CN105790265A

CN105790265A - AC power flow constraint-based uncertainty unit commitment model and solving method

Info

Publication number: CN105790265A
Application number: CN201610254532.7A
Authority: CN
Inventors: 杨楠; 周峥; 崔家展; 李宏圣; 王璇; 黎索亚
Original assignee: China Three Gorges University CTGU
Current assignee: China Three Gorges University CTGU
Priority date: 2016-04-21
Filing date: 2016-04-21
Publication date: 2016-07-20
Anticipated expiration: 2036-04-21
Also published as: CN105790265B

Abstract

The present invention relates to an uncertain unit combination model and a solution method considering AC power flow constraints. The present invention takes the minimum sum of fuel costs of thermal power units in 24 periods of a day as the optimization goal, and adopts a chance constraint method to describe the uncertainty of wind power output , construct network security constraints based on AC power flow model, and propose an uncertain unit combination model considering AC power flow security constraints. Aiming at the problem that the model is difficult to solve, a stochastic constrained order optimization method is proposed, which successfully realizes the fast solution of the model. Compared with the traditional uncertain unit combination model based on DC power flow constraints, the model proposed in the present invention effectively reduces the risk of grid voltage exceeding the limit after large-scale wind power access, and improves the effectiveness of day-ahead power generation planning decisions. It can also calculate the network loss of the system in a refined manner, so as to provide data reference for dispatchers. Simultaneously, the solution algorithm provided by the present invention has significantly improved compared with the traditional algorithm.

Description

An Uncertain Unit Combination Model Considering AC Power Flow Constraints and Its Solution Method

技术领域technical field

本发明属于电力系统及自动化研究领域，尤其是涉及一种考虑交流潮流约束的不确定性机组组合模型及求解方法。The invention belongs to the field of electric power system and automation research, and in particular relates to an uncertain unit combination model and a solution method considering the constraint of AC power flow.

背景技术Background technique

考虑安全约束的机组组合(SecurityConstraintUnitCommitment，SCUC)是电力系统日前调度决策的理论基础，也是其制定日前发电计划的主要依据。随着近年来出力具有不确定性的风电大规模接入，以及电网调度运行的精细化要求不断提高，考虑风电接入的电力系统机组组合问题日益成为人们的研究热点。Security Constraint Unit Commitment (SCUC) is the theoretical basis of power system day-ahead scheduling decision-making and the main basis for making day-ahead power generation plan. With the large-scale access of wind power with uncertain output in recent years and the continuous improvement of refinement requirements for power grid dispatching and operation, the problem of unit combination in power systems considering wind power access has increasingly become a research hotspot.

目前，在不考虑风电接入的传统电力系统中，普遍采用的SCUC模型是利用基于直流潮流模型的网络安全约束条件对决策方案进行安全稳定校核。由于直流潮流模型不考虑系统无功和电压因素，仅计算线路有功潮流，因而可以极大的降低模型求解难度。而对于风电大规模接入之后的电力系统，常用场景法、机会约束、鲁棒优化等对不确定性进行描述。然而，当集群风电的接入水平很高时，往往无法对无功补偿设备进行统一调控，故发电功率因数和线路压降与常规机组相比仍有较大差距，加之风电的调节能力普遍较差，从而导致简化网络安全约束模型的前提假设条件已经不存在。若在SCUC模型中继续采用直流潮流模型描述网络安全约束条件，则必然会导致决策方案有效性降低，电压越限风险增加。At present, in the traditional power system that does not consider wind power access, the widely used SCUC model uses the network security constraints based on the DC power flow model to check the safety and stability of the decision-making scheme. Since the DC power flow model does not consider the reactive power and voltage factors of the system, but only calculates the active power flow of the line, it can greatly reduce the difficulty of solving the model. For the power system after large-scale access to wind power, scenarios, chance constraints, and robust optimization are commonly used to describe uncertainties. However, when the access level of cluster wind power is very high, it is often impossible to uniformly regulate reactive power compensation equipment, so there is still a large gap between the power factor and line voltage drop compared with conventional units, and the adjustment ability of wind power is generally relatively weak. Poor, leading to the premise assumptions of the simplified network security constraint model no longer exist. If the SCUC model continues to use the DC power flow model to describe the network security constraints, it will inevitably lead to a decrease in the effectiveness of the decision-making scheme and an increase in the risk of voltage violation.

另外，SCUC模型本身是一个具有复杂约束的非线性混合整数规划问题，由于在不确定性环境下，交流潮流模型本身无法快速解析性的求解，通常需要借助于耗时的数值算法，因此，在不确定性SCUC模型中引入交流潮流约束将必然面临求解困难的问题。而现有基于Benders分解的求解思路的主要优势在于求解具有复杂约束的确定性优化问题，而对于同时考虑风电不确定性和交流潮流约束的SCUC模型则很难保证求解效率。因此亟需研究一种考虑交流潮流约束的不确定性机组组合模型及求解方法。In addition, the SCUC model itself is a nonlinear mixed integer programming problem with complex constraints. Since the AC power flow model itself cannot be quickly and analytically solved in an uncertain environment, time-consuming numerical algorithms are usually required. Therefore, in The introduction of AC power flow constraints into the uncertain SCUC model will inevitably face the problem of solving difficulties. The main advantage of the existing solution based on Benders decomposition is to solve deterministic optimization problems with complex constraints, but it is difficult to guarantee the solution efficiency for the SCUC model that considers wind power uncertainty and AC power flow constraints at the same time. Therefore, it is urgent to study an uncertain unit combination model and its solution method considering AC power flow constraints.

