Dynamic DC loop planning method for distributed photovoltaic distribution network

Abstract

A method for dynamic DC closed-loop planning of a distributed photovoltaic distribution network belongs to the field of AC / DC hybrid distribution networks. The purpose of the present invention is to provide a method for dynamic DC closed-loop planning of a distributed photovoltaic distribution network through quantitative analysis of photovoltaic uncertainty and power support capability and multi-objective DC closed-loop planning of network topology. The steps of the present invention are: GMM-based distribution network uncertainty modeling, power distribution optimization and evaluation, distribution network DC closed-loop multi-objective decision model, and decision model convexity transformation. The present invention realizes flexible power transfer between distribution lines, effectively optimizes the voltage distribution of network nodes, and significantly improves the distribution network's ability to accept distributed photovoltaics.

Description

Technical Field

[0001] The present invention belongs to the field of AC / DC hybrid distribution networks. Background Art

[0002] Traditional AC distribution networks typically feature a radial grid structure characterized by "closed-loop design, open-loop operation," and a "single-point to multi-point" approach. System power is naturally distributed and flows unidirectionally, with the source following the load, lacking the ability to regulate power flow. However, when a high proportion of distributed power sources are connected, their highly random fluctuations not only cause power flow reversals but also easily lead to power flow congestion, causing distribution lines to overload or operate, thereby increasing dispatch costs and limiting the absorption of renewable energy. If not promptly alleviated, these conditions can damage system components and even cause serious cascading failures. However, the use of DC networking technology to plan hybrid AC / DC distribution networks can effectively increase the diversity of system operating modes and the precision and flexibility of power flow regulation. It can also enable low-voltage remote power supply and asynchronous closing of multi-regional distribution networks, alleviate power flow congestion, reduce line power and voltage losses to a certain extent, and effectively improve the absorption of distributed renewable energy.

[0003] DC networking is an effective means of achieving flexible power flow control and optimizing node voltage distribution. Power flow control in distribution networks based on DC network planning and DC network reconstruction should comprehensively consider renewable energy output forecast errors and existing grid structural constraints. Power flow distribution can be optimized by improving power flow optimization objectives and expanding the definition of system operational and structural constraints. Existing models and methods for DC network planning for distribution networks fail to adequately consider the impact of random fluctuations and forecast errors in distributed generation (DGs), making them incapable of fully adapting to scenarios with high proportions of DGs and strong random fluctuations. Summary of the Invention

[0004] The purpose of the present invention is to provide a dynamic DC closed-loop planning method for distributed photovoltaic distribution networks through quantitative analysis of photovoltaic uncertainty and power support capability and multi-objective DC closed-loop planning of network topology.

[0005] The steps of the present invention are:

[0006] S1. Distribution network uncertainty modeling based on GMM

[0007] S1.1 Basic principles of GMM

[0008] The GMM probability density function can be expressed as:

[0009]

[0010] Where: M is the number of Gaussian components of GMM; is the kth one-dimensional Gaussian component; ω k 、μ k 、 are the weight, expectation and covariance of the kth Gaussian component respectively;

[0011] where ω k Normalization conditions should be met:

[0012]

[0013] Parameter ω in the Gaussian mixture model k 、μ k and The expectation maximization algorithm is used to solve the problem;

[0014] random variable Obey GMM, its marginal probability and conditional probability must obey GMM;

[0015] S1.2. Uncertainty Modeling of Photovoltaic Power Forecast Error

[0016] In a typical daily time series T, the distributed photovoltaic power prediction error of any node i connected to the distribution network is expressed as:

[0017] P Ei =P DGi -P prei (3)

[0018] Where: P DGi is the actual power of distributed photovoltaic connected to node i; P prei is the predicted value of the photovoltaic power connected to node i;

[0019] Let W be the total number of nodes in the system, then:

[0020]

[0021] In formula (3), the actual photovoltaic power P DGi , power prediction error P Ei They are all time series random variables, and together with T, they constitute a set of multidimensional random vectors;

[0022] Let Y = [P E T] T , then the joint probability density function of the photovoltaic power prediction error connected to any node i based on GMM is:

[0023]

[0024] Where:

[0025]

[0026]

[0027] S1.3. Uncertainty Modeling of Voltage Deviation at Distribution Network Nodes

[0028] The node voltage deviation affected by the photovoltaic power prediction error can be described as:

[0029] V E =[V E1 V E2 … V EW ] T (8)

[0030] Considering the impact of injected active power uncertainty on node voltage distribution, the node voltage deviation is expressed as:

[0031]

[0032] Where: A is the sensitivity coefficient matrix, where P i 、U i are the actual injected power and node voltage of node i respectively; ΔP Ei This is the probability density of the photovoltaic power prediction error of node i as shown in formula (5);

[0033] The conditional probability density function of the voltage deviation of any photovoltaic access node i also obeys k expectations Aμ ki , the covariance is The weighted superposition form of the Gaussian components is:

[0034]

[0035] Where:

[0036]

[0037] S2. Power distribution optimization evaluation

[0038] S2.1、Balancing power analysis of voltage-limited nodes

[0039] The conditional probability distribution of the voltage deviation of any photovoltaic access node in the distribution network caused by the photovoltaic power prediction error can be expressed as:

[0040]

[0041] Define any voltage-over-limit high-risk node as satisfying:

[0042] p(v Ei >ΔU over )≥ξ∪p(v Ei <ΔU low )≥ξ (13)

[0043] Where: p(Z) is the probability of event Z occurring; ΔUover , ΔU low are the upper and lower limits of voltage deviation respectively. If U N is the system rated voltage, then [U N -ΔU low ,U N +ΔU over ] is the allowable voltage deviation range; ξ is the voltage over-limit probability threshold;

