技术领域Technical Field
本发明涉及电力系统通信优化控制技术领域，尤其涉及一种针对网络化耦合系统的分布式Gossip协议和控制器联合设计方法。The present invention relates to the technical field of power system communication optimization control, and in particular to a distributed Gossip protocol and controller joint design method for a networked coupling system.
背景技术Background Art
许多工程系统都可以用大规模系统LSS模型来描述，例如电力系统。一般来说，大规模系统LSS已经研究了三种不同的控制策略，即集中控制、分散控制和分布式控制。分布式控制被认为是集中控制和分散控制之间的权衡，在过去几年中得到了广泛的研究。在大规模系统LSS分布式控制的研究中，通常假设每个子控制器在每个时刻都与其所有邻居进行通信。然而，当计算和通信资源有限时，这一假设在实际工程中并不容易满足。因此，使用各种通信协议来管理通信顺序。Many engineering systems can be described by the large-scale system LSS model, such as power systems. Generally speaking, three different control strategies have been studied for large-scale systems LSS, namely centralized control, decentralized control, and distributed control. Distributed control is considered to be a trade-off between centralized control and decentralized control and has been widely studied in the past few years. In the study of distributed control of large-scale systems LSS, it is usually assumed that each sub-controller communicates with all its neighbors at every moment. However, this assumption is not easy to meet in actual engineering when computing and communication resources are limited. Therefore, various communication protocols are used to manage the communication order.
传统的通信协议Gossip协议，每个子控制器等概率地仅从一个随机选择的邻居接收信息，而不是在每一时刻从所有邻居接收信息。因此，该协议的使用节省了网络带宽并减少了通信网络中的数据包传输。但是它忽略了在实际应用中，尤其在电力系统中，子系统之间的通信概率并不是等同一致，它会受到各种因素干扰如通信设备和技术、环境条件等，因此通过设计并优化通信概率对大规模互联系统的系统性能的提升具有显著影响。In the traditional communication protocol Gossip protocol, each sub-controller receives information from only one randomly selected neighbor with equal probability, rather than receiving information from all neighbors at every moment. Therefore, the use of this protocol saves network bandwidth and reduces the transmission of data packets in the communication network. However, it ignores the fact that in practical applications, especially in power systems, the communication probability between subsystems is not equal and consistent, and it will be interfered by various factors such as communication equipment and technology, environmental conditions, etc. Therefore, by designing and optimizing the communication probability, it has a significant impact on improving the system performance of large-scale interconnected systems.
发明内容Summary of the invention
针对现有技术的不足，本发明提供了一种针对网络化耦合系统的分布式Gossip协议和控制器联合设计方法，解决了传统分布式电力系统控制通信概率设计过程中存在非线性、非凸约束的技术问题，达到了提高大规模电力系统的鲁棒性与抗干扰性能，减少了计算负担与通信带宽的目的。In view of the shortcomings of the prior art, the present invention provides a distributed Gossip protocol and controller joint design method for networked coupled systems, which solves the technical problems of nonlinear and non-convex constraints in the control communication probability design process of traditional distributed power systems, thereby achieving the purpose of improving the robustness and anti-interference performance of large-scale power systems and reducing the computational burden and communication bandwidth.
