WO2020093295A1 - 一种电-气互联综合能源系统的多时段潮流优化方法 - Google Patents
一种电-气互联综合能源系统的多时段潮流优化方法 Download PDFInfo
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- G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
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- G06Q10/0631—Resource planning, allocation, distributing or scheduling for enterprises or organisations
- G06Q10/06312—Adjustment or analysis of established resource schedule, e.g. resource or task levelling, or dynamic rescheduling
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/008—Circuit arrangements for ac mains or ac distribution networks involving trading of energy or energy transmission rights
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
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- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
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- Y04S10/00—Systems supporting electrical power generation, transmission or distribution
- Y04S10/50—Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications
Definitions
- the invention relates to the technical field of electrical interconnection, and in particular to a multi-period power flow optimization method for an integrated electrical energy system with electrical interconnection.
- the two-way energy flow between the power system and the natural gas system is possible.
- the development of natural gas has transformed the power system and the natural gas system from independent to mutual coupling (gradually Developed into a strong coupling). Therefore, it is necessary to break the independent planning and operation mode of the existing energy system and construct a unified and integrated energy system with multiple heterogeneous energy interconnections.
- the energy Internet can be understood as the deep integration of Internet thinking and technology on the basis of multiple types of energy interconnection (ie, integrated energy system). Therefore, the construction of an integrated energy system will also become an important part of China's energy Internet strategy.
- the advantages of the integrated electricity-gas interconnected energy system are: 1) higher energy utilization efficiency and greater economic benefits; 2) promoting the large-scale development and grid connection of renewable energy; 3) Increase flexibility and energy complementarity between systems.
- Natural gas systems have slow dynamic characteristics, so in short-time scale scheduling, line-pack storage characteristics in natural gas system pipelines need to be considered.
- the natural gas system power flow model is essentially a nonlinear non-convex equation.
- For non-convex optimization it is often only possible to obtain a local optimal solution, and the convergence of the solution is easily affected by the initial value.
- the optimization of power system operation also faces the problem of non-convexity, but the DC linear power flow model has been able to replace the AC nonlinear power flow model in engineering practice, so the efficient linear power flow model in power system optimization is available.
- the existing power flow model linearization model uses a piecewise linear method, which requires the introduction of a large number of integer variables, which greatly increases the computational complexity. If a small number of piecewise integer variables are considered, the piecewise linear accuracy is difficult to meet engineering practice requirements . Therefore, the highly efficient convex optimization natural gas system flow is particularly important.
- the present invention provides a multi-period power flow optimization method for an integrated energy system of electric-gas interconnection.
- the method uses second-order cone optimization to ensure the efficiency and optimality of the understanding, and adopts DCP ( difference-of-convex) method to ensure the feasibility of understanding (ie to be able to meet the strict physical constraints of natural gas systems).
- DCP difference-of-convex
- the multi-period power flow optimization method of the integrated electric-gas interconnected energy system of the present invention includes:
- the power system information obtained in step (1) is: power grid topology, branch parameter information, generator parameter information, electric load information in the future period, wind power predicted value information;
- natural gas system parameter information is: natural gas Network topology, pipeline parameter information, current pipeline line-pack storage, gas source parameter information, and gas load information in the future period.
- the multi-period scheduling model of the integrated energy system of electricity-gas interconnection established in step (2) is specifically as follows:
- the superscript 0 represents the benchmark operation scenario
- the subscript t represents the time t, i, j, m, n represent the nodes in the energy system
- the superscript max represents the upper limit
- the superscript min represents the lower limit
- f 0 To optimize the objective function, N G is the generator set, N g is the gas turbine set, N s is the gas source set, N W is the wind farm set, T 0 is the number of time sections, C G, i is the generator cost coefficient, C S, m is the cost coefficient of the gas source, C W, i is the cost coefficient of abandoned wind, Is the wind curtailment percentage, Contribute to the generator, For the lower and upper output limits of the generator, To abandon the wind ratio, Expected output for wind power, P L, i, t is the active load, Is the line ij active power, EN (i) is the set of nodes connected to node i, b ij is the line ij susceptance, and ⁇
- step (3) specifically includes:
- the superscript 0 indicates the benchmark operation scenario
- the subscript t indicates the time t
- the superscript max indicates the corresponding upper limit value
- the superscript min indicates the corresponding lower limit value
- ⁇ > T indicates the convex envelope function of the square term
- ⁇ mn represents a square term convex envelope variable
- ⁇ mn represents a bilinear term convex envelope variable.