[0044] The transformed network should meet the following requirements:

[0045] p(v Ei >ΔU over )<ξ∩p(v Ei <ΔU low )<ξ (14)

[0046] The power distribution optimization process of the distribution network can be described as:

[0047]

[0048] Where: ΔP ij is the power to be balanced between node i and node j; and is the node voltage deviation quantile, and:

[0049]

[0050] S2.2. Feasibility Analysis of Interconnectable Nodes

[0051] For any two nodes i and j, according to the GMM conditional probability consistency principle, when the voltage of node i exceeds the limit, the conditional probability density of the voltage exceeding the limit of node j also obeys GMM, that is:

[0052]

[0053] Therefore, the voltage deviation v at node j is obtained Ej The marginal probability distribution of

[0054] According to the GMM marginal probability consistency principle, v Ej The probability density function of also obeys the distribution of formula (17), which can be expressed as:

[0055]

[0056] Its probability distribution can be expressed as:

[0057]

[0058] When the voltage over-limit probability of node i and node j satisfies equation (20), it is possible to optimize the network power distribution by flexible loop closing between the two nodes. Otherwise, loop closing is not possible.

[0059]

[0060] S2.3 Analysis of power support capability of contact nodes of voltage-over-limit nodes

[0061] The power to be balanced between the two nodes is calculated by calculating the voltage deviation of node j:

[0062]

[0063] Where: v Eij is the difference between the voltage deviations of nodes i and j;

[0064] If node i is a high-risk node with voltage exceeding the upper limit, node j can provide balancing power ΔP ij The probability is:

[0065]

[0066] If node i is a high-risk node with voltage exceeding the lower limit, node j can provide balancing power ΔP ij The probability is:

[0067]

[0068] Define p + 、p - When equation (24) is satisfied, the tie node j has sufficient power support capability for the voltage-over-limit node i.

[0069] p + ≥ζ∪p - ≥ζ (24)

[0070] Where: ζ is the power support probability threshold;

[0071] S3. Multi-objective decision-making model for DC closed loop distribution network

[0072] S3.1. Objective Function

[0073] The overall objective function includes minimizing the comprehensive investment cost, minimizing the system operation loss, and minimizing the system node voltage deviation. The weights of each sub-objective γ1, γ2, and γ3 can be determined by the hierarchical analysis method. Therefore, the overall objective F can be expressed as:

[0074]

[0075] (1) Comprehensive investment cost

[0076] The comprehensive investment cost of DC loop transformation of distribution network includes the cost of new VSC converter station and the cost of new DC circuit breaker, namely:

[0077]

[0078] Where: c VSC is the construction cost of the VSC converter station per unit capacity; S VSCn is the capacity of the nth VSC; c DB Cost of a single DC circuit breaker; N is the total number of newly built VSC converter stations; N DB The total number of newly added DC circuit breakers is N. DB =N;

[0079] (2) System operation loss

[0080] System operation losses include AC and DC line losses and converter losses Right now:

[0081]

[0082] The AC and DC line losses are:

[0083]

[0084] Where: are the total number of AC and DC lines in the system; I m , I l are the currents of the mth and lth branches respectively; R m 、R l are the resistances of the mth and lth branches respectively;

[0085] In the simplified VSC equivalent circuit: are the active and reactive powers input to the VSC from the AC side respectively; is the active power output on the DC side of the VSC; is the equivalent reactive power inside the VSC; are the AC and DC side voltages of VSC respectively; is the internal voltage of VSC; I n 、R n and X n are the equivalent branch current, resistance and reactance respectively. Therefore, the converter loss cost is:

[0086]

[0087] (3) The system node voltage deviation target is described as:

[0088]

[0089] S3.2 Constraints

[0090] S3.2.1. Network Closure Feasibility Constraints

[0091] The feasibility constraints of the network loop can be described by equations (20) and (24);

[0092] S3.2.2 System Operation Constraints

[0093] (1) AC network power flow constraints

[0094] Assuming that the three-phase AC distribution system is balanced, the DistFlow branch power flow equation is:

[0095]

[0096]

[0097]

[0098] Where: P ij , Q ij are the active and reactive power transmitted between nodes i and j respectively; I ij 、R ij and X ij are branch current, resistance and reactance respectively; P j , Q j and U j are the injected active power, reactive power and voltage amplitude of node j respectively; θ(j) and κ(j) represent the set of branch end and head end nodes with node j as the head and end node respectively;

[0099] (2) Power flow constraints of double-ended DC closed-loop networks

[0100] The double-terminal flexible DC line closing scheme is adopted, where the DC line power flow equation is:

[0101]

[0102]

[0103] The steady-state power flow constraint of the VSC converter is:

[0104]

[0105]

[0106] Where: α is the VSC DC voltage utilization rate; M n is the modulation ratio of the VSC converter, and 0≤Mn ≤1;

[0107] (3) The system node voltage safety constraint is:

[0108] U N -ΔU low ≤U i ≤U N +ΔU over (38)

[0109] (4) The transmission capacity constraints of AC and DC lines are:

[0110]

[0111]

[0112] Where: are the upper limits of the transmission capacity of AC and DC distribution lines, respectively. The relationship between the maximum power of the DC line and the transmission power of the AC line is:

[0113]

[0114] And there are:

[0115]

[0116] S4. Convexity transformation of decision model

[0117] (1) Second-order cone convex relaxation

[0118] The node voltage amplitude and branch current square terms are defined as:

[0119]

[0120] In satisfaction Under the conditions that the objective function is a strictly increasing function and the node load has no upper limit, Equations (33) and (41) are rewritten as:

[0121]

[0122]

[0123] Rewrite Equation (33) and Equation (41) into standard second-order cone form:

[0124]

[0125]

[0126] Formulas (28), (29), (31), (32), (34) to (36), and (38) in the decision model are replaced by the following formulas:

[0127]

[0128]

[0129]

[0130]

[0131]

[0132]

[0133]

[0134]

[0135] (2) Absolute value linearization

[0136] Formula (30) is the absolute value summation target, introducing the intermediate variable O i , rewrite it into inequality constraints as shown in Equation (55) and Equation (56):

[0137]

[0138]

[0139] (3) VSC steady-state voltage constraint linearization

[0140] Assume that VSC adopts SPWM modulation mode, then α is Then Equation (37) can be equivalent to the following linear constraint:

[0141]

[0142] Performing second-order cone relaxation on the above equation yields:

[0143]

[0144] (4) Linearization of AC Line Transmission Capacity Constraints

[0145] The AC line transmission capacity constraint shown in formula (39) is a quadratic constraint conditional formula. The linear approximation is performed using the quadratic circle constraint of the rotating regular polygon. The obtained linear constraint equation is:

[0146]

[0147] The present invention realizes flexible power transfer between distribution lines, effectively optimizes the voltage distribution of network nodes, and greatly improves the distribution network's ability to accept distributed photovoltaics. BRIEF DESCRIPTION OF THE DRAWINGS

[0148] Figure 1 This is the VSC equivalent circuit diagram;

[0149] Figure 2 Flowchart for planning method;

[0150] Figure 3 is a photovoltaic power curve diagram used in the embodiment;

[0151] Figure 4 This is a comparison chart of the prediction error simulation effect;

[0152] Figure 5 FIG. 1 is a diagram of the IEEE 33-node test system used in the embodiment;

[0153] Figure 6a This is the node voltage distribution result diagram of the original AC network without any optimization decision scenario;

[0154] Figure 6b The node voltage distribution result diagram is a diagram that only considers the feasibility of system loop closing without considering any other optimization conditions;

[0155] Figure 6c In order to consider the feasibility of system loop closing and comprehensive investment and operation costs, the node voltage distribution result diagram under the target scenario of system node voltage deviation is not considered;

[0156] Figure 6d This is a diagram of node voltage distribution results under the multi-objective decision model scenario proposed by the present invention;

[0157] Figure 7 This is a comparison of node voltage peaks under different photovoltaic penetration rates;

[0158] Figure 8 is the scatter plot of the second-order cone relaxation error. DETAILED DESCRIPTION

[0159] The following combination Figures 1 to 8 The present invention will be described in further detail. The specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0160] 1 Distribution Network Uncertainty Modeling Based on GMM

[0161] 1.1 Basic Principles of GMM

[0162] The Gaussian mixture model is a model that describes the probability density distribution of a mixture and is widely used in pattern recognition, image segmentation, cluster analysis, and other fields. It is not limited to a specific probability density function form assumption. Any probability density distribution can be approximated by a weighted linear combination of several Gaussian density functions. The GMM probability density function can be expressed as:

[0163]

[0164] Where: M is the number of Gaussian components of GMM; is the kth one-dimensional Gaussian component; ω k 、μ k 、 are the weight, expectation and covariance of the kth Gaussian component respectively.

[0165] where ω k Normalization conditions should be met:

[0166]

[0167] For the parameter ω in the Gaussian mixture model k 、μ k and The expectation maximization (EM) algorithm is usually used to solve the problem. The basic idea of the EM algorithm is to introduce implicit variables to solve the maximum likelihood estimate of the model distribution parameters, and then repeatedly iterate the implicit variable expectation formula and the model distribution parameter re-estimation formula until the likelihood function value converges. In addition, since GMM has the characteristics of marginal probability and conditional probability consistency, if the random variable If it obeys GMM, then its marginal probability and conditional probability must obey GMM.

[0168] 1.2 Uncertainty Modeling of Photovoltaic Power Forecast Error

[0169] In a typical daily time series T, the distributed photovoltaic power prediction error of any node i connected to the distribution network can be expressed as:

[0170] P Ei =P DGi -P prei (3)

[0171] Where: P DGi is the actual power of distributed photovoltaic connected to node i; P prei is the predicted value of the photovoltaic power connected to node i.

[0172] Let W be the total number of nodes in the system, then:

[0173]

[0174] In formula (3), the actual photovoltaic power P DGi , power prediction error P Ei They are all time series random variables, and together with T, they form a set of multidimensional random vectors. By establishing the joint probability density function of the multidimensional random vectors, the timing uncertainty of the node photovoltaic power can be described.

[0175] Let Y = [P E T] T , then the joint probability density function of the photovoltaic power prediction error connected to any node i based on GMM is:

[0176]

[0177] Where:

[0178]

[0179]

[0180] 1.3 Distribution network node voltage deviation uncertainty modeling

[0181] Based on the node photovoltaic power prediction error model derived in Section 1.2, a probabilistic power flow method is introduced to analyze the voltage over-limit risk of each node in the distribution network. The node voltage deviation affected by the photovoltaic power prediction error can be described as:

[0182] V E =[V E1 V E2 … V EW ] T (8)

[0183] Since the photovoltaic grid-connected inverters in the distribution network have certain reactive power regulation capabilities, the uncertainty of reactive power injected into each node is much smaller than the active power.

[0184] The present invention only considers the impact of injected active power uncertainty on node voltage distribution, so the node voltage deviation can be expressed as:

[0185]

[0186] Where: A is the sensitivity coefficient matrix, where P i 、U i are the actual injected power and node voltage of node i respectively; ΔP Ei This is the probability density of the photovoltaic power prediction error of node i as shown in formula (5).

