CN114156869A - A control method for electrified railway participating in frequency regulation of power system - Google Patents

A control method for electrified railway participating in frequency regulation of power system Download PDF

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CN114156869A
CN114156869A CN202111368431.XA CN202111368431A CN114156869A CN 114156869 A CN114156869 A CN 114156869A CN 202111368431 A CN202111368431 A CN 202111368431A CN 114156869 A CN114156869 A CN 114156869A
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万灿
何子涵
宋永华
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Zhejiang University ZJU
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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
    • H02J3/002—Flicker reduction, e.g. compensation of flicker introduced by non-linear load
    • 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
    • H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
    • H02J3/241—The oscillation concerning frequency
    • 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
    • H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
    • 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
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]

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Abstract

The invention discloses a control method for participating in frequency regulation of an electric power system by an electrified railway, and belongs to the field of load side management and frequency control of the electric power system. Firstly, establishing a kinematic model of a train under frequency modulation control, then providing a multi-train cooperative control method to meet the frequency modulation specification of a power system, and finally constructing an electrified railway frequency control framework comprising day-ahead capacity estimation, intra-day frequency modulation parameter distribution and real-time frequency response; in addition, a sequence secant plane algorithm is provided to effectively solve the nonlinear integer optimization problem constructed in the day-ahead capacity estimation and day-wide frequency modulation parameter distribution stage. The method utilizes the characteristic that the train can change the running state in a short time, jointly regulates and controls a plurality of trains to jointly provide frequency regulation auxiliary service meeting requirements, can effectively improve the frequency response dynamics of the power system, and has an obvious supporting effect on the running control of the high-proportion renewable energy power system.

Description

一种电气化铁路参与电力系统频率调节的控制方法A control method for electrified railway participating in frequency regulation of power system

技术领域technical field

本发明涉及一种电气化铁路参与电力系统频率调节的控制方法，属于负荷侧管理与电力系统频率控制领域。The invention relates to a control method for an electrified railway to participate in frequency regulation of a power system, and belongs to the fields of load side management and power system frequency control.

背景技术Background technique

电力系统的频率反映了源荷功率平衡，是电力系统最重要的参数之一。随着越来越多的可再生能源代替传统发电机组接入电网，电力系统的频率控制正面临着巨大的挑战。完全依靠发电机组进行频率调节的传统方法在高波动性、强间歇性可再生能源大量接入的情况下将变得不充分也不经济。近年来，负荷侧参与到电力系统的频率控制是负荷侧管理与电力系统频率领域的热点问题之一。大量研究表明空调、热泵、电动汽车等灵活性负荷具有参与电力系统频率控制的能力。与空调、热泵、电动汽车相比，电气化铁路的动态过程相对较快，单个列车无法长时间维持调节功率，目前尚没有公开发表的关于电气化铁路参与频率调节的研究。事实上，在不影响列车准点到站的前提下，列车具有短时间调整运动状态的能力，这使得电气化铁路具有参与频率调控的理论潜力。此外，现代电气化铁路具有自然的列车调度中心和分层结构，也具有车地双向通信装置，非常有利于集中管理，这也为电气化铁路参与频率调控提供了现实基础。The frequency of the power system reflects the source-load power balance and is one of the most important parameters of the power system. As more and more renewable energy sources are connected to the grid instead of traditional generator sets, the frequency control of the power system is facing huge challenges. The traditional method of relying solely on generator sets for frequency regulation will become insufficient and uneconomical in the presence of a large number of highly volatile, highly intermittent renewable energy sources. In recent years, the participation of the load side in the frequency control of the power system is one of the hot issues in the field of load side management and power system frequency. A large number of studies have shown that flexible loads such as air conditioners, heat pumps, and electric vehicles have the ability to participate in the frequency control of power systems. Compared with air conditioners, heat pumps, and electric vehicles, the dynamic process of electrified railways is relatively fast, and a single train cannot maintain regulation power for a long time. There is no published research on electrified railways participating in frequency regulation. In fact, without affecting the train's on-time arrival, the train has the ability to adjust its motion state in a short time, which makes the electrified railway have the theoretical potential to participate in frequency regulation. In addition, modern electrified railways have a natural train dispatch center and layered structure, as well as a two-way communication device between trains and ground, which is very conducive to centralized management, which also provides a realistic basis for electrified railways to participate in frequency regulation.

发明内容SUMMARY OF THE INVENTION

为了克服现有技术的不足，本发明的目的是提出一种电气化铁路参与电力系统频率调节的控制方法。In order to overcome the deficiencies of the prior art, the purpose of the present invention is to propose a control method for an electrified railway to participate in the frequency regulation of the power system.

为了实现上述目的，本发明采用了如下的技术方案：In order to achieve the above object, the present invention adopts the following technical scheme:

一种电气化铁路参与电力系统频率调节的控制方法，该方法首先建立列车在调频控制下的运动学模型；在此基础上，提出了一个包含日前容量估计、日内调频参数分配、实时频率响应在内的电气化铁路频率控制框架；为了有效求解在日前容量估计和日内调频参数分配阶段构建的非线性整数优化问题，提出了一种序列割平面算法。A control method for electrified railways to participate in the frequency regulation of the power system. The method firstly establishes the kinematic model of the train under frequency modulation control. In order to effectively solve the nonlinear integer optimization problem constructed in the stage of day-ahead capacity estimation and intra-day frequency regulation parameter allocation, a sequential cut plane algorithm is proposed.