- step (5) specifically includes:
- f 0 (x) is the optimization objective function of the multi-period scheduling model of the electric-gas interconnected integrated energy system
- x is the state variable
- X is the feasible region of x
- x r is the state variable solved at the rth iteration.
- the optimal solution s mn is a non-negative relaxation variable
- ⁇ r is the penalty weight coefficient
- r is the current number of iterations
- x * is the state variable value after the end of the current iteration, These are the corresponding values in the state variable x * .
- the present invention has significant advantages: the present invention uses second-order cone optimization to ensure the efficiency and optimality of understanding, and the DCP method to ensure the feasibility of understanding (that is, it can meet the strict requirements of natural gas systems Physical constraints).
- FIG. 1 is a schematic flowchart of an embodiment of the present invention
- Figure 2 is a diagram of a comprehensive energy system composed of an IEEE-39 node system and a Belgium 20-node system.
- This embodiment provides a multi-period power flow optimization method for an integrated electric-gas interconnected energy system. As shown in FIG. 1, the method includes the following steps:
- the power system information is: power grid topology, branch parameter information, generator parameter information, electric load information in the future period, wind power forecast value information;
- natural gas system parameter information is: natural gas network topology, pipeline parameter information, current The pipeline's line-pack storage capacity, gas source parameter information, and gas load information in the future period.
- superscript 0 represents the benchmark operation scenario
- subscript t represents the time t
- i, j, m, n represent the nodes in the energy system
- superscript max represents the upper limit value
- superscript min represents the lower limit value
- f 0 To optimize the objective function, N G is the generator set, N g is the gas turbine set, N s is the gas source set, N W is the wind farm set, T 0 is the wind curtailment ratio, and C G and i are the generator cost coefficients, C S, m is the cost coefficient of the gas source, C W, i is the cost coefficient of abandoned wind, Is the wind curtailment percentage, Contribute to the generator, For the lower and upper output limits of the generator, Is the number of time sections, Expected output for wind power, P L, i, t is the active load, Is the line ij active power, EN (i) is the set of nodes connected to node i, b ij is the line ij susceptance
- equation (1) is the multi-period optimization objective function, including the cost of non-gas-fired power generation, gas supply, and wind curtailment. It should be noted that the cost of gas supply indirectly includes the power generation cost of the gas turbine, so the power generation cost in (1) only accounts for non-gas-fired units.
- Equations (2)-(7) are power system operation constraints. Equation (2) is the node power balance constraint, equation (3) describes the linear relationship between the line power and the phase angle difference between the first and the end nodes in the DC power flow model; equations (4) and (5) are the upper and lower constraints of the generator, respectively And climbing constraints; Equation (6) is the line transmission capacity constraint. Equations (8)-(19) are the dynamic operating constraints of the natural gas system.
- Equation (8) is a node flow balance constraint. Equations (9) and (10) describe the nonlinear relationship between the average flow rate of the pipeline and the pressure at the node at the end of the pipeline; equation (11) indicates that the difference between the flow rate at the end and the end is equal to that in the pipeline Fluctuation of tube storage in two adjacent sections; Equation (12) indicates that the pipeline storage is proportional to the average pressure at the head and end; Equation (13) describes the linear relationship between the flow absorbed by the pressure station and the flow through the pressure station; 14) It is the pressure ratio constraint of the pressurization station; Equation (15) is the transportation capacity constraint of the pressurization station; Equations (16) and (17) are the gas supply capacity and climbing constraints; Equation (18) is the nodal pressure The lower limit constraint; Equation (19) is the lower limit constraint of the natural gas system master deposit at time T 0 .
- equation (9) is a nonlinear non-convex equation, and the corresponding nonlinear optimization model will inevitably encounter initial value sensitivity and numerical stability Poor and other issues.
- equation (9) can be relaxed to equation (20), and further, the standard second-order taper equation of equation (20) is shown in equation (21).
- Equing equation (9) into the second-order cone of equation (21) can effectively avoid the numerical stability problem.
- equation (21) may not be the same as equation (9), that is, the second-order cone relaxation may not be strict. of.
- the present invention proposes an enhanced second-order cone-shaped natural gas power flow model.