为解决上述技术问题，本发明提供了如下技术方案：一种针对网络化耦合系统的分布式Gossip协议和控制器联合设计方法，该方法包括以下步骤：To solve the above technical problems, the present invention provides the following technical solutions: a method for jointly designing a distributed Gossip protocol and a controller for a networked coupling system, the method comprising the following steps:
S1、获取被控多区域电力系统中每个子区域的系统参数，并基于系统参数建立每个子区域的连续时间系统状态空间模型；S1. Obtain system parameters of each sub-region in the controlled multi-region power system, and establish a continuous-time system state space model of each sub-region based on the system parameters;
S2、将连续时间系统状态空间模型离散化得到离散时间系统参数矩阵，并在Gossip协议下根据离散时间系统参数矩阵构建分布式控制器系统模型；S2. Discretize the continuous-time system state space model to obtain the discrete-time system parameter matrix , and according to the discrete time system parameter matrix under the Gossip protocol Build a distributed controller system model;
S3、基于分布式控制器的设计目标构建非线性矩阵不等式；S3, construct nonlinear matrix inequalities based on the design goals of distributed controllers;
S4、通过Schur引理以及不等式放缩对非线性矩阵不等式解耦，得到只含耦合项通信概率的矩阵不等式；S4. Decouple the nonlinear matrix inequality through Schur's lemma and inequality scaling to obtain the communication probability containing only the coupling term Matrix inequalities for ;
S5、采用GA遗传算法和LMI线性矩阵不等式结合的求解算法得到最优的通信概率；S5. Use the GA genetic algorithm and LMI linear matrix inequality solution algorithm to obtain the optimal communication probability ;
S6、将得到的最优通信概率代入到分布式控制系统模型的矩阵不等式中用以稳定多区域电力系统。S6. The optimal communication probability obtained Substitute it into the matrix inequality of the distributed control system model to stabilize the multi-regional power system.
借由上述技术方案，本发明提供了一种针对网络化耦合系统的分布式Gossip协议和控制器联合设计方法，至少具备以下有益效果：By means of the above technical solution, the present invention provides a method for jointly designing a distributed Gossip protocol and a controller for a networked coupling system, which has at least the following beneficial effects:
1、本发明所提出的分布式Gossip协议和控制器联合设计方法应用于互联电力系统中，相比于集中控制器需要来自所有子系统的信息，以及分散式控制中每个子控制器仅使用本地信息而导致的系统性能下降，所提出分布式Gossip协议和控制器联合设计方法能保证互联电力系统在稳定的前提下减少通信带宽。1. The distributed Gossip protocol and controller joint design method proposed in the present invention are applied to interconnected power systems. Compared with the centralized controller requiring information from all subsystems and the system performance degradation caused by each subcontroller in decentralized control using only local information, the proposed distributed Gossip protocol and controller joint design method can ensure that the interconnected power system reduces the communication bandwidth under the premise of stability.
2、本发明将Gossip协议应用于互联电力系统中，在由通信协议调度通信网络中的信息通信能避免数据冲突，减少通信和计算负担。同时，与传统的Gossip协议的等概率通信相比，本发明对通信概率进行优化设计，有效地最小化了有限时间的性能指标，提高了系统的鲁棒性。2. The present invention applies the Gossip protocol to the interconnected power system. The information communication in the communication network dispatched by the communication protocol can avoid data conflicts and reduce the communication and computing burden. At the same time, compared with the equal probability communication of the traditional Gossip protocol, the present invention optimizes the communication probability and effectively minimizes the limited time. performance indicators and improve the robustness of the system.
3、本发明通过在Gossip协议下优化通信概率的方法，将传统的LMI方法与GA遗传算法相结合进行求解得到最优通信概率，能够降低控制器设计中的保守性，同时有效提升系统性能；GA遗传算法的引入能够很好的处理分布式控制器求解的充分条件中的非凸、非线性项，同时显著减小有限时间的性能指标，从而提高系统性能。3. The present invention optimizes the communication probability under the Gossip protocol The method combines the traditional LMI method with the GA genetic algorithm to solve the optimal communication probability, which can reduce the conservatism in the controller design and effectively improve the system performance; the introduction of the GA genetic algorithm can well handle the non-convex and nonlinear terms in the sufficient conditions for solving the distributed controller, and significantly reduce the finite time performance indicators, thereby improving system performance.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
此处所说明的附图用来提供对本申请的进一步理解，构成本申请的一部分，本申请的示意性实施例及其说明用于解释本申请，并不构成对本申请的不当限定。在附图中：The drawings described herein are used to provide a further understanding of the present application and constitute a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:
图1为本发明控制方法的流程图；FIG1 is a flow chart of a control method of the present invention;
图2为本发明多区域电力系统中四个区域的电力系统框架示意图；FIG2 is a schematic diagram of a power system framework of four regions in a multi-region power system of the present invention;
图3为本发明GA遗传算法的执行流程图；FIG3 is an execution flow chart of the GA genetic algorithm of the present invention;
图4为本发明遗传算法的适应度函数值迭代曲线图；FIG4 is an iteration curve diagram of the fitness function value of the genetic algorithm of the present invention;
图5为本发明四区域电力系统的状态轨迹曲线图。FIG5 is a state trajectory curve diagram of the four-area power system of the present invention.
