Power distribution network interval voltage regulation method considering multi-dimensional meteorological factor coupling

Abstract

The invention relates to the technical field of power systems, and particularly discloses a power distribution network interval voltage regulation method considering multi-dimensional meteorological factor coupling, which comprises the following steps: S1, introducing the uncertainty of meteorological factors through an improved non-parametric kernel density estimation method of multi-meteorological factor coupling, and performing estimation by using a joint probability density function, generating a confidence interval of the meteorological factors; s2, through an affine algorithm based on a forced boundary and spatial approximation, calculating an interval of photovoltaic power generation power and load demand based on a meteorological factor confidence interval; and S3, constructing a power distribution network interval voltage regulation optimization model by taking the minimum total voltage regulation cost as a target, inputting the photovoltaic power generation power interval and the load demand interval into the power distribution network interval voltage regulation optimization model, and outputting an optimized voltage regulation scheme. The method has the advantages that the uncertainty caused by the previous correlation of a plurality of meteorological factors is solved, the voltage regulation optimization model is constructed to obtain an accurate voltage regulation scheme, and the voltage regulation cost is effectively reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of electric power systems, and in particular to a distribution network interval voltage regulation method taking into account the coupling of multi-dimensional meteorological factors. Background Art

[0002] In recent years, distributed renewable energy has achieved irreversible development due to its advantages of reducing electricity costs and promoting electricity self-use. However, with the high popularity of these distributed renewable energy sources, active distribution networks (ADN) have many technical problems, among which voltage over-limit plays a leading role. Voltage over-limit is mainly caused by the intermittent / volatile and undispatched nature of renewable energy, the growth of node load demand, and the unreasonable site selection of power sources. The voltage over-limit caused by the above reasons can cause serious economic losses, especially for voltage-sensitive users. In modern distribution networks with a high popularity of renewable energy, voltage regulation is one of the problems that need to be solved urgently.

[0003] At present, the methods for characterizing the uncertainty of voltage regulation can be roughly divided into four categories, namely, scenario-based methods, probability-based methods, fuzzy logic methods, and interval value methods. In the scenario-based method, multiple scenarios such as AC loads or photovoltaic power generation with different penetration levels are set to study the changes in voltage regulation strategies. However, in the process of processing a large amount of historical data, the scenario-based method inherently has the problem of large computational complexity and inaccuracy in rare or extreme scenarios. A probability-based method can also be used to describe the uncertainty of load demand and renewable energy resources through typical probability variables or probability density functions, and on this basis, the voltage regulation scheme is obtained through a probabilistic power flow model. However, this probability-based method is usually based on certain probability distribution assumptions, which may deviate from the actual results and further lead to inaccuracies. The uncertainty in the fuzzy logic method is represented by membership and fuzzy membership functions. The prior art 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 a voltage control scheme. Prior art A new fuzzy adaptive particle swarm optimization for non-smootheconomic dispatch utilizes fuzzification of control parameters to execute price-based Volt / Var control strategies for ADN. Although fuzzy logic methods are effective in the above-mentioned prior arts, fuzzy logic methods usually involve subjective judgments and personal preferences and cannot provide scientific explanations. Interval value methods use interval parameters instead of traditional point parameters to deal with uncertainty or variability. Prior art A transactive retail market mechanism for active distribution network integrated with large-scale distributed energy resources defines the uncertain output of distributed energy as an interval and proposes a voltage regulation interval that maximizes retailers' profits. Prior art Estimating DLMP confidence intervals in distribution networks with AC power flow model and uncertain renewable generation regards the volatility of renewable energy as an interval based on a polyhedron, and gives distribution network voltage regulation intervals at different confidence levels while considering node voltage constraints.In summary, there are two major drawbacks: First, the current uncertainty representation methods (such as scenario-based, probability-based, and interval-based), especially for photovoltaic power generation output and AC load demand, are not accurate enough and cannot be directly relied on historical data. The correlation between multidimensional meteorological factors plays a key role in generating this uncertainty. Second, the voltage regulation uncertainty information is still limited. Summary of the invention

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

[0005] The object of the present invention is achieved by the following technical solution: a distribution network interval voltage regulation method considering the coupling of multi-dimensional meteorological factors, the method comprising:

[0006] S1. The uncertainty of meteorological factors is introduced by the improved nonparametric kernel density estimation method of multiple meteorological elements coupling, and the confidence interval of meteorological factors is generated by estimation using the joint probability density function;

