Novel distributed state estimation method for the AC‐DC hybrid microgrid based on the Lagrangian relaxation method
2019; Institution of Engineering and Technology; Volume: 2019; Issue: 18 Linguagem: Inglês
10.1049/joe.2018.9329
ISSN2051-3305
AutoresPing Ling, Xiangrui Kong, Chen Fang, Zheng Yan,
Tópico(s)Islanding Detection in Power Systems
ResumoThe Journal of EngineeringVolume 2019, Issue 18 p. 4932-4936 The 7th International Conference on Renewable Power Generation (RPG 2018)Open Access Novel distributed state estimation method for the AC-DC hybrid microgrid based on the Lagrangian relaxation method Ling Ping, Ling Ping State Grid Shanghai Municipal Electric Power Company, Shanghai, People's Republic of ChinaSearch for more papers by this authorKong Xiangrui, Corresponding Author Kong Xiangrui xr_kong@sjtu.edu.cn Key Laboratory of Control of Power Transmision and Conversion (Department of Electrical Engineering, Shanghai Jiao Tong University), Ministry of Education, Shanghai, People's Republic of ChinaSearch for more papers by this authorFang Chen, Fang Chen State Grid Shanghai Municipal Electric Power Company, Shanghai, People's Republic of ChinaSearch for more papers by this authorYan Zheng, Yan Zheng Key Laboratory of Control of Power Transmision and Conversion (Department of Electrical Engineering, Shanghai Jiao Tong University), Ministry of Education, Shanghai, People's Republic of ChinaSearch for more papers by this author Ling Ping, Ling Ping State Grid Shanghai Municipal Electric Power Company, Shanghai, People's Republic of ChinaSearch for more papers by this authorKong Xiangrui, Corresponding Author Kong Xiangrui xr_kong@sjtu.edu.cn Key Laboratory of Control of Power Transmision and Conversion (Department of Electrical Engineering, Shanghai Jiao Tong University), Ministry of Education, Shanghai, People's Republic of ChinaSearch for more papers by this authorFang Chen, Fang Chen State Grid Shanghai Municipal Electric Power Company, Shanghai, People's Republic of ChinaSearch for more papers by this authorYan Zheng, Yan Zheng Key Laboratory of Control of Power Transmision and Conversion (Department of Electrical Engineering, Shanghai Jiao Tong University), Ministry of Education, Shanghai, People's Republic of ChinaSearch for more papers by this author First published: 04 June 2019 https://doi.org/10.1049/joe.2018.9329Citations: 5AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract The AC-DC hybrid microgrid is a credible evolution path for the microgrid. State estimation in complex distribution network is a significant foundation for the safe operation. In AC-DC hybrid microgrid, centralised state estimation algorithms have quite a few deficiencies such as large communication capacity and privacy protection. In response to these obstacles, this paper proposed a novel distributed state estimation algorithm. First, a three-stage state estimation model was established for AC-DC hybrid microgrid, in which the second stage is a nonlinear transform for the linearisation of the nonlinear state estimation progress so that the first and third stage can solve the linear state estimation problem. Furthermore, the Lagrangian relaxation method was ultilised for the distributed problem solution. In the proposed algorithm, AC subsystems and DC subsystems respectively execute state estimation through local information, and the overall consistency of the system state estimation can be eventually achieved according to the transfer iteration of the boundary information. The computational efficiency and convergence of the proposed method was ensured owing to the combination of bilinear theory and Lagrangian relaxation. Simulation results indicate that the proposed method can achieve its goal and be superior to existing method in efficiency. 1 Introduction 1.1 Motivations With the development of microgrid technology and renewable energy, AC/DC hybrid microgrid has aroused people's attention because it has the characteristics of the AC microgrid and DC microgrid at the same time: ① It includes an AC subsystem, a DC subsystem and an AC/DC converter (ILC). ② It can supply power to both AC and DC loads at the same time, reducing the power of electronic transformation and energy consumption. ③The power between AC and DC systems can flow bidirectionally [1-4]. The subsystems can also operate independently on the grid mode and islanding mode. Therefore, the AC/DC hybrid microgrid can more effectively integrate renewable generations, energy storage devices and various types of loads into the distribution network. However, the increasing penetration of distributed generations (DGs) brings uncertainty and noises to power grid operation, which enlarges the difficulty of distribution network monitoring. At present, there are many researches on the control and configuration of AC/DC hybrid microgrid [5, 6], but there are few researches on its state estimation. Moreover, most of them focus on centralised state estimation problem of the AC-DC hybrid microgrid, such as references [7, 8]. The centralised state estimator has the following disadvantages [9-11]: it needs to collect all the information in the system, calculate the state variables uniformly. Thus the high-dimensional calculation and large-scale communication traffic significantly reduce the computational efficiency. Furthermore, once the information data in one subsystem fails to be updated, the whole state estimation process will be interrupted immediately. So here are the critical questions: How to achieve meticulous monitoring for AC/DC hybrid microgrid with high penetration renewable energy integration? 