具体的方法如下：The specific method is as follows:

(1)建立列车在调频控制下的运动学模型(1) Establish the kinematics model of the train under frequency modulation control

列车在牵引挡位u下运动的动力学模型为：The dynamic model of the train moving in the traction gear u is:

Figure BDA0003361716680000021
Figure BDA0003361716680000021

Figure BDA0003361716680000022
Figure BDA0003361716680000022

其中M为列车质量，γ为回转系数，θ为铁轨坡度，g为重力加速度，a0,a1,a2为空气阻力系数，Pm为列车最大牵引功率。以当前速度v，当前位置x为初始条件,求解此微分方程在时间T处的值，得到列车运动的速度函数V(x,v,u,T)和位置函数X(x,v,u,T)。Where M is the mass of the train, γ is the coefficient of gyration, θ is the slope of the rail, g is the acceleration of gravity, a 0 , a 1 , and a 2 are the air resistance coefficients, and P m is the maximum traction power of the train. Taking the current speed v and current position x as the initial conditions, solve the value of this differential equation at time T, and obtain the speed function V(x, v, u, T) and the position function X(x, v, u, T).

为了保证列车能够在提供频率调控服务后仍能准点到站，提出一种使得列车尽快到站的边界驾驶策略，在边界驾驶策略下，列车仅仅在道路限速和本身牵引力的限制下行驶。只要在边界驾驶策略下列车能够准点到站，那么必存在一种更优的驾驶策略能够使得列车在提供调频服务后准点到站，这种更优的驾驶策略可由列车的自动驾驶系统计算得到。边界驾驶策略描述如下：In order to ensure that the train can still arrive at the station on time after the frequency regulation service is provided, a boundary driving strategy is proposed to make the train arrive at the station as soon as possible. As long as the train can arrive at the station on time under the boundary driving strategy, there must be a better driving strategy that enables the train to arrive at the station on time after providing the frequency modulation service. This better driving strategy can be calculated by the train's automatic driving system. The boundary driving strategy is described as follows:

a)列车首先以最大牵引挡位加速；a) The train first accelerates in the maximum traction gear;

b)如果列车在制动点前的速度到达了道路限速，则开始恒速巡航，否则列车仍然以最大牵引挡位运行；b) If the speed of the train before the braking point reaches the road speed limit, start constant speed cruise, otherwise the train still runs in the maximum traction gear;

c)列车到达制动点后以常用制动力开始制动直到到站。c) After the train reaches the braking point, it starts to brake with the usual braking force until it arrives at the station.

如果列车当前速度为v，当前位置为x，当前时间为t，在边界驾驶策略下的到站时间记为Tarr(x,v,t)。If the current speed of the train is v, the current position is x, and the current time is t, the arrival time under the boundary driving strategy is recorded as Tarr (x, v, t).

(2)提出一个包含日前容量估计、日内调频参数分配、实时频率响应在内的电气化铁路频率控制框架(2) Propose a frequency control framework for electrified railways including day-ahead capacity estimation, intra-day frequency modulation parameter allocation, and real-time frequency response

电气化铁路频率控制框架如图1所示，主要包含日前容量估计、日内调频参数分配、实时频率响应。日前容量估计：根据列车的计划运行信息估计列车最大调频容量

Figure BDA0003361716680000031
电力系统返回接受的容量Pup；日内调频参数分配：在每一个时间段内给每个列车分配下一时间段的触发频率ftri(uz)和触发频率的牵引挡位uz；实时频率响应：列车根据触发频率ftri(uz)和触发频率的牵引挡位uz实时响应电力系统的频率变化，辅助电力系统的频率调节。电气化铁路参与电力系统频率调节的整体流程如图2所示。The frequency control framework of electrified railway is shown in Fig. 1, which mainly includes day-ahead capacity estimation, intra-day frequency modulation parameter allocation, and real-time frequency response. Day-ahead capacity estimation: Estimate the maximum frequency regulation capacity of the train based on the planned operation information of the train
Figure BDA0003361716680000031
The power system returns the accepted capacity P up ; intraday frequency regulation parameter allocation: in each time period, each train is allocated the trigger frequency f tri (u z ) of the next time period and the traction gear uz of the trigger frequency; real-time frequency Response: The train responds to the frequency change of the power system in real time according to the trigger frequency f tri (u z ) and the traction gear u z of the trigger frequency, and assists the frequency regulation of the power system. The overall process of the electrified railway participating in the frequency regulation of the power system is shown in Figure 2.

由于列车在两个站点之间运行的时间总共只有十几到几十分钟，而电力系统规定的一次调频功率持续时间也为十几到几时分钟，单个列车很有可能无法按照电力系统的规定的时长维持一次调频功率，因此提出一种多车协同控制策略，通过构建日前容量估计优化问题和日内调频功率分配问题，协调控制多辆列车联合起来共同提供满足要求的调频服务。首先把时间间隔离散化，每一段间隔时长为T0，每辆列车可以选择以一定的功率在连续的几个时间间隔内提供频率响应，多辆列车联合起来共同提供满足要求的调频服务，具体的细节如下：Since the total time for a train to run between two stations is only ten to dozens of minutes, and the duration of the primary frequency modulation power specified by the power system is also ten to several hours, a single train may not be able to comply with the regulations of the power system. Therefore, a multi-vehicle cooperative control strategy is proposed. By constructing the optimization problem of day-ahead capacity estimation and the problem of intra-day frequency regulation power distribution, it can coordinate and control multiple trains to jointly provide frequency regulation services that meet the requirements. First, the time interval is discretized, and the duration of each interval is T 0 . Each train can choose to provide frequency response in several consecutive time intervals with a certain power. Multiple trains work together to provide frequency modulation services that meet the requirements. The details are as follows:

a)日前容量估计：设列车i的行车计划为：位置-时间关系

Figure BDA0003361716680000032
和速度-时间关系
Figure BDA0003361716680000041
列车i从时间段
Figure BDA0003361716680000042
到时间段
Figure BDA0003361716680000043
提供频率控制服务，列车在时间段
Figure BDA0003361716680000044
的初始时刻和时间段
Figure BDA0003361716680000045
的结束时刻的位置和速度分别记为
Figure BDA0003361716680000046
Figure BDA0003361716680000047
计算方法如下：a) Day-ahead capacity estimation: Let the travel plan of train i be: position-time relationship
Figure BDA0003361716680000032
and speed-time relationship
Figure BDA0003361716680000041
train i from time slot
Figure BDA0003361716680000042
to time period
Figure BDA0003361716680000043
Provide frequency control service, trains in time slot
Figure BDA0003361716680000044
the initial moment and time period of
Figure BDA0003361716680000045
The position and velocity at the end time of , respectively, are recorded as
Figure BDA0003361716680000046
Figure BDA0003361716680000047
The calculation method is as follows:

Figure BDA0003361716680000048
Figure BDA0003361716680000048

Figure BDA0003361716680000049
Figure BDA0003361716680000049

Figure BDA00033617166800000410
Figure BDA00033617166800000410

Figure BDA00033617166800000411
Figure BDA00033617166800000411

为了减少列车的速度波动，列车的速度应在一定范围内变化：In order to reduce the speed fluctuation of the train, the speed of the train should vary within a certain range:

Figure BDA00033617166800000412
Figure BDA00033617166800000412

其中，

Figure BDA00033617166800000413
是速度下限，
Figure BDA00033617166800000414
是铁路限速。为了保证列车准点到站，列车在边界驾驶策略下的到站时间应该早于规定的到站时间：in,
Figure BDA00033617166800000413
is the lower speed limit,
Figure BDA00033617166800000414
It's the railway speed limit. In order to ensure that the train arrives at the station on time, the arrival time of the train under the boundary driving strategy should be earlier than the specified arrival time:

Figure BDA00033617166800000415
Figure BDA00033617166800000415

其中

Figure BDA00033617166800000416
是规定的到站时间，
Figure BDA00033617166800000417
是预留的时间裕量。列车i在第n个时间段提供的调频功率可以表示为：in
Figure BDA00033617166800000416
is the specified arrival time,
Figure BDA00033617166800000417
is the reserved time margin. The FM power provided by train i in the nth time period can be expressed as:

Figure BDA00033617166800000418
Figure BDA00033617166800000418

其中，

Figure BDA00033617166800000419
是当前牵引挡位和最低调频牵引挡位的差；
Figure BDA00033617166800000420
表示特征函数：如果
Figure BDA00033617166800000421
否则
Figure BDA00033617166800000422
为了联合控制多个列车共同满足电力系统规定的调频功率和持续时间需求，列车的调频容量估计问题可以表示为一个优化问题，目标函数即为容量最大化：in,
Figure BDA00033617166800000419
is the difference between the current traction gear and the lowest FM traction gear;
Figure BDA00033617166800000420
Represents a characteristic function: if
Figure BDA00033617166800000421
otherwise
Figure BDA00033617166800000422
In order to jointly control multiple trains to meet the frequency regulation power and duration requirements specified by the power system, the frequency regulation capacity estimation problem of trains can be expressed as an optimization problem, and the objective function is to maximize the capacity:

Figure BDA00033617166800000423
Figure BDA00033617166800000423

其中NET是列车总数。where NET is the total number of trains.

b)日内调频参数分配：在日内调频参数分配阶段，需要在每个时间段内决定下一个时间段的频率控制参数。首先需要决定下一个时间段参与调频的列车i以及最低调频挡位

Figure BDA0003361716680000051
假设电力系统接受的调频容量为Pup，为了完全履行调频任务，要求每个时间段的总调频功率大于Pup：b) Intraday frequency modulation parameter allocation: In the intraday frequency modulation parameter allocation stage, the frequency control parameters of the next time period need to be determined in each time period. First of all, it is necessary to determine the train i participating in frequency regulation in the next time period and the lowest frequency regulation gear
Figure BDA0003361716680000051
Assuming that the frequency regulation capacity accepted by the power system is P up , in order to fully perform the frequency regulation task, the total frequency regulation power in each time period is required to be greater than P up :

Figure BDA0003361716680000052
Figure BDA0003361716680000052

除此之外，在a)中所述的保证列车准点到站的约束和列车速度波动范围的约束仍然应该满足。In addition to this, the constraints to ensure that the train arrives at the station on time and the constraints of the train speed fluctuation range described in a) should still be satisfied.

列车参与调频的代价可以用列车的代价系数qi乘上列车参与调频的能量表示：The cost of the train participating in frequency regulation can be expressed by multiplying the cost coefficient q i of the train by the energy of the train participating in the frequency regulation:

Figure BDA0003361716680000053
Figure BDA0003361716680000053

其中，NPDT是电力系统要求的调频功率持续时间。于是，下一个时间段参与调频的列车i以及最大的调频挡位

Figure BDA0003361716680000054
可以表示为优化问题，其目标函数为：where N PDT is the FM power duration required by the power system. Therefore, the train i participating in the frequency modulation in the next time period and the maximum frequency modulation gear
Figure BDA0003361716680000054
It can be expressed as an optimization problem, and its objective function is:

Figure BDA0003361716680000055
Figure BDA0003361716680000055

求解此优化问题得到下一时间段参与调频的列车i和最低调频挡位

Figure BDA0003361716680000056
在下一个时间段参与调频的列车根据它们的代价系数从低到高排序，为了提供更加接近线性的一次调频下垂曲线，如果在当前牵引挡位和最低调频挡位
Figure BDA0003361716680000057
之间还有其它牵引挡位
Figure BDA0003361716680000058
也为这些牵引挡位分配触发频率：Solve this optimization problem to get the train i participating in frequency modulation and the lowest frequency modulation gear in the next time period
Figure BDA0003361716680000056
The trains participating in FM in the next time period are sorted according to their cost coefficients from low to high.
Figure BDA0003361716680000057
There are other traction gears in between
Figure BDA0003361716680000058
Also assign trigger frequencies to these traction gears:

Figure BDA0003361716680000061
Figure BDA0003361716680000061

其中，Oi表示排在列车i之前的列车的集合，f0是系统正常频率，Δfdb是一次调频死区，Δfmax是最大频率偏差。Among them, O i represents the set of trains before train i, f 0 is the normal frequency of the system, Δf db is the primary frequency modulation dead zone, and Δf max is the maximum frequency deviation.

c)实时频率响应：在实时频率响应阶段，列车根据分配到的频率控制参数：触发频率ftri i(uz i)和触发频率的牵引挡位uz i对系统频率偏差进行实时响应。具体的，列车实时监控电网频率，如果电网频率低于触发频率ftri i(uz i)，那么列车将牵引挡位调整至uz i。c) Real-time frequency response: In the real-time frequency response stage, the train responds in real time to the system frequency deviation according to the assigned frequency control parameters: the trigger frequency f tri i ( u zi ) and the traction gear u zi of the trigger frequency. Specifically, the train monitors the grid frequency in real time, and if the grid frequency is lower than the trigger frequency f tri i (u zi ) , the train adjusts the traction gear to u zi .

(3)为了有效求解在日前容量估计和日内调频参数分配阶段构建的非线性整数优化问题，提出一种序列割平面算法(3) In order to effectively solve the nonlinear integer optimization problem constructed in the day-ahead capacity estimation and intra-day frequency modulation parameter allocation stages, a sequential cut plane algorithm is proposed.

由于所提的电气化铁路参与频率调节的流程中的容量估计问题和功率分配问题涉及到非线性整数优化问题的求解，因此提出一种序列割平面算法来有效求解这两个优化问题。Since the capacity estimation problem and power allocation problem in the proposed electrified railway participating in the frequency regulation process involve the solution of nonlinear integer optimization problems, a sequential cut plane algorithm is proposed to effectively solve these two optimization problems.

a)单独可行点集合：首先求解出每个列车单独的可行点集合，即能够保证本列车准点到站以及满足速度波动限制的调控点的集合：a) Separate feasible point set: First, solve the separate feasible point set of each train, that is, the set of control points that can ensure that the train arrives at the station on time and meet the speed fluctuation limit:

Figure BDA0003361716680000062
Figure BDA0003361716680000062

b)线性松弛：取Ωi的凸包，并将其用线性不等式表示：b) Linear relaxation: take the convex hull of Ω i and express it with a linear inequality:

Figure BDA0003361716680000063
Figure BDA0003361716680000063

其中Li,li分别是线性不等式的系数矩阵和右端向量。where L i , L i are the coefficient matrix and the right-hand vector of the linear inequality, respectively.

c)割平面：直接以

Figure BDA0003361716680000064
为约束求解优化问题，若松弛问题的解
Figure BDA0003361716680000065
不是原问题的可行解，即不在Ωi中，此时，可以找到一个在Ωi中的点
Figure BDA0003361716680000066
使得
Figure BDA0003361716680000067
最大。用一个割平面将
Figure BDA0003361716680000068
割掉并保留
Figure BDA0003361716680000071
同时尽可能多地保留Ωi中的可行点。设割平面方程为：c) Cutting plane: directly with
Figure BDA0003361716680000064
To solve the optimization problem for constraints, if the solution to the relaxed problem
Figure BDA0003361716680000065
is not a feasible solution to the original problem, i.e. not in Ω i , at this time, a point in Ω i can be found
Figure BDA0003361716680000066
make
Figure BDA0003361716680000067
maximum. with a cutting plane
Figure BDA0003361716680000068
cut and keep
Figure BDA0003361716680000071
At the same time, keep as many feasible points in Ω i as possible. Let the cutting plane equation be:

Ax+By+Cz+D≤0Ax+By+Cz+D≤0

若以bj＝1表示Ωi中的点未被此割平面割掉，则割平面的系数可以由如下优化问题决定：If b j = 1 indicates that the points in Ω i are not cut by this cutting plane, the coefficients of the cutting plane can be determined by the following optimization problem:

Figure BDA0003361716680000072
Figure BDA0003361716680000072

Figure BDA0003361716680000073
Figure BDA0003361716680000073

Figure BDA0003361716680000074
Figure BDA0003361716680000074

这是一个较小规模的混合整数线性规划问题，可以使用常规的混合整数线性规划求解器求解。This is a smaller-scale mixed-integer linear programming problem that can be solved using a regular mixed-integer linear programming solver.

d)迭代：设置变量β来存储优化问题的上界，设置变量α来存储优化问题的下界。持续进行b)和c)过程。d) Iteration: Set the variable β to store the upper bound of the optimization problem, and set the variable α to store the lower bound of the optimization problem. Processes b) and c) are continued.

在每一次迭代过程中，若松弛问题的解可行：则结束迭代。During each iteration, if the solution to the relaxation problem is feasible: end the iteration.

若松弛问题的解不可行：将这个解的目标函数值作为原始优化问题的一个上界，并更新最小上界变量β，形成割平面，得到使

Figure BDA0003361716680000075
最大的可行解，将此可行解对应的目标函数值作为原始优化问题的下界，并更新最大下界变量α；若上下界之间的差距在容忍范围δ内：If the solution of the relaxation problem is infeasible: take the objective function value of the solution as an upper bound of the original optimization problem, and update the minimum upper bound variable β to form a cutting plane, and obtain the
Figure BDA0003361716680000075
The maximum feasible solution, the objective function value corresponding to this feasible solution is taken as the lower bound of the original optimization problem, and the maximum lower bound variable α is updated; if the gap between the upper and lower bounds is within the tolerance range δ:

(β-α)/α＜δ(β-α)/α＜δ

则结束迭代，否则，将割平面加入到松弛问题的约束中继续迭代过程。Then end the iteration, otherwise, add the cut plane to the constraints of the relaxation problem to continue the iterative process.