[0007] S2, calculating the interval of photovoltaic power generation and load demand based on the confidence interval of meteorological factors through an affine algorithm based on forced boundaries and spatial approximation;

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

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

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

[0011]

[0012] Where 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 Represents the bandwidth matrix, which is a key indicator for determining the fitting accuracy of the sample set;

[0013] The simplified formula is:

[0014]

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

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

[0017]

[0018] Where, d i (H)=|f(x i )-f(X i )| represents the geometric distance of the i-th sampling point, based on d in formula (3) O (H) and d M (H), optimize the 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, H Z It is expressed as the optimal bandwidth to control the width of the kernel around each meteorological sampling point; the fixed H of the meteorological sampling point is determined by the following formula Z Whether to produce under-smoothing in local areas where observations are sparse or over-smoothing 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 the sampling interval l; d l (H Z )=∑ i∈l d i (H Z ) represents the geometric distance of the sampling interval l; represents the average geometric distance of the sampling interval l. If formula (5) holds, that is, there is a local adaptability problem in the sampling interval l, then adjust H Z for:

[0023]

[0024] In the formula, H l is the adjustment bandwidth of the sampling interval l; d l (H z ) mid is the median of the geometric distance of the sampling points in 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), the confidence interval of meteorological factors is generated by rejection sampling method and Bootstrap method.

[0028] Specifically, the photovoltaic power generation range P PV Calculated as:

[0029]

[0030] Where P STC Indicates the maximum power output under standard test conditions; G STC / G T is the standard / actual illumination; T τ / K is the standard test temperature and efficiency coefficient; T C is the PV module temperature, and the calculation formula is:

[0031]

[0032] Where, T a / D wt for air temperature and wind speed;

[0033] Load demand range for:

[0034]

[0035] In the formula, is the rated power of the air conditioner; τ on / τ off Indicates the air conditioner operation / stop time within a unit operation cycle, when the actual temperature T is lower than the set temperature T set Calculation at 0.5℃ lower / higher:

[0036]

[0037] Here, the actual temperature T is determined by 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 K is the outer / inner wall surface area and window area of ​​the air-conditioned room; wa / K wi is the wall / window transmission coefficient; T in / T out is the inner surface temperature of the inner / outer wall; T a / f is the outdoor temperature and its influencing parameters; C is the attribute parameter; Q AC is the AC cooling capacity; ρ in and c in is the air density and heat capacity; V is the volume of the room; T is the indoor air temperature; τ is the maintenance time of the AC air conditioner. Specifically, the specific steps of step S2 are:

[0040] Propose a mandatory boundary [x] = {x l ,x u}, where x l / x u Represents upper / lower mandatory boundaries, combining mandatory boundaries [x] and affine intervals The affine interval can be expressed as:

[0041]

[0042] In the formula, Indicates the top / top operation;

[0043] In order to further reduce the conservatism of the traditional affine algorithm, any affine binary operation is expressed as:

[0044]

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

[0046] Geometrically, equation (14) is interpreted as the relationship between two parallel planes in (x, y, z) space in a given domain U xy In the case of , it tightly surrounds the surface of z, as follows:

[0047]

[0048] Where A and B are partial derivatives at the central value;

[0049]

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

[0051]

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

[0053]

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

[0055]

[0056] Specifically, the distribution network interval voltage regulation optimization model is:

[0057]

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

[0059] In the formula, C is the voltage regulation fee; OLTC C is the OLTC voltage regulation fee; CB It is the voltage regulation fee of CB circuit breaker; It is the voltage regulation cost of photovoltaic power generation; is the voltage regulation cost of ES; P and σ Q It is the active / reactive power calculation coefficient; is the active power of TS; is the reactive power of TS; is the active / reactive output factor of node i; represents the active power reduction of PV of node i at time t; is the charge / discharge power of ES; is the active power of air conditioning load at node i at time t; is the maximum power generation of PV at node i at time t; is the active power loss of the optimal power flow at time t; represents the reactive power of PV of node i at time t; is the reactive power of CB of node i at time t; for is the optimal power flow reactive loss at time t; is the voltage difference of node i before and after voltage regulation; is the capacitance of CB at node j at time t; is the reactive power of PV of node i at time t; △V is the voltage sensitivity coefficient of active / reactive power injection into the node;1,t is the root node voltage when the OLTC tap is operated for the kth time; The highest number of gears of OLTC tap; d k,t is a binary variable; i and V err are the voltage offset coefficient and the maximum voltage offset respectively; α c,0 / α c,1 / α c,2 is the polygonal approximation coefficient; is the power of bus l; BSF lp,l-i / BSF lq,l-i It is the sensitivity factor of branch power flow when node active / reactive power is injected.

