ISSN 2196-5625 CN 32-1884/TK
Kafeel Ahmed , Mehdi Seyedmahmoudian , Saad Mekhilef , N. M. Mubarak , Alex Stojcevski
2021, 9(5):969-985. DOI: 10.35833/MPCE.2020.000068
Abstract:The demand of electricity and environmental issues associated with conventional power generation plants are increasing significantly. Modern technology has transformed the conventional power system through the integration of distributed generation (DG). With the help of modern power electronic technology, the conventional power system is able to support the integration of DGs based on renewable energy sources (RESs). The systematic combination of DGs with energy storage system forms a microgrid (MG), which can operate in islanded mode or grid-connected mode. The intermittent nature of RES and varying load pose substantial obstacles such as voltage and frequency instability, and the unreliability of RES. Unequal feeder impedances and non-linear loads are considered as present challenges in MG control. Hierarchical control has been useful in undertaking solutions to these issues. This paper covers the deep insight of different control methods applied at the primary and secondary control levels in hierarchical control. In primary control, the classification based on droop and non-droop controls is discussed. The virtual synchronization machine (VSM) based control method is reviewed. Voltage and frequency restoration control and economical operations at decentralized and centralized secondary control are analyzed in detail. Based on the existing literature, critical discussion on MG control and future trends are also presented to provide future research perspectives.
2021, 9(5):986-999. DOI: 10.35833/MPCE.2020.000312
Abstract:Addressed to the
2021, 9(5):1000-1006. DOI: 10.35833/MPCE.2020.000129
Abstract:Volt/var optimization (VVO) is a control function that is employed in distribution systems to keep the load voltages within the standard limits, and it includes secondary objectives such as loss minimization. The power flow based VVO is the way of choice in practical applications because it can handle a variety of objective functions and provides a solution even for large-scale network instances. This paper extends the power flow based VVO to account for uncertainty in both the load values and the power generation from photovoltaic sources. The proposed method employs circular arithmetic in complex variables to compute VVO settings that guard against load uncertainty and an optimized linear decision rule that modulates the reactive power of photovoltaic inverter in function of its active power. Finally, the proposed method is tested on distribution networks with up to 3146 nodes and is shown to produce optimal solutions that are robust against power variations.
Zhihang Zhou , Libao Shi , Yixuan Chen
2021, 9(5):1007-1017. DOI: 10.35833/MPCE.2020.000374
Abstract:This paper proposes an optimal over-frequency generator tripping strategy aiming at implementing the least amount of generator tripping for the regional power grid with high penetration level of wind/photovoltaic (PV), to handle the over-frequency problem in the sending-end power grid under large disturbances. A steady-state frequency abnormal index is defined to measure the degrees of generator over-tripping and under-tripping, and a transient frequency abnormal index is presented to assess the system abnormal frequency effect during the transient process, which reflects the frequency security margin during the generator tripping process. The scenario-based analysis method combined with the non-parametric kernel density estimation method is applied to model the uncertainty of the outgoing power caused by the stochastic fluctuations of wind/PV power and loads. Furthermore, an improved fireworks algorithm is utilized for the solution of the proposed optimization model. Finally, the simulations are performed on a real-sized regional power grid in Southern China to verify the effectiveness and adaptability of the proposed model and method.