具体实施方式DETAILED DESCRIPTION
为使本发明的上述目的、特征和优点能够更加明显易懂，下面结合附图和具体实施方式对本发明作进一步详细的说明。借此对本申请如何应用技术手段来解决技术问题并达成技术功效的实现过程能充分理解并据以实施。In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific implementation methods, so that the implementation process of how the present application uses technical means to solve technical problems and achieve technical effects can be fully understood and implemented accordingly.
近年来，大规模系统（LSS）的控制问题引起了广泛的研究关注。原因是许多工程系统都可以用LSS模型来描述，例如电力系统。LSS通常由大量互连的子系统组成。一个子系统的动力学会影响其他子系统的动力学，这使得LSS的控制成为一项具有挑战性的工作。一般来说，LSS已经研究了三种不同的控制策略，即集中控制、分散控制和分布式控制。然而，集中控制可能会承受沉重的通信和计算负担，因为集中控制器需要来自所有子系统的信息。另一方面，分散控制可能会导致系统性能下降，甚至破坏系统稳定性，因为每个子控制器仅使用本地信息。因此，分布式控制被认为是集中控制和分散控制之间的权衡，在过去几年中得到了广泛的研究。在该控制策略中，收集本地信息和来自邻居的信息以形成本地控制输入。在LSS分布式控制的研究中，通常假设每个子控制器在每个时刻都与其所有邻居进行通信。然而，当计算和通信资源有限时，这一假设在实际工程中并不容易满足。因此，使用各种通信协议来管理通信顺序。In recent years, the control problem of large-scale systems (LSS) has attracted extensive research attention. The reason is that many engineering systems can be described by LSS models, such as power systems. LSSs are usually composed of a large number of interconnected subsystems. The dynamics of one subsystem affects the dynamics of other subsystems, which makes the control of LSSs a challenging task. Generally speaking, three different control strategies have been studied for LSSs, namely centralized control, decentralized control, and distributed control. However, centralized control may suffer from heavy communication and computational burdens because the centralized controller requires information from all subsystems. On the other hand, decentralized control may lead to system performance degradation or even destroy system stability because each subcontroller only uses local information. Therefore, distributed control is considered to be a trade-off between centralized control and decentralized control and has been widely studied in the past few years. In this control strategy, local information and information from neighbors are collected to form local control inputs. In the study of distributed control of LSSs, it is usually assumed that each subcontroller communicates with all its neighbors at every moment. However, this assumption is not easy to meet in practical engineering when computing and communication resources are limited. Therefore, various communication protocols are used to manage the communication sequence.
传统的通信协议Gossip协议，每个子控制器等概率地仅从一个随机选择的邻居接收信息，而不是在每一时刻从所有邻居接收信息。因此，该协议的使用节省了网络带宽并减少了通信网络中的数据包传输。但是它忽略了在实际应用中，尤其在电力系统中，子系统之间的通信概率并不是等同一致，它会受到各种因素干扰如通信设备和技术、环境条件等，通过设计并优化通信概率对大规模互联系统的系统性能的提升具有显著影响。本发明引入遗传算法（GA）来对含有通信概率的耦合项进行处理，通过GA遗传算法与线性矩阵不等式LMI的结合，有效降低了控制器设计的保守性，最小化了有限时间的性能指标，提高了系统的鲁棒性。In the traditional communication protocol Gossip protocol, each sub-controller receives information from only one randomly selected neighbor with equal probability, rather than receiving information from all neighbors at every moment. Therefore, the use of this protocol saves network bandwidth and reduces the transmission of data packets in the communication network. However, it ignores the fact that in practical applications, especially in power systems, the communication probability between subsystems is not equal and consistent. It will be interfered by various factors such as communication equipment and technology, environmental conditions, etc. The design and optimization of communication probability has a significant impact on the improvement of system performance of large-scale interconnected systems. The present invention introduces a genetic algorithm (GA) to The coupling term of is processed, and the conservatism of controller design is effectively reduced by combining GA genetic algorithm with linear matrix inequality LMI, minimizing the finite time performance indicators and improve the robustness of the system.