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

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

[0062] In the formula, θ OLTC is the unit price of the switching action, δ t is the change in OLTC tap position between adjacent moments:

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

[0064] In the formula, tap t is the change in the OLTC tap position at time t, tap t With v ro,t The correlation between them is expressed as follows:

[0065]

[0066] Where k is the tap position index, d k,t is a binary variable, indicating the on / off state of the tap position k at time t; tap up is the maximum tap position of OLTC; V uni is the initial node voltage of the root node; ΔV uni Indicates the voltage adjustment range within one step.

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

[0068] C CB =C C ∑ i ∑ k λ i,k,t (26)

[0069] In the formula, C C is 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 k th State binary variable, indicating the i-th th The state of the kth capacitor in a CB at time t; i,k,t =c i,k,t ·c i,k,t+1 is an auxiliary variable.

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

[0073]

[0074] In the formula, α PV for Ratio to total photovoltaic investment cost; ρ P is the average active power price; represents the reactive power of the i-th PV at time t; tanθ is and ratio; Indicates the benefit / cost per unit PV active power; is the PV active / reactive loss coefficient; represents the active power reduction of the i-th PV at time t. During the VR process, the PV needs to overcome the capacity constraint:

[0075]

[0076] In the formula, For photovoltaic power generation.

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

[0078]

[0079] In the formula, represents the initial investment / maintenance cost of the i-th ES; Y ES Years of service as ES; and r are the investment capital recovery coefficient and discount rate; represents the life cycle of the i-th ES; where, is the total life cycle of ES at 100% depth of discharge (DoD); is the total life cycle of the i-th ES within one year; represents the loss period coefficient of the i-th ES at time t; N0 and k p is the discharge constant; represents 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 adjust the bandwidth within a specific sampling interval, so that the maximum distance, Euclidean distance and fitness of the proposed NPKDE model are reduced by 23.65%, 13.20% and 22.97% respectively. By comparison, it can be seen that the proposed NPKDE can effectively improve the fitting accuracy of multiple coupled meteorological factors; compared with the typical policy price and the traditional DLMP price, the INVP price proposed by the present invention is more evenly distributed and has a smaller peak, and the voltage regulation cost is reduced by 37.04% and 20.96% respectively. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 Demonstration diagram of the overshoot problem of the traditional affine algorithm;

[0083] Figure 2 Variable polytopes based on enforced boundaries under the proposed affine algorithm;

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

[0085] Figure 4 It is the wiring diagram of the 152-node distribution network;

[0086] Figure 5 Schematic diagram of 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 Schematic diagram of the output range of each voltage regulating device at three confidence levels of 95%, 85% and 75%. DETAILED DESCRIPTION

[0088] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention, that is, the embodiments described are only part of the embodiments of the present invention, rather than all of the embodiments. The components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0089] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without making creative work are within the scope of protection of the present invention.

[0090] It should be noted that relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "including a..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

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

[0092] S1. The uncertainty of meteorological factors is introduced by the improved nonparametric kernel density estimation method of multiple meteorological elements coupling, and the confidence interval of meteorological factors is generated by estimation using the joint probability density function;

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

[0094]

[0095] Where 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 Represents the bandwidth matrix, which is a key indicator for determining the fitting accuracy of the sample set;

[0096] The simplified formula is:

[0097]

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

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

[0100]

[0101] Where, d i (H)=|f(x i )-f(X i )| represents the geometric distance of the i-th sampling point, based on d in formula (3) O (H) and d M (H), optimize the 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 is expressed as the optimal bandwidth to control the width of the kernel around each meteorological sampling point; however, the fixed H Z Under-smoothing may occur in local areas with sparse observations, or over-smoothing may occur in the opposite case, which is called the local adaptability problem. In order to determine whether this problem exists, the present invention proposes a standard, namely:

[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; represents the average geometric distance of the sampling interval l. If formula (5) holds, that is, there is a local adaptability problem in the sampling interval l, then adjust H Z for:

[0106]

[0107] In the formula, H l is the adjustment bandwidth of the sampling interval l; d l (H z ) mid is the median of the geometric distance of the sampling points in 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 interval of meteorological factors is generated by the rejection sampling method and the Bootstrap method. The confidence interval of meteorological factors is generated by the bootstrap sampling method.