- the enhanced second-order cone-shaped natural gas power flow model is based on equation (21), and deeply considers equation (22).
- equation (22) there are two points that need to be explained here: 1) The combination of formula (21) and formula (22) is strictly equivalent to formula (9); 2) Unlike formula (21), formula (22) is still non-compliant Convex.
- the present invention further proposes to use the convex envelope (Convex envelope) method to relax the bilinear term (essentially non-convex term) in equation (22). Then the left bilinear term in equation (22) Equation (23) can be used instead, and for the non-convex term on the right in Equation (22), define Then the right part of formula (A-7) can be replaced by formula (24). Finally, using the convex envelope method, equations (23)-(25) can replace equation (22).
- Convex envelope convex envelope
- equations (21) and (23)-(25) constitute an enhanced second-order cone-shaped natural gas flow model.
- the DCP method linearizes the concave part of (22) (ie h mn (x)), and then converts (22) to the following form:
- x is the state variable
- X is the feasible field of x
- s mn is the non-negative relaxation variable
- ⁇ r is the penalty weight coefficient
- r is the number of iterations.
- equation (28) the relaxation variable s mn is introduced to ensure the solvability of equation (28).
- DCP iteratively solves equation (28), and gradually updates the value of x r until Gap c is sufficiently small in equation (29) (that is, the original nonlinear equation (9) is approximately true), and the iteration ends.
- Gap c is a constraint violation indicator
- the simulation test of the present invention is as follows.
- FIG. 2 is an integrated energy system composed of IEEE-39 nodes and Belgium 20-node systems.
- Table 1 shows the comparison between the optimization results of the second-order cone model and the enhanced second-order cone model. From the table, it can be seen that in the first-stage optimization, the dual gap Gap o of the enhanced second-order cone model is smaller than the second-order cone model (0.43% VS 0.91%), and the constraint violation index Gap c is smaller, indicating that the enhanced second-order cone model optimization results are more similar to the original nonlinear optimization results.