本发明的有益效果是：The beneficial effects of the present invention are:

本发明提出了一种电气化铁路参与电力系统频率调节的控制方法，该方法考虑了列车运动的快速动态，在保证列车准点到站的前提下，使列车有能力为电力系统提供一次调频服务；多列车联合响应策略协调控制多个列车共同提供满足电力系统规范的频率控制服务，克服了单个列车调节功率持续时间不足的问题；提出了电气化铁路频率控制框架，在不增加任何新的基础设施投资的情况下让电气化铁路参与到电力系统的频率控制中；提出一种序列割平面算法，能够有效求解在日前容量估计和日内调频参数分配阶段构建的非线性整数优化问题。本发明方法能够有效改善电力系统的频率响应动态，对高比例可再生能源电力系统的运行控制具有明显支撑作用。The invention proposes a control method for electrified railways to participate in the frequency regulation of the power system. The method takes into account the fast dynamics of the train movement, and enables the train to provide a primary frequency regulation service for the power system on the premise of ensuring that the train arrives at the station on time; The train joint response strategy coordinates and controls multiple trains to jointly provide frequency control services that meet the power system specifications, overcoming the problem of insufficient duration of single train regulation power; a frequency control framework for electrified railways is proposed, without adding any new infrastructure investment. In this paper, the electrified railway is involved in the frequency control of the power system under the circumstances. A sequential cut plane algorithm is proposed, which can effectively solve the nonlinear integer optimization problem constructed in the day-ahead capacity estimation and intraday frequency regulation parameter allocation stages. The method of the invention can effectively improve the frequency response dynamics of the power system, and has an obvious supporting effect on the operation control of the high-proportion renewable energy power system.

附图说明Description of drawings

图1为电气化铁路频率控制框架图；Fig. 1 is the frame diagram of frequency control of electrified railway;

图2为电气化铁路参与电力系统频率控制整体流程图；Figure 2 is the overall flow chart of the electrified railway participating in the frequency control of the power system;

图3为多车协同控制策略示意图。Figure 3 is a schematic diagram of a multi-vehicle cooperative control strategy.

具体实施方式Detailed ways

以下结合附图与实施实例对本发明做进一步说明。The present invention will be further described below with reference to the accompanying drawings and embodiments.

如图1所示为本发明提出的包含日前容量估计、日内调频参数分配、实时频率响应在内的电气化铁路频率控制框架。Figure 1 shows the frequency control framework for electrified railways proposed by the present invention including day-ahead capacity estimation, intra-day frequency modulation parameter allocation, and real-time frequency response.

图2为电气化铁路参与电力系统频率控制整体的流程图。下面介绍具体的执行流程。Figure 2 is a flow chart of the electrified railway participating in the overall frequency control of the power system. The specific execution flow is described below.

根据所提列车运动方程计算方法，离线计算速度函数V(x,v,u,T)、位置函数X(x,v,u,T)、边界驾驶策略下的到站时间函数Tarr(x,v,t)。According to the calculation method of the proposed train motion equation, the velocity function V(x,v,u,T), the position function X(x,v,u,T) and the arrival time function Tarr (x) under the boundary driving strategy are calculated offline. ,v,t).

多车协同控制策略的一个示意图如图3所示：首先把时间间隔离散化，每一段间隔时长为T0，T0在1分钟到3分钟左右。虚线表示电力系统要求的调频功率和持续时间，每一个标有ET的小长方形表示一辆电气化列车(ET，electric train)提供的调频服务，长方形的长表示调频功率的持续时间，长方形的高表示提供的调频功率。每辆列车可以选择以一定的功率在连续的几个时间间隔内提供频率响应，多辆列车联合起来共同提供满足要求的调频服务，在图中表现为12个小方块合起来覆盖了虚线所围的区域。A schematic diagram of the multi-vehicle cooperative control strategy is shown in Figure 3: First, the time interval is discretized, and the duration of each interval is T 0 , and T 0 is about 1 minute to 3 minutes. The dotted line represents the FM power and duration required by the power system. Each small rectangle marked with ET represents the FM service provided by an electric train (ET, electric train). The length of the rectangle represents the duration of the FM power, and the height of the rectangle represents the FM service. supplied FM power. Each train can choose to provide frequency response in several consecutive time intervals with a certain power. Multiple trains work together to provide a frequency modulation service that meets the requirements. In the figure, 12 small squares cover the area surrounded by the dotted line. Area.

日前容量估计：根据列车计划行车信息，即位置-时间关系

Figure BDA0003361716680000091
和速度-时间关系
Figure BDA0003361716680000092
指定列车能够提供频率控制的区域为从位置
Figure BDA0003361716680000093
到
Figure BDA0003361716680000094
计算列车计划到达和离开调频控制区域的时间为
Figure BDA0003361716680000095
和
Figure BDA0003361716680000096
计算其所在的离散时间段
Figure BDA0003361716680000097
和
Figure BDA0003361716680000098
构建日前容量估计优化问题，目标函数为：Day-ahead capacity estimation: based on train plan travel information, i.e. location-time relationship
Figure BDA0003361716680000091
and speed-time relationship
Figure BDA0003361716680000092
Designate the area where the train can provide frequency control as the slave position
Figure BDA0003361716680000093
arrive
Figure BDA0003361716680000094
Calculate the planned arrival and departure times of the trains in the FM control area as
Figure BDA0003361716680000095
and
Figure BDA0003361716680000096
Calculate the discrete time period in which it is located
Figure BDA0003361716680000097
and
Figure BDA0003361716680000098
Construct the optimization problem of day-ahead capacity estimation, and the objective function is:

Figure BDA0003361716680000099
Figure BDA0003361716680000099

约束为：The constraints are:

Figure BDA00033617166800000910
Figure BDA00033617166800000910

Figure BDA00033617166800000911
Figure BDA00033617166800000911

Figure BDA00033617166800000912
Figure BDA00033617166800000912

Figure BDA00033617166800000913
Figure BDA00033617166800000913

Figure BDA00033617166800000914
Figure BDA00033617166800000914

Figure BDA00033617166800000915
Figure BDA00033617166800000915

Figure BDA00033617166800000916
Figure BDA00033617166800000916

Figure BDA00033617166800000917
Figure BDA00033617166800000917

根据所提序列割平面算法，设置迭代结束时目标函数上下界差距的容忍范围δ，大约在0.5％到5％之间，迭代求解优化问题得到最大调频容量

Figure BDA00033617166800000918
将最大调频容量
Figure BDA00033617166800000919
提交给电力系统，电力系统返回接受的调频容量Pup。According to the proposed sequence cutting plane algorithm, set the tolerance range δ of the difference between the upper and lower bounds of the objective function at the end of the iteration, about 0.5% to 5%, and iteratively solve the optimization problem to obtain the maximum frequency modulation capacity
Figure BDA00033617166800000918
The maximum FM capacity
Figure BDA00033617166800000919
Submitted to the power system, the power system returns the accepted FM capacity P up .

日内调频参数分配：根据列车实时行车信息，即位置-时间关系

Figure BDA0003361716680000101
和速度-时间关系
Figure BDA0003361716680000102
构建功率分配问题，目标函数为：Intraday FM parameter allocation: according to the real-time running information of the train, that is, the position-time relationship
Figure BDA0003361716680000101
and speed-time relationship
Figure BDA0003361716680000102
Constructing the power distribution problem, the objective function is:

Figure BDA0003361716680000103
Figure BDA0003361716680000103

约束为：The constraints are:

Figure BDA0003361716680000104
Figure BDA0003361716680000104

Figure BDA0003361716680000105
Figure BDA0003361716680000105

Figure BDA0003361716680000106
Figure BDA0003361716680000106

Figure BDA0003361716680000107
Figure BDA0003361716680000107

Figure BDA0003361716680000108
Figure BDA0003361716680000108

Figure BDA0003361716680000109
Figure BDA0003361716680000109

Figure BDA00033617166800001010
Figure BDA00033617166800001010

Figure BDA00033617166800001011
Figure BDA00033617166800001011

Figure BDA00033617166800001012
Figure BDA00033617166800001012

Figure BDA00033617166800001013
Figure BDA00033617166800001013

根据所提序列割平面算法，设置迭代结束时目标函数上下界差距的容忍范围δ，大约在0.5％到5％之间，迭代求解优化问题得到下一时间段参与调频的列车i和最低调频挡位

Figure BDA00033617166800001014
在下一个时间段参与调频的列车根据代价系数从低到高排序，如果在当前牵引挡位和最低调频挡位
Figure BDA00033617166800001015
之间还有其它牵引挡位
Figure BDA00033617166800001016
为这些牵引挡位分配触发频率：According to the proposed sequence cutting plane algorithm, set the tolerance range δ of the difference between the upper and lower bounds of the objective function at the end of the iteration, which is about 0.5% to 5%, and iteratively solve the optimization problem to obtain the train i and the lowest frequency modulation block participating in the next time period. bit
Figure BDA00033617166800001014
The trains participating in frequency modulation in the next time period are sorted according to the cost coefficient from low to high, if the current traction gear and the lowest frequency modulation gear
Figure BDA00033617166800001015
There are other traction gears in between
Figure BDA00033617166800001016
Assign trigger frequencies to these traction gears:

Figure BDA0003361716680000111
Figure BDA0003361716680000111

实时频率响应：列车实时监控电网频率，如果电网频率低于触发频率ftri i(uz i)，那么列车将牵引挡位调整至uz i。Real-time frequency response: The train monitors the grid frequency in real time. If the grid frequency is lower than the trigger frequency f tri i (u zi ) , the train adjusts the traction gear to u zi .

以上结合附图对本发明的具体实施方式进行了描述，并非对本发明保护范围的限制，所有利用本发明说明书及附图内容所做的等效模型或等效算法流程，通过直接或间接运用于其他相关技术领域，均属本发明的专利保护范围内。The specific embodiments of the present invention have been described above with reference to the accompanying drawings, which are not intended to limit the scope of protection of the present invention. All equivalent models or equivalent algorithm processes made by using the contents of the description and the accompanying drawings of the present invention can be directly or indirectly applied to other The relevant technical fields are all within the scope of the patent protection of the present invention.

Claims (4)

