New energy consumption-oriented power transmission network optimal configuration modeling method

Abstract

The invention discloses a new energy consumption-oriented power transmission network optimal configuration modeling method, which comprises the following steps of: S1, constructing a target function by taking minimization of the investment construction cost of a power transmission network and maximization of the new energy consumption capability of a power system as targets; s2, establishing a first stage constraint; s3, establishing a second stage constraint; s4, according to the objective function, the first stage constraint and the second stage constraint, establishing a general model of transmission network optimal configuration for new energy consumption; and S5, solving the general model to obtain an optimization model. According to the modeling method, quantifiable guidance is provided for investment of the power transmission network and development of new energy, and complete consumption of a power system on new energy power generation is ensured; the balance between the investment cost of the power transmission network and the new energy consumption is quantified in a moderately conservative mode through the distributed robust combined opportunity constraint.

Description

Technical Field

[0001] The present invention relates to the technical field of power transmission network optimization configuration, and particularly relates to a modeling method for power transmission network optimization configuration for new energy consumption. Background Art

[0002] Power transmission network investment has the characteristics of high amount, wide coverage, and strong public attributes. Usually, the investment plan is centrally decided by the system operator. In some areas with rich new energy power generation resources but limited local load demand, for example, in some areas, it is difficult to consume large-scale new energy power generation only relying on local load demand, and wind and light abandonment often occur. As a countermeasure, power transmission network expansion can significantly enhance the power transmission capacity, improve the regional power grid interconnection level, better cope with the uncertainty of high proportion of new energy, and enhance the new energy power generation consumption capacity of the power system. However, the system operator needs to consider various uncertainty factors, resulting in the difficulty of solving the power transmission network optimization configuration problem. Traditionally, the uncertainty on the demand side is regarded as the main source of uncertainty, thus being widely concerned. However, with the continuous increase of new energy power generation penetration rate, the uncertainty on the power generation side has also intensified, so more attention needs to be paid.

[0003] In the research of power transmission network optimization configuration, the most commonly used methods for modeling uncertainty are stochastic optimization and robust optimization methods. There is currently no research to reveal and quantify the trade-off relationship between power transmission network investment cost and new energy consumption capacity. In terms of existing technology modeling, these stochastic optimization and robust optimization methods face challenges in practice. On the one hand, it is usually difficult to obtain the exact distribution of random variables, and these distribution parameters are necessary for stochastic optimization modeling and will affect the out-of-sample performance of the optimal result. As the number of scenarios increases, the calculation time will increase exponentially with exponential complexity. On the other hand, for the robust optimization method, the decision is made considering the worst-case scenario of uncertain parameters, thus resulting in a conservative solution. Summary of the Invention

[0004] The purpose of the present invention is to provide a modeling method for power transmission network optimization configuration for new energy consumption. It aims to solve the problems that in the existing research on power transmission network optimization configuration, the trade-off relationship between power transmission network investment cost and new energy consumption capacity cannot be directly quantified, and traditional stochastic optimization methods often have difficulty in obtaining the exact distribution of random variables or have high computational complexity, and traditional robust optimization methods are prone to leading to overly conservative solutions.

[0005] To achieve the above object, the present invention is realized through the following technical solutions:

[0006] The present invention provides a modeling method for power transmission network optimization configuration for new energy consumption, including:

[0007] Step S1: With the goal of minimizing the investment and construction cost of the transmission grid and maximizing the new - energy consumption capacity of the power system, a target function is constructed. The target function includes decision variables related to the investment and construction of the transmission grid and decision variables related to the new - energy consumption capacity.

[0008] Step S2: For the decision variables related to the investment and construction of the transmission grid, a first - stage constraint is established.

[0009] Step S3: For the decision variables related to the new - energy consumption capacity, a second - stage constraint is established.

[0010] Step S4: According to the target function, the first - stage constraint, and the second - stage constraint, a general model for the optimal configuration of the transmission grid for new - energy consumption is established.

[0011] Step S5: Solve the general model to obtain an optimal model for the optimal configuration of the transmission grid for new - energy consumption.

[0012] Optionally, the expression of the target function is:

[0013]

[0014] In the formula, min represents the minimization function; Ω represents the set of transmission corridors to be built; l represents the transmission corridor; C l represents the investment cost of a single line within the transmission corridor l. and represent the minimum and maximum number of transmission lines within the transmission corridor l, respectively. is whether the m - th line within the transmission corridor l is built. When , it means it is built; when , it means it is not built. δ represents the weight coefficient; u represents the probability that the power system fully consumes new energy. represents the investment cost of the newly built line, and δu represents the new - energy consumption capacity.

[0015] Optionally, the first - stage constraint includes: line - investment constraint, first - line power - flow constraint, first - power - balance constraint, and first - unit output constraint.

[0016] Optionally, in Step S2, the line - investment constraint is shown as the following formula and includes:

[0017]

[0018]

[0019] In the formula, represents the number of transmission lines within each transmission corridor, and α l (m-1)Indicates whether the (m-1)-th line in the transmission corridor l is to be built; M l Indicates the set of lines to be built in the transmission corridor l;

[0020] The first line power flow constraint is as shown in the following formula, including:

[0021]

[0022] In the formula, Indicates the maximum transmission power of the transmission corridor l; t represents the time period in the pre-scheduling; T represents the set of time periods; Is the power flow on the m-th line in the transmission corridor l at time period t in the pre-scheduling; N l Indicates the set of nodes connected to the transmission corridor l; N represents the set of all nodes; x l Is the impedance of the line in the transmission corridor l; And Respectively represent the phase angles of nodes i and j connected by the transmission corridor l at time period t in the pre-scheduling; Represents the phase angle of node n at time period t in the pre-scheduling;

[0023] The first power balance constraint is as shown in the following formula, including:

[0024]

[0025] In the formula, G represents the set of thermal power units; G(n) represents the set of thermal power units at node n; W represents the set of wind power; W(n) represents the set of wind power at node n; Ω(n) represents the set of transmission corridors connected to node n; Represents the predicted output of wind power w at time period t, d tn Represents the load of node n at time period t. The variable Represents the output of thermal power unit g at time period t in the pre-scheduling;

[0026] The first unit output constraint is as shown in the following formula, including:

[0027]

[0028] In the formula, Represents the upper limit of the output of thermal power unit g.

