-th PV at time t. During the VR process, the PV needs to overcome capacity constraints:

[0075]

[0076] In the formula, The power output of photovoltaic televisions.

[0077] Specifically, the voltage regulation cost of the ES for:

[0078]

[0079] In the formula, Y represents the initial investment / maintenance cost of the i-th ES; ES Service life of ES; Let r be the investment recovery factor and the discount rate; This represents the lifecycle of the i-th ES; where, This represents the total lifetime of the ES at 100% depth of discharge (DoD). The total lifecycle of the i-th ES within one year; N0 and k represent the loss period coefficient of the i-th ES at time t; p It is the discharge constant; Let represent the virtual DOD of the i-th ES at time t.

[0080] The present invention has the following advantages:

[0081] Compared with the fixed bandwidth of the traditional NPKDE method, the bandwidth of the proposed NPKDE method can be adjusted within a specific sampling interval, resulting in a 23.65% reduction in the maximum distance, Euclidean distance, and fitness of the proposed NPKDE model, respectively. The comparison shows that the proposed NPKDE can effectively improve the fitting accuracy of multiple coupled meteorological factors. Compared with typical policy prices and traditional DLMP prices, the INVP price proposed in this invention has a more uniform distribution and smaller peak values, reducing voltage regulation costs by 37.04% and 20.96%, respectively. Attached Figure Description

[0082] Figure 1 A diagram illustrating the overshoot problem in traditional affine algorithms;

[0083] Figure 2 The proposed affine algorithm for variable multicells based on forced boundaries;

[0084] Figure 3 The spatial approximation graph of the proposed affine algorithm;

[0085] Figure 4 Wiring diagram for a 152-node distribution network;

[0086] Figure 5 The diagram illustrates the results of photovoltaic power generation and load demand under four methods: MSAA algorithm considering multiple meteorological factors coupling, traditional AA considering multiple meteorological factors coupling, Monte Carlo method considering multiple meteorological factors coupling, and MSAA algorithm not considering multiple meteorological factors coupling.

[0087] Figure 6 A schematic diagram of the output range for each voltage regulator at three confidence levels: 95%, 85%, and 75%. Detailed Implementation

[0088] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only for explaining the invention and are not intended to limit the invention; that is, the described embodiments are merely some embodiments of the invention, and not all embodiments. The components of the embodiments of the invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0089] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0090] It should be noted that relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0091] The present invention will be further described below with reference to the accompanying drawings, but the scope of protection of the present invention is not limited to the following description. Figures 1 to 6 As shown, a voltage regulation method for distribution network sections considering the coupling of multi-dimensional meteorological factors is proposed. This method includes:

[0092] S1. An improved nonparametric kernel density estimation method with coupling of multiple meteorological elements is introduced to introduce the uncertainty of meteorological factors, and the joint probability density function is used for estimation to generate the confidence interval of meteorological factors.

[0093] Define X i =[X i,1 ,X i,2, …,X i,m ] T The meteorological vector for the i-th sampling point is represented by m = 3, where m is the number of meteorological factors. The uncertainty of the meteorological factors is represented by a random vector x = [x1, x2, ..., x]. m ] T The joint probability density function is expressed as:

[0094]

[0095] In the formula, n is the number of sampling points; K[·] is the kernel function, used in conjunction with the Gaussian function; H=diag[H i,i ]∈R m×m The bandwidth matrix is ​​a key indicator that determines the accuracy of fitting the sample set.

[0096] The simplified formula is:

[0097]

[0098] In the formula, h j For the j-th th The bandwidth of each meteorological factor; M(x) is a polynomial, denoted as ∑ j ((x i -X i,j ) / h j ) 2 ;

[0099] To improve the smoothness and accuracy of the probability density function, Euclidean distance d is introduced. O (H) and maximum distance d M (H):

[0100]

[0101] In the formula, d i (H)=|f(x i )-f(X i )| represents the geometric distance of the i-th sampling point, based on d in equation (3). O (H) and d M (H), optimize bandwidth H:

[0102] minR(H)=min[d O (H Z )+d M (H Z (4)

[0103] In the formula, R(H) is the fitness function, and H in formula (4) is... Z This is represented as the optimal bandwidth, controlling the width of the kernel around each meteorological sampling point; however, the fixed H for all meteorological sampling points... Z This can lead to undersmoothing in sparsely observed local regions or oversmoothing in the opposite case, a problem known as local adaptability. To determine if this problem exists, this invention proposes a criterion:

[0104]

[0105] In the formula, λ is a constant coefficient, l is a certain sampling interval; L is the number of meteorological sampling points in the sampling interval l; d l (H Z )=∑ i∈l d i (H Z ) represents the geometric distance of the sampling interval l; Let H represent the average geometric distance of the sampling interval l. If equation (5) holds, that is, if the sampling interval l has a local adaptive problem, then adjust H. Z for:

[0106]

[0107] In the formula, H l The adjusted bandwidth for the sampling interval l; d l (H z ) mid δ is the median of the geometric distance between sampling points within interval l; δ is the threshold of the kernel function;

[0108] According to formula (6), the final joint probability density function after bandwidth adjustment is expressed as:

[0109]

[0110] Based on formula (7), the confidence intervals of meteorological factors are generated using the rejection sampling method and the bootstrap method. The confidence intervals of meteorological factors are generated by the bootstrap sampling method.

[0111] Specifically, the photovoltaic power generation range P PV The calculation is as follows:

[0112]

[0113] In the formula, P STC Indicates the maximum power generation output under standard test conditions; G STC / G T Standard / actual illuminance; T τ / K represents the standard test temperature and efficiency coefficient; T C The temperature of the PV module is calculated using the following formula:

[0114]

[0115] In the formula, T a / D wt For temperature and wind speed; from equations (8) and (9), it can be seen that the photovoltaic power generation range P is jointly determined by light intensity, temperature and wind speed. PV This explains the basic principle that the coupling of three meteorological factors needs to be considered;

[0116] Range of load demand for:

[0117]

[0118] In the formula, Rated power of the air conditioner; τ on / τ off This indicates the air conditioner's operating / stopping time within a unit operating cycle, at the actual temperature T compared to the set temperature T. set Calculations at 0.5℃ lower / higher:

[0119]

[0120] In the formula, the actual temperature T is determined through the heat exchange process, including the heat between the indoor air and the inner surface of the wall or window:

[0121]

[0122] In the formula, A out / A in / A wi This refers to the surface area of ​​the exterior / interior walls and the area of ​​the windows in the air-conditioned room; K wa / K wi T is the wall / window transfer factor. in / T out T represents the inner surface temperature of the inner / outer wall. a / f represents the outdoor temperature and its influence parameters; C represents the attribute parameter; Q represents the outdoor temperature and its influence parameters. AC For AC cooling capacity; ρ in and c in S1 represents air density and heat capacity; V represents room volume; T represents indoor air temperature; τ represents AC air conditioner maintenance time; S2, calculate the range between photovoltaic power generation and load demand using an affine algorithm based on forced boundary and spatial approximation;

[0123] The traditional affine interval form is represented by a first-order polynomial, i.e. With x0 and ε i Using center values ​​and noise symbols, affine interval forms of addition, subtraction, multiplication, division, and exponential functions were developed to some extent. However, these operations based on nominal symmetric changes can lead to undershoot / overshoot problems. To illustrate this, let's take exponential operations as an example. Figure 1 In the affine interval [x] l ,x u The centrally symmetric affine interval [y] obtained by performing exponential operations l ',y u '] does not actually equal the actual result [y l ,y u ], yu and y u The difference between ' and ', i.e. δy, leads to the overshoot problem. To handle this overshoot problem, a forced boundary [x] = {x} is proposed. l ,x u}, where x l / x u Indicates the upper / lower forced boundary, combining the forced boundary [x] and the affine interval. The affine interval can be represented as:

[0124]

[0125] In the formula, This represents the top-down / top-down operation; through equation (13), overshoot can be eliminated, such as... Figure 2 As shown, the yellow area represents the removal of the domain in the affine interval calculation to enhance conservatism;

[0126] To further reduce the conservatism of traditional affine algorithms, a space approximation technique is proposed, which represents arbitrary affine binary operations as:

[0127]

[0128] In the formula, x, y, z are values ​​in spatial geometric coordinates, A, B, C, D are four coefficients, and ε is the noise figure located in [-1, 1].