[0187] Due to the consistency of conditional probability, similar to the probability distribution of node power deviation, the conditional probability density function of the voltage deviation of any photovoltaic access node i also obeys k expectations of Aμ ki , the covariance is The weighted superposition form of the Gaussian components is:

[0188]

[0189] Where:

[0190]

[0191] 2 Power Distribution Optimization Evaluation

[0192] 2.1 Analysis of the balancing power required for voltage-exceeding nodes From formula (10), we can see that the conditional probability distribution of the voltage deviation of any photovoltaic access node in the distribution network caused by the photovoltaic power prediction error can be expressed as:

[0193]

[0194] Therefore, any voltage-over-limit high-risk node is defined as satisfying:

[0195] p(v Ei >ΔU over )≥ξ∪p(v Ei <ΔU low )≥ξ (13)

[0196] Where: p(Z) is the probability of event Z occurring; ΔU over , ΔU low are the upper and lower limits of voltage deviation respectively. If U N is the system rated voltage, then [U N -ΔU low ,U N +ΔU over ] is the allowable voltage deviation range; ξ is the voltage over-limit probability threshold.

[0197] For the high-limit-crossing risk node described by equation (13), the voltage deviation probability within time period T is greater than or equal to ξ. The present invention optimizes the power distribution of the distribution network through flexible DC loop closing to reduce the voltage-crossing risk of network nodes. The modified network should meet the following requirements:

[0198] p(v Ei >ΔU over )<ξ∩p(v Ei <ΔU low )<ξ (14)

[0199] Therefore, the power distribution optimization process of the distribution network can be described as:

[0200]

[0201] Where: ΔP ij is the power to be balanced between node i and node j; and is the node voltage deviation quantile, and:

[0202]

[0203] 2.2 Feasibility Analysis of Interconnectable Node Rings

[0204] For any two nodes i and j, according to the GMM conditional probability consistency principle, when the voltage of node i exceeds the limit, the conditional probability density of the voltage exceeding the limit of node j also obeys GMM, that is:

[0205]

[0206] Therefore, the voltage deviation v at node j can be calculated Ej The marginal probability distribution of .

[0207] According to the GMM marginal probability consistency principle, v Ej The probability density function of also obeys the distribution of formula (17), which can be expressed as:

[0208]

[0209] Its probability distribution can be expressed as:

[0210]

[0211] When the voltage over-limit probability of node i and node j satisfies equation (20), it is possible to optimize the network power distribution by flexible loop closing between the two nodes; otherwise, loop closing is not possible.

[0212]

[0213] 2.3 Analysis of power support capability of contact nodes with voltage-over-limit nodes

[0214] The power to be balanced between the two nodes is calculated by calculating the voltage deviation of node j:

[0215]

[0216] Where: v Eij is the difference between the voltage deviations at nodes i and j.

[0217] If node i is a high-risk node with voltage exceeding the upper limit, node j can provide balancing power ΔP ij The probability is:

[0218]

[0219] If node i is a high-risk node with voltage exceeding the lower limit, node j can provide balancing power ΔP ij The probability is:

[0220]

[0221] Define p + 、p - When equation (24) is satisfied, the tie node j has sufficient power support capability for the voltage-over-limit node i.

[0222] p + ≥ζ∪p - ≥ζ (24)

[0223] Where: ζ is the power support probability threshold.

[0224] Therefore, the sequential power complementarity of interconnected nodes can be evaluated by calculating the power support capability under different scenarios, and the feasibility of alleviating node voltage over-limit through node interconnection can be further determined.

[0225] 3. Multi-objective decision-making model for DC closed loop of distribution network

[0226] 3.1 Objective Function

[0227] The proposed multi-objective DC closed-loop decision model for distribution networks has an overall objective function that minimizes comprehensive investment costs, minimizes system operating losses, and minimizes system node voltage deviations. The weights of each sub-objective, γ1, γ2, and γ3, can be determined using the analytic hierarchy process. Therefore, the overall objective F can be expressed as:

[0228]

[0229] (1) Comprehensive investment cost

[0230] The comprehensive investment cost of DC loop transformation of distribution network includes the cost of new VSC converter station and the cost of new DC circuit breaker, namely:

[0231]

[0232] Where: c VSC is the construction cost of the VSC converter station per unit capacity; S VSCn is the capacity of the nth VSC; c DB Cost of a single DC circuit breaker; N is the total number of newly built VSC converter stations; N DB The total number of newly added DC circuit breakers is N. DB =N.

[0233] (2) System operation loss

[0234] System operation losses include AC and DC line losses and converter losses Right now:

[0235]

[0236] The AC and DC line losses are:

[0237]

[0238] Where: are the total number of AC and DC lines in the system; I m , I l are the currents of the mth and lth branches respectively; R m 、R l are the resistances of the mth and lth branches respectively. Since there is no proximity effect and skin effect in DC lines, for the same type of wires, there are R dc =0.98R ac , where R ac and R dc are the AC and DC line resistances respectively.

[0239] The simplified VSC equivalent circuit is as follows: Figure 1 As shown, it consists of equal impedance and ideal VSC. are the active and reactive powers input to the VSC from the AC side respectively; is the active power output on the DC side of the VSC; is the equivalent reactive power inside the VSC; are the AC and DC side voltages of VSC respectively; is the internal voltage of VSC; I n 、R n and X n are the equivalent branch current, resistance and reactance respectively. Therefore, the converter loss cost is:

[0240]

[0241] (3) The system node voltage deviation target is described as:

[0242]

[0243] 3.2 Constraints

[0244] 3.2.1 Network Closure Feasibility Constraints

[0245] According to the discussion in Section 2 of the present invention, the distribution network can be closed-loop transformed through the flexible DC link only when the power mutual assistance conditions are met between the nodes. Therefore, the feasibility constraints of the network closing loop can be described by Equations (20) and (24), where ξ is taken as 0.5 and ζ is taken as 0.75.