[0111] Specifically, the photovoltaic power generation range P PV Calculated as:

[0112]

[0113] Where P STC Indicates the maximum power output under standard test conditions; G STC / G T is the standard / actual illumination; T τ / K is the standard test temperature and efficiency coefficient; T C is the PV module temperature, and the calculation formula is:

[0114]

[0115] Where, T a / D wt is the temperature and wind speed; from equations (8) and (9), it can be seen that the photovoltaic power generation interval P is determined by the light intensity, temperature and wind speed. PV The rationale for considering the coupling of three meteorological factors is explained;

[0116] Load demand range for:

[0117]

[0118] In the formula, is the rated power of the air conditioner; τ on / τ off Indicates the air conditioner operation / stop time within a unit operation cycle, when the actual temperature T is lower than the set temperature T set Calculation at 0.5℃ lower / higher:

[0119]

[0120] Here, the actual temperature T is determined by 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 K is the outer / inner wall surface area and window area of ​​the air-conditioned room; wa / K wi is the wall / window transmission coefficient; T in / T out is the inner surface temperature of the inner / outer wall; T a / f is the outdoor temperature and its influencing parameters; C is the attribute parameter; Q AC is the AC cooling capacity; ρ in and c in is the air density and heat capacity; V is the volume of the room; T is the indoor air temperature; τ is the AC air conditioner maintenance time; S2, the interval between photovoltaic power generation and load demand is calculated by an affine algorithm based on forced boundaries and spatial approximation;

[0123] The traditional affine interval form is expressed as a first-order polynomial, namely With x0 and ε i For the center value and noise symbol, the addition, subtraction, multiplication, division, exponential function and other operations in the affine interval form are developed to a certain extent. However, this operation based on nominal symmetry change may lead to undershoot / overshoot problems. To illustrate this point, take the exponential operation as an example. Figure 1 In the affine interval [x l ,x u ] is the central symmetric affine interval [y l ',y u '] is not actually equal to the actual result [y l ,y u ],yu and u The difference between ', i.e., δy, leads to the overshoot problem. To deal with this overshoot problem, we propose to force the boundary [x] = {x l ,x u}, where x l / x u Represents upper / lower mandatory boundaries, combining mandatory boundaries [x] and affine intervals The affine interval can be expressed as:

[0124]

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

[0126] In order to further reduce the conservatism of the traditional affine algorithm, a spatial approximation technique is proposed to express any affine binary operation as:

[0127]

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

[0129] Geometrically, equation (14) is interpreted as the relationship between two parallel planes in (x, y, z) space in a given domain U xy In the case of tightly enclosing the surface of z, such as Figure 3 , as follows:

[0130]

[0131] Where A and B are partial derivatives at the central value;

[0132]

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

[0134]

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

[0136]

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

[0138]

[0139] In order to provide a more direct formula (19), the following definitions are made:

[0140]

[0141] Since the difference between the product uv of formula (20) and d(x, y) in formula (19) is a constant, uv has the same extreme value as d(x, y) in formula (19), which obviously only occurs in the closed polygonal domain U uv On the boundary of the polygonal domain U uv Three points on any edge, namely the two endpoints and the point {(u,v)|u=c / 2a,v=c / 2b}, get the extreme value of uv. Assuming the edge equation is au+bv=c, the extreme value of uv is defined as E=min(uv), F=max(uv), then the affine approximation of multiplication xy can be transformed into:

[0142]

[0143] In order to further reduce the conservatism of formula (21), the lumped ε in formula (21) is distributed over all existing uncertainty symbols:

[0144]

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

[0146] The specific voltage regulation costs of the four voltage regulation equipment, on-load voltage regulating transformer OLTC, capacitor bank CB, photovoltaic PV, and energy storage ES are described as follows:

[0147] The OLTC voltage regulation cost is mainly determined by the number of switching actions in one working cycle δ t Decide:

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

[0149] In the formula, θ OLTC is the unit price of the switching action, δ 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 the tap further affects the voltage at all nodes along the distribution feeder. t With v ro,t The correlation between them is expressed as follows:

[0152]

[0153] Where, d k,t is a binary variable, indicating the on / off state of the tap position k at time t; tap up is the maximum tap position of OLTC, tap up Indicates that OLTC can be switched in both positive and negative modes; V Ini is the initial node voltage of the root node; ΔV uni Indicates the voltage adjustment range within one step.

