CN111030196B - Dynamic sensitivity-based dynamic reactive power reserve optimization method for receiving-end power grid - Google Patents

Dynamic sensitivity-based dynamic reactive power reserve optimization method for receiving-end power grid Download PDF

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CN111030196B
CN111030196B CN201911297768.9A CN201911297768A CN111030196B CN 111030196 B CN111030196 B CN 111030196B CN 201911297768 A CN201911297768 A CN 201911297768A CN 111030196 B CN111030196 B CN 111030196B
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reactive power
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fault
state
variables
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CN111030196A (en
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王彬
陈天华
郭庆来
陈建华
葛怀畅
杜磊
齐子杰
徐陆飞
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Tsinghua University
NARI Group Corp
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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
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
    • H02J3/50—Controlling the sharing of the out-of-phase component
    • 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
    • H02J3/12—Circuit arrangements for AC mains or AC distribution networks for adjusting voltage in AC networks by changing a characteristic of the network load
    • H02J3/16—Circuit arrangements for AC mains or AC distribution networks for adjusting voltage in AC networks by changing a characteristic of the network load by adjustment of reactive power
    • 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
    • H02J3/18—Arrangements for adjusting, eliminating or compensating reactive power in networks
    • 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
    • H02J3/36—Arrangements for transfer of electric power between AC networks via a high-tension DC link
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/30—Reactive power compensation
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y02E60/60—Arrangements for transfer of electric power between AC networks or generators via a high voltage DC link [HVCD]

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  • Power Engineering (AREA)
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Abstract

本发明涉及一种基于动态灵敏度的受端电网动态无功储备优化方法，属于电力系统安全和控制技术领域。该方法首先建立交直流混联系统的微分代数方程，并求取系统的一阶动态灵敏度；然后针对当前状况，建立动态无功储备优化模型，并求解。求解完成后，各动态无功控制设备根据优化结果，进行稳态无功值的调整，如发电机需要在计算出动态无功储备结果后预留出相应的无功储备量。本发明可确保交直流混联电网发生换相失败时仍然能够安全运行，提高电网运行的可靠性。The invention relates to a dynamic reactive power reserve optimization method of a receiving-end power grid based on dynamic sensitivity, and belongs to the technical field of power system security and control. The method firstly establishes the differential algebraic equation of the AC-DC hybrid system, and obtains the first-order dynamic sensitivity of the system; then, according to the current situation, the dynamic reactive power reserve optimization model is established and solved. After the solution is completed, each dynamic reactive power control device adjusts the steady-state reactive power value according to the optimization result. For example, the generator needs to reserve the corresponding reactive power reserve after calculating the dynamic reactive power reserve result. The invention can ensure that the AC-DC hybrid grid can still operate safely when the commutation failure occurs, and improve the reliability of the grid operation.

Description

一种基于动态灵敏度的受端电网动态无功储备优化方法An optimization method for dynamic reactive power reserve of receiving-end power grid based on dynamic sensitivity

技术领域technical field

本发明属于电力系统安全和控制技术领域，具体提出一种基于动态灵敏度的受端电网动态无功储备优化方法。The invention belongs to the technical field of power system security and control, and specifically proposes a dynamic reactive power reserve optimization method of a receiving-end power grid based on dynamic sensitivity.

背景技术Background technique

我国东部和中部已建成大规模多直流落点的受端电网，“强直弱交”的格局十分明显。作为受端电网常见的故障，换相失败在单个受端换流站一年内会出现十次到数十次。在换相失败发生期间，会消耗大量的动态无功功率。传统无功优化仅以稳态电压分布为目标控制容抗器组和发电机，故障情况下运行方式可能并不合理，一旦发生换相失败故障，因动态无功储备不足，电网安全存在重大隐患。因此，如何在稳态运行时进行动态无功储备优化，确定合理的无功设备运行方式，保障交直流混联电网的电压安全，十分重要。In the eastern and central parts of my country, large-scale receiving-end power grids with multiple DC distribution points have been built, and the pattern of "strong DC and weak AC" is very obvious. As a common fault of the receiving-end power grid, commutation failure will occur ten to dozens of times within a year in a single receiving-end converter station. During the occurrence of commutation failure, a large amount of dynamic reactive power is consumed. Traditional reactive power optimization only takes steady-state voltage distribution as the goal to control the capacitor reactor group and generator, and the operation mode may be unreasonable under fault conditions. Once a commutation failure occurs, due to insufficient dynamic reactive power reserve, there are major hidden dangers to power grid security. . Therefore, it is very important to optimize the dynamic reactive power reserve during steady-state operation, determine a reasonable operating mode of reactive power equipment, and ensure the voltage safety of the AC-DC hybrid grid.

发明内容SUMMARY OF THE INVENTION

本发明的目的是为克服已有技术的不足之处，提出一种基于动态灵敏度的受端电网动态无功储备优化方法。本发明可确保交直流混联电网发生换相失败时仍然能够安全运行，提高电网运行的可靠性。The purpose of the present invention is to propose a dynamic reactive power reserve optimization method of the receiving end power grid based on dynamic sensitivity in order to overcome the deficiencies of the prior art. The invention can ensure that the AC-DC hybrid grid can still operate safely when the commutation failure occurs, and improve the reliability of the grid operation.

