技术领域technical field
本发明属于电力系统调度运行技术领域，涉及到电力系统非线性区间经济调度建模求解方法，特别涉及区间经济调度中双层非线性悲观解的解法问题。The invention belongs to the technical field of electric power system dispatching operation, relates to a modeling and solving method for the nonlinear interval economic dispatching of the electric power system, and particularly relates to the solution problem of the double-layer nonlinear pessimistic solution in the interval economic dispatching.
背景技术Background technique
近年来，风能作为一种新能源广泛的应用在电力系统运行中，但是风能具有间歇性和随机性，为电力系统安全稳定运行带来新的难题。In recent years, wind energy has been widely used in power system operation as a new energy source, but wind energy is intermittent and random, which brings new problems to the safe and stable operation of power system.
通常对于含风电不确定性的经济调度模型主要有概率模型，模糊模型及区间模型。概率模型建模中需考虑样本空间极其概率分布，模糊模型中需建立隶属度函数，这些都包含了人为的主观因素在内。而区间方法只需知道区间上下边界，无需得到不确定量的概率分布，并且得到的区间结果能够直观的提供目标的上下边界，为电力系统安全稳定运行提供依据，因此具有广泛的应用前景。Usually, the economic dispatch models with wind power uncertainty mainly include probability models, fuzzy models and interval models. The sample space and its probability distribution need to be considered in probabilistic model modeling, and the membership function needs to be established in fuzzy model, all of which include human subjective factors. The interval method only needs to know the upper and lower boundaries of the interval, and does not need to obtain the probability distribution of uncertain quantities, and the obtained interval results can intuitively provide the upper and lower boundaries of the target, providing a basis for the safe and stable operation of the power system, so it has a wide range of application prospects.
当风电接入电网后，风电不确定性对电力系统经济调度运行带来了影响，如何解决引入风电区间变量后的电力系统经济调度模型求解是区间经济调度研究的重点。含区间变量的电力系统经济调度问题的优化目标是寻求目标函数的区间解，即目标函数对应的乐观解和悲观解，其模型分别用双层优化模型表示。其中乐观解是在不确定扰动区间范围内的最优解，表示为“min-min”形式，悲观解是在不确定扰动区间范围内的最差解，表示为“max-min”形式。通过求解区间经济调度问题，不仅得到目标函数即成本的区间估计，还得到相应的发电机出力。When wind power is connected to the grid, the uncertainty of wind power has an impact on the economic dispatching operation of the power system. How to solve the economic dispatching model of the power system after introducing the interval variable of wind power is the focus of the research on interval economic dispatching. The optimization goal of the power system economic dispatching problem with interval variables is to seek the interval solution of the objective function, that is, the optimistic solution and the pessimistic solution corresponding to the objective function, and their models are represented by a two-layer optimization model. Among them, the optimistic solution is the optimal solution within the range of uncertain disturbance interval, expressed as "min-min" form, and the pessimistic solution is the worst solution within the range of uncertain disturbance interval, expressed as "max-min" form. By solving the interval economic scheduling problem, not only the interval estimation of the objective function, namely the cost, but also the corresponding generator output can be obtained.
在实际电网中，电力系统的经济调度模型包含大量的非线性因素，例如含阀点效应的目标函数以及电网的线路约束等等。目前针对区间经济调度的乐观解及悲观解的求法都具有局限性，由于乐观解及悲观解都是双层优化模型，现有的一些方法是将目标函数及约束条件进行线性化后，对内层模型采用线性对偶转换为单层模型再采用优化方法进行求解，或者解决针对二次规划的函数模型，没有直接对非线性区间经济调度问题进行求解。In the actual power grid, the economic dispatch model of the power system contains a large number of nonlinear factors, such as the objective function including the valve point effect and the line constraints of the power grid and so on. At present, the optimistic solution and the pessimistic solution for interval economic dispatch have limitations. Since the optimistic solution and the pessimistic solution are two-layer optimization models, some existing methods are to linearize the objective function and constraints, and then internally The layer model is converted into a single layer model by linear duality and then solved by optimization method, or solves the function model for quadratic programming, and does not directly solve the nonlinear interval economic scheduling problem.