发明内容Contents of the invention

本发明提出了一种考虑交流潮流约束的不确定性机组组合模型及求解方法，该模型采用机会约束方法描述风电出力的不确定性，并且基于交流潮流模型对网络安全进行校核。针对模型求解困难的问题，提出了一种随机约束序优化方法，成功实现对模型的快速求解。基于修改的IEEE-118节点电力系统的实施例，验证了本发明所提建模方法的正确性和有效性，相比与传统基于直流潮流约束的不确定性SCUC模型，本发明所提模型有效降低了风电大规模接入后电网电压越限的风险，提升了日前发电计划决策的有效性，同时本发明所建模型还可以精细化的计算系统网络损耗，从而为调度人员提供数据参考。The present invention proposes an uncertain unit combination model and a solution method considering AC power flow constraints. The model uses a chance constraint method to describe the uncertainty of wind power output, and checks network security based on the AC power flow model. Aiming at the problem that the model is difficult to solve, a stochastic constrained order optimization method is proposed, which successfully realizes the fast solution of the model. Based on the embodiment of the modified IEEE-118 node power system, the correctness and effectiveness of the modeling method proposed by the present invention are verified. Compared with the traditional uncertain SCUC model based on DC power flow constraints, the model proposed by the present invention is effective It reduces the risk of the grid voltage exceeding the limit after large-scale access of wind power, and improves the effectiveness of the decision-making of the power generation plan. At the same time, the model built by the invention can also calculate the network loss of the system in a refined manner, so as to provide data reference for dispatchers.

本发明所采用的技术方案是：The technical scheme adopted in the present invention is:

一种考虑交流潮流安全约束的不确定性机组组合建模方法，考虑风电出力的不确定性，并且以交流潮流约束对其进行安全校核，使总运行成本最小，其目标函数为：An uncertain unit combination modeling method considering AC power flow safety constraints, considering the uncertainty of wind power output, and checking it with AC power flow constraints to minimize the total operating cost, its objective function is:

$min min {F f}_{G G t t} = = {Σ Σ}_{t t = = 11}^{24 twenty four} {Σ Σ}_{i i = = 11}^{M m} [[{U u}_{G G i i t t} {Y Y}_{i i t t} (({P P}_{G G i i t t})) + + {U u}_{G G i i t t} ((11 - - {U u}_{G G i i t t - - 11})) {S S}_{i i t t} (({τ τ}_{i i}))]] - - - - - - ((11))$

式中：F_Gt为系统的总运行成本，系统中的发电机组个数为M，P_Git和U_Git分别表示第i号机组在t时段的有功出力和启停状态，U_Git＝0表示发电机组处于停机状态，U_Git＝1表示发电机组处于开机状态。Y_it(P_Git)为发电机组的运行成本，S_it(τ_i)为发电机的启停成本；In the formula: F _Gt is the total operating cost of the system, the number of generator sets in the system is M, P _Git and U _Git respectively represent the active output and start-stop status of the i-th unit in the period t, and U _Git = 0 means power generation The generator set is in shutdown state, and U _Git = 1 means that the generator set is in startup state. Y _it (P _Git ) is the operating cost of the generator set, S _it (τ _i ) is the start-stop cost of the generator;

其中，发电机组的运行成本、启停成本的具体数学表达形式如下：Among them, the specific mathematical expressions of the operating cost and start-stop cost of the generator set are as follows:

${Y Y}_{i i t t} (({P P}_{G G i i t t})) = = {α α}_{i i} + + {β β}_{i i} {P P}_{G G i i t t} + + {γ γ}_{i i} {P P}_{G G i i t t}^{22} - - - - - - ((22))$

${S S}_{i i t t} (({τ τ}_{i i})) = = {S S}_{00 i i} + + {S S}_{11 i i} ((11 - - {e e}^{{τ τ}_{i i} / / {ω ω}_{i i}})) - - - - - - ((33))$

式中：α_i、β_i、γ_i为机组运行成本参数。S_0i、S_1i、τ_i为i号机组的停机时间，ω_i为启停成本参数；In the formula: α _i , β _i , γ _i are the operating cost parameters of the unit. S _0i , S _1i , τ _i are the downtime of unit i, and ω _i is the start-stop cost parameter;

决策变量通常满足以下常规约束条件：系统有功功率平衡约束；发电机组有功、无功出力上下限约束；最小启停次数约束；机组爬坡约束；Decision variables usually meet the following conventional constraints: system active power balance constraints; generator set active and reactive output upper and lower limits; minimum start and stop times constraints; unit climbing constraints;

除上述常规约束条件外，本发明提出的网络安全约束条件如下：In addition to the above conventional constraints, the network security constraints proposed by the present invention are as follows:

-P_l,max≤P_l,t≤P_l,max(4)-P _l,max ≤P _l,t ≤P _l,max (4)

-Q_l,max≤Q_l,t≤Q_l,max(5)-Q _l,max ≤Q _l,t ≤Q _l,max (5)

V_b,min≤V_bt≤V_b,max(6)V _b,min ≤V _bt ≤V _b,max (6)

式中：P_l,t、Q_l,t分别为线路l在t时段的有功功率和无功功率，V_bt为节点b在t时段的电压，P_l,max、Q_l,max为分别线路l允许的最大有功、无功容量；V_b,min，V_b,max分别为节点b允许的最小最大电压；In the formula: P _l,t , Q _l,t are the active power and reactive power of line l in period t respectively, V _bt is the voltage of node b in period t, P _l,max and Q _l,max are line l The maximum active and reactive capacity allowed; V _b,min , V _b,max are the minimum and maximum voltages allowed by node b respectively;

公式(4-6)中的变量P_l,max、Q_l,max、V_bt需要经过交流潮流方程求出。其具体形式如下：The variables P _l,max , Q _l,max , and V _bt in the formula (4-6) need to be obtained through the AC power flow equation. Its specific form is as follows:

$\{\begin{matrix} Δ Δ P P = = {V V}_{b b} \underset{c c &Element; &Element; b b}{Σ Σ} {V V}_{c c} (({G G}_{b b c c} {cosθ cosθ}_{b b c c} + + {B B}_{b b c c} {sinθ sinθ}_{b b c c})) \\ Δ Δ Q Q = = {V V}_{b b} \underset{c c &Element; &Element; b b}{Σ Σ} {V V}_{c c} (({G G}_{b b c c} {sinθ sinθ}_{b b c c} - - {B B}_{b b c c} {cosθ cosθ}_{b b c c})) \end{matrix} - - - - - - ((77))$