本发明提出一种基于动态灵敏度的受端电网动态无功储备优化方法，其特征在于，该方法包括以下步骤：The present invention provides a method for optimizing the dynamic reactive power reserve of the receiving-end power grid based on dynamic sensitivity, which is characterized in that the method comprises the following steps:

1)建立交直流混联系统方程，求取系统的一阶动态灵敏度；具体步骤如下：1) Establish an AC-DC hybrid system equation to obtain the first-order dynamic sensitivity of the system; the specific steps are as follows:

1-1)建立稳态运行时的受端电网方程，如式(1)所示：1-1) Establish the receiver power grid equation during steady-state operation, as shown in formula (1):

Figure GDA0002705411510000011
Figure GDA0002705411510000011

其中，x代表系统的状态变量，包括发电机内电势、功角、励磁电压、直流电流变量；y代表代数变量，包括系统的母线电压幅值和母线电压的相角；u代表控制变量，包括稳态运行时发电机无功出力

Figure GDA0002705411510000012
和容抗器的无功出力
Figure GDA0002705411510000013
Among them, x represents the state variables of the system, including generator internal potential, power angle, excitation voltage, and DC current variables; y represents algebraic variables, including the bus voltage amplitude of the system and the phase angle of the bus voltage; u represents the control variables, including Generator reactive output during steady state operation
Figure GDA0002705411510000012
and the reactive output of the capacitive reactor
Figure GDA0002705411510000013

1-2)故障发生之后，式(1)中第一个表达式保持不变；1-2) After the fault occurs, the first expression in formula (1) remains unchanged;

对于故障发生后清除前时段，用式(2)替代式(1)中第二个表达式；For the period before clearing after the fault occurs, replace the second expression in Equation (1) with Equation (2);

对于故障发生后且故障清除后时段，用式(3)替代式(1)中第二个表达式；分别得到表达式如下：For the period after the fault occurs and after the fault is cleared, the second expression in the formula (1) is replaced by the formula (3); the expressions are respectively obtained as follows:

0＝gs(x,y,u) (2)0=g s (x, y, u) (2)

0＝gs,c(x,y,u) (3)0=g s, c (x, y, u) (3)

式中，s代表故障编号；c代表清除；In the formula, s represents the fault number; c represents clearing;

1-3)令

Figure GDA0002705411510000021
和
Figure GDA0002705411510000022
分别表示故障发生后的初始状态时状态变量和代数变量对控制变量的偏导数，分别用式(4)和式(5)求取：1-3) Order
Figure GDA0002705411510000021
and
Figure GDA0002705411510000022
Respectively represent the partial derivatives of the state variables and algebraic variables to the control variables in the initial state after the fault occurs, and are calculated by equations (4) and (5) respectively:

Figure GDA0002705411510000023
Figure GDA0002705411510000023

Figure GDA0002705411510000024
Figure GDA0002705411510000024

其中，t0表示故障发生时刻；

Figure GDA0002705411510000025
表示故障发生前的初始时刻；
Figure GDA0002705411510000026
表示故障发生后的初始时刻；Among them, t 0 represents the moment when the fault occurs;
Figure GDA0002705411510000025
Represents the initial moment before the failure occurs;
Figure GDA0002705411510000026
Represents the initial moment after the failure occurs;

Figure GDA0002705411510000027
表示故障发生前的初始状态下，状态变量对控制变量的偏导数；
Figure GDA0002705411510000028
分别表示发生第s个故障后的初始状态下，式(1)中的第二个表达式对代数变量和控制变量的偏导数；
Figure GDA0002705411510000027
Represents the partial derivative of the state variable to the control variable in the initial state before the fault occurs;
Figure GDA0002705411510000028
respectively represent the partial derivatives of the second expression in equation (1) with respect to the algebraic variable and the control variable in the initial state after the occurrence of the sth fault;

1-4)令

Figure GDA0002705411510000029
和
Figure GDA00027054115100000210
分别表示故障清除后的初始状态时状态变量和代数变量对控制变量的偏导数，分别用式(6)和式(7)式求取：1-4) Order
Figure GDA0002705411510000029
and
Figure GDA00027054115100000210
respectively represent the partial derivatives of the state variables and algebraic variables to the control variables in the initial state after the fault is cleared, and are obtained by equations (6) and (7) respectively:

Figure GDA00027054115100000211
Figure GDA00027054115100000211

Figure GDA00027054115100000212
Figure GDA00027054115100000212

其中，tc表示故障清除时刻，

Figure GDA00027054115100000213
表示故障清除前的初始时刻，
Figure GDA00027054115100000214
表示故障清除后的初始时刻，
Figure GDA00027054115100000215
表示故障发生前的初始状态下，状态变量对控制变量的偏导数；
Figure GDA00027054115100000216
分别表示发生清除第s个故障后的初始状态下，式(1)中的第二个表达式对代数变量和控制变量的偏导数；Among them, t c represents the fault clearing time,
Figure GDA00027054115100000213
represents the initial moment before the fault is cleared,
Figure GDA00027054115100000214
represents the initial moment after the fault is cleared,
Figure GDA00027054115100000215
Represents the partial derivative of the state variable to the control variable in the initial state before the fault occurs;
Figure GDA00027054115100000216
respectively represent the partial derivatives of the second expression in formula (1) to the algebraic variable and the control variable in the initial state after the sth fault is cleared;

1-5)在故障发生时段内任意时刻

Figure GDA00027054115100000217
令T＝t，计算T时刻的灵敏度
Figure GDA00027054115100000218
利用式(8)计算T+1时刻的灵敏度
Figure GDA00027054115100000219
1-5) Any time during the fault occurrence period
Figure GDA00027054115100000217
Let T=t, calculate the sensitivity at time T
Figure GDA00027054115100000218
Use formula (8) to calculate the sensitivity at time T+1
Figure GDA00027054115100000219