为了解决传统分布式电力系统控制通信概率设计过程中存在非线性、非凸约束的技术问题，请参照图1-图5，本实施例提出了一种针对网络化耦合系统的分布式Gossip协议和控制器联合设计方法，本实施例通过在Gossip通信协议下优化子系统之间的通信概率并使用遗传算法Genetic Algorithm，GA结合线性矩阵不等式LMI进行控制器设计，以实现对互联电力系统强鲁棒、快速响应的控制效果，同时优化了分布式控制器的最小化有限时间的性能指标。该方法包括以下步骤：In order to solve the technical problems of nonlinear and non-convex constraints in the control communication probability design process of traditional distributed power systems, please refer to Figures 1 to 5. This embodiment proposes a distributed Gossip protocol and controller joint design method for networked coupling systems. This embodiment optimizes the communication probability between subsystems under the Gossip communication protocol. The Genetic Algorithm (GA) is used in combination with the Linear Matrix Inequality (LMI) to design the controller to achieve a strong and fast response control effect on the interconnected power system, while optimizing the minimum finite time of the distributed controller. The method comprises the following steps:
S1、获取被控多区域电力系统中每个子区域的系统参数，并基于系统参数建立每个子区域的连续时间系统状态空间模型；系统参数包括频率偏移、联络线功率偏差、发电机输出功率偏差、发电机阀门位置偏差、发电机组的阻尼常数、速度下降系数、发电机惯量、频率偏差常量、汽轮机时间系数、调速器时间系数以及联络线之间的同步模数，其中。S1. Obtain the system parameters of each sub-region in the controlled multi-region power system, and establish a continuous-time system state space model for each sub-region based on the system parameters; the system parameters include frequency offset , Interconnection line power deviation , Generator output power deviation , Generator valve position deviation , the damping constant of the generator set , speed reduction coefficient , Generator inertia , frequency deviation constant , Turbine time coefficient , Governor time coefficient And the synchronous modulus between the tie lines ,in .
每个子区域的连续时间系统状态空间模型为：The continuous-time system state space model for each sub-region is:
； ;
其中，in,
； ;
； ;
； ;
其中，为频率偏移；为联络线功率偏差；为发电机输出功率偏差；为发电机阀门位置偏差；为频率偏差常量；为发电机组的阻尼常数；发电机惯量；为速度下降系数；为汽轮机时间系数；为调速器时间系数；为联络线之间的同步模数；为的转置；为的转置；，意味着第i个离散时间系统模型的邻居集；为负载扰动；为的导数。in, is the frequency offset; is the tie line power deviation; is the generator output power deviation; is the generator valve position deviation; is the frequency deviation constant; is the damping constant of the generator set; Generator inertia; is the speed reduction coefficient; is the turbine time coefficient; is the governor time coefficient; is the synchronous modulus between the tie lines; for The transpose of for The transpose of , means the neighbor set of the i-th discrete-time system model; is the load disturbance; for The derivative of .
S2、将连续时间系统状态空间模型离散化得到离散时间系统参数矩阵，并在Gossip协议下根据离散时间系统参数矩阵构建分布式控制器系统模型；在本实施例中选用的四区域电力系统框架图如图2所示，该系统由四个子区域组成，其中区域1与区域2存在互联，区域2与区域1和区域3存在互联，区域3与区域和区域4存在互联，区域4与区域3存在互联；在第i个区域中存在若干个个观测器观测该区域的系统输出，采集到的信息传输到分布式控制层的第i个控制器中，第i个控制器产生的控制信号作为控制输出传输给第i个区域，控制器和观测器之间的通信网络由Gossip协议调度。S2. Discretize the continuous-time system state space model to obtain the discrete-time system parameter matrix , and according to the discrete time system parameter matrix under the Gossip protocol Construct a distributed controller system model; the framework diagram of the four-area power system selected in this embodiment is shown in Figure 2, and the system consists of four sub-areas, among which area 1 is interconnected with area 2, area 2 is interconnected with area 1 and area 3, area 3 is interconnected with area 4, and area 4 is interconnected with area 3; in the i-th area, there are several observers to observe the system output of the area, and the collected information is transmitted to the i-th controller of the distributed control layer, and the control signal generated by the i-th controller is transmitted to the i-th area as the control output, and the communication network between the controller and the observer is scheduled by the Gossip protocol.