Yaping Deng , Xinghua Liu , Rong Jia , Qi Huang , Gaoxi Xiao , Peng Wang
2021, 9(5):1018-1031. DOI: 10.35833/MPCE.2020.000528
Abstract:Accurate sag source location and precise sag type recognition are both essential to verifying the responsible party for the sag and taking countermeasures to improve power quality. In this paper, an attention-based independently recurrent neural network (IndRNN) for sag source location and sag type recognition in sparsely monitored power system is proposed. Specially, the given inputs are voltage waveforms collected by limited meters in sparsely monitored power system, and the desired outputs simultaneously contain the following information: the located lines where sag occurs; the corresponding sag types, including motor starting, transformer energizing and short circuit; and the fault phase for short circuit. In essence, the responsibility of the proposed method is to automatically establish a nonlinear function that relates the given inputs to the desired outputs with categorization labels as few as possible. A favorable feature of the proposed method is that it can be realized without system parameters or models. The proposed method is validated by IEEE 30-bus system and a real 134-bus system. Experimental results demonstrate that the accuracy of sag source location is higher than 99% for all lines, and the accuracy of sag type recognition is also higher than 99% for various sag sources including motor starting, transformer energizing and 7 different types of short circuits. Furthermore, a comparison among different monitor placements for the proposed method is conducted, which illustrates that the observability of power networks should be ensured to achieve satisfactory performance.
Jigneshkumar P. Desai , Vijay H. Makwana
2021, 9(5):1032-1042. DOI: 10.35833/MPCE.2020.000277
Abstract:The existing out-of-step (OOS) protection schemes have proven to be deficient in the prevention of significant outages. OOS protection schemes must not operate in stable power swing, and rapidly isolate an asynchronous generator or group of generators from the rest of the power system in case of unstable power swing. The paper proposes a novel phasor measurement unit (PMU) incorporating a polygon-shaped graphical algorithm for OOS protection of the synchronous generator. The unique PMU-based logic works further to classify the type of swing once the graphical scheme detects it, which can identify the complex power swing produced in the modern power system. The proposed algorithm can take the correct relaying decision in the event of power swing due to renewable energy integration, load encroachment, and transient faults. In this paper, the original and modified Kundur two-area system with a power system stabilizer (PSS) is used to test the proposed algorithm. In the end, it provides assessment results of the proposed relay on the Indian power system during the blackout in July 2012. The results demonstrate that the proposed algorithm is fast, accurate, and adaptive in the modern power system and shows better performance than the existing OOS protection schemes.
Guanyu Tian , Yingzhong Gu , Di Shi , Jing Fu , Zhe Yu , Qun Zhou
2021, 9(5):1043-1053. DOI: 10.35833/MPCE.2020.000362
Abstract:This paper proposes a neural-network-based state estimation (NNSE) method that aims to achieve higher time efficiency, improved robustness against noise, and extended observability when compared with the conventional weighted least squares (WLS) state estimation method. NNSE consists of two parts, the linear state estimation neural network (LSE-net) and the unobservable state estimation neural network (USE-net). The LSE-net functions as an adaptive approximator of linear state estimation (LSE) equations to estimate the nominally observable states. The inputs of LSE-net are the vectors of synchrophasors while the outputs are the estimated states. The USE-net operates as the complementary estimator on the nominally unobservable states. The inputs are the estimated observable states from LSE-net while the outputs are the estimation of nominally unobservable states. USE-net is trained off-line to approximate the veiled relationship between observable states and unobservable states. Two test cases are conducted to validate the performance of the proposed approach. The first case, which is based on the IEEE 118-bus system, shows the comprehensive performance of convergence, accuracy, and robustness of the proposed approach. The second case study adopts real-world synchrophasor measurements, and is based on the Jiangsu power grid, which is one of the largest provincial power systems in China.