Figure GDA0002705411510000031
Figure GDA0002705411510000031

式中，h代表仿真步长，I代表单位矩阵，J代表系统的雅克比矩阵；

Figure GDA0002705411510000032
分别代表T时刻，系统状态变量和代数变量对控制变量的偏导数；
Figure GDA0002705411510000033
分别代表T+1时刻，系统状态变量和代数变量对控制变量的偏导数；
Figure GDA0002705411510000034
分别代表T时刻，式(1)中第一个表达式对状态变量和代数变量的偏导数；
Figure GDA0002705411510000035
分别代表T时刻，式(1)中第二个表达式对状态变量和代数变量的偏导数；
Figure GDA0002705411510000036
分别代表T和T+1时刻式(1)中第一个表达式对控制变量的偏导数；
Figure GDA0002705411510000037
分别代表T和T+1时刻(1)式中第二个公式对控制变量的偏导数；where h represents the simulation step size, I represents the identity matrix, and J represents the Jacobian matrix of the system;
Figure GDA0002705411510000032
Represent the partial derivatives of the system state variables and algebraic variables to the control variables at time T, respectively;
Figure GDA0002705411510000033
respectively represent the partial derivatives of the system state variables and algebraic variables to the control variables at time T+1;
Figure GDA0002705411510000034
respectively represent the time T, the partial derivative of the first expression in equation (1) to the state variable and algebraic variable;
Figure GDA0002705411510000035
respectively represent time T, the partial derivative of the second expression in formula (1) to the state variable and algebraic variable;
Figure GDA0002705411510000036
represent the partial derivatives of the first expression in equation (1) to the control variable at time T and T+1, respectively;
Figure GDA0002705411510000037
represent the partial derivatives of the second formula in formula (1) to the control variable at time T and T+1, respectively;

2)建立动态无功储备优化模型，该模型由目标函数和约束条件构成；具体步骤如下：2-1)建立动态无功储备优化模型的目标函数，如(9)所示：2) Establish a dynamic reactive power reserve optimization model, which consists of an objective function and constraints; the specific steps are as follows: 2-1) Establish an objective function of the dynamic reactive power reserve optimization model, as shown in (9):

Figure GDA0002705411510000038
Figure GDA0002705411510000038

其中，Nstation表示容抗器总数，

Figure GDA0002705411510000039
Nc,i分别表示第i个容抗器当前的投入组数和优化后的投入组数；Among them, N station represents the total number of capacitive reactors,
Figure GDA0002705411510000039
N c,i respectively represent the current input group number and the optimized input group number of the ith capacitive reactor;

2-2)确定动态无功储备优化模型的约束条件，具体如下：2-2) Determine the constraints of the dynamic reactive power reserve optimization model, as follows:

2-2-1)各场站容抗器投入的组数约束，如式(10)所示：2-2-1) Constraints on the number of groups of capacitor reactor input at each station, as shown in formula (10):

Figure GDA00027054115100000310
Figure GDA00027054115100000310

其中，Nc ,

Figure GDA00027054115100000311
分别代表各容抗器投入组数的下限值和上限值；where, N c ,
Figure GDA00027054115100000311
Represent the lower limit value and upper limit value of each capacitor input group number;

2-2-2)发电机稳态时的无功出力约束，如式(11)所示：2-2-2) The reactive power output constraint of the generator in steady state, as shown in formula (11):

Figure GDA00027054115100000312
Figure GDA00027054115100000312

其中，

Figure GDA00027054115100000313
代表稳态时发电机无功出力的优化值，
Figure GDA00027054115100000314
分别代表稳态时发电机无功出力的下限值与上限值；in,
Figure GDA00027054115100000313
represents the optimal value of the generator reactive power output at steady state,
Figure GDA00027054115100000314
respectively represent the lower limit and upper limit of the generator reactive power output in steady state;

2-2-3)换相失败故障后的N-1安全约束条件，如式(12)所示：2-2-3) N-1 safety constraints after commutation failure failure, as shown in formula (12):

Figure GDA00027054115100000315
Figure GDA00027054115100000315

其中，

Figure GDA00027054115100000316
代表换流站交流母线电压故障后的临界电压恢复值；
Figure GDA00027054115100000317
分别代表第s个故障发生后，Tend时刻换流站交流母线电压的优化值和当前值；Tend表示换相恢复的时间；
Figure GDA00027054115100000318
分别代表稳态运行时发电机无功出力的优化值和当前值；in,
Figure GDA00027054115100000316
Represents the critical voltage recovery value after the AC bus voltage failure of the converter station;
Figure GDA00027054115100000317
respectively represent the optimized value and current value of the AC bus voltage of the converter station at the moment T end after the sth fault occurs; T end represents the commutation recovery time;
Figure GDA00027054115100000318
Represent the optimized value and current value of the generator reactive power output during steady-state operation, respectively;

Figure GDA0002705411510000041
分别代表稳态运行时容抗器无功出力的优化值和当前值；
Figure GDA0002705411510000042
分别代表第s个故障下，Tend时刻
Figure GDA0002705411510000043
对
Figure GDA0002705411510000044
和
Figure GDA0002705411510000045
的动态灵敏度，该灵敏度值由步骤1)求出；
Figure GDA0002705411510000041
Represent the optimized value and current value of the reactive power output of the capacitive reactor during steady-state operation;
Figure GDA0002705411510000042
Respectively represent the time of T end under the sth fault
Figure GDA0002705411510000043
right
Figure GDA0002705411510000044
and
Figure GDA0002705411510000045
The dynamic sensitivity of , the sensitivity value is obtained by step 1);