- both the second-order cone model and the enhanced second-order cone model can recover feasible solutions in the second stage (Gap c is small enough), but the enhanced second-order cone model is closer to the original nonlinear model ( Its Gap o is smaller), so the results in Table 1 verify the effectiveness of the proposed enhanced second-order cone model.
- Gap o is the relative error between the second-order cone model and the nonlinear model optimization target value
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Abstract
本发明公开了一种电-气互联综合能源系统的多时段潮流优化方法，该方法包括：(1)获取电-气互联综合能源系统信息；(2)根据系统信息构建电-气互联综合能源系统多时段调度模型；(3)将所述电-气互联综合能源系统多时段调度模型中的天然气管道流量与压力的非线性非凸方程转化为增强二阶锥约束形式的天然气潮流模型；(4)对转化后的电-气互联综合能源系统多时段调度模型进行求解得到最优解；(5)将所述最优解作为初值，并采用DCP方法对转化后的电-气互联综合能源系统多时段调度模型进行线性化迭代求解，直至天然气系统严格的满足潮流约束；(6)将迭代结束时的最终解作为未来时段内的最优潮流解进行输出。本发明可以有效地进行多时段潮流优化。
Description
本发明涉及电气互联技术领域，尤其涉及一种电-气互联综合能源系统的多时段潮流优化方法。
鉴于燃气轮机在发电侧比重的提升以及电转气技术在电力系统中应用，使电力系统与天然气系统间的双向能量流成为可能，天然气的发展使得电力系统与天然气系统由相互独立转变为相互耦合(逐步发展为强耦合)。因此有必要打破现有能源系统间独立规划、运行的模式，并构造统一的、多种异质能源互联的综合能源系统。进一步而言，能源互联网可理解为在多类型能源互联(即综合能源系统)的基础上，互联网思维与技术的深度融入，因而综合能源系统的构建也将成为我国能源互联网战略的重要环节。相比于现有能源系统，电－气互联综合能源系统的优势在于：1)更高的能源利用效率、更大的经济利益；2)促进可再生能源的规模化开发与并网；3)增加系统间的灵活性与能源互补性。
天然气系统存在慢动态特性，因而在短时间尺度调度中，需要考虑天然气系统管道中line-pack存储特性。同时，天然气系统潮流模型本质上为非线性非凸方程，对于非凸优化而言，往往只能获取局部最优解，且解的收敛性易受到初值影响。电力系统的运行优化同样面临非凸的难题，但直流线性潮流模型在工程实践中已能够替代交流非线性潮流模型，因此电力系统优化中高效的线性潮流模型是可获取的。然而对于天然气系统，现有潮流模型线性化模型采用分段线性方法，需引入大量整数变量，极大的增加计算复杂度，若考虑少量的分段整数变量，分段线性精度难以满足工程实践要求。因而高效的凸优化形式的天然气系统潮流显得尤为重要。
发明内容
发明目的：本发明针对现有技术存在的问题，提供一种电-气互联综合能源系统的多时段潮流优化方法，方法中采用二阶锥优化保证了解的高效性与最优性，采用DCP(difference‐of‐convex)方法保证了解的可行性(即能够满足天然气系统严格的物理约束)。
技术方案：本发明所述的电-气互联综合能源系统的多时段潮流优化方法包括：
(1)分别获取电-气互联综合能源系统的电力系统信息和天然气系统信息；
(2)根据所述电力系统信息和天然气系统信息，构建电-气互联综合能源系统多时段调度模型；
(3)将所述电-气互联综合能源系统多时段调度模型中的天然气管道流量与压力的非线性非凸方程转化为增强二阶锥约束形式的天然气潮流模型；
(4)对转化后的电-气互联综合能源系统多时段调度模型进行求解得到最优解；
(5)将所述最优解作为初值，并采用DCP方法对转化后的电-气互联综合能源系统多时段调度模型进行线性化迭代求解，直至天然气系统严格的满足潮流约束；