[0246] 3.2.2 System Operation Constraints

[0247] (1) AC network power flow constraints

[0248] Assuming that the three-phase AC distribution system is balanced, the DistFlow branch power flow equation is:

[0249]

[0250]

[0251]

[0252] Where: P ij , Q ij are the active and reactive power transmitted between nodes i and j respectively; I ij 、R ij and X ij are branch current, resistance and reactance respectively; P j , Q j and U j are the injected active power, reactive power and voltage amplitude of node j respectively; θ(j) and κ(j) represent the set of branch end and head end nodes with node j as the head and end node respectively.

[0253] (2) Power flow constraints of double-ended DC closed-loop networks

[0254] The present invention adopts a double-ended flexible DC line loop closing scheme, wherein the DC line power flow equation is:

[0255]

[0256]

[0257] Depend on Figure 1 It can be seen that the steady-state power flow constraint of the VSC converter is:

[0258]

[0259]

[0260] Where: α is the VSC DC voltage utilization rate; M n is the modulation ratio of the VSC converter, and 0≤M n ≤1.

[0261] (3) The system node voltage safety constraint is:

[0262] U N -ΔU low ≤U i ≤U N +ΔU over (38)

[0263] (4) The transmission capacity constraints of AC and DC lines are:

[0264]

[0265]

[0266] Where: are the upper limits of the transmission capacity of AC and DC distribution lines, respectively. Referring to the conclusions of existing literature, the relationship between the maximum power of the DC line and the transmission power of the AC line is:

[0267]

[0268] And there are:

[0269]

[0270] In summary, the process of the dynamic DC closed loop planning method for distributed photovoltaic distribution network considering node power mutual assistance proposed by the present invention is as follows: Figure 2 shown.

[0271] 4 Convexity transformation of decision model

[0272] The dynamic DC closed-loop planning model for a distributed photovoltaic distribution network, including node power mutualization, is a typical mixed-integer non-convex programming problem, making it difficult to solve directly and quickly. Therefore, it is necessary to linearize the model and transform it into a convex one, constructing a mixed-integer linear convex optimization model to effectively reduce the solution difficulty.

[0273] (1) Second-order cone convex relaxation

[0274] The node voltage amplitude and branch current square terms are defined as:

[0275]

[0276] In satisfaction Under the conditions that the objective function is a strictly increasing function and the node load has no upper limit, equations (33) and (41) can be rewritten as:

[0277]

[0278]

[0279] Therefore, Equation (33) and Equation (41) are rewritten into standard second-order cone forms:

[0280]

[0281]

[0282] In addition, equations (28), (29), (31), (32), (34) to (36), and (38) in the decision model can be replaced by the following equations:

[0283]

[0284]

[0285]

[0286]

[0287]

[0288]

[0289]

[0290]

[0291] (2) Absolute value linearization

[0292] Formula (30) is the absolute value summation target, introducing the intermediate variable O i , rewrite it into inequality constraints as shown in Equation (55) and Equation (56):

[0293]

[0294]

[0295] (3) VSC steady-state voltage constraint linearization

[0296] Assume that VSC adopts SPWM modulation mode, then α is Then Equation (37) can be equivalent to the following linear constraint:

[0297]

[0298] Performing second-order cone relaxation on the above equation yields:

[0299]

[0300] (4) Linearization of AC Line Transmission Capacity Constraints

[0301] The AC line transmission capacity constraint shown in formula (39) is a quadratic constraint conditional formula. The linear approximation is performed using the quadratic circle constraint of the rotating regular polygon. The obtained linear constraint equation is:

[0302]

[0303] After the above transformation, the original model becomes a mixed integer second-order cone convex programming problem, which can be efficiently solved by commercial solvers.

[0304] 5 Case Analysis

[0305] 5.1 GMM photovoltaic power prediction error simulation

[0306] The uncertainty analysis of photovoltaic power is conducted based on the effective data of a typical day of a photovoltaic power station in a certain province of China. The actual photovoltaic power and the predicted power curve are as follows: Figure 3 As shown in the figure, the data time scale is 24 hours per day, and the data set resolution is 15 minutes. The number of sub-Gaussians of GMM is 3. In order to facilitate the comparison of fitting effects with other distribution models, the error data distribution to be fitted is first mapped to the interval [0,1]. Then, the Normal distribution, Gamma distribution, Beta distribution, Weibull distribution and GMM are selected to compare the simulation effects of the given photovoltaic power data prediction error, as shown in the figure. Figure 4 As shown. The fitting error of each distribution model is represented by the absolute average error X MAE (mean absolute error, MAE), cosine angle transformation formula X cos For quantization, equations (61) and (62) are respectively X MAE and X cos The calculation formula is, where MAE is used to represent the average error of the model. The smaller the value, the higher the fitting accuracy. cos The model fitting effect can be verified. When X cos The closer it is to 0, the more similar the fitted model is to the original distribution curve. The calculation results of each model index are shown in Table 1.

[0307]

[0308]

[0309] Table 1 Fitting errors of different distribution models

[0310]

[0311] The comparison results in Table 1 show that the absolute mean error and cosine angle transform index of the GMM model are significantly lower than those of all other models, indicating that the average error after fitting this model is small, and its fitting curve is most similar to the original curve. This verifies the superiority of the GMM in this invention for modeling photovoltaic power forecast error uncertainty.