发明内容Contents of the invention
本发明目的是提供一种求解含风电的区间经济调度非线性对偶优化方法，主要针对模型中双层非线性悲观解模型进行求解。针对实际电网中双层非线性悲观解模型采用非线性对偶模型结合原对偶内点法对其进行优化计算，得到发电成本的区间估计及其相应的发电机出力，为发电决策提供依据。The purpose of the present invention is to provide a nonlinear dual optimization method for solving interval economic dispatch including wind power, which is mainly aimed at solving the double-layer nonlinear pessimistic solution model in the model. For the double-layer nonlinear pessimistic solution model in the actual power grid, the nonlinear dual model combined with the original dual interior point method is used to optimize the calculation, and the interval estimation of the power generation cost and the corresponding generator output are obtained, which provides a basis for power generation decision-making.
本发明的技术方案是：Technical scheme of the present invention is:
1.建立电力系统区间经济调度模型1. Establish a power system interval economic dispatch model
传统经济调度问题的目标是在满足负荷和运行约束的前提下，合理地分配电网中各发电机组的出力使得调度周期发电总成本最小，而区间经济调度模型中含有风电的不确定区间出力，每一个区间内的风电取值对应一个目标函数优化解，因此，区间经济调度模型根据风电区间变量求得目标函数的乐观解及悲观解。此外，电力系统经济调度中，汽轮机进气阀突然开启时出现的拔丝现象会在机组耗量曲线上叠加一个脉动效应，产生阀点效应。因此，区间经济调度模型如式(1)所示。The goal of the traditional economic dispatch problem is to rationally distribute the output of each generating unit in the power grid under the premise of satisfying the load and operation constraints so that the total cost of power generation in the dispatch cycle is minimized. However, the interval economic dispatch model contains the uncertain interval output of wind power. The value of wind power in an interval corresponds to an optimal solution of the objective function. Therefore, the interval economic dispatch model obtains the optimistic and pessimistic solutions of the objective function according to the variable of wind power interval. In addition, in the economic dispatching of the power system, the wire drawing phenomenon that occurs when the inlet valve of the steam turbine is suddenly opened will superimpose a pulsation effect on the unit consumption curve, resulting in a valve point effect. Therefore, the interval economic dispatch model is shown in formula (1).
其中，a，b，c，e，f为燃料费用系数，Pi为发电机出力。Pi,j为j时段发电机i的出力，PDj为j时段总负荷数。为j时段风力发电机组出力总和，Wi为第i台风力发电机组的出力，Wi为第i台风力发电机组出力下限，为第i台风力发电机组出力上限。Pimin为第i台发电机出力下限，Pimax为第i台发电机出力上限。URi为第i台发电机组向上爬坡率约束，DRi为第i台发电机组向下爬坡率约束。Among them, a, b, c, e, f are fuel cost coefficients, and Pi is generator output. Pi, j is the output of generator i in period j, and PDj is the total load in period j. is the total output of wind turbines in period j, Wi is the output of the i-th wind turbine,Wi is the lower limit of the output of the i-th wind turbine, It is the output upper limit of the i-th wind turbine. Pimin is the lower limit of the output of the i-th generator, and Pimax is the upper limit of the output of the i-th generator. URi is the upward ramp rate constraint of the i-th generator set, and DRi is the downward ramp rate constraint of the i-th generator set.