(6)将迭代结束时的最终解作为未来时段内的最优潮流解进行输出。
进一步的，步骤(1)中获取的电力系统信息为：电网拓扑、支路参数信息，发电机参数信息，未来时段内的电负荷信息，风电的预测值信息；天然气系统的参数信息为：天然气网拓扑、管道参数信息，当前管道的line-pack存储量，气源的参数信息，未来时段内的气负荷信息。
进一步的，步骤(2)中建立的电-气互联综合能源系统多时段调度模型具体为：
式中，上标0表示基准运行场景，下标t表示t时刻，i、j、m、n表示能源系统中的节点；上标max表示上限值，上标min表示下限值；f
0为优化目标函数，N
G为发电机集合，N
g为燃气轮机集合，N
s为气源集合，N
W为风电场集合，T
0为时间断面数，C
G,i为发电机成本系数，C
S,m为气源成本系数，C
W,i为弃风成本系数，
为弃风百分比，
为发电机出力，
为发电机出力下限和上限，
为弃风比，
为风电期望出力，P
L,i,t为有功负荷，
为线路i-j有功功率，EN(i)为与节点i相连节点集合，b
ij为线路i-j电纳，θ为节点相角向量，
为线路i-j有功功率下限和上限；
为燃气轮机消耗的天然气量，η为燃气轮机组转化效率，
为气源出力，F
D,m,t为天然气负荷，GC(m)、GP(m)、GN(m)分别为节点m连接的加压站、燃气轮机及管道集合，
为加压站k的吸收流量，
为流经加压站k的流量；
及
分别为管道m-n首端、末端以及平均流量，C
mn为管道m-n压降常量，π
m与π
n分别为节点m、n压力，
分别为节点m压力下限和上限；GL
mn为管道m-n的line-pack储气量，K
mn为管道m-n的line-pack参数；
为燃气驱动加压站耗能系数，
为发电机最大有功爬坡，
分别为加压站首、末端压力，
与
为加压站升压比上限和下限，
为气源出力下限和上限，
为气源最大爬坡，
为管道m-n管道量，GL
min为管道的管道量下限，GB为管道集合。
进一步的，步骤(3)具体包括：
将天然气管道流量与压力的非线性非凸方程
转化为如下的增强二阶锥约束形式的天然气潮流模型：
式中，上标0表示基准运行场景，下标t表示t时刻，
上标max表示对应上限值，上标min表示对应下限值，< >
T表示平方项凸包络函数，
表示双线性项凸包络函数，κ
mn表示平方项凸包络变量，λ
mn表示双线性项凸包络变量。
进一步的，步骤(5)具体包括：
(5.1)对所述电-气互联综合能源系统多时段调度模型进行求解得到最优解x
0；
(5.2)建立凸优化问题：
s.t.s
mn≥0,x∈X
式中，f
0(x)为电-气互联综合能源系统多时段调度模型的优化目标函数，x为状态变量，X为x的可行域，x
r为第r次迭代时求解的状态变量最优解，s
mn为非负松弛变量，β
r为惩罚权重系数，r为当前迭代次数，
(5.3)将x
0作为凸优化问题的初值，进行DCP迭代求解，逐步更新x
r数值，直至 天然气约束违反指标Gap
c小于预设值，结束迭代。
进一步的，步骤(5.3)中天然气约束违反指标Gap
c计算公式为：
式中：x
*为当前次迭代结束后的状态变量值，
分别为状态变量x
*中对应值。
有益效果：本发明与现有技术相比，其显著优点是：本发明采用二阶锥优化保证了解的高效性与最优性，采用DCP方法保证了解的可行性(即能够满足天然气系统严格的物理约束)。
图1是本发明的一个实施例的流程示意图；
图2是IEEE‐39节点系统与比利时20节点系统构成的综合能源系统图。
本实施例提供了一种电-气互联综合能源系统的多时段潮流优化方法，如图1所示，包括如下步骤：
S1、分别获取电-气互联综合能源系统的电力系统信息和天然气系统信息。
其中，电力系统信息为：电网拓扑、支路参数信息，发电机参数信息，未来时段内的电负荷信息，风电的预测值信息；天然气系统的参数信息为：天然气网拓扑、管道参数信息，当前管道的line-pack存储量，气源的参数信息，未来时段内的气负荷信息。
S2、根据所述电力系统信息和天然气系统信息，构建电-气互联综合能源系统多时段调度模型：
式中：上标0表示基准运行场景，下标t表示t时刻，i、j、m、n表示能源系统中的节点；上标max表示上限值，上标min表示下限值；f
0为优化目标函数，N
G为发电机集合，N
g为燃气轮机集合，N
s为气源集合，N
W为风电场集合，T
0为弃风比，C
G,i为发电机成本系数，C
S,m为气源成本系数，C
W,i为弃风成本系数，
为弃风百分比，
为发电机出力，
为发电机出力下限和上限，
为时间断面数，
为风电期望出力，P
L,i,t为有功负荷，
为线路i-j有功功率，EN(i)为与节点i相连节点集合，b
ij为线路i-j电纳，θ为节点相角向量，
为线路i-j有功功率下限和上限；
为燃气轮机消耗的天然气量，η为燃气轮机组转化效率，
为气源出力，F
D,m,t为天然气负荷，GC(m)、GP(m)、GN(m)分别为节点m连接的加压站、燃气轮机 及管道集合，