[0312] 5.2 Simulation and Analysis of Modified IEEE 33-Node Test System Example

[0313] In order to verify the correctness and effectiveness of the dynamic DC closed-loop planning method for distribution network considering the uncertainty of photovoltaic power prediction error proposed in this paper, a modified 33-node test case was established on the Matlab 2020a platform to analyze and verify it. Figure 5 As shown in the example, nodes 8, 13, 16, 25 and 32 are connected to distributed photovoltaics. Since the distribution network covers a small area, there is no significant difference in the light intensity, temperature and other factors of each node. Therefore, the output of each photovoltaic power station is set to be the same as Figure 3 The curves are consistent, and the photovoltaic installed capacity at each node is 2.1MW, with a power factor of 0.95; the load and branch admittance parameters of each node in the example system are shown in Appendix A Table A1.

[0314] The loop feasibility constraints determine that the loop-closing routes are: 8-21, 12-22, and 25-29. To further verify the effectiveness of the loop-closing planning proposed in this invention, the following four scenarios are set for detailed comparative analysis:

[0315] Case 1: Original communication network, without any optimization decision;

[0316] Case 2: Only the feasibility of system closure is considered without considering any other optimization conditions;

[0317] Case 3: Considering the system loop feasibility and comprehensive investment and operating costs, without considering the system node voltage deviation target;

[0318] Case 4: The multi-objective decision-making model proposed in this invention.

[0319] 5.2.1 Node voltage distribution analysis

[0320] Figure 6 shows the node voltage distribution at different times of grid optimization results for the four scenarios described above. In the figure, nodes with voltage limits exceeding the upper and lower limits are circled in red and blue, respectively. As shown in Figure 6, in scenario 1, where no loop lines are added, node voltages exceed limits to varying degrees during both peak and valley times of the PV power station's output. However, scenarios 2 and 3 only experience minor node voltage limits exceeding limits during peak PV output times. Because scenario 3 prioritizes economic efficiency as its primary optimization objective, it does not fully address node voltage limit violations. Scenario 4, which takes voltage deviation into account, does not experience any node voltage limit violations. The frequency and mean of node voltage limits are shown in Table 2.

[0321] Table 2 Node voltage over-limit frequency and mean value under different scenarios

[0322]

[0323] 5.2.2 Analysis of Photovoltaic Acceptance Capacity

[0324] Due to the different closing conditions considered in the four scenarios, the photovoltaic acceptance capacity of the system in each scenario is different. Figure 7 The figure shows a comparison of node voltage peaks for various scenarios at different PV penetration rates. The dashed line in the figure represents the node voltage upper limit of 1.07 per unit, set by the present invention. It can be seen that the maximum acceptable PV penetration rate for scenario 4 in this system is 280%, while the node voltage peak for scenario 1 reaches 1.07 at a PV penetration rate of 85%. The PV acceptance capacity curves for scenarios 2 and 3 are not clearly distinguishable, but their acceptance capacities lie between those of scenarios 1 and 4. This demonstrates that the proposed DC closed-loop planning method for distribution networks can effectively improve the system's PV acceptance capacity.

[0325] 5.2.3 Analysis of the influence of second-order cone convex relaxation

[0326] In addition, to verify the effect of second-order cone relaxation on the accuracy of the model proposed in this invention, the branch parameter error in a single planning cycle is described by the infinite norm of all branch deviations contained in the system at a certain moment, that is:

[0327]

[0328] The scatter plot of the second-order cone relaxation error obtained by the above formula is as follows Figure 8 As shown in the figure, the square deviation vector of the branch current amplitude after relaxation is very small, only 10 -3The magnitude meets the planning requirements, so it can be shown that the second-order cone relaxation formula is accurate. The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be considered within the scope of protection of the present invention.

[0329] Appendix A

[0330] Table A1 IEEE 33-node test system parameters

[0331]

[0332] Note: The system head-end reference voltage is 12.66kV, the three-phase power reference value is 10MVA, and the total system load is 5084.26+j2547.32kW.

[0333] The Chinese names of the symbols involved in the present invention are as follows:

[0334] M is the number of Gaussian components of GMM

[0335] is the kth one-dimensional Gaussian component

[0336] ω k is the weight of the kth Gaussian component

[0337] μ k is the expectation of the kth Gaussian component

[0338] is the covariance of the kth Gaussian component

[0339] X is any random variable

[0340] T is the time series

[0341] P Ei is the distributed photovoltaic power prediction error of node i

[0342] P DGi is the actual power of distributed photovoltaic connected to node i

[0343] P prei is the predicted value of the photovoltaic power connected to node i

[0344] W is the total number of nodes in the system

[0345] Y is the joint vector of PV power forecast error and time series

[0346] V Ei is the voltage deviation caused by the photovoltaic power prediction error at node i

[0347] A is the sensitivity coefficient matrix

[0348] P i is the actual injected power of node i

[0349] U i is the actual node voltage of node i

[0350] ΔP Ei is the probability density of the photovoltaic power prediction error of node i

[0351] μ' k is the expectation of the conditional probability density function of the node voltage deviation

[0352] σ' k 2 is the covariance of the conditional probability density function of the node voltage deviation

[0353] Conditional probability distribution of voltage deviation at node i

[0354] Conditional probability distribution of the kth one-dimensional Gaussian component of the voltage deviation at node i

[0355] Z is any event

[0356] p(Z) is the probability of any event occurring where Z is the

[0357] ΔU over The upper limit of the node voltage deviation

[0358] ΔU low The lower limit of the node voltage deviation

[0359] U N The rated voltage of the system

[0360] ξ is the voltage over-limit probability threshold

[0361] is the upper quantile of the node voltage deviation

[0362] is the lower quantile of the node voltage deviation

[0363] μ″ k is the expectation of the marginal probability density function of node voltage deviation