目标函数中的阀点效应燃料成本部分采用凝聚函数将其进行光滑化处理等价为式(2)所示：The fuel cost part of the valve point effect in the objective function is smoothed by the agglomeration function, which is equivalent to formula (2):
含区间变量的电力系统经济调度问题的优化目标是寻求目标函数的区间解，即目标函数对应的乐观解和悲观解，其模型分别用双层优化模型表示。其中乐观解表示在不确定扰动区间范围内的最优值，表示为“min-min”形式，悲观解表示在不确定扰动区间范围内的最差解，表示为“max-min”形式。乐观解模型为：The optimization goal of the power system economic dispatching problem with interval variables is to seek the interval solution of the objective function, that is, the optimistic solution and the pessimistic solution corresponding to the objective function, and their models are represented by a two-layer optimization model. Among them, the optimistic solution represents the optimal value within the range of the uncertain disturbance interval, expressed in the form of "min-min", and the pessimistic solution represents the worst solution within the range of the uncertain disturbance interval, expressed in the form of "max-min". The optimistic solution model is:
悲观解模型为：The pessimistic solution model is:
对于乐观解模型，内外层都事求取目标函数最小，合并为单层求最小优化模型，而悲观解模型，内外层求取目标不同，需先进行对偶转换为单层优化模型后再求解。For the optimistic solution model, the inner and outer layers both seek to minimize the objective function, and are merged into a single-layer optimization model to find the minimum. For the pessimistic solution model, the inner and outer layers have different objectives, and it is necessary to perform dual conversion into a single-layer optimization model before solving.
2.非线性对偶方法2. Nonlinear dual method
设原问题模型如式(5)所示：Suppose the original problem model is shown in formula (5):
则所对应的对偶问题模型如式(6)所示:Then the corresponding dual problem model is shown in formula (6):
其中，x为原问题优化变量，u对偶问题的新增变量；x,u分别为n×1阶和m×1阶向量，uT为u的转置；f(x)为原问题目标函数，是x组成的纯量函数；h(x)为原问题约束条件，由hi(x)(i＝1,2,…,m)组成，即：Among them, x is the optimization variable of the original problem, and the new variable of u dual problem; x, u are n×1 order and m×1 order vectors respectively, uT is the transpose of u; f(x) is the objective function of the original problem , is a scalar function composed of x; h(x) is the constraint condition of the original problem, composed of hi (x)(i=1,2,…,m), namely:
Z(x,u)为对偶问题的目标函数。Z(x,u) is the objective function of the dual problem.
Vxf(x)表示由f(x)关于xi(i＝1,2,…,n)的偏导数所组成的n×1阶向量，即：Vx f(x) represents an n×1 order vector composed of partial derivatives of f(x) with respect to xi (i=1,2,…,n), namely:
同理，Vxh(x)表示h(x)关于xi(i＝1,2,…,n)的偏导数所组成的n×m阶矩阵，即：Similarly, Vx h(x) represents an n×m order matrix composed of partial derivatives of h(x) with respect to xi (i=1,2,…,n), namely:
本发明的效果和益处是：提供了一种求解含风电的区间经济调度的非线性对偶优化方法，主要针对悲观解模型中双层非线性悲观解模型进行求解。本发明直接对双层非线性悲观解模型进行优化计算，解决了实际电网的经济调度运行中对于双层的非线性区间经济调度模型求解困难的问题。The effects and benefits of the present invention are: a nonlinear dual optimization method for solving interval economic dispatch including wind power is provided, which mainly solves the double-layer nonlinear pessimistic solution model in the pessimistic solution model. The invention directly optimizes and calculates the double-layer nonlinear pessimistic solution model, and solves the problem of difficulty in solving the double-layer nonlinear interval economic dispatch model in the economic dispatch operation of the actual power grid.
附图说明Description of drawings
附图是双层非线性悲观解模型求解流程图。The accompanying drawing is a flow chart of solving the double-layer nonlinear pessimistic solution model.
具体实施方式detailed description
以下结合技术方案和附图详细叙述本发明的具体实施方式。The specific embodiments of the present invention will be described in detail below in conjunction with the technical solutions and accompanying drawings.
步骤1.建立非线性区间经济调度模型，将第9台机组作为风电出力机组，并转换为相应的乐观解模型及悲观解模型。含风电的区间经济调度悲观解模型如式(10)所示：Step 1. Establish a nonlinear interval economic dispatch model, take the ninth unit as a wind power output unit, and convert it into the corresponding optimistic solution model and pessimistic solution model. The pessimistic solution model of interval economic dispatch including wind power is shown in formula (10):
步骤2.将步骤1中提到的乐观解模型直接内外层合并，构成普通非线性优化模型，并采用原对偶内点法求解，得到乐观解。Step 2. Combine the inner and outer layers of the optimistic solution model mentioned in step 1 directly to form an ordinary nonlinear optimization model, and use the primal dual interior point method to solve it to obtain an optimistic solution.