[0129] Geometrically, formula (14) can be interpreted as two parallel planes in the (x,y,z) space lying in a given domain U. xy In the case of tightly surrounding the surface of z, such as Figure 3 As shown in the following formula:

[0130]

[0131] In the formula, A and B are the partial derivatives at the central value;

[0132]

[0133] The solution to formula (15) is expressed as:

[0134]

[0135] In the formula, d(x,y) is the distance function. To provide a clear perspective on the spatial approximation techniques in equations (16) and (17), let's take multiplication as an example, where the values ​​of A and B are:

[0136]

[0137] According to equation (18), the specific distance function d(x,y) is calculated as follows:

[0138]

[0139] To provide a more direct expression (19), the following is defined:

[0140]

[0141] Since the difference between the product uv in formula (20) and d(x,y) in formula (19) is a constant, uv and d(x,y) in formula (19) have the same extrema. This obviously only occurs in the closed polygon domain U. uv On the boundary, based on this, it is possible to compare the polygonal domain U uv For any three points on an edge, i.e., the two endpoints and the point {(u,v)|u=c / 2a,v=c / 2b}, we obtain the extreme values ​​of uv. Assuming the equation of the edge is au + bv=c, and defining the extreme values ​​of uv as E=min(uv) and F=max(uv), then the affine approximation of multiplication xy can be transformed into:

[0142]

[0143] To further reduce the conservatism of Equation (21), the lumped ε in Equation (21) is distributed over all existing uncertainty symbols:

[0144]

[0145] In the formula, z0=x0y0 represents The center value of z; i =x0y i +x i y0 represents the real coefficient of the partial variance in the affine form. Combining this with the forced boundary in formula (13), formula (22) can be finally reduced to... S3. Construct a distribution network interval voltage regulation optimization model with the goal of minimizing total voltage regulation cost. Input the confidence interval of meteorological factors and the interval between photovoltaic power generation and load demand into the distribution network interval voltage regulation optimization model, and output the optimized voltage regulation scheme.

[0146] The specific voltage regulation costs for four types of voltage regulation equipment—on-load tap-changing transformers (OLTC), capacitor banks (CB), photovoltaic (PV), and energy storage (ES)—are detailed below:

[0147] The cost of OLTC voltage regulation is mainly determined by the number of switching actions (δ) within a working cycle. t Decide:

[0148] C OLTC =θ OLTC ∑ t δ t (twenty three)

[0149] In the formula, θ OLTC δ represents the unit price of the switching action. t It is calculated by the movement of the OLTC tap position between two adjacent cycles, i.e., tap t and tap t+1 :

[0150] tap t+1 -tap t ≤δ t , tap t -tap t+1 ≤δ t (twenty four)

[0151] In the formula, tap t For adjusting node v ro,t The voltage at that point further affects the voltage at all nodes along the distribution feeder. t With v ro,t The correlation between them is expressed by the following formula:

[0152]

[0153] In the formula, d k,t This is a binary variable representing the on / off state of tap position k at time t; tap up This is the maximum tap position for OLTC. up This indicates that OLTC can switch between positive and negative modes; V Ini ΔV is the initial node voltage at the root node. uni This indicates the voltage adjustment range within a one-click step.

[0154] The voltage regulation cost of a CB circuit breaker is mainly determined by the total number of capacitor switching operations (λ). i,k,t Decide:

[0155] C CB =C C ∑ i ∑ k λ i,k,t (26)

[0156] In the formula, C C The unit cost of the capacitor switch; i / k is the number of nodes / capacitors, λ i,k,t Calculated by the following formula:

[0157]

[0158] In the formula, c i,k,t For k th The state binary variable represents the i-th... th The state of the k-th capacitor in each CB at time t; ai,k,t =c i,k,t ·c i,k,t+1 It is an auxiliary variable; the voltage regulation of CB is achieved by discretely switching the reactive power of each capacitor, that is... in For the kth th The capacitance of each capacitor.