式中：△P、△Q表示节点注入有功和无功；b＝1,2,LK为节点数；c∈b表示与节点b相连的节点c；V表示节点电压；G_bc、B_bc分别是节点b和节点c之间的网络导纳的实部和虚部；In the formula: △P, △Q represent the active and reactive power injected by the node; b=1, 2, LK is the number of nodes; c∈b represents the node c connected to node b; V represents the node voltage; G _bc and B _bc respectively are the real and imaginary parts of the network admittance between nodes b and c;

采用机会约束方法描述机组组合问题中的风电出力不确定性，分别构建系统正负旋转备用风险指标。The uncertainty of wind power output in the unit combination problem is described by the chance constraint method, and the positive and negative spinning reserve risk indicators of the system are respectively constructed.

Q_d≤λ(13)Q _d ≤ λ(13)

Q_u≤λ(14)Q _u ≤ λ(14)

式中：Q_d、Q_u分别为正、负旋转备用风险指数；λ为旋转备用风险槛值，系统调度部门可利用年总费用最小法获取可靠性标准后换算而得，通常取0～10％之间。In the formula: Q _d , Q _u are the positive and negative spinning reserve risk indices respectively; λ is the spinning reserve risk threshold, which can be converted by the system dispatching department by using the minimum annual total cost method to obtain the reliability standard, usually 0 to 10 %between.

一种考虑交流潮流安全约束的不确定性机组组合模型求解方法，从融入交流潮流约束的不确定性SCUC模型本身的特点出发，提出了一种适用于SCUC模型求解的随机约束序优化方法。针对模型的离散决策变量U_Git和连续决策变量P_Git，分别构造序优化粗糙模型和精确模型，在进行序比较的同时实现混合整数决策变量的解耦。A method for solving an uncertain unit combination model considering the safety constraints of AC power flow. Starting from the characteristics of the uncertain SCUC model integrated with AC power flow constraints, a stochastic constrained order optimization method suitable for solving the SCUC model is proposed. Aiming at the discrete decision variable U _Git and the continuous decision variable P _Git of the model, the sequence optimization rough model and precise model are respectively constructed, and the decoupling of the mixed integer decision variables is realized while performing sequence comparison.

步骤1：构造粗糙模型对机组启停状态解空间进行预筛选，依照均匀分布抽取N个可行解构成表征集合Ω，N的个数与解空间的大小密切相关，，在解空间小于10⁸时，N的个数一般选1000。其具体粗糙模型为：Step 1: Construct a rough model to pre-screen the solution space of the start-stop state of the unit, and extract N feasible solutions according to the uniform distribution to form a representation set Ω. The number of N is closely related to the size of the solution space. When the solution space is less than 10 ⁸ , the number of N is generally selected as 1000. Its specific rough model is:

(1)功率平衡约束(1) Power balance constraints

机组启停状态向量需保证开机机组的最大最小发电能力应满足系统的负荷及备用需求，即：The start-stop state vector of the unit needs to ensure that the maximum and minimum generating capacity of the start-up unit should meet the load and backup requirements of the system, namely:

${Σ Σ}_{i i = = 11}^{M m} {U u}_{G G i i t t} {P P}_{G G i i m m a a x x} + + {P P}_{W W t t} &GreaterEqual; &Greater Equal; {P P}_{D D. t t} + + {R R}_{D D. p p} - - - - - - ((1515))$

${Σ Σ}_{i i = = 11}^{M m} {U u}_{G G i i t t} {P P}_{G G i i min min} + + {P P}_{W W t t} \leq \leq {P P}_{D D. t t} - - {R R}_{D D. n no} - - - - - - ((1616))$

式中：R_Dp、R_Dn分别为考虑风电接入后，系统所需的正旋转备用和负旋转备用。In the formula: R _Dp and R _Dn are the positive spinning reserve and negative spinning reserve required by the system after considering the wind power access, respectively.

(2)机组爬坡约束(2) Crew climbing constraint

在粗糙模型之中，机组爬坡速率约束体现为相邻时段内机组最大爬坡能力和最大滑坡能力之和大于负荷变化绝对值，即：In the rough model, the unit’s ramp rate constraint is reflected in the fact that the sum of the unit’s maximum ramping capacity and maximum landslide capacity in adjacent periods is greater than the absolute value of the load change, that is:

${Σ Σ}_{i i = = 11}^{M m} [[{U u}_{G G i i t t} {ΔP ΔP}_{G G i i}^{u u p p} + + {P P}_{G G i i min min} (({U u}_{G G i i t t} - - {U u}_{G G i i t t - - 11}))]] &GreaterEqual; &Greater Equal; | | {P P}_{D D. t t} - - {P P}_{D D. t t - - 11} | | - - - - - - ((1717))$

${Σ Σ}_{i i = = 11}^{M m} [[{U u}_{G G i i t t} {ΔP ΔP}_{G G i i}^{d d o o w w n no} + + {P P}_{G G i i min min} (({U u}_{G G i i t t} - - {U u}_{G G i i t t - - 11}))]] &GreaterEqual; &Greater Equal; | | {P P}_{D D. t t} - - {P P}_{D D. t t - - 11} | | - - - - - - ((1818))$

(3)网络安全约束(3) Network security constraints

${Σ Σ}_{i i = = 11}^{k k - - 11} (({a a}_{l l,, {i i}_{n no}} - - {a a}_{l l,, {i i}_{k k}})) {P P}_{G G i i m m a a x x} + + {Σ Σ}_{i i = = k k + + 11}^{N N} (({a a}_{l l,, {i i}_{n no}} - - {a a}_{l l,, {i i}_{k k}})) {P P}_{G G i i min min} + + {a a}_{l l,, {i i}_{k k}} \leq \leq {B B}_{l l,, t t} - - - - - - ((1919))$