为加压站k的吸收流量，
为流经加压站k的流量；
及
分别为管道m-n首端、末端以及平均流量，C
mn为管道m-n压降常量，π
m与π
n分别为节点m、n压力，
分别为节点m压力下限和上限；GL
mn为管道m-n的line-pack储气量，K
mn为管道m-n的line-pack参数；
为燃气驱动加压站耗能系数，
为发电机最大有功爬坡，
分别为加压站首、末端压力，
与
为加压站升压比上限和下限，
为气源出力下限和上限，
为气源最大爬坡，
为管道m-n管道量，GL
min为管道的管道量下限，GB为管道集合。
我中，式(1)为多时段优化目标函数，包括非燃气机组发电成本、供气成本以及弃风成本。需要说明的是，供气成本间接包含了燃气轮机的发电成本，因而(1)中的发电成本仅计及非燃气机组。式(2)-(7)为电力系统运行约束。式(2)为节点功率平衡约束，式(3)描述了直流潮流模型中线路功率与首末端节点相角差之间的线性关系；式(4)和式(5)分别为发电机上下限约束和爬坡约束；式(6)为线路输电容量约束。式(8)-(19)为天然气系统动态运行约束。式(8)为节点流量平衡约束，式(9)与式(10)描述了管道平均流量与管道首末端节点压力之间的非线性关系；式(11)表示首末端流量之差等于管道中相邻两断面管存波动；式(12)表示管道管存正比于首末端平均压力；式(13)描述了加压站吸收的流量与流经加压站流量之间的线性关系；式(14)为加压站升压比约束；式(15)为加压站输送容量约束；式(16)和式(17)为气源供应容量和爬坡约束；式(18)为节点压力上下限约束；式(19)为T
0时刻天然气系统总管存下限约束。
S3、将所述电-气互联综合能源系统多时段调度模型中的天然气管道流量与压力的非线性非凸方程转化为增强二阶锥约束形式的天然气潮流模型。
由式(1)-(19)构成的综合能源系统多断面运行调度模型中，式(9)为非线性非凸方程，对应的非线性优化模型难免会遇到对初值敏感、数值稳定性不佳等问题。首先式(9)可松弛为式(20)，进一步的，式(20)的标准二阶锥形式如式(21)所示。
将式(9)松弛为式(21)二阶锥形式，可有效避免数值稳定问题，然而在最优解运行点， 式(21)未必与式(9)，即二阶锥松弛未必是严格的。基于此，本发明提出一种增强二阶锥形式的天然气潮流模型。
增强二阶锥形式的天然气潮流模型在式(21)基础上，深入考虑式(22)。此处针对式(22)，有两点需要说明：1)式(21)与式(22)结合与式(9)严格等价；2)不同于式(21)，式(22)依然是非凸的。
本发明进一步提出采用凸包络(Convex envelope)的方法松弛式(22)中的双线性项(本质非线性非凸项)。则式(22)中左侧双线性项
可采用式(23)代替，而对于式(22)中右侧的非凸项，定义
则式(A-7)右侧部分可采用式(24)代替。最后，采用凸包络的方法，式(23)-(25)可代替式(22)。
至此，式(21)与式(23)-(25)构成了增强二阶锥形式的天然气潮流模型。
S4、对转化后的电-气互联综合能源系统多时段调度模型进行求解得到最优解。
S5、将所述最优解作为初值，并采用DCP方法对转化后的电-气互联综合能源系统多时段调度模型进行线性化迭代求解，直至天然气系统严格的满足潮流约束。
可以注意到，相比于二阶锥天然气潮流模型，增强二阶锥模型能够提供更为严格的最优解，然而最优解仍然未必满足式(9)，即松弛非严格成立，因而本发明进一步提出采用DCP的方法恢复天然气潮流的可行解。定义：
则式(22)可表述为：
g
mn(x)-h
mn(x)≤0 (26)
基于当前的最优解x
r，DCP方法线性化式(22)凹部分(即h
mn(x))，则将(22)转化为如下形式：
基于式(27)，DCP求解如下凸优化问题：
式中：x为状态变量，X为x的可行域；s
mn为非负松弛变量，β
r为惩罚权重系数，r为迭代次数。
式(28)中，引入松弛变量s
mn可保证式(28)的可解性。DCP迭代求解式(28)，逐步更新x
r数值，直至式(29)中Gap
c足够小(即原始非线性方程式(9)近似成立)，结束迭代。
式中：Gap
c为约束违反指标。
S6、将迭代结束时的最终解作为未来时段内的最优潮流解进行输出。
下面对本发明进行仿真测试。
本发明测试的算例如图2所示，由IEEE-39节点和比利时20节点系统构成的综合能源系统。表1给出了二阶锥与增强二阶锥模型优化结果比较，由该表可知，在第一阶段优化中，相比于二阶锥模型，增强二阶锥模型的对偶间隙Gap
o更小(0.43％VS 0.91％)，且约束违反指标Gap
c更小，说明增强二阶锥模型优化结果与原始非线性优化结果更相近。进一步的，基于第一阶段结果，二阶锥模型和增强二阶锥模型在第二阶段均能恢复可行解(Gap
c足够小)，但增强二阶锥模型与原始非线性模型更为接近(其Gap
o更小)，因而表1结果验证了所提增强二阶锥模型的有效性。
表1 二阶锥与增强二阶锥模型优化结果比较