[0159] Voltage regulation costs for photovoltaic systems Reactive power capacity cost Opportunity cost and active / reactive power loss costs composition:

[0160]

[0161] In the formula, α PV for The ratio of total photovoltaic investment cost; ρ P The average active power price; Let tanθ represent the reactive power of the i-th PV at time t; tanθ is... and The ratio; This represents the revenue / cost per unit of active power in a given PV unit. PV active / reactive power loss coefficient; This represents the reduction in active power of the i-th PV at time t. During the VR process, the PV needs to overcome capacity constraints:

[0162]

[0163]

[0164] ES voltage regulation cost Determined by a shortened lifespan:

[0165]

[0166] In the formula, Y represents the initial investment / maintenance cost of the i-th ES; ES Service life of ES; Let r be the investment recovery factor and the discount rate; This represents the lifecycle of the i-th ES; where, This represents the total lifetime of the ES at 100% depth of discharge (DoD). The total lifecycle of the i-th ES within one year; N0 and k represent the loss period coefficient of the i-th ES at time t; p It is the discharge constant; Let represent the virtual DOD of the i-th ES at time t; it can be seen that equations (32b), (32d), and (32e) are nonlinear. Regarding equation (32d), a piecewise technique is introduced to eliminate nonlinearity, i.e.:

[0167]

[0168] In the formula, s DoD For segmentation The total number of segments in the middle; and s th The slope and intercept of the segment; This represents the state variable of the i-th segment ES at time t; Indicates the sth th The lower / upper DoD bounds of the segment are linearized in a similar manner, which is omitted here for simplicity. For equation (32e), the Big M method is used for linearization:

[0169]

[0170] In the formula, The difference in virtual SOC between the i-th ES of adjacent points; It is an auxiliary binary variable; M DoD It is a very large constant; Indicates the virtual state of charge (SOC) of the i-th ES at time t:

[0171]

[0172] In the formula, For state variables, it involves the SOC extreme point information of the i-th ES at time t; The SOC of the i-th ES at time t is calculated using the following formula:

[0173]

[0174] In the formula For charge and discharge efficiency; This serves as the lower / upper bound of the system's State of Charge (SOC). The charging / discharging power of the ES can be obtained as follows:

[0175]

[0176] In the formula, This refers to the rated power of the ES. and It is a charge / discharge state variable, through and We can obtain:

[0177]

[0178] in, and This includes state variables and information about state transitions between charging and discharging; and It is an auxiliary variable for the transition of equilibrium state;

[0179] To achieve voltage regulation in an ADN while considering the uncertainties of photovoltaic power generation and load demand, a virtual reality interval optimization model was established. The objective function is to minimize the total voltage regulation cost, including the voltage regulation costs of the four types of equipment mentioned above and the costs of purchasing / selling active and reactive power from the transmission network (TN). The distribution network interval voltage regulation optimization model is as follows:

[0180]

[0181] Eq.(24)-(25),(27),(30)-(31),(33)-(37) (39h)

[0182] In the formula, For pressure regulation costs; C OLTC For OLTC voltage regulation costs; C CB For voltage regulation fees of CB circuit breakers; The cost of voltage regulation for photovoltaic systems; For the voltage regulation cost of ES; σ P and σ Q The active / reactive power calculation coefficient; The active power of TS; The reactive power of TS; The active / reactive output factor of node i; To represent the reduction in active power of PV at node i at time t; This refers to the charging / discharging power of the ES. The active power of the air conditioning load at time t is the value of node i. Let be the maximum power output of PV at node i at time t; The optimal power flow loss at time t; This represents the reactive power of PV at node i at time t; Let be the reactive power of CB at node i at time t; for The optimal power flow reactive power loss at time t; The voltage difference at node i before and after voltage regulation; Let be the capacitance of CB at time t at node j; Let be the reactive power of PV at node i at time t; Voltage sensitivity factor injected into the active / reactive power of a node; ΔV 1,t V is the root node voltage during the k-th tap operation of the OLTC. σ For each adjustment step of OLTC; d represents the highest number of taps on an OLTC tap changer; k,t For binary variables; λ i and V err These are the voltage offset coefficient and the maximum voltage offset, respectively; α c,0 / α c,1 / α c,2 These are the polygon approximation coefficients; Power of bus l; BSF lp,l-i / BSF lq,l-i Sensitivity factor for branch power flow when active / reactive power is injected into a node.

[0183] The above description is merely a preferred embodiment of the present invention and does not constitute any limitation on the present invention. Any person skilled in the art can make many possible variations and modifications to the technical solution of the present invention, or modify it into equivalent embodiments, without departing from the scope of the present invention. Therefore, any modifications, equivalent changes, and alterations made to the above embodiments based on the technology of the present invention without departing from the scope of the present invention are within the protection scope of the present invention.