[0029] Optionally, in step S3, the second-stage constraints include: operating state constraints, new energy consumption range constraints, and distributionally robust joint chance constraints.

[0030] Optionally, the operating state constraints, the new energy consumption range constraints, and the distributionally robust joint chance constraints specifically include:

[0031] The operating state constraints include: second-line power flow constraint, second power balance constraint, and second generator output constraint;

[0032] The second-line power flow constraint is shown as follows and includes:

[0033]

[0034] In the formula, represents the power flow on the m-th line in the transmission corridor l at time t in actual dispatch; θ ti and θ tj respectively represent the phase angles of nodes i and j connected by the transmission corridor l at time t in actual dispatch; θ tn represents the phase angle of node n at time t in actual dispatch; ξ t represents the prediction error of the output of all wind power at time t;

[0035] The second power balance constraint is shown as follows and includes:

[0036]

[0037] In the formula, represents the output of thermal power unit g at time t in actual dispatch; ξ tw represents the prediction error of the output of wind power w at time t;

[0038] The second generator output constraint is shown as follows and includes:

[0039]

[0040] The new energy consumption range constraint is shown as follows and includes:

[0041]

[0042] In the formula, U represents the upper bound; L represents the lower bound; and respectively represent the upper and lower bounds of the consumption range of wind power w at time t;

[0043] The establishment of the distributionally robust joint chance constraint specifically includes the following steps:

[0044] Step S3.1: Establish a fuzzy set D. The fuzzy set D is shown as follows and includes:

[0045]

[0046] In the formula, represents the probability distribution of the prediction error of the output of wind turbines based on historical data; represents the probability distribution expectation; ξ tw represents the prediction error of the output of the wind turbine generator; μ tw represents the mean value of the prediction error of the output of the wind turbine generator; Var represents variance calculation; represents the variance of the prediction error of the output of the wind turbine generator;

[0047] Step S3.2: Establish a new energy consumption capacity model to quantify the probability that wind power is fully consumed by the power system. The new energy consumption capacity model is shown as follows and includes:

[0048]

[0049] u0 ≤ u ≤ 1;

[0050] In the formula, and respectively represent the upper and lower bounds of all wind power prediction errors that the system can consume in period t; u represents the probability that the power system fully consumes new energy; u0 represents the minimum value of the minimum consumption probability.

[0051] Optionally, in step S4, the general model is shown as follows and includes:

[0052]

[0053] α ∈ {0, 1};

[0054]

[0055] Qξ L ≤ q, Rξ U ≤ r;

[0056] In the formula, α represents the decision variable for the investment and construction of the transmission network; C represents the cost coefficient in the objective function; y(ξ) represents the decision variable related to the new energy consumption capacity; Q and q represent the parameters related to the lower limit of the random variable ξ; R and r represent the parameters related to the upper limit of the random variable ξ.

[0057] Optionally, in step S5, solving the general model specifically includes:

[0058] According to the linear affine decision rule, mathematical transformation and duality principle, transform each constraint in the general model into a constraint without the upper and lower bounds of the variable, and obtain the optimization model for the optimal configuration of the transmission network for new energy consumption.

[0059] Optionally, in step S5, the steps for solving the general model specifically include:

[0060] Step S5.1: Assume that the operating state variable in the second-stage constraint is the prediction error ξ of the output of the wind turbine generatortw Subject to the affine decision rule as follows:

[0061] y(ξ) = Bξ + b;

[0062] Step S5.2: Based on the Bonferroni approximation, Gaussian inequality, and second-order cone relaxation, transform the distributionally robust joint chance constraint into the second-order cone form as shown in the following formula, including:

[0063]

[0064] where g tw , v tw and z tw are auxiliary variables, and the parameters μ tw and σ tw are the mean and standard deviation of the random variable fuzzy set, respectively;

[0065] Step S5.3: Define E := diag(ξ U - ξ L ), then the random variable ξ can be written as ξ L + Ev, v ∈ [0, e], where e represents the column vector with all elements being 1; transform the formula in the general model to obtain the transformed formula as:

[0066]

[0067] Replace the quadratic terms BE and Bξ L with S and s respectively, to obtain:

[0068]

[0069] Then the expression of the standard robust form is:

[0070]

[0071] According to the duality principle, dualize the expression of the standard robust form as shown in the following formula:

[0072] Re ≤ Jξ L - T(x) - Ws;

[0073] R ≥ WS - JE, R ≥ 0.

[0074] Optionally, by solving the general model, the final optimized model includes:

[0075] The optimized objective function is as shown in the following formula:

[0076]

[0077] In the formula, E tw , v tw , z tw and g tg are auxiliary variables;

[0078] The optimized second-line power flow constraint is shown as follows:

[0079]

[0080] The optimized second power balance constraint is shown as follows:

[0081]

[0082] The optimized second generator output constraint is shown as follows:

[0083]

[0084] The constraints related to the auxiliary variables are shown as follows:

[0085]

[0086] The optimized distributionally robust joint chance constraint is shown as follows:

[0087]

[0088]

[0089] And the other constraints in the optimization model are the same as those in the general model.