1.2 Contributions In this paper, we propose a novel three-stage state estimation model of the AC-DC microgrid firstly and the decoupling of AC microgrid and DC microgrid state estimation is achieved via the utilisation of the Lagrangian relaxation algorithm. Then a distributed state estimation method is proposed for the AC/DC hybrid microgrid. Simulation results indicate that the proposed method can achieve its goal and be superior to the existing method in efficiency. 2 AC-DC hybrid microgrid structure Fig. 1 shows a typical AC-DC hybrid microgrid. In Fig. 1, the voltage converter achieves the connection of AC subsystem and DC subsystem for the coordinated operation between subsystems. Every subsystem in the hybrid microgrid has strong independence and autonomy. Moreover, Fig. 1 indicates the equivalent circuit of the voltage converter. Fig. 1Open in figure viewerPowerPoint AC and DC microgrid structure and the equivalent circuit of the voltage converter 2.1 Three-stage distributed state estimation method for AC-DC hybrid microgrid The AC/DC microgrid state estimation model in [12] is (1) In the equations, and are the state variables of the AC microgrid and the DC microgrid, and are the AC state estimation function and DC state estimation function, respectively. represents the active power flowing from the DC side to the AC side, and represents the active power flowing from the AC side to the DC side, is the transmission factor. The literature [12] assumes that the system measurement equation is linear, but generally speaking, the quantity measurement and state variables in the power system are nonlinear. Therefore, the state estimation model for AC-DC hybrid microgrid via the weighted least square algorithm is non-convex, and the distributed optimisation method is no longer applicable. Targeting the above obstacles, we propose a three-stage distributed state estimation method for the AC-DC hybrid microgrid. Then we utilise a Lagrangian relaxation method to decouple the AC and DC state estimation. 2.2 First-stage linear state estimation model In the proposed method, the first stage is the linear state estimation. Through the Lagrangian relaxation method, equality constraint in the centralised state estimation model is relaxed, so that the iterative update and the exchange of boundary variables between AC and DC microgrid can be achieved through the Lagrange multiplier. Thus, the purpose of the distributed solution is ultimately achieved. In the AC microgrid, state variables can be defined as (2) (3) As in (2) and (3), and indicate the voltage amplitude and phase angle of node i. The state variable consists of 、 and . The measurement can be linearly expressed by . For the reason that there is no node phase angle in the DC microgrid, the first-stage model can be described as (4) As in (4), and are the objective function through the weighted least square algorithm. The first-stage model is processed in Fig. 2. Fig. 2Open in figure viewerPowerPoint Demonstration of the first-stage centralized state estimation The Lagrange function can be constructed as follows for the above model： (5) (6) λ in (5) is the Lagrange multiplier, and it is updated via the second derivative algorithm. λ can achieve the coordination of and . Thus, the relaxation of the equation constraints can be ensured. In (6),ρ indicates the penalty factor. The solution steps of (4) are as follows: (7) (8) Equations (7) and (8) are the distributed state estimation process of the AC-DC hybrid microgrid in the first linear stage and k represents the number of iterations. The conditions for convergence are (9) Fig. 3 is a schematic diagram of the first-stage linear distributed state estimation implementation mechanism based on the Lagrangian relaxation method. Equations (7) and (8) are solved by the AC microgrid state estimator and the DC microgrid state estimator in parallel according to the local measurement and topology parameters, and the calculation results are transmitted to each other to finally satisfy the convergence condition. Fig. 3Open in figure viewerPowerPoint Mechanism of the first-stage centralized state estimation 2.3 Non-linear transformation stage of the intermediate variables The intermediate variable u can be split into the AC part and the DC part. In (10)–(12), represents the intermediate variables of the AC subsystem and represents the intermediate variables of the DC subsystem. (10) (11) (12) The second stage is the non-linear transformation stage of intermediate variables. According to the results of the first stage, the intermediate variables of the AC-DC microgrid are achieved through the nonlinear function (13) and (14): (13) (14) 2.4 Third-stage distributed state estimation In the AC subsystem, can make linearly expressed as: . Similarly, of the DC subsystem can be associated with elements from . Define variables and , where . Expand to , then can be linearly represented by . (15) (16) The detailed expression of can be shown as (17) In (18) and (19), the sub-objective functions for the state estimation of AC and DC subsystems are defined. In (20), the third stage system state estimation model is expressed as the equivalent problem. Wherein, the