Claims

1. A method for voltage regulation in distribution network sections considering the coupling of multidimensional meteorological factors, characterized in that: The method includes: S1. An improved nonparametric kernel density estimation method with coupling of multiple meteorological elements is introduced to introduce the uncertainty of meteorological factors, and the joint probability density function is used for estimation to generate the confidence interval of meteorological factors. S2. Using an affine algorithm based on forced boundary and spatial approximation, calculate the interval between photovoltaic power generation and load demand based on the confidence interval of meteorological factors. S3. Construct a distribution network interval voltage regulation optimization model with the goal of minimizing the total voltage regulation cost. Input the photovoltaic power generation range and the load demand range into the distribution network interval voltage regulation optimization model and output the optimized voltage regulation scheme. The specific steps of step S1 are as follows: definition As the first i The meteorological vectors of sampling points, where m=3 is the number of meteorological factors, and the uncertainty of the meteorological factors is represented by a random vector. The joint probability density function is expressed as: (1) In the formula, n The number of sampling points; This is a kernel function, used in conjunction with the Gaussian function; The bandwidth matrix is ​​a key indicator that determines the accuracy of fitting the sample set. The simplified formula is: (2) In the formula, For the first Bandwidth of each meteorological factor; It is a polynomial, represented as ; To improve the smoothness and accuracy of the probability density function, Euclidean distance is introduced. and maximum distance : (3) In the formula, Indicates the first i The geometric distance of each sampling point is based on equation (3). and Regarding bandwidth H Optimize: (4) In the formula, For the fitness function, This is represented as the optimal bandwidth, used to control the width of the kernel surrounding each meteorological sampling point; The following formula is used to determine the fixity of meteorological sampling points. Does it produce undersmoothing in sparse local areas of observation, or oversmoothing in the opposite case? (5) In the formula, It is a constant coefficient; For a certain sampling interval; L Sampling interval The number of meteorological sampling points; Indicates sampling interval l geometric distance; Indicates sampling interval l The average geometric distance, if formula (5) holds, that is, the sampling interval l If local adaptation issues exist, then adjust. for: (6) In the formula, Sampling interval l Adjust bandwidth; For interval l The median of the geometric distance between the inner sampling points; The threshold of the kernel function; According to formula (6), the final joint probability density function after bandwidth adjustment is expressed as: （7） Based on formula (7), confidence intervals for meteorological factors are generated using rejection sampling and bootstrap methods.

2. The distribution network interval voltage regulation method considering the coupling of multi-dimensional meteorological factors according to claim 1, characterized in that: Photovoltaic power generation range The calculation is as follows: (8) In the formula, This indicates the maximum power generation output under standard test conditions; Standard / actual illuminance; The standard test temperature and efficiency coefficient are used. The temperature of the PV module is calculated using the following formula: (9) In the formula, For temperature and wind speed; Range of load demand for: (10) In the formula, This refers to the rated power of the air conditioner. This indicates the air conditioner's on / off time within a unit operating cycle, at the actual temperature. T Compared to the set temperature Calculations at 0.5℃ lower / higher: (11) In the formula, the actual temperature T It is determined through the heat exchange process, including the heat between indoor air and the inner surfaces of walls or windows: (12) In the formula, This includes the surface area of ​​the exterior / interior walls and the area of ​​the windows in the air-conditioned room. For wall / window transfer coefficient; The inner surface temperature of the inner / outer wall; Outdoor temperature and its influencing parameters; C For attribute parameters; For AC cooling capacity; and For air density and heat capacity; V It refers to the volume of the room; T Indoor air temperature; This refers to the repair time for AC air conditioners.