在步骤S2中，具体过程包括以下步骤：In step S2, the specific process includes the following steps:
S21、将连续时间系统状态空间模型离散化得到离散时间系统模型，其中离散时间系统模型为：S21. Discretize the continuous-time system state space model to obtain a discrete-time system model, wherein the discrete-time system model is:
； ;
其中，in,
； ;
其中，k代表离散时间系统模型的第k个采样时刻；、分别代表第i个离散时间系统模型的状态向量、控制输入和外部扰动；，意味着第i个离散时间系统模型的邻居集；为第i个子系统的邻居j的带时延项的状态；Where k represents the kth sampling moment of the discrete-time system model; , Represent the state vector, control input and external disturbance of the i-th discrete-time system model respectively; , means the neighbor set of the i-th discrete-time system model; is the delayed term of neighbor j of the ith subsystem Status;
S22、基于离散时间系统模型得到离散时间系统参数矩阵；根据离散时间系统模型即可得到参数矩阵。S22. Obtain discrete time system parameter matrix based on discrete time system model ; According to the discrete time system model, the parameter matrix can be obtained .
S23、在Gossip协议中引入随机变量，并构建基于观测器的分布式控制器，其中，，意味着第i个子控制器接收到来自第j个子控制器的状态向量和状态估计，其中，具体的，分布式控制器为：S23. Introducing random variables in the Gossip protocol , and construct an observer-based distributed controller, where , which means that the i-th sub-controller receives the state vector from the j-th sub-controller and state estimation ,in ,Specifically, the distributed controller is:
； ;
其中，，代表第i个分布式控制器的估计状态；矩阵表示观测器增益；矩阵表示控制器增益；；，表示第i个分布式控制器的测量输出；分别为系统方程的已知矩阵，来源于，代表第i个子系统，j代表第i个子系统的邻居j；为第i个子系统的邻居j的带时延项的状态估计；为i个子系统的邻居j的带时延项的测量输出。in, , represents the estimated state of the i-th distributed controller; the matrix represents the observer gain; the matrix represents the controller gain; ; , represents the measured output of the i-th distributed controller; are the known matrices of the system equations, derived from , represents the ith subsystem, j represents the neighbor j of the ith subsystem; is the delayed term of neighbor j of the ith subsystem state estimation; is the delayed term of neighbor j of subsystem i The measurement output.
S24、建立分布式控制器在Gossip协议中通信变量的概率分布，在Gossip协议中，每个子系统在某一时刻只能随机接收到它其中一个邻居传递的信息，因此通信变量需满足以下的概率分布：S24. Establish the probability distribution of communication variables of the distributed controller in the Gossip protocol. In the Gossip protocol, each subsystem can only randomly receive information transmitted by one of its neighbors at a certain time. Therefore, the communication variables must satisfy the following probability distribution:
； ;
其中，为通信概率；为随机变量的概率分布；为随机变量，为区别于；m为代表第i个子系统的邻居，为区别于j。in, is the communication probability; is a random variable The probability distribution of is a random variable, which is different from ; m represents the neighbor of the i-th subsystem, which is different from j.
S25、根据分布式控制器构建分布式控制系统模型，所构建的分布式控制系统模型为：S25. Construct a distributed control system model according to the distributed controller. The constructed distributed control system model is:
； ;
其中，k代表离散时间系统的第k个采样时刻；分别代表第i个分布式控制器的状态向量、控制输入、外部扰动、性能输出与测量输出；均为适当维数的实矩阵；，意味着第i个子系统的邻居集，代表的基数；，且，为常数。Where k represents the kth sampling moment of the discrete-time system; Represent the state vector, control input, external disturbance, performance output and measurement output of the i-th distributed controller respectively; are all real matrices of appropriate dimension; , which means the neighbor set of the ith subsystem, represent The cardinality of ,and , is a constant.