式中：a_l,t、B_l,t分别为直流潮流系数矩阵A、B_t中第l行元素；k为整数，满足以下约束条件：In the formula: a _{l, t} and B _{l, t} are the elements of row l in the DC power flow coefficient matrix A and B _t respectively; k is an integer, which satisfies the following constraints:

${Σ Σ}_{i i = = 11}^{k k - - 11} (({P P}_{G G i i max max} - - {P P}_{G G i i min min})) \leq \leq {P P}_{D D. t t} - - {Σ Σ}_{i i = = 11}^{M m} {P P}_{G G i i min min} \leq \leq {Σ Σ}_{i i = = 11}^{k k} (({P P}_{G G i i max max} - - {P P}_{G G i i min min})) - - - - - - ((2020))$

步骤2：利用特定的挑选规则从表征集合中进一步挑选出s个解作为选定集合S，集合S需保证以至少α％的概率包含k个足够好解。Step 2: Use specific selection rules to further select s solutions from the representation set as the selected set S, and the set S needs to be guaranteed to contain k good enough solutions with at least α% probability.

本发明采用盲选法确定选定集合S，其数学模型为：The present invention adopts blind selection method to determine selected set S, and its mathematical model is:

$\begin{matrix} P P ((| | G G \cap \cap S S | | &GreaterEqual; &Greater Equal; k k)) \\ = = {Σ Σ}_{j j = = k k}^{min min ((g g,, s the s))} {Σ Σ}_{i i = = 00}^{s the s - - j j} \frac{{C C}_{g g}^{j j} {C C}_{N N - - g g}^{s the s - - i i - - j j}}{{C C}_{N N}^{s the s - - i i}} {C C}_{s the s}^{i i} {q q}^{s the s - - i i} {((11 - - q q))}^{i i} &GreaterEqual; &Greater Equal; η η \end{matrix} - - - - - - ((21 twenty one))$

式中：P(·)为对准概率，g为足够好解集G中解的个数，s为选定集合S中解的个数，k表示选定集合中至少有k个真实足够好解，η表示选定集合S中包含k个足够好解的概率，通常η取0.95，q为解空间中真实观察到可行解的概率。In the formula: P( ) is the alignment probability, g is the number of solutions in the good enough solution set G, s is the number of solutions in the selected set S, k means that there are at least k real good enough solutions in the selected set solution, η represents the probability that the selected set S contains k good enough solutions, usually η is 0.95, and q is the probability of actually observing a feasible solution in the solution space.

上式中，足够好解集G、选定集合S、表征集合Ω的关系如图2所示。In the above formula, the relationship between the good enough solution set G, the selected set S, and the representation set Ω is shown in Figure 2.

步骤3：以机组运行总成本最小为目标函数，考虑与机组出力相关的约束条件，构建针对连续变量P_Git的精确模型，针对选定集合S中的每一个机组启停状态，求解与之对应的机组出力和运行成本，并对选定集合进行进一步排序，求取最优解。所构造序优化精确模型为：Step 3: Taking the minimum total operating cost of the unit as the objective function, considering the constraints related to the unit output, construct an accurate model for the continuous variable P _Git , and solve the corresponding The output and operating cost of the unit, and further sort the selected set to find the optimal solution. The exact model of sequence optimization constructed is:

$\{\begin{matrix} min min {F f}_{G G t t} = = {Σ Σ}_{t t = = 11}^{24 twenty four} {Σ Σ}_{i i = = 11}^{M m} [[{U u}_{G G i i t t} {Y Y}_{i i t t} (({P P}_{G G i i t t})) + + {U u}_{G G i i t t} ((11 - - {U u}_{G G i i t t - - 11})) {S S}_{i i t t} (({τ τ}_{i i}))]] \\ s the s . . t t . . {P P}_{G G i i min min} \leq \leq {P P}_{G G i i t t} \leq \leq {P P}_{G G i i m m a a x x} \\ {Q Q}_{G G i i min min} \leq \leq {Q Q}_{G G i i t t} \leq \leq {Q Q}_{G G i i m m a a x x} \\ - - {P P}_{l l max max} \leq \leq {P P}_{l l t t} \leq \leq {P P}_{l l m m a a x x} \\ - - {Q Q}_{l l max max} \leq \leq {Q Q}_{l l t t} \leq \leq {Q Q}_{l l max max} \\ {V V}_{b b m m i i x x} \leq \leq {V V}_{b b t t} \leq \leq {V V}_{b b max max} \end{matrix} - - - - - - ((22 twenty two))$

精确模型的求解思路是，将选定集合中的每一个机组组合状态矩阵U_G作为已知参数代入公式(21)中，利用内点法求解相应的发电机有功出力矩阵P_G，并利用F_Gt对解进行排序，求取最优解。The idea of solving the exact model is to substitute the combined state matrix U _G of each unit in the selected set into the formula (21) as a known parameter, use the interior point method to solve the corresponding generator active output matrix _PG , and use F _Gt sorts the solutions to find the optimal solution.

与现有方法相比，本发明提出的考虑交流潮流约束的不确定性机组组合模型及求解方法，具有以下优点和有益效果：Compared with existing methods, the uncertain unit combination model and solution method considering AC power flow constraints proposed by the present invention have the following advantages and beneficial effects:

(1)、本发明提出的融入交流潮流安全约束的不确定性SCUC模型，采用更为精确地交流潮流模型对调度决策方案进行安全稳定校核，有效避免了系统电压越限情况的出现，提升了日前调度决策的精确性和有效性。(1) The uncertain SCUC model integrated into the AC power flow security constraints proposed by the present invention uses a more accurate AC power flow model to check the safety and stability of the scheduling decision-making scheme, effectively avoiding the occurrence of system voltage over-limit situations, and improving The accuracy and effectiveness of the day-ahead scheduling decision.