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

[0155] C CB =C C ∑ i ∑ k λ i,k,t (26)

[0156] In the formula, C C is 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 k th State binary variable, indicating the i-th th The state of the kth capacitor in a CB at time t;i,k,t =c i,k,t ·c i,k,t+1 is an auxiliary variable, and the voltage regulation of CB is achieved by discretely switching the reactive power of each capacitor, that is, in For the kth th The capacity of a capacitor.

[0159] Photovoltaic voltage regulation costs Reactive capacity cost Opportunity Cost and active / reactive power loss costs composition:

[0160]

[0161] In the formula, α PV for Ratio to total photovoltaic investment cost; ρ P is the average active power price; represents the reactive power of the i-th PV at time t; tanθ is and ratio; Indicates the benefit / cost per unit PV active power; is the PV active / reactive loss coefficient; represents the active power reduction of the i-th PV at time t. During the VR process, the PV needs to overcome the capacity constraint:

[0162]

[0163]

[0164] ES voltage regulation cost Determined by the shortened life cycle:

[0165]

[0166] In the formula, represents the initial investment / maintenance cost of the i-th ES; Y ES Years of service as ES; and r are the investment capital recovery coefficient and discount rate; represents the life cycle of the i-th ES; where, is the total life cycle of ES at 100% depth of discharge (DoD); is the total life cycle of the i-th ES within one year; represents the loss period coefficient of the i-th ES at time t; N0 and k p is the discharge constant; represents the virtual DOD of the i-th ES at time t; it can be seen that equations (32b), (32d), and (32e) are nonlinear. As for equation (32d), the segmentation technology is introduced to eliminate the nonlinearity, that is:

[0167]

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

[0169]

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

[0171]

[0172] In the formula, is a state variable, involving the SOC extreme point information of the i-th ES at time t; represents the SOC of the i-th ES at time t, and the calculation formula is:

[0173]

[0174] In the formula is the charge and discharge efficiency; is the lower / upper bound of the system SOC; is the charge / discharge power of ES, we can get:

[0175]

[0176] In the formula, is the rated power of ES; and is the charge / discharge state variable, through and You can get:

[0177]

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

[0179] In order to realize voltage regulation in ADN considering the uncertainty of photovoltaic power generation and load demand, a virtual reality interval optimization model is established. The objective function is to minimize the total voltage regulation cost, including the voltage regulation costs of the above four types of equipment and the cost of buying / selling active and reactive power to the transmission network (TN). The distribution network interval voltage regulation optimization model is:

[0180]

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

[0182] In the formula, C is the voltage regulation fee; OLTC C is the OLTC voltage regulation fee; CB It is the voltage regulation fee of CB circuit breaker; It is the voltage regulation cost of photovoltaic power generation; is the voltage regulation cost of ES; P and σ Q It is the active / reactive power calculation coefficient; is the active power of TS; is the reactive power of TS; is the active / reactive output factor of node i; represents the active power reduction of PV of node i at time t; is the charge / discharge power of ES; is the active power of air conditioning load at node i at time t; is the maximum power generation of PV at node i at time t; is the active power loss of the optimal power flow at time t; represents the reactive power of PV of node i at time t; is the reactive power of CB of node i at time t; for is the optimal power flow reactive loss at time t; is the voltage difference of node i before and after voltage regulation; is the capacitance of CB at node j at time t; is the reactive power of PV of node i at time t; △V is the voltage sensitivity coefficient of active / reactive power injection into the node; 1,t is the root node voltage when the OLTC tap is operated for the kth time; V σ is the adjustment step size of OLTC; The highest number of gears of OLTC tap; d k,t is a binary variable; i and V err are the voltage offset coefficient and the maximum voltage offset respectively; α c,0 / α c,1 / α c,2 is the polygonal approximation coefficient; is the power of bus l; BSF lp,l-i / BSF lq,l-i It is the sensitivity factor of branch power flow when node active / reactive power is injected.

[0183] The above is only a preferred embodiment of the present invention and does not limit the present invention in any form. Any technician familiar with the art can make many possible changes and modifications to the technical solution of the present invention by using the above-mentioned technical content without departing from the scope of the technical solution of the present invention, or modify it into an equivalent embodiment of equivalent changes. Therefore, any changes, modifications, equivalent changes and modifications made to the above embodiments based on the technology of the present invention without departing from the content of the technical solution of the present invention belong to the protection scope of the present technical solution.