[0090] Compared with the prior art, the present invention has the following beneficial effects:

[0091] Considering the distributionally robust joint chance constraint, the present invention synergistically optimizes the investment in the transmission network and the new energy consumption capacity. On the one hand, it provides a quantifiable guidance for the investment in the transmission network and the development of new energy, and at the same time ensures the complete consumption of new energy power generation by the power system; on the other hand, the distributionally robust joint chance constraint quantifies the trade-off between the investment cost of the transmission network and the new energy consumption capacity in a moderately conservative manner, with clear physical meanings;

[0092] The optimization model proposed by the present invention is a two-stage distributionally robust optimization model, which reformulates the distributionally robust joint chance constraint into a second-order cone form, and replaces the random variable with a combination of the lower bound variable of the random variable and the auxiliary variable to further apply duality for solution, realizing the transformation of the general model into the single-stage robust optimization model, and can be efficiently solved by a commercial solver. Description of the Drawings

[0093] To more clearly illustrate the technical solution of the present invention, the accompanying drawings required in the description will be briefly introduced below. Obviously, the accompanying drawings in the following description are an embodiment of the present invention. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can be obtained based on these drawings:

[0094] Figure 1 It is a flowchart of a modeling method for optimizing the configuration of a transmission network for new energy accommodation provided by an embodiment of the present invention;

[0095] Figure 2 It is a topological diagram of a 6-node system provided by an embodiment of the present invention;

[0096] Figure 3 It is a schematic diagram of the trade-off between investment cost and accommodation range in the system provided by an embodiment of the present invention;

[0097] Figure 4 It is a schematic diagram of the out-of-sample test results of the system provided by an embodiment of the present invention;

[0098] Figure 5 It is a topological diagram of the IEEE 118-node system provided by an embodiment of the present invention;

[0099] Figure 6 It is a schematic diagram of the trade-off between investment cost and accommodation range in the IEEE 118-node system provided by an embodiment of the present invention;

[0100] Figure 7 It is a schematic diagram of the out-of-sample test results of the IEEE 118-node system provided by an embodiment of the present invention. Detailed implementation manners

[0101] The following further elaborates in detail on the modeling method for optimizing the configuration of a transmission network for new energy accommodation proposed by the present invention in combination with the Figures 1 to 7 detailed implementation manners. According to the following description, the advantages and features of the present invention will be clearer. It should be noted that the accompanying drawings are in a very simplified form and all use non-precise scales, only for conveniently and clearly assisting in explaining the purpose of the embodiments of the present invention. In order to make the purpose, features, and advantages of the present invention more obvious and understandable, please refer to the accompanying drawings. It should be known that the structures, scales, sizes, etc. shown in the drawings of this specification are only used to cooperate with the content disclosed in the specification for those familiar with this technology to understand and read, and are not used to limit the limiting conditions for the implementation of the present invention. Therefore, they do not have technical essence. Any modification of the structure, change of the proportional relationship, or adjustment of the size, without affecting the effects that the present invention can produce and the purposes that can be achieved, should still fall within the scope covered by the technical content disclosed by the present invention.

[0102] In view of the fact that in the research on the optimal configuration of the transmission network in the existing technology, the trade-off relationship between the investment cost of the transmission network and the new energy consumption capacity cannot be directly quantified, and traditional stochastic optimization methods often have difficulty in obtaining the exact distribution of random variables or have high computational complexity, and traditional robust optimization methods are prone to lead to overly conservative solutions. As Figure 1 shown, this embodiment provides a modeling method for the optimal configuration of a transmission network for new energy consumption, including:

[0103] Step S1: With the goal of minimizing the investment and construction cost of the transmission network and maximizing the new energy consumption capacity of the power system at the same time, a target function is constructed, and the target function includes: decision variables for the investment and construction of the transmission network and decision variables related to the new energy consumption capacity.

[0104] The expression of the target function is:

[0105]

[0106] In the formula, min represents the minimization function; Ω represents the set of transmission corridors to be built; l represents the transmission corridor; C l represents the investment cost of a single line within the transmission corridor l; and respectively represent the minimum and maximum number of transmission lines within the transmission corridor l; is whether the m-th line within the transmission corridor l is built. When it means it is built; when it means it is not built; δ represents the weight coefficient, and δ is used to adjust the weights of the two goals in step S1; u represents the probability that the power system fully consumes new energy; represents the investment cost of the newly built line, and δu represents the new energy consumption capacity.

[0107] Step S2: For the decision variables of the investment and construction of the transmission network, a first-stage constraint is established. The first-stage constraint includes: line investment constraint, first line power flow constraint, first power balance constraint, and first unit output constraint.

[0108] The line investment constraint is shown as follows and includes:

[0109]

[0110] In the formula, represents the number of transmission lines within each transmission corridor, and α l (m-1) is whether the (m - 1)-th line within the transmission corridor l is built; M l represents the set of lines to be built within the transmission corridor l.

[0111] Equation (2) indicates whether each line is to be built. When it indicates building; when it indicates not building. Equation (3) is used to ensure that the number of transmission lines within each transmission corridor is within the maximum and minimum number ranges, and Equation (4) indicates that new lines should be built in sequence.