(2)、本发明所建模型可以精细化的计算系统网络损耗，从而为调度人员提供数据支持。(2) The model built by the present invention can calculate the network loss of the system in a refined manner, so as to provide data support for dispatchers.

(3)、本发明提出的基于随机约束序优化的求解算法，有效的解决了本发明所建模型的求解难题，与传统的Benders分解法相比，在计算效率方面具有显著优势。(3), the solution algorithm based on stochastic constraint order optimization proposed by the present invention effectively solves the difficult problem of solving the model built by the present invention, and has a significant advantage in computational efficiency compared with the traditional Benders decomposition method.

附图说明Description of drawings

图1是本发明算法总体思路框图。Fig. 1 is a block diagram of the overall idea of the algorithm of the present invention.

图2是本发明约束序优化概念示意图。Fig. 2 is a schematic diagram of the concept of constraint order optimization in the present invention.

图3是本发明实施例中的风电场出力曲线图。Fig. 3 is a graph of the wind farm output in the embodiment of the present invention.

图4是本发明实施例中的各个时刻有功网损。Fig. 4 shows active network losses at various moments in the embodiment of the present invention.

具体实施方式detailed description

$min min {F f}_{G G t t} = = {Σ Σ}_{t t = = i i}^{24 twenty four} {Σ Σ}_{i i = = 11}^{M m} [[{U u}_{G G i i t t} {Y Y}_{i i t t} (({P P}_{G G i i t t})) + + {U u}_{G G i i t t} ((11 - - {U u}_{G G i i t t - - 11})) {S S}_{i i t t} (({τ τ}_{i i}))]] - - - - - - ((11))$

-P_l,max≤P_l,t≤P_l,max(4)-P _l,max ≤P _l,t ≤P _l,max (4)

-Q_l,max≤Q_l,t≤Q_l,max(5)-Q _l,max ≤Q _l,t ≤Q _l,max (5)

V_b,min≤V_bt≤V_b,max(6)V _b,min ≤V _bt ≤V _b,max (6)

Q_d≤λ(13)Q _d ≤ λ(13)

Q_u≤λ(14)Q _u ≤ λ(14)

(1)功率平衡约束(1) Power balance constraints

${Σ Σ}_{i i = = 11}^{M m} {U u}_{G G i i t t} {P P}_{G G i i max max} + + {P P}_{W W t t} &GreaterEqual; &Greater Equal; {P P}_{D D. t t} + + {R R}_{D D. p p} - - - - - - ((1515))$

(2)机组爬坡约束(2) Crew climbing constraint

${Σ Σ}_{i i = = 11}^{M m} [[{U u}_{G G i i t t} {ΔP ΔP}_{G G i i}^{d d o o w w n no} + + {P P}_{G G i i m m i i n no} (({U u}_{G G i i t t} - - {U u}_{G G i i t t - - 11}))]] &GreaterEqual; &Greater Equal; | | {P P}_{D D. t t} - - {P P}_{D D. t t - - 11} | | - - - - - - ((1818))$

(3)网络安全约束(3) Network security constraints

${Σ Σ}_{i i = = 11}^{k k - - 11} (({P P}_{G G i i max max} - - {P P}_{G G i i min min})) \leq \leq {P P}_{D D. t t} - - {Σ Σ}_{i i = = 11}^{M m} {P P}_{G G i i min min} \leq \leq {Σ Σ}_{i i = = 11}^{k k} {P P}_{G G i i max max} - - {P P}_{G G i i min min})) - - - - - - ((2020))$

$\begin{matrix} P P ((| | G G \cap \cap S S | | &GreaterEqual; &Greater Equal; k k)) \\ = = {Σ Σ}_{j j = = k k}^{min min ((g g,, s the s))} {Σ Σ}_{i i = = 00}^{s the s - - j j} \frac{{C C}_{g g}^{j j} {C C}_{N N - - g g}^{s the s - - i i - - j j}}{{C C}_{N N}^{s the s - - i i}} {C C}_{s the s}^{j j} {q q}^{s the s - - i i} {((11 - - q q))}^{i i} &GreaterEqual; &Greater Equal; η η \end{matrix} - - - - - - ((21 twenty one))$

实施例：Example:

本发明以修改的IEEE-118节点电力系统为例，该系统包含54台火电机组，3个风力发电场，91个负荷点，其中风电场分别位于节点14，54，95上，其额定功率分别为100MW、200MW、250MW，有功出力如图3所示。系统中常规机组正旋转备用需求为系统最大负荷的8％，负旋转备用需求为系统最小负荷的2％，旋转备用风险指标为0.01。相关计算均在英特尔酷睿i3-3240处理器3.40GHz，4G内存计算机上完成，采用Matlab8.0和Cplex12.5对算例进行编程求解。The present invention takes the modified IEEE-118 node power system as an example. The system includes 54 thermal power units, 3 wind farms, and 91 load points, wherein the wind farms are respectively located on nodes 14, 54, and 95, and their rated power 100MW, 200MW, 250MW, the active output is shown in Figure 3. The positive spinning reserve demand of conventional units in the system is 8% of the maximum system load, the negative spinning reserve demand is 2% of the minimum system load, and the spinning reserve risk index is 0.01. Relevant calculations are completed on a computer with Intel Core i3-3240 processor 3.40GHz and 4G memory, and Matlab8.0 and Cplex12.5 are used to program and solve the calculation examples.

1)、模型求解：1), model solution:

利用机会约束方法求取的系统及各风电场所需的旋转备用如表1所示。Table 1 shows the system obtained by using the chance constraint method and the spinning reserve required by each wind farm.

表1各风电场的旋转备用(MW)Table 1 Spinning reserve (MW) of each wind farm

利用本发明所建的融入交流潮流约束的SCUC模型以及相应的求解方法，求解IEEE-118节点仿真算例中54台发电机组24小时内的启停计划如表2所示。Using the SCUC model integrated with the AC power flow constraints built by the present invention and the corresponding solution method, the start-stop plan of 54 generating units within 24 hours in the IEEE-118 node simulation example is solved, as shown in Table 2.