[0364] is the covariance of the marginal probability density function of node voltage deviation

[0365] ΔP ij The power to be balanced between two nodes i and j

[0366] v Eij The difference between the voltage deviations at nodes i and j

[0367] p + Node j can provide balancing power ΔP for node i whose voltage exceeds the upper limit ij Probability

[0368] p - Node j can provide balancing power ΔP for node i whose voltage exceeds the lower limit ij Probability

[0369] ζ is the power support probability threshold

[0370] F is the overall goal of the planning model

[0371] F1, F2 and F3 are sub-goals of the planning model

[0372] γ1, γ2 and γ3 are the weight coefficients of each sub-goal

[0373] c VSC The construction cost of the VSC converter station per unit capacity is

[0374] S VSCn is the capacity of the nth VSC

[0375] c DB Cost of a single DC circuit breaker

[0376] N is the total number of newly built VSC converter stations

[0377] N DB Total number of newly added DC circuit breakers

[0378] is the AC / DC distribution line loss

[0379] is the converter loss

[0380] The total number of AC lines in the system

[0381] is the total number of DC lines in the system

[0382] I m , I l The currents of the mth and lth branches are

[0383] R m 、R l The resistances of the mth and lth branches are

[0384] R ac and R dc are AC and DC line resistances respectively

[0385] are the active and reactive power input to the VSC from the AC side

[0386] Active power output on the VSC DC side

[0387] is the VSC internal equivalent reactive power

[0388] VSC AC and DC side voltages respectively

[0389] VSC internal voltage

[0390] I n 、R n and X n are the equivalent branch current, resistance and reactance respectively

[0391] P ij , Q ij are the active and reactive power transmitted between nodes i and j respectively

[0392] I ij 、R ij and X ij are the current, resistance and reactance of branch ij respectively

[0393] P j , Q j and U j are the injected active power, reactive power and voltage amplitude of node j respectively

[0394] P jk , Q jk are the active and reactive power transmitted between nodes j and k respectively

[0395] θ(j) and κ(j) represent the set of branch end and head node with node j as the head and end node respectively.

[0396] α is the VSC DC voltage utilization rate

[0397] M n is the modulation ratio of the VSC converter

[0398] are the active and reactive power transmitted by the AC line between nodes i and j, respectively.

[0399] is the active power transmitted by the DC line between nodes i and j

[0400] The upper limits of the transmission capacity of AC and DC distribution lines are

[0401] The upper limits of active power transmission for AC and DC distribution lines are

[0402] is the actual node voltage of DC node i

[0403] is the current transmitted by the DC line between nodes i and j

[0404] They are the node voltage amplitude U i and branch current I ij The square term of

[0405] O i is the intermediate variable for the convex transformation of the absolute value function

[0406] They are and The square term of

[0407] X MAE is the absolute mean error

[0408] X cos is the cosine angle transformation

[0409] P' Ei is the fitting result of the distributed photovoltaic power prediction error of node i

[0410] n is the number of sampling points of the photovoltaic power curve

[0411] is the parameter error of branch ij within a single planning cycle.

Claims

1. A method for dynamic DC closed-loop planning of a distributed photovoltaic distribution network, characterized by: The steps are: S1. Distribution network uncertainty modeling based on GMM S1.1 Basic principles of GMM The GMM probability density function can be expressed as: Where: M is the number of Gaussian components of GMM; is the kth one-dimensional Gaussian component; ω k 、μ k 、 are the weight, expectation and covariance of the kth Gaussian component respectively; where ω k Normalization conditions should be met: Parameter ω in the Gaussian mixture model k 、μ k and The expectation maximization algorithm is used to solve the problem; random variable Obey GMM, its marginal probability and conditional probability must obey GMM; S1.

2. Uncertainty Modeling of Photovoltaic Power Forecast Error In a typical daily time series T, the distributed photovoltaic power prediction error of any node i connected to the distribution network is expressed as: P Ei =P DGi -P prei (3) Where: P DGi is the actual power of distributed photovoltaic connected to node i; P prei is the predicted value of the photovoltaic power connected to node i; Let W be the total number of nodes in the system, then: In formula (3), the actual photovoltaic power P DGi , power prediction error P Ei are all time series random variables, and together with T, they form a set of multidimensional random vectors; let Y = [P E T] T , then the joint probability density function of the photovoltaic power prediction error connected to any node i based on GMM is: Where: S1.

3. Uncertainty Modeling of Voltage Deviation at Distribution Network Nodes The node voltage deviation affected by the photovoltaic power prediction error can be described as: V E =[V E1 V E2 … V EW ] T (8) Considering the impact of injected active power uncertainty on node voltage distribution, the node voltage deviation is expressed as: Where: A is the sensitivity coefficient matrix, where P i 、U i are the actual injected power and node voltage of node i respectively; ΔP Ei This is the probability density of the photovoltaic power prediction error of node i as shown in formula (5); The conditional probability density function of the voltage deviation of any photovoltaic access node i also obeys k expectations Aμ ki , the covariance is The weighted superposition form of the Gaussian components is: Where: S2. Power distribution optimization evaluation S2.1、Balancing power analysis of voltage-exceeding nodes The conditional probability distribution of the voltage deviation of any photovoltaic access node in the distribution network caused by the photovoltaic power prediction error can be expressed as: Define any voltage-over-limit high-risk node as satisfying: p(v Ei >ΔU over )≥ξ∪p(v Ei <ΔU low )≥ξ (13) Where: p(Z) is the probability of event Z occurring; ΔU over , ΔU low are the upper and lower limits of voltage deviation respectively. If U N is the system rated voltage, then [U N -ΔU low ,U N +ΔU over ] is the allowable voltage deviation range; ξ is the voltage over-limit probability threshold; The transformed network should meet the following requirements: p(v Ei >ΔU over )<ξ∩p(v Ei <ΔU low )<ξ (14) The power distribution optimization process of the distribution network can be described as: Where: ΔP ij is the power to be balanced between node i and node j; and is the node voltage deviation quantile, and: S2.