Mohammad Kamruzzaman Khan Prince , Graduate , Mohammad T. Arif , Ameen Gargoom , Aman M. T. Oo , Md Enamul Haque
2021, 9(5):1054-1065. DOI: 10.35833/MPCE.2020.000601
Abstract:The design of reliable controllers for wind energy conversion systems (WECSs) requires a dynamic model and accurate parameters of the wind generator. In this paper, a dynamic model and the parameter measurement and control of a direct-drive variable-speed WECS with a permanent magnet synchronous generator (PMSG) are presented. An experimental method is developed for measuring the key parameters of the PMSG. The measured parameters are used in the design of the controllers. The generator-side converter is controlled using a vector control scheme that maximizes the power extraction under varying wind speeds. A model predictive controller (MPC) is designed for the grid-side voltage source converter (VSC) to regulate the active and reactive power flows to the power grid by controlling the d- and q-axis currents in the synchronous reference frame. The MPC predicts the future values of the control variables and takes control actions based on the minimum value of the cost functions. To comply with the grid code requirement, a modified design approach for an
Xue Lyu , Youwei Jia , Zhaoyang Dong
2021, 9(5):1066-1075. DOI: 10.35833/MPCE.2020.000237
Abstract:With the increasing share of wind power, it is expected that wind turbines would provide frequency regulation ancillary service. However, the complex wake effect intensifies the difficulty in controlling wind turbines and evaluating the frequency regulation potential from the wind farm. We propose a novel frequency control scheme for doubly-fed induction generator (DFIG)-based wind turbines, in which the wake effect is considered. The proposed control scheme is developed by incorporating the virtual inertia control and primary frequency control in a holistic way. To facilitate frequency regulation in time-varying operation status, the control gains are adaptively adjusted according to wind turbine operation status in the proposed controller. Besides, different kinds of power reserve control approaches are explicitly investigated. Finally, extensive case studies are conducted and simulation results verify that the frequency behavior is significantly improved via the proposed control scheme.
Pengwei Chen , Chenchen Qi , Xin Chen
2021, 9(5):1076-1087. DOI: 10.35833/MPCE.2020.000908
Abstract:With the increasing penetration of wind power, using wind turbines to participate in the frequency regulation to support power system has become a clear consensus. To accurately quantify the inertia provided by the doubly-fed induction generator (DFIG) based wind farm, the frequency response model of DFIG with additional frequency control is established, and then by using Routh approximation, the explicit expression of the virtual moment of inertia is derived for the DFIG grid-connected system. To further enhance the availability of the expression, an estimation method is proposed based on the matrix pencil method and the least squares algorithm for estimating the virtual moment of inertia provided by the wind farm. Finally, numerical results tested by a DFIG grid-connected system and a modified IEEE 30-bus system verify the derived expression of the virtual moment of inertia and the proposed estimation method.
Yixin Huang , Zhenzhi Lin , Xinyi Liu , Li Yang , Yangqing Dan , Yanwei Zhu , Yi Ding , Qin Wang
2021, 9(5):1088-1100. DOI: 10.35833/MPCE.2020.000335
Abstract:Due to the uncertainty and fluctuation of distributed generation (DG) and load, the operation of active distribution network (ADN) is affected by multi-dimension factors which are described by massive operation scenarios. Efficient and accurate screening of severely restricted scenarios (SRSs) has become a new challenge in ADN planning. In this paper, a novel bi-level coordinated planning model which combines the short-time-scale operation problem with the long-time-scale planning problem is proposed. At the upper level, the demand response (DR) resource, an effective non-component planning resource characterized by low capacity price, high energy price, and short contract term, is co-optimized with the configuration of lines and energy storage systems (ESSs) to achieve the economic trade-off between the investment cost and the operation cost under SRSs. At the lower level, with the planning scheme obtained from the upper level, massive operation problems are optimized to minimize the daily operation cost; and the SRSs are provided to the upper level through a shadow-price-based scenario screening method, which simulates the planning information (i.e., the restricted degrees of operation scenarios) feedback process from ADN operators to ADN planners. Case studies on a 62-node distribution system in Jianshan New District, Zhejiang Province, China, illustrate the effectiveness of the proposed bi-level coordinated planning model considering DR resources and SRSs.