表2交流潮流约束下启停方案Table 2 Start-stop scheme under AC power flow constraints

本发明所建模型还可以详细计算系统的输电网损，从而为系统调度人员提供更为精细化的数据支持。利用本发明所建AC-SCUC模型计算系统24个时段的输电网损如图4所示。The model built by the invention can also calculate the transmission network loss of the system in detail, thereby providing more refined data support for system dispatchers. The AC-SCUC model built by the present invention is used to calculate the transmission network loss in 24 time periods of the system as shown in Fig. 4 .

由图4可知，系统输电网损的变化趋势与负荷变化趋势基本一致，在20点最大，为176.11MW，在4点最小，为29.71MW。It can be seen from Figure 4 that the change trend of the system transmission network loss is basically consistent with the load change trend, the largest at 20 points, 176.11MW, and the smallest at 4 points, 29.71MW.

2)、对比分析：2), comparative analysis:

(1)、直流潮流安全约束与交流潮流安全约束对比分析：(1) Comparative analysis of DC power flow security constraints and AC power flow security constraints:

为验证本发明所提模型的先进性，利用基于直流潮流网络安全约束的SCUC模型对本发明算例进行求解，然后利用交流潮流约束对仿真结果进行校核，对比分析其运行成本，输电网络越限情况如表3所示，在表中基于直流潮流网络安全约束的SCUC模型和本发明所建模型分别用DC-SCUC和AC-SCUC表示。In order to verify the advanced nature of the model proposed in the present invention, the calculation example of the present invention is solved using the SCUC model based on the security constraints of the DC power flow network, and then the simulation results are checked using the AC power flow constraints, and the operating costs are compared and analyzed. The situation is shown in Table 3. In the table, the SCUC model based on the DC power flow network security constraints and the model built by the present invention are represented by DC-SCUC and AC-SCUC respectively.

表3直流约束与交流约束比较结果Table 3 Comparison results of DC constraints and AC constraints

由表3可知，就系统运行成本而言，AC-SCUC模型制定的方案比DC-SCUC模型增加了57950$，而在24小时的调度时段内，两个方案导致的线路有功越限数均为0，但DC-SCUC模型制定的调度方案却出现了105次节点电压越限的情况。It can be seen from Table 3 that, in terms of system operating costs, the scheme formulated by the AC-SCUC model is 57950$ more than the DC-SCUC model, and in the 24-hour scheduling period, the number of active power violations caused by the two schemes is 0, but the scheduling scheme formulated by the DC-SCUC model has 105 node voltage violations.

结果表明，无论是DC-SCUC模型还是本发明提出的AC-SCUC模型，都可以有效避免输电线路出现有功潮流越限。因为考虑了更为精确的电压、无功等约束条件，相比于DC-SCUC模型，本发明所建模型制定的调度方案成本虽然有所增加，但是其有效避免了节点电压越限的情况出现，从而提升了日前调度决策方案的有效性，保证了系统安全可靠运行。The results show that both the DC-SCUC model and the AC-SCUC model proposed by the present invention can effectively prevent the active power flow from exceeding the limit in the transmission line. Because more accurate constraints such as voltage and reactive power are considered, compared with the DC-SCUC model, although the cost of the dispatching plan formulated by the model built by the present invention has increased, it effectively avoids the occurrence of node voltage exceeding the limit , thus improving the effectiveness of the day-ahead scheduling decision-making scheme and ensuring the safe and reliable operation of the system.

基于DC-SCUC模型制定的调度方案下，出现电压越限的节点编号及最大越限电压如表4所示。Under the scheduling scheme based on the DC-SCUC model, the node numbers and the maximum voltage violations are shown in Table 4.

表4各时刻下越限电压Table 4 Lower limit voltage at each moment

由表4可知，由于DC-SCUC模型未能对节点电压约束进行校核，系统在各时刻均出现低电压情况。其中29、31、53三条支路在24个时段均出现电压越限，是整个系统最脆弱的输电断面。It can be seen from Table 4 that because the DC-SCUC model fails to check the node voltage constraints, the system has low voltage at each moment. Among them, the three branches 29, 31, and 53 all had voltage violations in 24 time periods, and they were the most vulnerable transmission sections of the entire system.

(2)、风电场对电力系统运行影响分析：(2) Analysis of the influence of the wind farm on the operation of the power system:

为分析风电场对电力系统运行安全的影响，采用DC-SCUC模型分别对含风电与不含风电的电力系统进行优化计算，并采用交流潮流模型对仿真结果进行安全校核，其结果如表5所示。In order to analyze the impact of wind farms on the safety of power system operation, the DC-SCUC model is used to optimize the calculation of power systems with and without wind power, and the AC power flow model is used to check the safety of the simulation results. The results are shown in Table 5 shown.

表5风电场对电力系统运行影响Table 5 Impact of wind farms on power system operation

由表5可知，风电接入后，虽然可以降低系统的运行成本，但是也会导致系统电压越限节点数增加，其原因是风电场在运行过程中会在一定程度上吸收无功功率。由此可见，在风电大规模接入的形势下，传统DC-SCUC模型将很难保证日前调度决策的有效性。It can be seen from Table 5 that although wind power access can reduce the operating cost of the system, it will also lead to an increase in the number of nodes whose voltage exceeds the limit of the system. The reason is that the wind farm will absorb reactive power to a certain extent during operation. It can be seen that under the situation of large-scale access to wind power, the traditional DC-SCUC model will hardly guarantee the effectiveness of day-ahead scheduling decisions.