S3、基于分布式控制器的设计目标构建非线性矩阵不等式；其中，设计目标为使多区域电力系统满足在外部扰动下的指数稳定以及零初始条件下有限时间最小，设计目标为：S3. Construct nonlinear matrix inequalities based on the design objectives of distributed controllers; the design objective is to make the multi-regional power system meet the requirements of external disturbances. Exponential stability under zero initial conditions and finite time Minimum, design goals are:
； ;
其中，为干扰衰减水平指标；N为子控制器的数量；k为采样时刻；分别代表第i个分布式控制器的状态向量、外部扰动、性能输出；E为数学期望。in, is the interference attenuation level index; N is the number of sub-controllers; k is the sampling time; They represent the state vector, external disturbance and performance output of the i-th distributed controller respectively; E is the mathematical expectation.
本实例通过李雅普诺夫方程来证明多区域电力系统的稳定性与满足有限时间最小性能指标，李雅普诺夫方程为：This example uses the Lyapunov equation to prove the stability of the multi-regional power system and the finite time Minimum performance index , the Lyapunov equation is:
； ;
其中，，为的转置；均为正定矩阵；t和分别为延迟项的求和变量。in, , for The transpose of are all positive definite matrices; t and are the summation variables of the delayed terms, respectively.
控制器的非线性矩阵不等式为：The nonlinear matrix inequality of the controller is:
； ;
其中，in,
； ;
； ;
； ;
且需满足；And must meet ;
上式中，代表的基数；为通信概率；均为适当维数的实矩阵；为干扰衰减水平指标；均为正定的未知矩阵；为第个子系统第个邻居对的通信概率；分别为第个子系统对自己的控制增益和的第个邻居对的控制增益；分别为第个子系统对自己的观测增益和的第个邻居对的观测增益；为第个子系统第个邻居对的关联矩阵；为第个子系统第个邻居的关联矩阵；为单位阵；都为大于0的未知常数。In the above formula, represent The cardinality of is the communication probability; are all real matrices of appropriate dimension; It is the interference attenuation level indicator; All unknown matrices are positive definite; For the Subsystem Neighbors The communication probability of Respectively The control gain and No. Neighbors The control gain of Respectively The observation gain and No. Neighbors The observation gain of For the Subsystem Neighbors The correlation matrix of for Subsystem Neighbor's Correlation matrix; is the unit matrix; are all unknown constants greater than 0.
S4、通过Schur引理以及不等式放缩对非线性矩阵不等式解耦，得到只含耦合项通信概率的矩阵不等式；除了通信概率的耦合项，上述矩阵不等式还存在类似于的非线性项，针对于这种非线性项，在步骤S4中，具体为：S4. Decouple the nonlinear matrix inequality through Schur's lemma and inequality scaling to obtain the communication probability containing only the coupling term Matrix inequality of; except for the communication probability The above matrix inequality also has coupling terms similar to For this nonlinear term, in step S4, specifically:
采用Schur引理对非线性矩阵不等式左乘以及右乘它的转置，再利用两种不等式放缩可得到新的只含通信概率耦合项的矩阵不等式，即：Using Schur's lemma to multiply the nonlinear matrix inequality on the left and on the right by its transpose, and then scaling the two inequalities, we can get a new communication-only probability The matrix inequality of the coupling term is:
对得到的非线性矩阵不等式左乘：Multiply the resulting nonlinear matrix inequality on the left:
； ;
其中，为对角阵；为单位阵；均为正定矩阵；为子系统的邻居数；均为，代表零空间的基；、分别为表示乘以大矩阵里面项的部分以及乘以大矩阵里面项的部分；in, is a diagonal matrix; is the unit matrix; All are positive definite matrices; For subsystem The number of neighbors of Both , represents the basis of the null space; , They represent multiplication by the large matrix. The part of the term and multiplying by the large matrix Part of an item;
右乘它的转置：Right multiply by its transpose:
； ;
其中，为正定矩阵；为；in, is a positive definite matrix; for ;
利用两种不等式放缩得到新的只含通信概率耦合项的矩阵不等式，即：Using the two inequalities to scale up and down, we can get a new communication-only probability The matrix inequality of the coupling term is:
； ;
其中，in,
； ;
； ;
； ;
； ;
其中，in,
； ;
； ;
； ;
； ;
； ;
； ;
上式中，都为正定矩阵；都为维度合适的未知矩阵；分别为和的邻居j取子系统i的个邻居；为邻居j的邻居数；为子系统i的邻居数。In the above formula, are all positive definite matrices; are all unknown matrices of appropriate dimensions; They are and The neighbor j of subsystem i Neighbors; is the number of neighbors of neighbor j; is the number of neighbors of subsystem i.