3)对步骤2)建立的模型求解，得到最优解

Figure GDA0002705411510000046
利用式(13)计算无功补偿设备预留的最少动态无功储备，优化结束；3) Solve the model established in step 2) to obtain the optimal solution
Figure GDA0002705411510000046
Use formula (13) to calculate the minimum dynamic reactive power reserve reserved by the reactive power compensation equipment, and the optimization is over;

Figure GDA0002705411510000047
Figure GDA0002705411510000047

式中，

Figure GDA0002705411510000048
为无功补偿设备的最少动态无功储备，下标g表示发电机。In the formula,
Figure GDA0002705411510000048
It is the minimum dynamic reactive power reserve of reactive power compensation equipment, and the subscript g represents the generator.

本发明的特点及有益效果在于：The characteristics and beneficial effects of the present invention are:

本发明针对传统无功优化仅考虑稳态而不考虑故障情况的不足，提出考虑故障情况下的电压安全约束的动态无功储备优化模型，给出稳态时的容抗器组、发电机的运行方式。本发明可指导调度人员合理制定无功设备的运行方式，保证在故障情况下有足够的动态无功储备避免换相失败等故障引发的电压安全问题，提升电力系统的安全性。Aiming at the insufficiency of traditional reactive power optimization that only considers the steady state without considering the fault condition, the invention proposes a dynamic reactive power reserve optimization model considering the voltage safety constraint under the fault condition. Operation mode. The invention can guide dispatchers to rationally formulate the operation mode of reactive power equipment, ensure sufficient dynamic reactive power reserve under fault conditions, avoid voltage safety problems caused by faults such as commutation failure, and improve the safety of the power system.

具体实施方式Detailed ways

本发明提出的一种基于动态灵敏度的受端电网动态无功储备优化方法，下面结合具体实施例进一步详细说明如下。A method for optimizing the dynamic reactive power reserve of the receiving-end power grid based on the dynamic sensitivity proposed by the present invention is further described in detail below with reference to specific embodiments.

本发明提出一种基于动态灵敏度的受端电网动态无功储备优化方法，包括以下步骤：The present invention proposes a method for optimizing the dynamic reactive power reserve of the receiving-end power grid based on dynamic sensitivity, comprising the following steps:

1)建立交直流混联系统方程，求取系统的一阶动态灵敏度；具体步骤如下：1) Establish an AC-DC hybrid system equation to obtain the first-order dynamic sensitivity of the system; the specific steps are as follows:

1-1)建立稳态运行时的受端电网方程，用式(1)表示。式(1)中的两个方程分别描述了系统的动态过程和系统变量之间的代数关系。其中，x代表系统的状态变量，包括发电机内电势、功角、励磁电压、直流电流变量；y代表代数变量，包括系统的母线电压幅值和母线电压的相角；u代表控制变量，包括稳态运行时发电机无功出力

Figure GDA0002705411510000049
和容抗器的无功出力
Figure GDA00027054115100000410
1-1) Establish the receiving-end power grid equation during steady-state operation, which is represented by formula (1). The two equations in Eq. (1) describe the dynamic process of the system and the algebraic relationship between the system variables, respectively. Among them, x represents the state variables of the system, including generator internal potential, power angle, excitation voltage, and DC current variables; y represents algebraic variables, including the bus voltage amplitude of the system and the phase angle of the bus voltage; u represents the control variables, including Generator reactive output during steady state operation
Figure GDA0002705411510000049
and the reactive output of the capacitive reactor
Figure GDA00027054115100000410

Figure GDA00027054115100000411
Figure GDA00027054115100000411

1-2)故障发生之后，式(1)中，第一个公式是不变的，第二个公式会改变；分别用(2)式和(3)式代表故障发生后清除前和故障清除后时段。式中，s代表故障编号，c代表清除。1-2) After the fault occurs, in formula (1), the first formula is unchanged, and the second formula will change; formulas (2) and (3) are used to represent the fault before and after the fault is cleared. later period. In the formula, s represents the fault number, and c represents clearing.

0＝gs(x,y,u) (2)0=g s (x, y, u) (2)

0＝gs,c(x,y,u) (3)0=g s, c (x, y, u) (3)

下文中，t0表示故障发生时刻，tc表示故障清除时刻；

Figure GDA0002705411510000051
和
Figure GDA0002705411510000052
分别表示故障发生前和故障清除前的初始时刻；
Figure GDA0002705411510000053
和
Figure GDA0002705411510000054
分别表示故障发生后和故障清除后的初始时刻。In the following, t 0 represents the moment when the fault occurs, and t c represents the moment when the fault is cleared;
Figure GDA0002705411510000051
and
Figure GDA0002705411510000052
represent the initial moments before the fault occurs and before the fault is cleared, respectively;
Figure GDA0002705411510000053
and
Figure GDA0002705411510000054
represent the initial moments after the fault occurs and after the fault is cleared, respectively.