[0112] The first line power flow constraint is shown as follows and includes:

[0113]

[0114] In the formula, represents the maximum transmission power of transmission corridor l; t represents the time period in the pre-scheduling; T represents the set of time periods; is the power flow on the m-th line within transmission corridor l at time period t in the pre-scheduling; N l represents the set of nodes connected to transmission corridor l; N represents the set of all nodes; x l is the impedance of the line within transmission corridor l; and respectively represent the phase angles of node i and node j connected by transmission corridor l at time period t in the pre-scheduling; represents the phase angle of node n at time period t in the pre-scheduling.

[0115] Equation (5) ensures that the power flow on each line of transmission corridor l at time period t is within the line transmission capacity. Equation (6) represents the DC power flow constraint of the line. If the line is not built, this constraint will be relaxed. Equation (7) is the node phase angle constraint.

[0116] The first power balance constraint is shown as follows and includes:

[0117]

[0118] In the formula, G represents the set of thermal power units; G(n) represents the set of thermal power units at node n; W represents the set of wind power; W(n) represents the set of wind power at node n; Ω(n) represents the set of transmission corridors connected to node n; represents the predicted output of wind power w at time period t, d tn represents the load of node n at time period t. The variable represents the output of thermal power unit g at time period t in the pre-scheduling. Equation (8) is used to represent the node power balance.

[0119] The first unit output constraint is shown as follows and includes:

[0120]

[0121] In the formula, Denotes the upper limit of the output of the thermal power unit g. Equation (9) is the technical constraint for the output of the thermal power unit.

[0122] Step S3: Establish the second-stage constraints for the decision variables related to the new energy consumption capacity.

[0123] The decisions in the second stage occur after the first-stage decisions are completed, and at this time the uncertainties have been revealed. Therefore, the second-stage constraints include the random variable ξ tw , which is the prediction error of the wind power w output in time period t. Correspondingly, the second-stage variables also include some operating state variables related to ξ tw , such as power flow, node phase angle, and thermal power unit output.

[0124] The second-stage constraints include: operating state constraints, new energy consumption range constraints, and distributionally robust joint chance constraints.

[0125] The operating state constraints include: the second line power flow constraint, the second power balance constraint, and the second unit output constraint.

[0126] The second line power flow constraint is shown as follows and includes:

[0127]

[0128] In the formula, Denotes the power flow on the m-th line in the transmission corridor l at time period t in the actual dispatch; θ ti and θ tj Respectively denote the phase angles of nodes i and j connected by the transmission corridor l at time period t in the actual dispatch; θ tn Denotes the phase angle of node n at time period t in the actual dispatch; ξ t Denotes the prediction error of the output of all wind power at time period t. Equation (10) ensures that the power flow on each line of the transmission corridor l is within the line transmission capacity. Equation (11) represents the DC power flow constraint of the line when , and this constraint will be relaxed when , and Equation (12) is the node phase angle constraint.

[0129] The second power balance constraint is shown as follows and includes:

[0130]

[0131] In the formula, Denotes the output of the thermal power unit g at time period t in the actual dispatch; ξ tw Denotes the prediction error of the output of the wind power w at time period t. Equation (13) is used to represent the node power balance.

[0132] The output constraint of the second unit is shown in the following formula and includes:

[0133]

[0134] Formula (14) represents the technical range of the thermal power unit output.

[0135] The new energy accommodation range constraint is shown in the following formula and includes:

[0136]

[0137] In the formula, U represents the upper bound; L represents the lower bound; and respectively represent the upper and lower bounds of the accommodation range of wind power w at time t. This accommodation range is defined as when the output prediction error of wind power w at time t is greater than and less than At this time, the system can accommodate the wind power generation at this time and there will be no wind curtailment behavior. After the decision variable in the first stage, that is, the investment plan of the transmission grid, is given, the accommodation range of wind power should also be given accordingly, that is

[0138] The larger the range, the higher the probability that the wind power is completely accommodated, and the stronger the ability of the power system to accommodate wind power. Therefore, the problem of maximizing the wind power accommodation ability is transformed into an optimization problem of solving the upper and lower wind power accommodation boundaries under certain constraint conditions, and the technical constraints to be satisfied are shown in formula (15).

[0139] The establishment of the distributionally robust joint chance constraint specifically includes the following steps:

[0140] Step S3.1: Establish a fuzzy set D, which has the following two characteristics: (1) ξ tw has the same mean μ tw and variance That is, the following formula (16); (2) ξ tw is unimodal with respect to μ tw That is, the probability density function of ξ tw is non-decreasing from 0 to μ tw and non-increasing after μ tw The fuzzy set D is shown in the following formula and includes:

[0141]

[0142] In the formula, represents the probability distribution of the prediction error of the wind turbine output based on historical data; represents the expectation of the probability distribution ; ξ twdenotes the prediction error of the output of the wind turbine generator; μ tw denotes the mean value of the prediction error of the output of the wind turbine generator; Var denotes variance calculation; denotes the variance of the prediction error of the output of the wind turbine generator;

[0143] Step S3.2: Establish a new - energy accommodation capacity model to quantify the probability that wind power is fully accommodated by the power system, that is, the probability that the wind - power prediction error falls within the range, and use this to characterize the accommodation capacity of new energy. The new - energy accommodation capacity model is shown as follows and includes:

[0144]

[0145] u0≤u≤1(18)

[0146] In the formula, and respectively represent the upper and lower bounds of all wind - power prediction errors that the system can accommodate in time period t; u represents the probability that the power system fully accommodates new energy; u0 represents the minimum value of the minimum accommodation probability. Equation (17) represents the requirements that the probability that the prediction error of wind - power output falls within the range that the system can accommodate should meet, and equation (18) represents the upper and lower - limit constraints of the minimum probability.