Claims

1. A distribution network interval voltage regulation method considering the coupling of multi-dimensional meteorological factors, characterized by: The method includes: S1. The uncertainty of meteorological factors is introduced by the improved nonparametric kernel density estimation method of multiple meteorological elements coupling, and the confidence interval of meteorological factors is generated by estimation using the joint probability density function; S2, calculating the interval of photovoltaic power generation and load demand based on the confidence interval of meteorological factors through an affine algorithm based on forced boundaries and spatial approximation; 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 power interval and the load demand interval into the distribution network interval voltage regulation optimization model, and output the optimized voltage regulation plan.

2. A 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 S1 are: Define X i =[X i,1 ,X i,2, …,X i,m ] T As the meteorological vector of the i-th sampling point, m = 3 is the number of meteorological factors, and the uncertainty of meteorological factors is represented by a random vector x = [x1, x2, …, x m ] T , the joint probability density function is expressed as: Where 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 Represents the bandwidth matrix, which is a key indicator for determining the fitting accuracy of the sample set; The simplified formula is: In the formula, h j For the jth th The bandwidth of meteorological factors; M(x) is a polynomial, expressed as ∑ j ((x i -X i,j ) / h j ) 2 ; In order to improve the smoothness and accuracy of the probability density function, the Euclidean distance d is introduced O (H) and the maximum distance d M (H): Where, d i (H)=|f(x i )-f(X i )| represents the geometric distance of the i-th sampling point, based on d in formula (3) O (H) and d M (H), optimize the bandwidth H: minR(H)=min[d O (H Z )+d M (H Z )] (4) In the formula, R(H) is the fitness function, H Z It is expressed as the optimal bandwidth to control the width of the kernel around each meteorological sampling point; the fixed H of the meteorological sampling point is determined by the following formula Z Whether to produce under-smoothing in local areas where observations are sparse or over-smoothing in the opposite case: 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; represents the average geometric distance of the sampling interval l. If formula (5) holds, that is, there is a local adaptability problem in the sampling interval l, then adjust H Z for: In the formula, H l is the adjustment bandwidth of the sampling interval l; d l (H z ) mid is the median of the geometric distance of the sampling points in interval l; δ is the threshold of the kernel function; According to formula (6), the final joint probability density function after bandwidth adjustment is expressed as: Based on formula (7), the confidence interval of meteorological factors is generated by rejection sampling method and Bootstrap method.

3. A 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 P PV Calculated as: Where P STC Indicates the maximum power output under standard test conditions; G STC / G T is the standard / actual illumination; T τ / K is the standard test temperature and efficiency coefficient; T C is the PV module temperature, and the calculation formula is: Where, T a / D wt for air temperature and wind speed; Load demand range for: In the formula, is the rated power of the air conditioner; τ on / τ off Indicates the air conditioner operation / stop time within a unit operation cycle, when the actual temperature T is lower than the set temperature T set Calculation at 0.5℃ lower / higher: Here, the actual temperature T is determined by the heat exchange process, including the heat between the indoor air and the inner surface of the wall or window: In the formula, A out / A in / A wi K is the surface area of ​​the exterior / interior walls and windows of the air-conditioned room; wa / K wi is the wall / window transmission coefficient; T in / T out is the inner surface temperature of the inner / outer wall; T a / f is the outdoor temperature and its influencing parameters; C is the attribute parameter; Q AC is the AC cooling capacity; ρ in and c in is the air density and heat capacity; V is the volume of the room; T is the indoor air temperature; τ is the maintenance time of the AC air conditioner.

4. A 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: Propose a mandatory boundary [x] = {x l ,x u }, where x l / x u Represents upper / lower mandatory boundaries, combining mandatory boundaries [x] and affine intervals The affine interval can be expressed as: In the formula, Indicates the top / top operation; In order to further reduce the conservatism of the traditional affine algorithm, any affine binary operation is expressed as: In the formula, x, y, z are all values ​​of spatial geometric coordinates, A, B, C, D are four coefficients, and ε is the noise coefficient located in [-1, 1]; Geometrically, equation (14) is interpreted as the relationship between two parallel planes in (x, y, z) space in a given domain U xy In the case of , it tightly surrounds the surface of z, as follows: Where A and B are partial derivatives at the central value; The solution of formula (15) is expressed as: In the formula, d(x, y) is the distance function. In order to provide a clear perspective on the spatial approximation techniques in equations (16) and (17), we take multiplication as an example, where the values ​​of A and B are: According to formula (18), the specific distance function d(x,y) is calculated as:

5. A distribution network interval voltage regulation method considering the coupling of multi-dimensional meteorological factors according to claim 4, characterized in that: The distribution network interval voltage regulation optimization model is: In the formula, C is the voltage regulation fee; OLTC C is the OLTC voltage regulation fee; CB It is the voltage regulation fee of CB circuit breaker; It is the voltage regulation cost of photovoltaic power generation; is the voltage regulation cost of ES; P and σ Q It is the active / reactive power calculation coefficient; is the active power of TS; is the reactive power of TS; is the active / reactive output factor of node i; represents the active power reduction of PV of node i at time t; is the charge / discharge power of ES; is the active power of air conditioning load at node i at time t; is the maximum power generation of PV at node i at time t; is the active power loss of the optimal power flow at time t; represents the reactive power of PV of node i at time t; is the reactive power of CB of node i at time t; for is the optimal power flow reactive loss at time t; is the voltage difference of node i before and after voltage regulation; is the capacitance of CB at node j at time t; is the reactive power of PV of node i at time t; △V is the voltage sensitivity coefficient of active / reactive power injection into the node; 1,t is the root node voltage when the OLTC tap is operated for the kth time; V σ is the adjustment step size of OLTC; The highest number of gears of OLTC tap; d k,t is a binary variable; i and V err are the voltage offset coefficient and the maximum voltage offset respectively; α c,0 / α c,1 / α c,2 is the polygonal approximation coefficient; is the power of bus l; BSF lp,l-i / BSF lq,l-i It is the sensitivity factor of branch power flow when node active / reactive power is injected.

6. A distribution network interval voltage regulation method considering the coupling of multi-dimensional meteorological factors according to claim 5, characterized in that: The OLTC voltage regulation fee C OLTC for: C OLTC =θ OLTC ∑ t d t (23) In the formula, θ OLTC is the unit price of the switching action, δ t is the change in OLTC tap position between adjacent moments: loss t+1 -loss t ≤δ t , loss t -loss t+1 ≤δ t (24) In the formula, tap t is the change in the OLTC tap position at time t, tap t With v ro,t The correlation between them is expressed as follows: Where k is the tap position index, d k,t is a binary variable, indicating the on / off state of the tap position k at time t; tap up is the maximum tap position of OLTC; V uni is the initial node voltage of the root node; ΔV uni Indicates the voltage adjustment range within one step.

7. A distribution network interval voltage regulation method considering the coupling of multi-dimensional meteorological factors according to claim 5, characterized in that: The voltage regulation cost of the CB circuit breaker is C CB for: C CB =C C ∑ i ∑ k l i,k,t (26) In the formula, C C is the unit cost of the capacitor switch; i / k is the number of nodes / capacitors, λ i,k,t Calculated by the following formula: In the formula, c i,k,t k th State binary variable, indicating the i th The state of the kth capacitor in a CB at time t; i,k,t =c i,k,t ·c i,k,t+1 is an auxiliary variable.

8. The method for voltage regulation in distribution network considering coupling of multi-dimensional meteorological factors according to claim 5 is characterized in that: The photovoltaic voltage regulation cost for: In the formula, α PV for Ratio to total photovoltaic investment cost; ρ P is the average active power price; represents the reactive power of the i-th PV at time t; tanθ is and ratio; Indicates the benefit / cost per unit PV active power; is the PV active / reactive loss coefficient; represents the active power reduction of the i-th PV at time t. During the VR process, the PV needs to overcome the capacity constraint: In the formula, For photovoltaic power generation.

9. A distribution network interval voltage regulation method considering the coupling of multi-dimensional meteorological factors according to claim 5, characterized in that: The voltage regulation cost of the ES for: In the formula, represents the initial investment / maintenance cost of the i-th ES; Y ES Years of service as ES; and r are the investment capital recovery coefficient and discount rate; represents the life cycle of the i-th ES; where, is the total life cycle of ES at 100% depth of discharge (DoD); is the total life cycle of the i-th ES within one year; represents the loss period coefficient of the i-th ES at time t; N0 and k p is the discharge constant; represents the virtual DOD of the i-th ES at time t.

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