overlap between the AC and DC state variables can be included as the form of an equality constraint. (18) (19) (20) It is not difficult to find that the first and third phase state estimation models are similar to each other. Therefore, in this stage, the same principle as the first stage can be utilised. The specific solution process is as follows: (21) (22) (23) (24) The final iteration convergence condition can be set as follows: (25) It can be found that the AC and DC subsystem state estimator estimate the state of the subsystem according to (21) and (22), and transfer the boundary values and to each other. Through (23) and (24), the iterative multipliers can be updated, and so on until it converges. The flow chart of the proposed method is shown in Fig. 4. Fig. 4Open in figure viewerPowerPoint Flow chart of the proposed method The state estimation processes are in the first and third phases. The decoupling for AC-DC subsystem is achieved through the Lagrangian relaxation method, enabling a distributed solution for system state estimation. The second phase is a nonlinear transformation, in which the AC-DC subsystem calculates the value of the intermediate variable of the subsystem based on the result of the first stage, and utilises it as the equivalent measurement of the third level of the subsystem. 3 Simulations and results This article uses the AC-DC microgrid in the literature [12] as a simulation system, as shown in Fig. 5. The AC/DC microgrid is a 5-node system, and the #1 DC node is connected to the #5 AC node. Measured values are obtained by superimposing random normal distribution errors on the basis of load flow calculations. DC side measurements include: voltage amplitude measurement at node 1-5 (standard deviation 0.2%); pseudo measurement of injection power at node 1-5 (standard deviation 2%); the current amplitude measurement (standard deviation 0.3%) of lines from node 1-2 and node 1-3. AC side measurement includes: measurement of voltage amplitude at node 1-5 (standard deviation is 0.2%); pseudo-measurement of injection power at node 1-5 (standard deviation is 2%); current amplitude measurement (standard deviation 0.3%) of lines from node 3-5 and node 2-4. In the case of non-special instructions, shall be 20 and . The simulation results were obtained on a desktop computer with an Intel dual-core 2.4 GHz CPU and 2G memory. The optimisation problem solutions were obtained by calling CPLEX with Matlab. Fig. 5Open in figure viewerPowerPoint AC/DC microgrid simulation system In order to verify the accuracy of the proposed three-stage state estimation model, the direct solution of (1) is compared with the results obtained by the proposed method. From Table 1, it can be found that there is a certain error between the proposed method and the direct solution of (1), but the error is minimal and can be ignored in practical applications. Table 1. Accuracy of the proposed state estimation method State variables AC voltage amplitude AC phase angel DC voltage amplitude Error (%) 6.7007e−03 1.1958e−02 3.1524e−03 Next, the simulation analysis of the distributed state estimation algorithm for the first linear stage is emphasised. Fig. 6 shows the iterative process of medium-size constraints of (4) while takes {10,20,30,40,50}. It can be seen from Fig. 6 that through the iterative solution between the AC and DC microgrids, eventually tend to 0 and the equality constraints are satisfied. The results in Fig. 6 and Table 2 show that the proposed method has promising convergence. Fig. 6Open in figure viewerPowerPoint Iteration analysis of the first-stage equation constrains Table 2. Convergence analysis of the proposed method Convergence times 10 26 33 40 20 13 18 23 30 8 11 14 40 5 7 9 50 3 4 5 Moreover, the comparison with existing method indicates that the proposed distributed state estimation method performs better in execution time (Table 3). Table 3. Comparison of execution time Execution time/s 10 20 30 40 50 existing method 7.27646 9.42179 7.56370 7.03978 6.31972 proposed method 6.19880 4.18020 2.47991 2.32335 1.41185 4 Conclusions This paper presents a distributed state estimation method for AC-DC microgrids. The method is divided into three stages: the first stage is a linear state estimation process. The Lagrange relaxation method is used to relax the equality constraints in the centralised state estimation model. By the exchange of the Lagrange multipliers and the exchange of boundary variables between the AC and DC microgrids will eventually achieve the purpose of a distributed solution. The second stage is the nonlinear transformation of intermediate variables, and the AC-DC microgrid obtains intermediate variables through nonlinear functions according to the results of the first phase. The third linear stage takes the intermediate variable resulted from the second stage as an equivalent measure. The AC-DC microgrid establishes the weighted least squares model and calculates the state variables of each node. This process is also calculated by the AC-DC microgrid in parallel. The proposed distributed state estimation method does not require an intermediate coordination mechanism compared to the centralised algorithm. The AC-DC subsystem only needs to pass the boundary information to each other and update the Lagrangian multiplier according to the interaction information. 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