步骤3.针对步骤1中的悲观解内层模型，将其按照非线性对偶原理进行转换求解，其中风电区间变量为外层变量，内层模型在求解过程中，区间变量为已知量，则求解目标函数关于变量Pi,t的偏导，得到9×1的导数列向量f(Pi,t)。如式(11)所示：Step 3. For the inner model of the pessimistic solution in step 1, it is converted and solved according to the principle of nonlinear duality, wherein the interval variable of wind power is the outer variable, and the interval variable is a known quantity during the solution of the inner model, then Solve the partial derivative of the objective function with respect to the variable Pi,t , and obtain a 9×1 derivative column vector f(Pi,t ). As shown in formula (11):
步骤4.分别对约束中的变量求导，得到导数矩阵将约束条件转换为式(12)所示状态，Step 4. Differentiate the variables in the constraint respectively to obtain the derivative matrix Transform the constraints into the state shown in formula (12),
分别对式中的变量Pi,t和Pi,t-1求导，得到导数矩阵得到(9×24)×(24×9×2+23×9×2+2)的导数矩阵，其中24为时段数，9为机组数，23为每台机组爬坡率约束的Pi,t和Pi,t-1变量数。Differentiate the variables Pi, t and Pi, t-1 in the formula to obtain the derivative matrix Obtain the derivative matrix of (9×24)×(24×9×2+23×9×2+2), where 24 is the number of time periods, 9 is the number of units, and 23 is the Pi constrained by the ramp rate of each unit, t and Pi,t-1 variable number.
步骤5.区间变量的上下限如表1中Unit10机组的约束所示，根据步骤3和步骤4中得到的导数矩阵行列数，引入临时变量u构成式(13)所示新的非线性优化模型，此时的区间变量将区间变量转换为常规优化变量：Step 5. The upper and lower limits of the interval variable are shown in the constraints of Unit10 in Table 1. According to the number of rows and columns of the derivative matrix obtained in Step 3 and Step 4, a new nonlinear optimization model shown in the composition formula (13) of the temporary variable u is introduced , the interval variable at this time converts the interval variable into a regular optimization variable:
步骤6.利用原对偶内点法对步骤5中的模型进行求解，得到区间变量Wi的优化解，即式(1)中Wi为已知量。将此优化解带入原双层悲观解模型中，双层悲观解模型转换为单层优化模型，公式如式(14)所示，采用原对偶内点法优化计算，得到的目标函数值即为悲观解。Step 6. Use the primal dual interior point method to solve the model in step 5, and obtain the optimal solution of the interval variable Wi , that is, Wi in formula (1) is a known quantity. Bring this optimization solution into the original double-layer pessimistic solution model, and convert the double-layer pessimistic solution model into a single-layer optimization model. For a pessimistic solution.
乐观解模型的目标函数为1762387.25$，悲观解模型的目标函数为4063941.84$，则求得的目标函数区间结果为[1762387.25,4063941.84],单位为$。The objective function of the optimistic solution model is 1762387.25$, and the objective function of the pessimistic solution model is 4063941.84$, then the obtained objective function interval result is [1762387.25, 4063941.84], and the unit is $.
十机组系统负荷表如表1所示。The system load table of the ten units is shown in Table 1.
表1十机组系统负荷表Table 1 System load table of ten units
十机组系统参数表如表2所示。The system parameters of the ten units are shown in Table 2.
表2十机组系统参数表Table 2 System parameter list of ten units
求解乐观解模型得到的十机组系统各时段各发电机组出力如表3所示。The output of each generator set in each period of the ten-unit system obtained by solving the optimistic solution model is shown in Table 3.
表3乐观解模型各时段下各发电机组出力Table 3 The output of each generator set in each time period of the optimistic solution model
求解悲观解模型得到的十机组系统各时段各发电机组出力如表4所示。The output of each generator set in each period of the ten-unit system obtained by solving the pessimistic solution model is shown in Table 4.
表4悲观解模型各时段下各发电机组出力Table 4 The output of each generator set in each time period of the pessimistic solution model
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