1.一种电气化铁路参与电力系统频率调节的控制方法，其特征在于，该方法是：建立列车在调频控制下的运动学模型；在此基础上，提出了包含日前容量估计、日内调频参数分配、实时频率响应在内的电气化铁路参与电力系统频率控制的框架；提出了一种序列割平面算法来有效求解在日前容量估计和日内调频参数分配阶段构建的非线性整数优化问题。1. an electrified railway participates in the control method of frequency regulation of electric power system, it is characterized in that, this method is: establish the kinematics model of train under frequency modulation control; , a framework for electrified railways to participate in power system frequency control including real-time frequency response; a sequential cut plane algorithm is proposed to effectively solve the nonlinear integer optimization problem constructed in the day-ahead capacity estimation and intraday frequency regulation parameter allocation stages. 2.根据权利要求1所述的电气化铁路参与电力系统频率调节的控制方法，其特征在于，所建立的列车在调频控制下的运动学模型包括速度函数V(x,v,u,T)、位置函数X(x,v,u,T)、边界驾驶策略下的到站时间函数Tarr(x,v,t)；其中，v表示当前速度，x表示当前位置，t表示当前时间，u表示牵引挡位，T表示牵引时间；速度函数V(x,v,u,T)和位置函数X(x,v,u,T)通过求解列车动力学方程直接得到；边界驾驶策略的构建过程如下：2. the control method that the electrified railway according to claim 1 participates in power system frequency regulation, it is characterized in that, the kinematics model of the established train under frequency modulation control comprises velocity function V (x, v, u, T), Position function X(x, v, u, T), arrival time function Tarr (x, v, t) under the boundary driving strategy; where v represents the current speed, x represents the current position, t represents the current time, and u represents the traction gear, and T represents the traction time; the speed function V(x,v,u,T) and the position function X(x,v,u,T) are directly obtained by solving the train dynamics equation; the construction process of the boundary driving strategy as follows: a)列车首先以最大牵引挡位加速，a) The train first accelerates in the maximum traction gear, b)如果列车在制动点前的速度到达了道路限速，则开始恒速巡航，否则列车仍然以最大牵引挡位运行，b) If the speed of the train before the braking point reaches the road speed limit, start constant speed cruise, otherwise the train still runs in the maximum traction gear, c)列车到达制动点后以常用制动力开始制动直到到站；c) After the train reaches the braking point, it starts to brake with the usual braking force until it arrives at the station; 边界驾驶策略下的到站时间函数Tarr(x,v,t)根据此驾驶过程直接计算得到。The arrival time function Tarr (x,v,t) under the boundary driving strategy is directly calculated according to this driving process. 3.根据权利要求1所述的控制电气化铁路参与电力系统频率调节的方法，其特征在于，所述的电气化铁路参与电力系统频率控制的框架具体为：3. The method for controlling electrified railway to participate in power system frequency regulation according to claim 1, it is characterized in that, the framework that described electrified railway participates in power system frequency control is specifically: a)日前容量估计：日前容量估计是根据列车行车计划，即列车的位置-时间关系
Figure FDA0003361716670000011
和速度-时间关系
Figure FDA0003361716670000012
以保证列车准点到站为约束，以开始调频时间段
Figure FDA0003361716670000013
结束调频时间段
Figure FDA0003361716670000014
调频牵引挡位
Figure FDA0003361716670000015
为决策变量，以最大化列车调频容量为目标函数建立的优化问题：a) Day-ahead capacity estimation: Day-ahead capacity estimation is based on the train schedule, that is, the position-time relationship of the train
Figure FDA0003361716670000011
and speed-time relationship
Figure FDA0003361716670000012
Constrained to ensure that the train arrives at the station on time, to start the frequency modulation time period
Figure FDA0003361716670000013
End FM period
Figure FDA0003361716670000014
FM traction gear
Figure FDA0003361716670000015
As the decision variable, the optimization problem established with the objective function of maximizing the frequency regulation capacity of the train: 目标函数为：The objective function is:
Figure FDA0003361716670000021
Figure FDA0003361716670000021
 约束为：The constraints are:
Figure FDA0003361716670000022
Figure FDA0003361716670000022
Figure FDA0003361716670000023
Figure FDA0003361716670000023
Figure FDA0003361716670000024
Figure FDA0003361716670000024
 其中，NET是列车总数，
Figure FDA0003361716670000025
是速度下限，
Figure FDA0003361716670000026
是铁路限速，
Figure FDA0003361716670000027
是规定的到站时间，
Figure FDA0003361716670000028
是预留的时间裕量；
Figure FDA0003361716670000029
分别为时间段
Figure FDA00033617166700000210
的初始时刻和时间段
Figure FDA00033617166700000211
的结束时刻的位置和速度，计算方法如下：where N ET is the total number of trains,
Figure FDA0003361716670000025
is the lower speed limit,
Figure FDA0003361716670000026
the railway speed limit,
Figure FDA0003361716670000027
is the specified arrival time,
Figure FDA0003361716670000028
is the reserved time margin;
Figure FDA0003361716670000029
time period
Figure FDA00033617166700000210
the initial moment and time period of
Figure FDA00033617166700000211
The position and velocity at the end time of , are calculated as follows:
Figure FDA00033617166700000212
Figure FDA00033617166700000212
Figure FDA00033617166700000213
Figure FDA00033617166700000213
Figure FDA00033617166700000214
Figure FDA00033617166700000214
Figure FDA00033617166700000215
Figure FDA00033617166700000215
 ΔPi(n)为列车i在第n个时间段提供的调频功率，可以表示为：ΔP i (n) is the frequency modulation power provided by train i in the nth time period, which can be expressed as:
Figure FDA00033617166700000216
Figure FDA00033617166700000216
 其中，
Figure FDA00033617166700000217
是当前牵引挡位和最低调频牵引挡位的差；
Figure FDA00033617166700000218
表示特征函数：如果
Figure FDA00033617166700000219
否则
Figure FDA00033617166700000220
in,
Figure FDA00033617166700000217
is the difference between the current traction gear and the lowest FM traction gear;
Figure FDA00033617166700000218
Represents a characteristic function: if
Figure FDA00033617166700000219
otherwise
Figure FDA00033617166700000220
 b)日内调频参数分配：日内调频参数分配是在每个时间段内决定下一个时间段的频率控制参数；日内调频参数分配根据列车实时运行信息，即列车的位置-时间关系
Figure FDA00033617166700000221
和速度-时间关系
Figure FDA00033617166700000222
以保证列车准点到站和满足调频要求为约束，以开始调频时间段
Figure FDA0003361716670000031
结束调频时间段
Figure FDA0003361716670000032
调频牵引挡位
Figure FDA0003361716670000033