S5、采用GA遗传算法和LMI线性矩阵不等式结合的求解算法得到最优的通信概率；针对于耦合项也就是通信概率的问题，本实施例采用了GA遗传算法，由于是概率问题，本实施例很好的将初始值控制在0到1之间，为后续运用GA遗传算法提供一个好的种群初始化范围，使得搜索空间更有效。S5. Use the GA genetic algorithm and LMI linear matrix inequality solution algorithm to obtain the optimal communication probability ; For the coupling term, that is, the communication probability To solve the problem, this embodiment adopts the GA genetic algorithm. Since it is a probability problem, this embodiment controls the initial value between 0 and 1 very well, providing a good population initialization range for the subsequent use of the GA genetic algorithm, making the search space more efficient.
作为步骤S5的优选实施方式，应用GA遗传算法与LMI线性矩阵不等式结合的求解算法得到最优的通信概率，请参照图3，为优化通信概率所用的GA遗传算法的执行流程图。具体过程包括以下步骤：As a preferred implementation of step S5, the optimal communication probability is obtained by applying a solution algorithm combining a GA genetic algorithm and an LMI linear matrix inequality. , please refer to Figure 3, to optimize the communication probability The execution flow chart of the GA genetic algorithm used. The specific process includes the following steps:
S51、根据概率属于[0,1]初始化范围随机生成初始种群；S51, randomly generate an initial population according to the probability of belonging to the initialization range [0,1];
S52、由于含有等式约束，引入动态惩罚函数，其中，，为迭代次数；S52, due to the equality constraints , introduce dynamic penalty function ,in, , is the number of iterations;
S53、利用LMI工具为每个个体求解线性矩阵不等式组，若有解则计算对应的适应度函数值；若无解则为该个体的适应度函数值赋一个足够大的值；考虑到步骤S52的等式约束以及动态惩罚函数，GA遗传算法的适应度函数表示为：S53, using the LMI tool to solve the linear matrix inequality group for each individual, if there is a solution, calculate the corresponding fitness function value; if there is no solution, assign a sufficiently large value to the fitness function value of the individual; considering the equality constraints of step S52 and the dynamic penalty function , the fitness function of GA genetic algorithm is expressed as:
； ;
其中，in,
； ;
； ;
其中，为转置。in, is transposed.
由于本实施例的目标是最小化干扰衰减水平指标，为了让适应度函数值大的解保留下来，本实施例选择的倒数来满足这种要求。Since the goal of this embodiment is to minimize the interference attenuation level index In order to keep the solution with large fitness function value, this embodiment selects to meet this requirement.
S54、执行选择、交叉、变异、精英保留GA操作进行迭代，若达到最大迭代次数则保存迭代过程中得到的最优个体，即为最优的通信概率；否则返回步骤S53。S54, perform selection, crossover, mutation, and elite retention GA operations for iteration. If the maximum number of iterations is reached, the optimal individual obtained during the iteration is saved, which is the optimal communication probability. ; Otherwise return to step S53.