[0147] Step S4: According to the objective function, the first - stage constraints, and the second - stage constraints, establish a general model for the optimal configuration of the transmission network for new - energy accommodation;

[0148] In step S4, the general model is shown as follows and includes:

[0149]

[0150] α∈{0,1} (20)

[0151]

[0152] Qξ L ≤q,Rξ U ≤r (23)

[0153] In the formula, α represents the decision variable for the investment and construction of the transmission network; C represents the cost coefficient in the objective function; y(ξ) represents the decision variable related to new - energy accommodation capacity, including power flow, phase angle, and the output of thermal power units; Q and q represent the parameters related to the lower limit of the random variable ξ; R and r represent the parameters related to the upper limit of the random variable ξ. Equation (19) is the objective function, equation (20) represents the first - stage constraints, equation (21) represents the operating - state constraints of the second stage, equation (22) is the distribution - robust joint - chance constraint of the second stage, and equation (23) represents the relevant constraints on the upper and lower limits of the accommodation range.

[0154] Step S5: Solve the general model to obtain the optimization model for the optimal configuration of the transmission network for new energy accommodation.

[0155] Specifically, solving the general model includes: according to the linear affine decision rule, mathematical transformation, and duality principle, transforming the constraints in the general model into constraints of random variables without variable upper and lower bounds, to obtain the optimization model for the optimal configuration of the transmission network for new energy accommodation.

[0156] Step S5.1: Assume that the prediction error ξ of the output power of the wind turbine by the operating state variable in the second-stage constraint tw obeys the following affine decision rule:

[0157] y(ξ) = Bξ + b (24)

[0158] The physical meaning of this mathematical assumption is the response behavior of the system after the uncertainty of wind power is revealed, simulating the adjustment response of AGC (Automatic Generation Control) in the power system. Taking the output power of thermal power unit g at time t in actual dispatching as an example, its expression is as follows: For example, its expression is as follows:

[0159]

[0160] In the formula, the variable B tgw and b tg represent the response of the output power of the thermal power unit to the prediction deviation of the wind power output.

[0161] By using this affine decision rule, the optimization space of the original optimization problem is restricted within the affine function range, reducing the difficulty of solution.

[0162] Step S5.2: Based on Bonferroni approximation, Gaussian inequality, and second-order cone relaxation, transform the distributionally robust joint chance constraint described in Equation (17) into the second-order cone form as shown in the following equation, including:

[0163]

[0164] In the formula, g tw , v tw and z tw are auxiliary variables, and μ tw and σ tw are the mean and standard deviation of the fuzzy set of random variables respectively.

[0165] Step S5.3: Define E := diag(ξ U - ξ L ), then the random variable ξ can be written as ξL +Ev, where v ∈ [0, e], and e represents a column vector with all elements being 1; transform the formula (21) in the general model to obtain the transformed formula as follows:

[0166]

[0167] Replace the quadratic terms BE and Bξ L with S and s respectively, to obtain:

[0168]

[0169] Then the expression of the standard robust form of equation (33) is:

[0170]

[0171] According to the duality principle, dualize equation (34) as shown in the following equation:

[0172] Re ≤ Jξ L -T(x) - Ws (35)

[0173] R ≥ WS - JE, R ≥ 0 (36)

[0174] By solving the general model, the final optimized model includes:

[0175] The optimized objective function is as shown in the following equation:

[0176]

[0177] The optimized second-line power flow constraint is as shown in the following equation:

[0178]

[0179]

[0180] The optimized second power balance constraint is as shown in the following equation:

[0181]

[0182] The optimized second generator output constraint is as shown in the following equation:

[0183]

[0184] The constraints related to the auxiliary variables are as shown in the following equation:

[0185]

[0186]

[0187] In formulas (48) - (51), E tw , v tw , z tw and g tg are auxiliary variables.

[0188] The optimized distributionally robust joint chance constraint is shown as follows:

[0189]

[0190] And the other constraints in the optimization model are the same as those in the general model. The other constraints in the optimization model include: the first-stage constraints, namely formulas (2) - (9); the new energy accommodation range constraint, namely formula (15), and the upper and lower limits of the minimum accommodation probability, namely formula (18).

[0191] Furthermore, numerical simulations are carried out on the model proposed in the above embodiments, specifically including:

[0192] A 6-node system and an IEEE 118-node system are used as test systems. All examples are programmed and solved based on the required solver on the simulation platform. The tolerance of the relative optimal gap is set to 0.01%. This numerical simulation is carried out on a central processing unit of the same model. In the example analysis, one day in each of the four seasons of spring, summer, autumn, and winter is selected as a typical day (T = 96h). When showing the wind power accommodation range, the results of the summer typical day are selected for display.

[0193] To simulate the uncertainty of wind power, a set of wind power prediction errors that follow a Gaussian distribution are generated, with the mean set to 0 and the variance increasing with time within each day: starting from 10% of the installed capacity and increasing in steps of 0.1% of the installed capacity. In this embodiment, 1000 sets of out-of-sample tests are run to verify the effectiveness of the proposed method.

[0194] In practice, the appropriate weight coefficient δ is determined through experiments. First is the rough adjustment. Roughly estimate the order of magnitude of the investment cost, such as 1×106M$ or 1×107M$, and then set a δ that is much smaller than the relative investment cost, such as 100 or 1000. By using this δ, the optimal investment cost and the optimal wind power accommodation capacity u are obtained by solving *So far, we have a certain understanding of the investment cost and the wind power accommodation capacity. Next is the fine-tuning: Set δ to be equal to the investment cost obtained previously. Since the wind power accommodation capacity u is a value between 0 and 1, usually between 0.6 and 1, the product of δ and u is close to and less than the investment cost. Then, by gradually increasing δ with an appropriate step size, a set of optimal investment costs and optimal wind power accommodation capacities are obtained. Finally, according to the actual investment budget and the new energy policy goals, an appropriate δ can be determined to balance the investment cost of the transmission grid and the new energy accommodation capacity.