(3)、随机约束序优化的有效性分析：(3) Effectiveness analysis of stochastic constrained order optimization:

为验证本发明所提求解算法的有效性，分别利用目前最常用的Benders分解法和本发明提出的COO算法对AC-SCUC模型进行求解，其计算时间及寻优结果如表6所示。In order to verify the effectiveness of the solution algorithm proposed by the present invention, the most commonly used Benders decomposition method and the COO algorithm proposed by the present invention are used to solve the AC-SCUC model respectively. The calculation time and optimization results are shown in Table 6.

表6求解算法比较Table 6 Comparison of solving algorithms

由表6可知，本发明提出的COO算法在寻优能力方面与Benders分解法比较接近，但在计算效率方面具有显著优势。It can be seen from Table 6 that the COO algorithm proposed by the present invention is relatively close to the Benders decomposition method in terms of optimization ability, but has a significant advantage in calculation efficiency.

Claims

1. An uncertain unit combination modeling method considering AC power flow safety constraints, characterized in that the uncertainty of wind power output is considered, and it is checked for safety with AC power flow constraints, and its objective function is:

{minF minF}_{G G t t} = = {Σ Σ}_{t t = = 11}^{24 twenty four} {Σ Σ}_{i i = = 11}^{M m} [[{U u}_{G G i i t t} {Y Y}_{i i t t} (({P P}_{G G i i t t})) + + {U u}_{G G i i t t} ((11 - - {U u}_{G G i i t t - - 11})) {S S}_{i i t t} (({τ τ}_{i i}))]] - - - - - - ((11))

In the formula: F _Gt is the total operating cost of the system, the number of generator sets in the system is M, P _Git and U _Git respectively represent the active output and start-stop status of the i-th unit in the period t, and U _Git = 0 means power generation The generator set is in shutdown state, and U _Git = 1 means that the generator set is in startup state. Y _it (P _Git ) is the operating cost of the generator set, S _it (τ _i ) is the start-stop cost of the generator;

Among them, the specific mathematical expressions of the operating cost and start-stop cost of the generator set are as follows:

{Y Y}_{i i t t} (({P P}_{G G i i t t})) = = {α α}_{i i} + + {β β}_{i i} {P P}_{G G i i t t} + + {γ γ}_{i i} {P P}_{G G i i t t}^{22} - - - - - - ((22))

{S S}_{i i t t} (({τ τ}_{i i})) = = {S S}_{00 i i} + + {S S}_{11 i i} ((11 - - {e e}^{{τ τ}_{i i} / / {ω ω}_{i i}})) - - - - - - ((33))

In the formula: α _i , β _i , γ _i are the unit operating cost parameters, S _0i , S _1i , τ _i are the downtime of unit i, and ω _i is the start-stop cost parameter;

Decision variables usually meet the following conventional constraints: system active power balance constraints; generator set active and reactive output upper and lower limits; minimum start and stop times constraints; unit climbing constraints;

In addition to the above general constraints, the network security constraints proposed by this method are as follows:

-P _l,max ≤P _l,t ≤P _l,max (4)

-Q _l,max ≤Q _l,t ≤Q _l,max (5)

V _b,min ≤V _bt ≤V _b,max (6)

In the formula: P _l,t , Q _l,t are the active power and reactive power of line l in period t respectively, V _bt is the voltage of node b in period t, P _l,max and Q _l,max are line l The maximum active and reactive capacity allowed; V _b,min , V _b,max are the minimum and maximum voltages allowed by node b respectively;

The variables P _l,max , Q _l,max , and V _bt in formula (4-6) need to be obtained through the AC power flow equation, and their specific forms are as follows:

\{\begin{matrix} Δ Δ P P = = {V V}_{b b} \underset{c c &Element; &Element; b b}{Σ Σ} {V V}_{c c} (({G G}_{b b c c} {cosθ cosθ}_{b b c c} + + {B B}_{b b c c} {sinθ sinθ}_{b b c c})) \\ Δ Δ Q Q = = {V V}_{b b} \underset{c c &Element; &Element; b b}{Σ Σ} {V V}_{c c} (({G G}_{b b c c} {sinθ sinθ}_{b b c c} - - {B B}_{b b c c} {cosθ cosθ}_{b b c c})) \end{matrix} - - - - - - ((77))

In the formula: △P, △Q represent the active and reactive power injected by the node; b=1, 2, LK is the number of nodes; c∈b represents the node c connected to node b; V represents the node voltage; G _bc and B _bc respectively are the real and imaginary parts of the network admittance between nodes b and c;

The uncertainty of wind power output in the unit combination problem is described by the chance constraint method, and the positive and negative spinning reserve risk indicators of the system are constructed respectively:

Q _d ≤ λ(13)

Q _u ≤ λ(14)

In the formula: Q _d , Q _u are the positive and negative spinning reserve risk indices respectively; λ is the spinning reserve risk threshold, which can be converted by the system dispatching department by using the minimum annual total cost method to obtain the reliability standard, usually 0 to 10 %between.

2. A method for solving the uncertain unit combination model considering the safety constraints of AC power flow, characterized in that, starting from the characteristics of the uncertain SCUC model integrated into the AC power flow constraints, a stochastic model suitable for solving the SCUC model is proposed Constrained order optimization method; for the discrete decision variable U _Git and the continuous decision variable P _Git of the model, the order optimization rough model and the precise model are respectively constructed, and the decoupling of mixed integer decision variables is realized while performing order comparison.