3. The distribution network interval voltage regulation method considering the coupling of multi-dimensional meteorological factors according to claim 1, characterized in that: The specific steps of step S2 are as follows: Propose mandatory boundaries ,in Indicates upper / lower forced boundaries, combined with forced boundaries and affine interval The affine interval can be represented as: (13) In the formula, , This represents the top / bottom operation; To further reduce the conservatism of traditional affine algorithms, arbitrary affine binary operations are represented as: (14) In the formula, x , y , z All values ​​are in spatial geometric coordinates, and A, B, C, and D are four coefficients. The noise figure is located in [-1, 1]. Geometrically, formula (14) is interpreted as ( x , y , z Two parallel planes in space within a given domain In the case of tightly surrounding z The surface is as follows: (15) In the formula, A and B are the partial derivatives at the central value; (16) The solution to formula (15) is expressed as: (17) In the formula, d ( x , y Let be the distance function. To provide a clear perspective on the spatial approximation techniques in equations (16) and (17), let's take multiplication as an example, where the values ​​of A and B are: (18) According to equation (18), the specific distance function d ( x , y The calculation is as follows: (19)。 4. The distribution network interval voltage regulation method considering the coupling of multi-dimensional meteorological factors according to claim 3, characterized in that: The voltage regulation optimization model for the distribution network section is as follows: (39a) (39b) (39c) (39d) (39e) (39f) (39g) In the formula, For pressure regulation costs; Cost of OLTC voltage regulation; for CB Circuit breaker voltage regulation fee; The cost of voltage regulation for photovoltaic systems; The cost of voltage regulation for ES; and The active / reactive power calculation coefficient; for TS The active power; for TS reactive power; For nodes i The active / reactive power output factor; To represent nodes i exist t The active power of PV is reduced at any time; This refers to the charging / discharging power of the ES. for i node t The air conditioning load is active at all times; For PV at the node i time t Maximum power generation capacity; for t Optimal power flow loss at all times; Represents a node i exist t The reactive power of PV at any given time; For nodes i The reactive power of CB at time t; for t Optimal power flow and reactive power loss at all times; For the nodes before and after voltage regulation i Voltage difference; For nodes j time t The capacitance of CB at that time; For nodes j exist t The reactive power of PV at any given time; Voltage sensitivity coefficient injected into the active / reactive power of a node; For OLTC k Root node voltage during the next tap operation; For each adjustment step of OLTC; This refers to the highest number of taps on an OLTC tap. It is a binary variable; and These are the voltage offset coefficient and the maximum voltage offset, respectively. These are the polygon approximation coefficients; busbar l The power; Sensitivity factor for branch power flow when active / reactive power is injected into a node.

5. A distribution network interval voltage regulation method considering the coupling of multidimensional meteorological factors according to claim 4, characterized in that: The OLTC voltage regulation cost for: (23) In the formula, The unit price for the switching action. The change in OLTC tap position between adjacent time points: (24) In the formula, for t The amount of change in the tap position of the OLTC tap changer at any given time. and The correlation between them is expressed by the following formula: (25) In the formula, For the tap position index, This is a binary variable representing the tap position. At any moment t On / off state; This is the maximum tap position for OLTC; The initial node voltage of the root node; This indicates the voltage adjustment range within a one-click step.

6. A distribution network interval voltage regulation method considering the coupling of multidimensional meteorological factors according to claim 4, characterized in that: The CB Circuit breaker voltage regulation cost for: (26) In the formula, The unit cost of capacitor switches; Number of nodes / capacitors Calculated by the following formula: (27) In the formula, for The state binary variable represents the first... indivual CB The Middle k One capacitor in t The state at any given moment; It is an auxiliary variable.

7. A distribution network interval voltage regulation method considering the coupling of multidimensional meteorological factors according to claim 4, characterized in that: The voltage regulation cost of the photovoltaic for: (28) (29) In the formula, for The ratio to the total photovoltaic investment cost; The average active power price; Indicates the first i PV in t Reactive power at any given moment; tan θ for and The ratio; This represents the revenue / cost per unit of active power in a PV unit. PV active / reactive power loss coefficient; Indicates the first i PV in t During the VR process, the PV needs to overcome capacity constraints due to the constant reduction of active power. (30) (31) In the formula, The power output of photovoltaic televisions.

8. A distribution network interval voltage regulation method considering the coupling of multidimensional meteorological factors according to claim 4, characterized in that: The voltage regulation cost of the ES for: (32a) (32b) (32c) (32d) (32e) In the formula, Indicates the first i Initial investment / maintenance costs for each ES; Service life of ES; and r The investment recovery factor and discount rate; Indicates the first i The lifecycle of each Elasticsearch instance; among which... This represents the total lifetime of the ES at 100% depth of discharge (DoD). For the first time in a year i The total lifecycle of each Elasticsearch instance; Indicates the first i One ES in t The loss period coefficient at any given time; and It is the discharge constant; Indicates the first i One ES in t The virtual DOD of a moment.

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