*此处Gap
o为二阶锥模型与非线性模型优化目标值之间的相对误差
以上所揭露的仅为本发明一种较佳实施例而已，不能以此来限定本发明之权利范围，因此依本发明权利要求所作的等同变化，仍属本发明所涵盖的范围。
Claims (6)
- 一种电-气互联综合能源系统的多时段潮流优化方法，其特征在于该方法包括：(1)分别获取电-气互联综合能源系统的电力系统信息和天然气系统信息；(2)根据所述电力系统信息和天然气系统信息，构建电-气互联综合能源系统多时段调度模型；(3)将所述电-气互联综合能源系统多时段调度模型中的天然气管道流量与压力的非线性非凸方程转化为增强二阶锥约束形式的天然气潮流模型；(4)对转化后的电-气互联综合能源系统多时段调度模型进行求解得到最优解；(5)将所述最优解作为初值，并采用DCP方法对转化后的电-气互联综合能源系统多时段调度模型进行线性化迭代求解，直至天然气系统严格的满足潮流约束；(6)将迭代结束时的最终解作为未来时段内的最优潮流解进行输出。
- 根据权利要求1所述的电-气互联综合能源系统的多时段潮流优化方法，其特征在于：步骤(1)中获取的电力系统信息为：电网拓扑、支路参数信息，发电机参数信息，未来时段内的电负荷信息，风电的预测值信息；天然气系统的参数信息为：天然气网拓扑、管道参数信息，当前管道的line-pack存储量，气源的参数信息，未来时段内的气负荷信息。
- 根据权利要求1所述的电-气互联综合能源系统的多时段潮流优化方法，其特征在于：步骤(2)中建立的电-气互联综合能源系统多时段调度模型具体为：
式中，上标0表示基准运行场景，下标t表示t时刻，i、j、m、n表示能源系统中的节点；上标max表示上限值，上标min表示下限值；f 0为优化目标函数，N G为发电机集合，N g为燃气轮机集合，N s为气源集合，N W为风电场集合，T 0为时间断面数，C G,i为发电机成本系数，C S,m为气源成本系数，C W,i为弃风成本系数，为弃风百分比，
为发电机出力，
为发电机出力下限和上限，
为弃风比，
为风电期望出力，P L,i,t为有功负荷，
为线路i-j有功功率，EN(i)为与节点i相连节点集合，b ij为线路i-j电纳，θ为节点相角向量，
为线路i-j有功功率下限和上限；
为燃气轮机消耗的天然气量，η为燃气轮机组转化效率，
为气源出力，F D,m,t为天然气负荷，GC(m)、GP(m)、GN(m)分别为与节点m连接的加压站、燃气轮机及管道集合，
为加压站k的吸收流量，
为流经加压站k的流量；
及
分别为管道m-n首端、末端以及平均流量，C mn为管道m-n压降常量，π m与π n分别为节点m、n压力，
分别为节点m压力下限和上限；GL mn为管道m-n的line-pack储气量，K mn为管道m-n的line-pack参数；
为燃气驱动加压站耗能系数，
为发电机最大有功爬坡，
分别为加压站首、末端压力，
与
为加压站升压比上限和下限，
为气源出力下限和上限，
为气源最大爬坡，
为管道m-n管道量，GL min为管道的管道量下限，GB为管道集合。
- 根据权利要求3所述的电-气互联综合能源系统的多时段潮流优化方法，其特征在于：步骤(3)具体包括：将天然气管道流量与压力的非线性非凸方程转化为如下的增强二阶锥约束形式的天然气潮流模型：
式中，上标0表示基准运行场景，下标t表示t时刻，
上标max表示对应上限值，上标min表示对应下限值，<> T表示平方项凸包络函数，
表示双线性项凸包络函数，κ mn表示平方项凸包络变量，λ mn表示双线性项凸包络变量。
- 根据权利要求4所述的电-气互联综合能源系统的多时段潮流优化方法，其特征在于：步骤(5)具体包括：(5.1)对所述电-气互联综合能源系统多时段调度模型进行求解得到最优解x 0；(5.2)建立凸优化问题：
s.t.s mn≥0,x∈X
式中，f 0(x)为电-气互联综合能源系统多时段调度模型的优化目标函数，x为状态变量，X为x的可行域，x r为第r次迭代时求解的状态变量最优解，s mn为非负松弛变量，β r为惩罚权重系数，r为当前迭代次数，
(5.3)将x 0作为凸优化问题的初值，进行DCP迭代求解，逐步更新x r数值，直至天然气约束违反指标Gap c小于预设值，结束迭代。 - 根据权利要求5所述的电-气互联综合能源系统的多时段潮流优化方法，其特征在于：步骤(5.3)中天然气约束违反指标Gap c计算公式为：
式中：x *为当前次迭代结束后的状态变量值，分别为状态变量x *中对应值。
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| CN111768036B (zh) * | 2020-06-29 | 2023-11-03 | 国网上海市电力公司 | 一种综合能源配电系统与上级电网交互运行的功率优化方法 |
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