Figure GDA0002705411510000055
和
Figure GDA0002705411510000056
分别表示故障发生后的初始状态时，状态变量和代数变量对控制变量的偏导数，分别用(4)式和(5)式求取。其中，
Figure GDA0002705411510000057
表示故障发生前的初始状态下，状态变量对控制变量的偏导数。
Figure GDA0002705411510000058
分别表示发生第s个故障后的初始状态下，(1)式中的第二个公式对代数变量和控制变量的偏导数。
Figure GDA0002705411510000055
and
Figure GDA0002705411510000056
When respectively representing the initial state after the fault occurs, the partial derivatives of the state variables and algebraic variables to the control variables are obtained by equations (4) and (5) respectively. in,
Figure GDA0002705411510000057
It represents the partial derivative of the state variable to the control variable in the initial state before the fault occurs.
Figure GDA0002705411510000058
respectively represent the partial derivatives of the second formula in formula (1) to the algebraic variable and the control variable in the initial state after the occurrence of the sth fault.

Figure GDA0002705411510000059
Figure GDA0002705411510000059

Figure GDA00027054115100000510
Figure GDA00027054115100000510

Figure GDA00027054115100000511
和
Figure GDA00027054115100000512
分别表示故障清除后的初始状态时，状态变量和代数变量对控制变量的偏导数，分别用(6)式和(7)式求取。其中，
Figure GDA00027054115100000513
表示故障发生前的初始状态下，状态变量对控制变量的偏导数。
Figure GDA00027054115100000514
分别表示发生清除第s个故障后的初始状态下，(1)式中的第二个公式对代数变量和控制变量的偏导数。
Figure GDA00027054115100000511
and
Figure GDA00027054115100000512
When the initial state after the fault is cleared, respectively, the partial derivatives of the state variable and the algebraic variable to the control variable are obtained by equation (6) and equation (7). in,
Figure GDA00027054115100000513
It represents the partial derivative of the state variable to the control variable in the initial state before the fault occurs.
Figure GDA00027054115100000514
respectively represent the partial derivatives of the second formula in formula (1) to the algebraic variable and the control variable in the initial state after the sth fault is cleared.

Figure GDA00027054115100000515
Figure GDA00027054115100000515

Figure GDA00027054115100000516
Figure GDA00027054115100000516

在故障发生时段内任意时刻

Figure GDA00027054115100000517
令T＝t，可计算出T时刻的值
Figure GDA00027054115100000518
其为T时刻的灵敏度。利用(8)式算出T+1时刻的值
Figure GDA00027054115100000519
其为T+1时刻的灵敏度。Any time during the fault period
Figure GDA00027054115100000517
Let T=t, the value at time T can be calculated
Figure GDA00027054115100000518
It is the sensitivity at time T. Calculate the value at time T+1 using equation (8)
Figure GDA00027054115100000519
It is the sensitivity at time T+1.

Figure GDA00027054115100000520
Figure GDA00027054115100000520

式中，h代表仿真步长，I代表单位矩阵，J代表系统的雅克比矩阵。

Figure GDA00027054115100000521
分别代表T时刻，系统状态变量和代数变量对控制变量的偏导数；
Figure GDA00027054115100000522
分别代表T+1时刻，系统状态变量和代数变量对控制变量的偏导数；
Figure GDA00027054115100000523
分别代表T时刻，(1)式中第一个公式对状态变量和代数变量的偏导数；
Figure GDA00027054115100000524
分别代表T时刻，(1)式中第二个公式对状态变量和代数变量的偏导数；
Figure GDA00027054115100000525
分别代表T和T+1时刻(1)式中第一个公式对控制变量的偏导数；
Figure GDA00027054115100000526
分别代表T和T+1时刻(1)式中第二个公式对控制变量的偏导数。In the formula, h represents the simulation step size, I represents the identity matrix, and J represents the Jacobian matrix of the system.
Figure GDA00027054115100000521
Represent the partial derivatives of the system state variables and algebraic variables to the control variables at time T, respectively;
Figure GDA00027054115100000522
respectively represent the partial derivatives of the system state variables and algebraic variables to the control variables at time T+1;
Figure GDA00027054115100000523
respectively represent the time T, the partial derivatives of the first formula in (1) to the state variables and algebraic variables;
Figure GDA00027054115100000524
respectively represent time T, the partial derivative of the second formula in (1) to the state variable and algebraic variable;
Figure GDA00027054115100000525
represent the partial derivatives of the first formula in formula (1) to the control variable at time T and T+1, respectively;
Figure GDA00027054115100000526
represent the partial derivatives of the second formula in formula (1) with respect to the control variable at time T and T+1, respectively.

2)针对系统当前状况，建立动态无功储备优化模型，该模型由目标函数和约束条件构成；具体步骤如下：2) According to the current state of the system, establish a dynamic reactive power reserve optimization model, which consists of an objective function and constraints; the specific steps are as follows:

2-1)建立动态无功储备优化模型的目标函数，如(9)所示：2-1) Establish the objective function of the dynamic reactive power reserve optimization model, as shown in (9):

Figure GDA0002705411510000061
Figure GDA0002705411510000061

式(9)表示了优化后所有发电机需要投入的容抗器最小数之和。其中，Nstation表示容抗器总数，

Figure GDA0002705411510000062
Nc,i分别表示第i个容抗器当前的投入组数和优化后的投入组数。Equation (9) represents the sum of the minimum number of capacitors that all generators need to put into after optimization. Among them, N station represents the total number of capacitive reactors,
Figure GDA0002705411510000062
N c,i respectively represent the current input group number and the optimized input group number of the ith capacitive reactor.