在本实施例中，本发明中的基于Gossip协议优化通信概率的分布式控制器设计方法，通过将传统的LMI方法与GA遗传算法相结合，能够降低控制器设计过程中的保守性，同时有效提升系统性能；GA遗传算法的引入能够很好的处理控制器求解的充分条件中的非线性项，更有效地最小化干扰衰减水平指标，抑制干扰对系统的影响，从而提高系统性能。In this embodiment, the Gossip protocol based communication probability optimization in the present invention The distributed controller design method combines the traditional LMI method with the GA genetic algorithm to reduce the conservatism in the controller design process and effectively improve the system performance. The introduction of the GA genetic algorithm can well handle the nonlinear terms in the sufficient conditions for solving the controller and more effectively minimize the interference attenuation level index. , suppress the impact of interference on the system, thereby improving system performance.
S6、将得到的最优通信概率代入到分布式控制系统模型的矩阵不等式中用以稳定多区域电力系统。S6. The optimal communication probability obtained Substitute it into the matrix inequality of the distributed control system model to stabilize the multi-regional power system.
综上，执行GA遗传算法辅助优化通信概率设计算法中得到的适应度函数值，迭代曲线如图4所示，图中红色实线代表的是以往Gossip协议中子系统之间等概率通信所得到有限时间的性能指标，红色虚线代表的是GA遗传算法迭代过程中最优个体的值，蓝色实线代表GA遗传算法迭代过程中平均适应度值。本发明所提出的方法得到的求解值便明显低于现有技术求解值。In summary, the GA genetic algorithm is used to assist in optimizing the communication probability. The fitness function value obtained in the design algorithm and the iteration curve are shown in Figure 4. The red solid line in the figure represents the finite time obtained by the equal probability communication between subsystems in the previous Gossip protocol. Performance indicators The red dotted line represents the optimal individual in the GA genetic algorithm iteration process. The blue solid line represents the average fitness value during the iteration of the GA genetic algorithm. The solution value obtained by the method proposed in the present invention is significantly lower than the solution value of the prior art.
将优化后的通信概率应用于电力系统，系统的状态曲线如图5所示。图中的四个子图描述了电力系统四个子区域的四个状态分量的状态轨迹图，分别为区域1、区域2、区域3以及区域4。四个状态分量的状态分别为频率偏差、联络线功率偏差、发电机输出功率偏差、发电机阀门位置偏差。从图5中可以看到每个子区域的每个状态分量均能收敛，即在规定时间内（本实施例中为30秒）达到有限时间稳定的性能要求。The optimized communication probability Applied to the power system, the state curve of the system is shown in Figure 5. The four sub-graphs in the figure describe the state trajectory diagrams of the four state components of the four sub-areas of the power system, namely area 1, area 2, area 3 and area 4. The states of the four state components are frequency deviation , Interconnection line power deviation , Generator output power deviation , Generator valve position deviation It can be seen from FIG5 that each state component of each sub-region can converge, that is, the performance requirement of finite-time stability is achieved within a specified time (30 seconds in this embodiment).
本领域普通技术人员可以理解实现上述实施例方法中的全部或部分步骤是可以通过程序来指令相关的硬件来完成，因此，本申请可采用完全硬件实施例、完全软件实施例、或结合软件和硬件方面的实施例的形式。而且，本申请可采用在一个或多个其中包含有计算机可用程序代码的计算机可用存储介质(包括但不限于磁盘存储器、CD-ROM、光学存储器等)上实施的计算机程序产品的形式。Those skilled in the art can understand that all or part of the steps in the above-mentioned embodiment method can be completed by instructing the relevant hardware through a program, so the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.
本说明书中的各个实施例均采用递进的方式描述，每个实施例重点说明的都是与其他实施例的不同之处，各个实施例之间相同或相似的部分互相参见即可。对于以上各实施例而言，由于其与方法实施例基本相似，所以描述的比较简单，相关之处参见方法实施例的部分说明即可。Each embodiment in this specification is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the above embodiments, since they are basically similar to the method embodiments, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiments.
以上实施方式对本发明进行了详细介绍，本文中应用了具体个例对本发明的原理及实施方式进行了阐述，以上实施例的说明只是用于帮助理解本发明的方法及其核心思想；同时，对于本领域的一般技术人员，依据本发明的思想，在具体实施方式及应用范围上均会有改变之处，综上所述，本说明书内容不应理解为对本发明的限制。The above implementation methods have been described in detail. Specific examples are used herein to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.
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