为决策变量，以最小化列车调频代价为目标函数建立优化问题：b) Intraday frequency modulation parameter allocation: intraday frequency modulation parameter allocation is to determine the frequency control parameters of the next time period in each time period; intraday frequency modulation parameter allocation is based on the real-time train operation information, that is, the position-time relationship of the train
Figure FDA00033617166700000221
and speed-time relationship
Figure FDA00033617166700000222
Constrained to ensure that the train arrives at the station on time and meets the frequency regulation requirements, to start the frequency regulation time period
Figure FDA0003361716670000031
End FM period
Figure FDA0003361716670000032
FM traction gear
Figure FDA0003361716670000033
As the decision variable, an optimization problem is established with the objective function of minimizing the cost of train frequency regulation: 目标函数为：The objective function is:
Figure FDA0003361716670000034
Figure FDA0003361716670000034
 约束为：The constraints are:
Figure FDA0003361716670000035
Figure FDA0003361716670000035
Figure FDA0003361716670000036
Figure FDA0003361716670000036
Figure FDA0003361716670000037
Figure FDA0003361716670000037
Figure FDA0003361716670000038
Figure FDA0003361716670000038
Figure FDA0003361716670000039
Figure FDA0003361716670000039
 求解此优化问题得到下一时间段参与调频的列车i和最低调频挡位
Figure FDA00033617166700000310
如果在当前牵引挡位和最低调频挡位
Figure FDA00033617166700000311
之间还有其它牵引挡位
Figure FDA00033617166700000312
那么也为这些牵引挡位分配触发频率：Solve this optimization problem to get the train i participating in frequency modulation and the lowest frequency modulation gear in the next time period
Figure FDA00033617166700000310
If in the current traction gear and the lowest FM gear
Figure FDA00033617166700000311
There are other traction gears in between
Figure FDA00033617166700000312
Then also assign trigger frequencies to these traction gears:
Figure FDA00033617166700000313
Figure FDA00033617166700000313
 其中，Oi表示排在列车i之前的列车的集合，f0是系统正常频率，Δfdb是一次调频死区，Δfmax是最大频率偏差；Among them, O i represents the set of trains before train i, f 0 is the normal frequency of the system, Δf db is the primary frequency modulation dead zone, and Δf max is the maximum frequency deviation; c)实时频率响应：实时频率响应是列车根据分配到的触发频率ftri i(uz i)和触发频率对应的牵引挡位uz i对系统频率偏差进行响应；具体地，列车实时监控电网频率，如果电网频率低于触发频率ftri i(uz i)，那么列车将牵引挡位调整至uz i。c) Real-time frequency response: The real-time frequency response is that the train responds to the system frequency deviation according to the assigned trigger frequency f tri i ( u zi ) and the traction gear u zi corresponding to the trigger frequency; specifically, the train monitors the power grid in real time. frequency, if the grid frequency is lower than the trigger frequency f tri i (u zi ) , the train will adjust the traction gear to u zi . 4.根据权利要求1所述的电气化铁路参与电力系统频率调节的控制方法，其特征在于，所述的序列割平面算法包含求解单独可行点集合、线性松弛、割平面、迭代四个步骤：4. the control method that electrified railway participates in frequency regulation of electric power system according to claim 1, it is characterized in that, described sequence cut plane algorithm comprises four steps of solving independent feasible point set, linear relaxation, cutting plane, iteration: a)求解单独可行点集合：求解出能够保证本列车准点到站以及满足速度波动限制的调控点的集合：a) Solve the set of independent feasible points: Solve the set of control points that can ensure that the train arrives at the station on time and meet the speed fluctuation limit:
Figure FDA0003361716670000041
Figure FDA0003361716670000041
 b)线性松弛：取Ωi的凸包，并将其用线性不等式表示：b) Linear relaxation: take the convex hull of Ω i and express it with a linear inequality:
Figure FDA0003361716670000042
Figure FDA0003361716670000042
 其中Li,li是线性不等式的系数矩阵和右端向量；where L i , li are the coefficient matrix and right-hand vector of the linear inequality; c)割平面：直接以
Figure FDA0003361716670000043
为约束求解优化问题，若所得到的松弛问题的解
Figure FDA0003361716670000044
不在Ωi中，则找到一个可行解
Figure FDA0003361716670000045
使得
Figure FDA0003361716670000046
最大；用一个割平面将
Figure FDA0003361716670000047
割掉并保留
Figure FDA0003361716670000048
而且同时尽可能地保留Ωi中的可行点；设割平面方程为：c) Cutting plane: directly with
Figure FDA0003361716670000043
Solving the optimization problem for constraints, if the obtained solution to the relaxed problem
Figure FDA0003361716670000044
is not in Ω i , then a feasible solution is found
Figure FDA0003361716670000045
make
Figure FDA0003361716670000046
maximum; use a cutting plane to
Figure FDA0003361716670000047
cut and keep
Figure FDA0003361716670000048
And at the same time keep the feasible points in Ω i as much as possible; let the equation of cutting plane be: Ax+By+Cz+D≤0Ax+By+Cz+D≤0 用bj＝1表示Ωi中的点未被此割平面割掉，则割平面的系数可以由如下优化问题决定：Use b j = 1 to indicate that the points in Ω i are not cut by this cutting plane, then the coefficient of the cutting plane can be determined by the following optimization problem:
Figure FDA0003361716670000049
Figure FDA0003361716670000049
Figure FDA00033617166700000410
Figure FDA00033617166700000410
Figure FDA00033617166700000411
Figure FDA00033617166700000411
 d)迭代：持续进行b)和c)过程；d) Iteration: the process of b) and c) is continuously performed; 在每一次迭代过程中：During each iteration: 若松弛问题的解可行则结束迭代；If the solution to the relaxation problem is feasible, end the iteration; 若松弛问题的解不可行，则将这个解作为原始优化问题的一个上界，形成割平面，得到使
Figure FDA0003361716670000051
最大的可行解，将此可行解对应的目标函数值作为原始优化问题的下界；若上下界之间的差距在容忍范围内，则结束迭代，否则，将割平面加入到松弛问题的约束中继续迭代过程。If the solution to the relaxation problem is infeasible, take this solution as an upper bound of the original optimization problem to form a cutting plane, and obtain the
Figure FDA0003361716670000051
The largest feasible solution, and the objective function value corresponding to this feasible solution is used as the lower bound of the original optimization problem; if the gap between the upper and lower bounds is within the tolerance range, the iteration ends, otherwise, the cut plane is added to the constraints of the relaxation problem to continue Iteration process.
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