2-2)确定动态无功储备优化模型的约束条件，具体如下：2-2) Determine the constraints of the dynamic reactive power reserve optimization model, as follows:

2-2-1)各场站容抗器投入的组数约束，如式(10)所示：2-2-1) Constraints on the number of groups of capacitor reactor input at each station, as shown in formula (10):

Figure GDA0002705411510000063
Figure GDA0002705411510000063

其中，Nc,i ,

Figure GDA0002705411510000064
分别代表各容抗器投入组数的下限值和上限值。Among them, N c,i ,
Figure GDA0002705411510000064
Represent the lower limit and upper limit of each capacitor input group number respectively.

2-2-2)发电机稳态时的无功出力约束，如式(11)所示：2-2-2) The reactive power output constraint of the generator in steady state, as shown in formula (11):

Figure GDA0002705411510000065
Figure GDA0002705411510000065

其中，

Figure GDA0002705411510000066
代表稳态运行时发电机无功出力构成的列向量，即优化后的取值。
Figure GDA0002705411510000067
分别代表稳态时发电机无功出力的下限值与上限值；in,
Figure GDA0002705411510000066
Represents the column vector formed by the reactive power output of the generator during steady-state operation, that is, the optimized value.
Figure GDA0002705411510000067
respectively represent the lower limit and upper limit of the generator reactive power output in steady state;

2-2-3)换相失败故障后的N-1安全约束条件，如式(12)所示：2-2-3) N-1 safety constraints after commutation failure failure, as shown in formula (12):

Figure GDA0002705411510000068
Figure GDA0002705411510000068

其中，

Figure GDA0002705411510000069
代表换流站交流母线电压故障后的临界电压恢复值。
Figure GDA00027054115100000610
分别代表第s个故障发生后，Tend时刻换流站交流母线电压的优化值和当前值。通常Tend由电网给定，表示换相恢复的要求时间。
Figure GDA00027054115100000611
分别代表稳态运行时发电机无功出力的优化值和当前值。
Figure GDA00027054115100000612
分别代表稳态运行时容抗器无功出力的优化值和当前值。
Figure GDA00027054115100000613
分别代表第s个故障下，Tend时刻
Figure GDA00027054115100000614
对
Figure GDA00027054115100000615
和
Figure GDA00027054115100000616
的动态灵敏度，该灵敏度值可由步骤1)求出。需要说明的是，步骤1)中的控制变量u是由
Figure GDA00027054115100000617
和
Figure GDA00027054115100000618
构成的向量，即
Figure GDA00027054115100000619
in,
Figure GDA0002705411510000069
Represents the critical voltage recovery value after the AC bus voltage failure of the converter station.
Figure GDA00027054115100000610
respectively represent the optimized value and current value of the AC bus voltage of the converter station at the time T end after the sth fault occurs. Usually T end is given by the grid and represents the required time for commutation recovery.
Figure GDA00027054115100000611
Represent the optimized value and current value of the generator reactive power output during steady-state operation, respectively.
Figure GDA00027054115100000612
Represent the optimized value and current value of reactive power output of the capacitive reactor during steady-state operation, respectively.
Figure GDA00027054115100000613
Respectively represent the time of T end under the sth fault
Figure GDA00027054115100000614
right
Figure GDA00027054115100000615
and
Figure GDA00027054115100000616
The dynamic sensitivity of , the sensitivity value can be obtained from step 1). It should be noted that the control variable u in step 1) is determined by
Figure GDA00027054115100000617
and
Figure GDA00027054115100000618
constituted vector, that is
Figure GDA00027054115100000619

3)利用CPLEX对步骤2)建立的模型求解，得到无功补偿设备求得对应的最优解

Figure GDA00027054115100000620
后，利用式(13)计算要预留的最少动态无功储备：3) Use CPLEX to solve the model established in step 2) to obtain the corresponding optimal solution for reactive power compensation equipment
Figure GDA00027054115100000620
Then, use formula (13) to calculate the minimum dynamic reactive power reserve to be reserved:

Figure GDA00027054115100000621
Figure GDA00027054115100000621

式中

Figure GDA00027054115100000622
为无功补偿设备的最少动态无功储备，g表示发电机。发电机需按照所求的
Figure GDA00027054115100000623
预留出无功储备量。in the formula
Figure GDA00027054115100000622
It is the minimum dynamic reactive power reserve of reactive power compensation equipment, and g represents the generator. Generator as required
Figure GDA00027054115100000623
Reserve a reactive power reserve.

Claims (1)