2. Feasibility Analysis of Interconnectable Nodes For any two nodes i and j, according to the GMM conditional probability consistency principle, when the voltage of node i exceeds the limit, the conditional probability density of the voltage exceeding the limit of node j also obeys GMM, that is: Therefore, the voltage deviation v at node j is obtained Ej The marginal probability distribution of According to the GMM marginal probability consistency principle, v Ej The probability density function of also obeys the distribution of formula (17), which can be expressed as: Its probability distribution can be expressed as: When the voltage over-limit probability of node i and node j satisfies equation (20), it is possible to optimize the network power distribution by flexible loop closing between the two nodes. Otherwise, loop closing is not possible. S2.3 Analysis of power support capability of contact nodes of voltage-over-limit nodes The power to be balanced between the two nodes is calculated by calculating the voltage deviation of node j: Where: v Eij is the difference between the voltage deviations of nodes i and j; If node i is a high-risk node with voltage exceeding the upper limit, node j can provide balancing power ΔP ij The probability is: If node i is a high-risk node with voltage exceeding the lower limit, node j can provide balancing power ΔP ij The probability is: Define p + 、p - When equation (24) is satisfied, the tie node j has sufficient power support capability for the voltage-over-limit node i; p + ≥ζ∪p - ≥ζ (24) Where: ζ is the power support probability threshold; S3. Multi-objective decision-making model for DC closed loop distribution network S3.

1. Objective Function The overall objective function includes minimizing the comprehensive investment cost, minimizing the system operation loss, and minimizing the system node voltage deviation. The weights of each sub-objective γ1, γ2, and γ3 can be determined by the hierarchical analysis method. Therefore, the overall objective F can be expressed as: (1) Comprehensive investment cost The comprehensive investment cost of DC loop transformation of distribution network includes the cost of new VSC converter station and the cost of new DC circuit breaker, namely: Where: c VSC is the construction cost of the VSC converter station per unit capacity; S VSCn is the capacity of the nth VSC; c DB Cost of a single DC circuit breaker; N is the total number of newly built VSC converter stations; N DB The total number of newly added DC circuit breakers is N. DB =N; (2) System operation loss System operation losses include AC and DC line losses and converter losses Right now: The AC and DC line losses are: Where: are the total number of AC and DC lines in the system; I m , I l are the currents of the mth and lth branches respectively; R m 、R l are the resistances of the mth and lth branches respectively; In the simplified VSC equivalent circuit: are the active and reactive powers input to the VSC from the AC side respectively; is the active power output on the DC side of the VSC; is the equivalent reactive power inside the VSC; are the AC and DC side voltages of VSC respectively; is the internal voltage of VSC; I n 、R n and X n are the equivalent branch current, resistance and reactance respectively, so the converter loss cost is: (3) The system node voltage deviation target is described as: S3.2 Constraints S3.2.

1. Network Closure Feasibility Constraints The feasibility constraints of the network loop can be described by equations (20) and (24); S3.2.2 System Operation Constraints (1) AC network power flow constraints Assuming that the three-phase AC distribution system is balanced, the DistFlow branch power flow equation is: Where: P ij , Q ij are the active and reactive power transmitted between nodes i and j respectively; I ij 、R ij and X ij are branch current, resistance and reactance respectively; P j , Q j and U j are the injected active power, reactive power and voltage amplitude of node j respectively; θ(j) and κ(j) represent the set of branch end and head node with node j as the head and end node, respectively; (2) Power flow constraints of double-ended DC closed-loop networks The double-terminal flexible DC line loop closing scheme is adopted, where the DC line power flow equation is: The steady-state power flow constraint of the VSC converter is: Where: α is the VSC DC voltage utilization rate; M n is the modulation ratio of the VSC converter, and 0≤M n ≤1; (3) The system node voltage safety constraint is: U N -ΔU low ≤U i ≤U N +ΔU over (38) (4) The transmission capacity constraints of AC and DC lines are: Where: are the upper limits of the transmission capacity of AC and DC distribution lines, respectively. The relationship between the maximum power of the DC line and the transmission power of the AC line is: And there are: S4. Convexity transformation of decision model (1) Second-order cone convex relaxation The node voltage amplitude and branch current square terms are defined as: In satisfaction Under the conditions that the objective function is a strictly increasing function and the node load has no upper limit, Equation (33) is rewritten as: Rewrite Equation (44) and Equation (45) into standard second-order cone form: Formulas (28), (29), (31), (32), (34) to (36), and (38) in the decision model are replaced by the following formulas: (2) Absolute value linearization Formula (30) is the absolute value summation target, introducing the intermediate variable O i , rewrite it into inequality constraints as shown in Equation (55) and Equation (56): (3) VSC steady-state voltage constraint linearization Assume that VSC adopts SPWM modulation mode, then α is Then Equation (37) can be equivalent to the following linear constraint: Performing second-order cone relaxation on the above equation yields: (4) Linearization of AC Line Transmission Capacity Constraints The AC line transmission capacity constraint shown in formula (39) is a quadratic constraint conditional formula. The linear approximation is performed using the quadratic circle constraint of the rotating regular polygon. The obtained linear constraint equation is:

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