[0195] In the 6-node system, the modified system is used to illustrate the impact of the uncertainty of new energy power generation on the investment decision of the transmission grid. The system topology structure diagram is referred to Figure 2 as shown, and the parameters of the lines to be built refer to Table 1 below. Note that node 6 was initially isolated, and the line parameters of the 2-6 transmission corridor and the 4-6 transmission corridor given in the table refer to the parameters of the lines to be built. The maximum number of transmission lines in each corridor is 6. In addition, the new construction cost per kilometer is 20k$.

[0196] Table 1 Parameters of the Modified System

[0197]

[0198]

[0199] Trade-off relationship between investment cost and new energy accommodation range:

[0200] The optimal investment plans under different δ are shown in Table 2. It can be seen from the table that when δ increases, more new lines will be built, requiring a higher investment cost. This is because δ is the weight coefficient of the wind power accommodation capacity in the objective function and can be understood as the willingness of the system to accommodate wind power. The increase of δ means that the system wants to accommodate more wind power, so this requires more new transmission lines, thus increasing the investment cost.

[0201] Table 2 System Investment Plan Based on the Proposed Method

[0202]

[0203] To demonstrate the trade-off between investment cost and the wind power accommodation range, the value of δ is gradually increased, and the proposed model is solved for each δ to obtain the corresponding wind power accommodation range. Since the investment cost does not change continuously, a change in δ does not necessarily cause a change in the investment cost each time. For example, when δ changes from 100 to 10,000, the investment cost remains unchanged at 6600 k$. When δ changes from 17,000 to 18,000, the investment cost changes from 6600 k$ to 7600 k$, which can be regarded as a change point here. For the sake of simplicity, only these change points are selected for demonstration. The trade-off between the investment cost and the new energy accommodation range is shown in Figure 3 as follows.

[0204] Taking the cost of 6600 k$ as an example, the space between the upper solid red line and the lower dashed red line represents the wind power range that the system can fully accommodate. In other words, it is necessary to spend at least 6600 k$ to strengthen the transmission network to adapt to any wind power size between the upper and lower red lines. The results show that when the investment cost increases, the wind power accommodation level will increase. At time t = 15 h, the new energy accommodation ranges corresponding to 6600 k$, 7600 k$, and 8600 k$ are 143.42 - 444.9 MW, 74.22 - 505.44 MW, and 10.45 - 584.84 MW, respectively. When the investment increases, more transmission lines will be built, thus having a more reliable transmission network. The newly built transmission network has better wind power accommodation capacity.

[0205] It should be noted that although the yellow dashed line is lower than the blue dashed line in some time periods (for example, at t = 2 h and t = 3 h), the interval width of the yellow line is still smaller than that of the blue line. For example, at t = 2 h, the accommodation ranges corresponding to the investment costs of 7600 k$ and 8600 k$ are 6.23 - 491.90 MW and 35.73 - 570.41 MW, respectively. At t = 3 h, the accommodation ranges corresponding to the yellow line and the blue line are 0 - 517.56 MW and 27.28 - 570.26 MW, respectively.

[0206] Comparison with the traditional robust method:

[0207] To compare the method proposed in the present invention with the traditional robust method, the optimal investment plan obtained using the traditional robust method is given in Table 3 below. The out-of-sample performances of the method proposed in the present invention and the traditional robust method are compared, as shown in Figure 4 as follows.

[0208] Table 3 Investment plan of the system based on the traditional robust optimization method

[0209]

[0210] On the one hand, it can be seen that when the investment cost rises, the probability of full accommodation of wind power increases, that is, the system's ability to accommodate wind power is enhanced. For example, when the investment cost is 6600k$, the probability of wind power accommodation is 0.785, which means that when 6600k$ is spent on expanding the transmission network, the probability of full accommodation of wind power is 0.785, and the probability of the system bearing the risk of curtailed wind is 0.215. On the other hand, compared with the modeling method proposed in this embodiment, the traditional robust optimization method shows conservatism. To achieve the same probability of wind power accommodation, the traditional robust optimization method requires a higher investment cost. For example, using the method proposed in the present invention, the system needs to spend 7600k$ to obtain a wind power accommodation probability of 0.991, while for the traditional robust optimization method, the system needs to pay 7800k$ to obtain a wind power accommodation probability of 0.874. This is because the method proposed in the present invention takes into account the expectation of the worst-case scenario probability distribution, rather than the single worst-case scenario considered in the traditional robust method, thus improving the conservatism compared with the traditional robust optimization method.

[0211] The modified IEEE 118-bus system is used below to verify the effectiveness of the modeling method proposed in this embodiment in a large system. Two wind farms with an installed capacity of 300 MW each are located at buses 32 and 88 respectively, and 30 candidate transmission corridors are marked in red. Refer to Figure 5 as shown. It is assumed that the length of each transmission corridor is the integer part of the floor of 250 times the corresponding reactance. Other parameters are the same as those of the 6-bus system.

[0212] Consistent with the simulation results of the 6-bus system, when δ increases, more new lines will be built, resulting in a higher investment cost, as shown in Table 4 below. This is because δ represents the weight coefficient of the wind power accommodation ability, indicating the willingness of the system to accommodate wind power.