1.一种基于动态灵敏度的受端电网动态无功储备优化方法，其特征在于，该方法包括以下步骤：1. a method for optimizing the dynamic reactive power reserve of a receiving end power grid based on dynamic sensitivity, is characterized in that, the method comprises the following steps: 1)建立交直流混联系统方程，求取系统的一阶动态灵敏度；具体步骤如下：1) Establish an AC-DC hybrid system equation to obtain the first-order dynamic sensitivity of the system; the specific steps are as follows: 1-1)建立稳态运行时的受端电网方程，如式(1)所示：1-1) Establish the receiver power grid equation during steady-state operation, as shown in formula (1):
Figure FDA0002321024880000011
Figure FDA0002321024880000011
 其中，x代表系统的状态变量，包括发电机内电势、功角、励磁电压、直流电流变量；y代表代数变量，包括系统的母线电压幅值和母线电压的相角；u代表控制变量，包括稳态运行时发电机无功出力
Figure FDA0002321024880000014
和容抗器的无功出力
Figure FDA0002321024880000015
Among them, x represents the state variables of the system, including generator internal potential, power angle, excitation voltage, and DC current variables; y represents algebraic variables, including the bus voltage amplitude of the system and the phase angle of the bus voltage; u represents the control variables, including Generator reactive output during steady state operation
Figure FDA0002321024880000014
and the reactive output of the capacitive reactor
Figure FDA0002321024880000015
 1-2)故障发生之后，式(1)中第一个表达式保持不变；1-2) After the fault occurs, the first expression in formula (1) remains unchanged; 对于故障发生后清除前时段，用式(2)替代式(1)中第二个表达式；For the period before clearing after the fault occurs, replace the second expression in Equation (1) with Equation (2); 对于故障发生后且故障清除后时段，用式(3)替代式(1)中第二个表达式；分别得到表达式如下：For the period after the fault occurs and after the fault is cleared, the second expression in the formula (1) is replaced by the formula (3); the expressions are respectively obtained as follows: 0＝gs(x,y,u) (2)0=g s (x, y, u) (2) 0＝gs,c(x,y,u) (3)0=g s, c (x, y, u) (3) 式中，s代表故障编号；c代表清除；In the formula, s represents the fault number; c represents clearing; 1-3)令
Figure FDA0002321024880000016
和
Figure FDA0002321024880000017
分别表示故障发生后的初始状态时状态变量和代数变量对控制变量的偏导数，分别用式(4)和式(5)求取：1-3) Order
Figure FDA0002321024880000016
and
Figure FDA0002321024880000017
Respectively represent the partial derivatives of the state variables and algebraic variables to the control variables in the initial state after the fault occurs, and are calculated by equations (4) and (5) respectively:
Figure FDA0002321024880000012
Figure FDA0002321024880000012
Figure FDA0002321024880000013
Figure FDA0002321024880000013
 其中，t0表示故障发生时刻；
Figure FDA0002321024880000018
表示故障发生前的初始时刻；
Figure FDA0002321024880000019
表示故障发生后的初始时刻；Among them, t 0 represents the moment when the fault occurs;
Figure FDA0002321024880000018
Represents the initial moment before the failure occurs;
Figure FDA0002321024880000019
Represents the initial moment after the failure occurs;
Figure FDA00023210248800000110
表示故障发生前的初始状态下，状态变量对控制变量的偏导数；
Figure FDA00023210248800000111
分别表示发生第s个故障后的初始状态下，式(1)中的第二个表达式对代数变量和控制变量的偏导数；
Figure FDA00023210248800000110
Represents the partial derivative of the state variable to the control variable in the initial state before the fault occurs;
Figure FDA00023210248800000111
respectively represent the partial derivatives of the second expression in equation (1) with respect to the algebraic variable and the control variable in the initial state after the occurrence of the sth fault; 1-4)令
Figure FDA0002321024880000025
和
Figure FDA0002321024880000026
分别表示故障清除后的初始状态时状态变量和代数变量对控制变量的偏导数，分别用式(6)和式(7)式求取：1-4) Order
Figure FDA0002321024880000025
and
Figure FDA0002321024880000026
respectively represent the partial derivatives of the state variables and algebraic variables to the control variables in the initial state after the fault is cleared, and are obtained by equations (6) and (7) respectively:
Figure FDA0002321024880000021
Figure FDA0002321024880000021
Figure FDA0002321024880000022
Figure FDA0002321024880000022
 其中，tc表示故障清除时刻，
Figure FDA0002321024880000027
表示故障清除前的初始时刻，
Figure FDA0002321024880000028
表示故障清除后的初始时刻，
Figure FDA0002321024880000029
表示故障发生前的初始状态下，状态变量对控制变量的偏导数；
Figure FDA00023210248800000210
分别表示发生清除第s个故障后的初始状态下，式(1)中的第二个表达式对代数变量和控制变量的偏导数；Among them, t c represents the fault clearing time,
Figure FDA0002321024880000027
represents the initial moment before the fault is cleared,
Figure FDA0002321024880000028
represents the initial moment after the fault is cleared,
Figure FDA0002321024880000029
Represents the partial derivative of the state variable to the control variable in the initial state before the fault occurs;
Figure FDA00023210248800000210
respectively represent the partial derivatives of the second expression in formula (1) to the algebraic variable and the control variable in the initial state after the sth fault is cleared; 1-5)在故障发生时段内任意时刻
Figure FDA00023210248800000211
令T＝t，计算T时刻的灵敏度
Figure FDA00023210248800000212
利用式(8)计算T+1时刻的灵敏度
Figure FDA00023210248800000213
1-5) Any time during the fault occurrence period
Figure FDA00023210248800000211
Let T=t, calculate the sensitivity at time T
Figure FDA00023210248800000212
Use formula (8) to calculate the sensitivity at time T+1
Figure FDA00023210248800000213
Figure FDA0002321024880000023
Figure FDA0002321024880000023
 式中，h代表仿真步长，I代表单位矩阵，J代表系统的雅克比矩阵；
Figure FDA00023210248800000214
分别代表T时刻，系统状态变量和代数变量对控制变量的偏导数；
Figure FDA00023210248800000215
分别代表T+1时刻，系统状态变量和代数变量对控制变量的偏导数；
Figure FDA00023210248800000216
分别代表T时刻，式(1)中第一个表达式对状态变量和代数变量的偏导数；