3. According to claim 2, a method for solving the uncertain unit combination model considering AC power flow security constraints, is characterized in that it comprises the following steps:

Step 1: Construct a rough model to pre-screen the solution space of the start-stop state of the unit, and extract N feasible solutions according to the uniform distribution to form a representation set Ω. The number of N is closely related to the size of the solution space. When the solution space is less than ¹⁰⁸ , The number of N is generally selected as 1000, and the specific rough model is:

(1), power balance constraints:

The start-stop state vector of the unit needs to ensure that the maximum and minimum generating capacity of the start-up unit should meet the load and backup requirements of the system, namely:

{Σ Σ}_{i i = = 11}^{M m} {U u}_{G G i i t t} {P P}_{G G i i m m a a x x} + + {P P}_{W W t t} &GreaterEqual; &Greater Equal; {P P}_{D D. t t} + + {R R}_{D D. p p} - - - - - - ((1515))

{Σ Σ}_{i i = = 11}^{M m} {U u}_{G G i i t t} {P P}_{G G i i min min} + + {P P}_{W W t t} \leq \leq {P P}_{D D. t t} - - {R R}_{D D. n no} - - - - - - ((1616))

In the formula: R _Dp and R _Dn are the positive spinning reserve and negative spinning reserve required by the system after considering the wind power connection;

(2) Unit climbing constraints:

In the rough model, the unit’s ramp rate constraint is reflected in the fact that the sum of the unit’s maximum ramping capacity and maximum landslide capacity in adjacent periods is greater than the absolute value of the load change, that is:

{Σ Σ}_{i i = = 11}^{M m} [[{U u}_{G G i i t t} {ΔP ΔP}_{G G i i}^{u u p p} + + {P P}_{G G i i min min} (({U u}_{G G i i t t} - - {U u}_{G G i i t t - - 11}))]] &GreaterEqual; &Greater Equal; | | {P P}_{D D. t t} - - {P P}_{D D. t t - - 11} | | - - - - - - ((1717))

{Σ Σ}_{i i = = 11}^{M m} [[{U u}_{G G i i t t} {ΔP ΔP}_{G G i i}^{d d o o w w n no} + + {P P}_{G G i i min min} (({U u}_{G G i i t t} - - {U u}_{G G i i t t - - 11}))]] &GreaterEqual; &Greater Equal; | | {P P}_{D D. t t} - - {P P}_{D D. t t - - 11} | | - - - - - - ((1818))

(3) Network security constraints

{Σ Σ}_{i i = = 11}^{k k - - 11} (({a a}_{l l,, {i i}_{n no}} - - {a a}_{l l,, {i i}_{k k}})) {P P}_{G G i i max max} + + {Σ Σ}_{i i = = k k + + 11}^{N N} (({a a}_{l l,, {i i}_{n no}} - - {a a}_{l l,, {i i}_{k k}})) {P P}_{G G i i min min} + + {a a}_{l l,, {i i}_{k k}} \leq \leq {B B}_{l l,, t t} - - - - - - ((1919))

In the formula: a _{l, t} and B _{l, t} are the elements of row l in the DC power flow coefficient matrix A and B _t respectively; k is an integer, which satisfies the following constraints:

{Σ Σ}_{i i = = 11}^{k k - - 11} (({P P}_{G G i i max max} - - {P P}_{G G i i min min})) \leq \leq {P P}_{D D. t t} - - {Σ Σ}_{i i = = 11}^{M m} {P P}_{G G i i min min} \leq \leq {Σ Σ}_{i i = = 11}^{k k} (({P P}_{G G i i max max} - - {P P}_{G G i i min min})) - - - - - - ((2020))

Step 2: use specific selection rules to further select s solutions from the representation set as the selected set S, and the set S needs to be guaranteed to contain k good enough solutions with a probability of at least α%;

The present invention adopts blind selection method to determine selected set S, and its mathematical model is:

\begin{matrix} P P ((| | G G \cap \cap S S | | &GreaterEqual; &Greater Equal; k k)) \\ = = {Σ Σ}_{j j = = k k}^{min min ((g g,, s the s))} {Σ Σ}_{i i = = 00}^{s the s - - j j} \frac{{C C}_{g g}^{j j} {C C}_{N N - - g g}^{s the s - - i i - - j j}}{{C C}_{N N}^{s the s - - i i}} {C C}_{s the s}^{i i} {q q}^{s the s - - i i} {((11 - - q q))}^{i i} &GreaterEqual; &Greater Equal; η η \end{matrix} - - - - - - ((21 twenty one))

In the formula: P( ) is the alignment probability, g is the number of solutions in the good enough solution set G, s is the number of solutions in the selected set S, k means that there are at least k real good enough solutions in the selected set Solution, η represents the probability that the selected set S contains k good enough solutions, usually η is 0.95, and q is the probability of actually observing a feasible solution in the solution space;

Step 3: Taking the minimum total operating cost of the unit as the objective function, considering the constraints related to the unit output, construct an accurate model for the continuous variable P _Git , and solve the corresponding The output and operating cost of the unit, and further sort the selected set to find the optimal solution. The exact model of sequence optimization constructed is:

\{\begin{matrix} {minF minF}_{G G t t} = = {Σ Σ}_{t t = = 11}^{24 twenty four} {Σ Σ}_{i i = = 11}^{M m} [[{U u}_{G G i i t t} {Y Y}_{i i t t} (({P P}_{G G i i t t})) + + {U u}_{G G i i t t} ((11 - - {U u}_{G G i i t t - - 11})) {S S}_{i i t t} (({τ τ}_{i i}))]] \\ s the s . . t t . . {P P}_{G G i i min min} \leq \leq {P P}_{G G i i t t} \leq \leq {P P}_{G G i i max max} \\ {Q Q}_{G G i i min min} \leq \leq {Q Q}_{G G i i t t} \leq \leq {Q Q}_{G G i i max max} \\ - - {P P}_{l l max max} \leq \leq {P P}_{l l t t} \leq \leq {P P}_{l l max max} \\ - - {Q Q}_{l l max max} \leq \leq {Q Q}_{l l t t} \leq \leq {Q Q}_{l l max max} \\ {V V}_{b b m m i i x x} \leq \leq {V V}_{b b t t} \leq \leq {V V}_{b b max max} \end{matrix} - - - - - - ((22 twenty two))

The idea of solving the exact model is to substitute the combined state matrix U _G of each unit in the selected set into the formula (21) as a known parameter, use the interior point method to solve the corresponding generator active output matrix _PG , and use F _Gt sorts the solutions to find the optimal solution.