[0213] Table 4 Investment plan of the IEEE 118-bus system based on the proposed method

[0214]

[0215] The trade-off relationship between the investment cost and the wind power accommodation range of the IEEE 118-bus system is referred to Figure 6 as shown. The results show that when the investment cost increases, the wind power accommodation range increases. At t = 15h, the regulation ranges corresponding to 20k$, 360k$ and 700k$ are 51.15 - 391.61 MW, 25.99 - 405.25 MW and 0 - 422.10 MW respectively. In addition, refer to Figure 7 as shown, when the investment cost increases, the wind power accommodation probability increases.

[0216] In summary, this embodiment proposes a modeling method for the optimal configuration of a power transmission network for new energy consumption, which co-optimizes the investment cost of the power transmission network and the new energy consumption capacity under the consideration of distributionally robust joint chance constraints. On the one hand, it provides a quantifiable guidance for the investment in the power transmission network and the development of new energy, while ensuring the complete consumption of new energy generation by the power system. On the other hand, the distributionally robust joint chance constraints quantify the trade-off between the investment cost of the power transmission network and the new energy consumption capacity in a moderately conservative manner, with clear physical meanings. The model proposed in this embodiment is a two-stage distributionally robust optimization model, which reformulates the distributionally robust joint chance constraints into a second-order cone form. And it replaces the random variables with the combination of the lower bound variables of the random variables and the auxiliary variables to further apply duality to solve. It realizes the transformation of the general model into the single-stage robust optimization model, and can be efficiently solved by a commercial solver. This embodiment verifies the effectiveness and scalability of the proposed method in a 6-node system and an IEEE 118-node system. The test results show that, under the given weight coefficients (representing the willingness of system planners for new energy consumption), the modeling method of this embodiment can obtain the minimum investment cost and the maximum new energy consumption capacity. Compared with traditional robust optimization, the modeling method of this embodiment improves the conservativeness of the traditional method. And the modeling method of this embodiment demonstrates scalability in large system tests.

[0217] It should be noted that in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements not only includes those elements, but also includes other elements not expressly listed, or further includes elements inherent to such process, method, article or device. Without further limitation, an element defined by the statement "comprising an..." does not exclude the existence of additional identical elements in the process, method, article or device comprising the element.

[0218] It should be noted that the devices and methods disclosed in the embodiments of this article can also be implemented in other ways. The device embodiments described above are merely illustrative. For example, the flowcharts and block diagrams in the accompanying drawings show the possible architectures, functions, and operations of devices, methods, and computer program products according to multiple embodiments of this article. In this regard, each block in the flowchart or block diagram can represent a module, program, or part of code that contains one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than that marked in the accompanying drawings. For example, two consecutive blocks can actually be executed substantially in parallel, and they can sometimes be executed in the reverse order, depending on the functions involved. It should also be noted that each block in the block diagram and / or flowchart, as well as the combination of blocks in the block diagram and / or flowchart, can be implemented by a dedicated hardware-based system for performing the specified functions or actions, or can be implemented by a combination of dedicated hardware and computer instructions.

[0219] In addition, each functional module in the various embodiments of this article can be integrated together to form an independent part, or each module can exist alone, or two or more modules can be integrated to form an independent part.

[0220] Although the content of the present invention has been introduced in detail through the above preferred embodiments, it should be recognized that the above description should not be considered as a limitation of the present invention. After those skilled in the art have read the above content, various modifications and alternatives to the present invention will be obvious. Therefore, the protection scope of the present invention should be defined by the appended claims.

Claims

1. A transmission network optimization configuration modeling method for new energy consumption, characterized in that: include: Step S1: constructing an objective function with the goal of minimizing the investment and construction cost of the transmission network and maximizing the new energy absorption capacity of the power system, wherein the objective function includes: decision variables for the investment and construction of the transmission network and decision variables related to the new energy absorption capacity; Step S2: establishing first-stage constraints for the decision variables of the transmission network investment and construction; Step S3: establishing second-stage constraints for decision variables related to the new energy consumption capacity; Step S4: establishing a general model for optimal configuration of a transmission network for accommodating new energy sources according to the objective function, the first-stage constraints and the second-stage constraints; Step S5: Solve the general model to obtain an optimization model for the optimal configuration of the transmission network for the consumption of new energy.

2. The transmission network optimization configuration modeling method for new energy consumption according to claim 1 is characterized in that: The expression of the objective function is: In the formula, min represents the minimization function; Ω represents the set of transmission corridors to be built; l represents the transmission corridor; C l represents the investment cost of a single line within the transmission corridor l; and They represent the minimum and maximum number of transmission lines in the transmission corridor l respectively; is whether the mth line in the transmission corridor l is built. When it means construction; when When , it means no construction; δ represents the weight coefficient; u represents the probability of the power system fully absorbing new energy; It represents the investment cost of new lines, and δu represents the new energy consumption capacity.

3. The transmission network optimization configuration modeling method for new energy consumption according to claim 2 is characterized in that: The first stage constraints include: line investment constraints, first line flow constraints, first power balance constraints and first unit output constraints.