Figure FDA00023210248800000217
分别代表T时刻，式(1)中第二个表达式对状态变量和代数变量的偏导数；
Figure FDA00023210248800000218
分别代表T和T+1时刻式(1)中第一个表达式对控制变量的偏导数；
Figure FDA00023210248800000219
分别代表T和T+1时刻(1)式中第二个公式对控制变量的偏导数；where h represents the simulation step size, I represents the identity matrix, and J represents the Jacobian matrix of the system;
Figure FDA00023210248800000214
Represent the partial derivatives of the system state variables and algebraic variables to the control variables at time T, respectively;
Figure FDA00023210248800000215
respectively represent the partial derivatives of the system state variables and algebraic variables to the control variables at time T+1;
Figure FDA00023210248800000216
respectively represent the time T, the partial derivative of the first expression in equation (1) to the state variable and algebraic variable;
Figure FDA00023210248800000217
respectively represent time T, the partial derivative of the second expression in formula (1) to the state variable and algebraic variable;
Figure FDA00023210248800000218
represent the partial derivatives of the first expression in equation (1) to the control variable at time T and T+1, respectively;
Figure FDA00023210248800000219
represent the partial derivatives of the second formula in formula (1) to the control variable at time T and T+1, respectively; 2)建立动态无功储备优化模型，该模型由目标函数和约束条件构成；具体步骤如下：2) Establish a dynamic reactive power reserve optimization model, which consists of an objective function and constraints; the specific steps are as follows: 2-1)建立动态无功储备优化模型的目标函数，如(9)所示：2-1) Establish the objective function of the dynamic reactive power reserve optimization model, as shown in (9):
Figure FDA0002321024880000024
Figure FDA0002321024880000024
 其中，Nstation表示容抗器总数，
Figure FDA00023210248800000220
Nc,i分别表示第i个容抗器当前的投入组数和优化后的投入组数；Among them, N station represents the total number of capacitive reactors,
Figure FDA00023210248800000220
N c,i respectively represent the current input group number and the optimized input group number of the ith capacitive reactor; 2-2)确定动态无功储备优化模型的约束条件，具体如下：2-2) Determine the constraints of the dynamic reactive power reserve optimization model, as follows: 2-2-1)各场站容抗器投入的组数约束，如式(10)所示：2-2-1) Constraints on the number of groups of capacitor reactor input at each station, as shown in formula (10):
Figure FDA0002321024880000031
Figure FDA0002321024880000031
 其中，Nc ,
Figure FDA0002321024880000035
分别代表各容抗器投入组数的下限值和上限值；where, N c ,
Figure FDA0002321024880000035
Represent the lower limit value and upper limit value of each capacitor input group number; 2-2-2)发电机稳态时的无功出力约束，如式(11)所示：2-2-2) The reactive power output constraint of the generator in steady state, as shown in formula (11):
Figure FDA0002321024880000032
Figure FDA0002321024880000032
 其中，
Figure FDA0002321024880000036
代表稳态时发电机无功出力的优化值，
Figure FDA0002321024880000037
分别代表稳态时发电机无功出力的下限值与上限值；in,
Figure FDA0002321024880000036
represents the optimal value of the generator reactive power output at steady state,
Figure FDA0002321024880000037
respectively represent the lower limit and upper limit of the generator reactive power output in steady state; 2-2-3)换相失败故障后的N-1安全约束条件，如式(12)所示：2-2-3) N-1 safety constraints after commutation failure failure, as shown in formula (12):
Figure FDA0002321024880000033
Figure FDA0002321024880000033
 其中，
Figure FDA0002321024880000038
代表换流站交流母线电压故障后的临界电压恢复值；
Figure FDA0002321024880000039
分别代表第s个故障发生后，Tend时刻换流站交流母线电压的优化值和当前值；Tend表示换相恢复的时间；
Figure FDA00023210248800000310
分别代表稳态运行时发电机无功出力的优化值和当前值；
Figure FDA00023210248800000311
分别代表稳态运行时容抗器无功出力的优化值和当前值；
Figure FDA00023210248800000312
分别代表第s个故障下，Tend时刻
Figure FDA00023210248800000313
对
Figure FDA00023210248800000314
和
Figure FDA00023210248800000315
的动态灵敏度，该灵敏度值由步骤1)求出；in,
Figure FDA0002321024880000038
Represents the critical voltage recovery value after the AC bus voltage failure of the converter station;
Figure FDA0002321024880000039
respectively represent the optimized value and current value of the AC bus voltage of the converter station at the moment T end after the sth fault occurs; T end represents the commutation recovery time;
Figure FDA00023210248800000310
Represent the optimized value and current value of the generator reactive power output during steady-state operation, respectively;
Figure FDA00023210248800000311
Represent the optimized value and current value of the reactive power output of the capacitive reactor during steady-state operation;
Figure FDA00023210248800000312
Respectively represent the time of T end under the sth fault
Figure FDA00023210248800000313
right
Figure FDA00023210248800000314
and
Figure FDA00023210248800000315
The dynamic sensitivity of , the sensitivity value is obtained by step 1); 3)对步骤2)建立的模型求解，得到最优解
Figure FDA00023210248800000316
利用式(13)计算无功补偿设备预留的最少动态无功储备，优化结束；3) Solve the model established in step 2) to obtain the optimal solution
Figure FDA00023210248800000316
Use formula (13) to calculate the minimum dynamic reactive power reserve reserved by the reactive power compensation equipment, and the optimization is over;
Figure FDA0002321024880000034
Figure FDA0002321024880000034
 式中，
Figure FDA00023210248800000317
为无功补偿设备的最少动态无功储备，下标g表示发电机。In the formula,
Figure FDA00023210248800000317
It is the minimum dynamic reactive power reserve of reactive power compensation equipment, and the subscript g represents the generator.
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