4. The transmission network optimization configuration modeling method for new energy consumption according to claim 3 is characterized in that: In step S2, the line investment constraint is as shown in the following formula, including: In the formula, represents the number of transmission lines in each transmission corridor, α l (m-1) Indicates whether the m-1th line in the transmission corridor l is built; M l represents the set of lines to be built in the transmission corridor l; The first line power flow constraint is shown in the following formula, including: In the formula, represents the maximum transmission power of transmission corridor l; t represents the pre-scheduling period; T represents the time period set; is the power flow on the mth line in the transmission corridor l during the pre-dispatching period t; N l represents the set of nodes connected to the transmission corridor l; N represents the set of all nodes; x l is the impedance of the line in the transmission corridor l; and They represent the phase angles of nodes i and j connected by transmission corridor l in time period t in the pre-scheduling respectively; represents the phase angle of node n in time period t in the pre-scheduling; The first power balance constraint is shown in the following formula, including: In the formula, G represents the set of thermal power units; G(n) represents the set of thermal power units at node n; W represents the set of wind power units; W(n) represents the set of wind power units at node n; Ω(n) represents the set of transmission corridors connected to node n; represents the predicted output of wind power w in period t, d tn represents the load of node n in time period t; variable represents the output of thermal power unit g in time period t in pre-dispatch; The output constraint of the first unit is as shown in the following formula, including: In the formula, Indicates the output upper limit of thermal power unit g.

5. The transmission network optimization configuration modeling method for new energy consumption according to claim 4 is characterized in that: In step S3, the second stage constraints include: operating state constraints, new energy consumption range constraints and distributed robust joint opportunity constraints.

6. The transmission network optimization configuration modeling method for new energy consumption according to claim 5 is characterized in that: The operating state constraint, the new energy consumption range constraint and the distributed robust joint opportunity constraint specifically include: The operating state constraints include: a second line flow constraint, a second power balance constraint, and a second unit output constraint; The second line power flow constraint is shown in the following formula, including: In the formula, represents the power flow on the mth line in the transmission corridor l during period t in actual scheduling; θ ti and θ tj They represent the phase angles of nodes i and j connected by transmission corridor l in time period t in actual scheduling; θ tn represents the phase angle of node n in time period t in actual scheduling; ξ t represents the prediction error of all wind power output in time period t; The second power balance constraint is shown in the following formula, including: In the formula, represents the output of thermal power unit g in time period t in actual scheduling; ξ tw represents the prediction error of wind power w in time period t; The output constraint of the second unit is as shown in the following formula, including: The new energy consumption range constraint is as shown in the following formula, including: In the formula, U represents the upper bound; L represents the lower bound; and They represent the upper and lower limits of the wind power consumption range w in time period t respectively; The establishment of the distributed robust joint opportunity constraint specifically includes the following steps: Step S3.1: Establish a fuzzy set D, which is shown in the following formula, including: In the formula, represents the probability distribution of the forecast error of wind turbine output based on historical data; Represents probability distribution expectations; tw Represents the prediction error of wind turbine output; μ tw It represents the mean of the prediction error of wind turbine output; Var represents the variance calculation; Represents the variance of the prediction error of wind turbine output; Step S3.2: Establish a new energy absorption capacity model to quantify the probability of wind power being fully absorbed by the power system. The new energy absorption capacity model is shown in the following formula, including: u0≤u≤1; In the formula, and They respectively represent the upper and lower bounds of the forecast errors of all wind power that the system can absorb in time period t; u represents the probability of the power system fully absorbing renewable energy; u0 represents the minimum value of the minimum absorption probability.

7. The transmission network optimization configuration modeling method for new energy consumption according to claim 6 is characterized in that: In step S4, the general model is shown in the following formula, including: α∈{0,1}； Qξ L ≤q,Rξ U ≤r; Wherein, α represents the decision variable for the investment and construction of the transmission network; C represents the cost coefficient in the objective function; y(ξ) represents the decision variable related to the new energy absorption capacity; Q and q represent parameters related to the lower limit of the random variable ξ; R and r represent parameters related to the upper limit of the random variable ξ.

8. The transmission network optimization configuration modeling method for new energy consumption according to claim 7 is characterized in that: In step S5, solving the general model specifically includes: According to the linear affine decision rule, mathematical transformation and duality principle, each constraint in the general model is transformed into a constraint of a random variable without variable upper and lower bounds, and an optimization model for the optimal configuration of the transmission network for the consumption of new energy is obtained.

9. The transmission network optimization configuration modeling method for new energy consumption according to claim 8 is characterized in that: In step S5, the step of solving the general model specifically includes: Step S5.1: Assume that the prediction error ξ of the wind turbine output by the operating state variables in the second stage constraints tw It obeys the following affine decision rule: y(ξ)=Bξ+b; Step S5.2: Based on the Bonferroni approximation, Gaussian inequality and second-order cone relaxation, the distributed robust joint chance constraint is converted into a second-order cone form as shown in the following formula, including: In the formula, g tw 、v tw and z tw is an auxiliary variable, parameter μ tw and σ tw are the mean and standard deviation of the fuzzy set of random variables respectively; Step S5.3: Define E:=diag(ξ U -ξ L ), then the random variable ξ can be written as ξ L +Ev, v∈[0,e], where e represents a column vector whose elements are all 1; for the formula in the general model After transformation, the transformed formula is: Substituting the quadratic terms BE and Bξ L Substituting S and s respectively, we get: Then the standard robust form is expressed as: According to the duality principle, the expression of the standard robust form is dualized as shown below: Re≤Jξ L -T(x)-Ws; R≥WS-JE,R≥0.

10. The transmission network optimization configuration modeling method for new energy consumption according to claim 9, characterized in that: By solving the general model, the final optimization model is obtained including: The optimized objective function is shown as follows: In the formula, E tw 、v tw 、z tw and g tg All are auxiliary variables; The optimized power flow constraint of the second line is as follows: The optimized second power balance constraint is as follows: The optimized output constraint of the second unit is as follows: The constraints related to auxiliary variables are as follows: The optimized distributed robust joint opportunity constraint is as follows: And the other constraints in the optimization model are consistent with those in the general model.

Images