Di Cao , Weihao Hu , Xiao Xu , Qiuwei Wu , Qi Huang , Zhe Chen , Frede Blaabjerg
2021, 9(5):1101-1110. DOI: 10.35833/MPCE.2020.000557
Abstract:This study proposes a deep reinforcement learning (DRL) based approach to analyze the optimal power flow (OPF) of distribution networks (DNs) embedded with renewable energy and storage devices. First, the OPF of the DN is formulated as a stochastic nonlinear programming problem. Then, the multi-period nonlinear programming decision problem is formulated as a Markov decision process (MDP), which is composed of multiple single-time-step sub-problems. Subsequently, the state-of-the-art DRL algorithm, i.e., proximal policy optimization (PPO), is used to solve the MDP sequentially considering the impact on the future. Neural networks are used to extract operation knowledge from historical data offline and provide online decisions according to the real-time state of the DN. The proposed approach fully exploits the historical data and reduces the influence of the prediction error on the optimization results. The proposed real-time control strategy can provide more flexible decisions and achieve better performance than the pre-determined ones. Comparative results demonstrate the effectiveness of the proposed approach.
Lu Shen , Xiaobo Dou , Huan Long , Chen Li , Ji Zhou , Kang Chen
2021, 9(5):1111-1120. DOI: 10.35833/MPCE.2019.000582
Abstract:With the increasing penetration of renewable energy generation, uncertainty and randomness pose great challenges for optimal dispatching in distribution networks. We propose a cloud-edge cooperative dispatching (CECD) method to exploit the new opportunities offered by Internet of Things (IoT) technology. To alleviate the huge pressure on the modeling and computing of large-scale distribution system, the method deploys edge nodes in small-scale transformer areas in which robust optimization subproblem models are introduced to address the photovoltaic (PV) uncertainty. Considering the limited communication and computing capabilities of the edge nodes, the cloud center in the distribution automation system (DAS) establishes a utility grid master problem model that enforces the consistency between the solution at each edge node with the utility grid based on the alternating direction method of multipliers (ADMM). Furthermore, the voltage constraint derived from the linear power flow equations is adopted for enhancing the operation security of the distribution network. We perform a cloud-edge system simulation of the proposed CECD method and demonstrate a dispatching application. The case study is carried out on a modified 33-node system to verify the remarkable performance of the proposed model and method.
Himan Hamedi , Vahid Talavat , Ali Tofighi , Reza Ghanizadeh
2021, 9(5):1121-1129. DOI: 10.35833/MPCE.2020.000415
Abstract:This paper presents a risk-based competitive bi-level framework for optimal decision-making in energy sales by a distribution company (DISCO) in an active distribution network (ADN). At the upper level of this framework, the DISCO and a rival retailer compete for selling energy. The DISCO intends to maximize its profit in the competitive market. Therefore, it is very important for the DISCO to make a decision and offer an optimal price for attracting customers and winning the competition. Networked microgrids (MGs) at the lower level, as the costumers, intend to purchase energy from less expensive sources in order to minimize costs. There is a bi-level framework with two different targets. The genetic algorithm is used to solve this problem. The DISCO needs to be cautious, so it uses the conditional value at risk (CVaR) to reduce the risk and increase the probability of making the desired profit. The effect of this index on the trade between the two levels is studied. The simulation results show that the proposed method can reduce the cost of MGs as the costumers, and can enable the DISCO as the seller to win the competition with its rivals.
2021, 9(5):1130-1136. DOI: 10.35833/MPCE.2019.000246
Abstract:Enhancing distribution system resilience is a new challenge for researchers. Supplying distribution loads, especially the residential customers and high-priority loads after disasters, is vital for this purpose. In this paper, the internal combustion engine (ICE) vehicles are firstly introduced as valuable backup energy sources in the aftermath of disasters and the use of this technology is explained. Then, the improvement of distribution system resilience is investigated through supplying smart residential customers and injecting extra power to the main grid. In this method, it is assumed that the infrastructure of distribution system is partially damaged (common cases) and it can be restored in less than one day. The extra power of residential customer can be delivered to other loads. A novel formulation for increasing the injected power of the smart home to the main grid using ICE vehicles is proposed. Moreover, the maximum backup duration in case of extensive damages in the distribution system is calculated for some commercial ICE vehicles. In this case, the smart home cannot deliver extra energy to the main grid because of its survivability. Simulation results demonstrate the effectiveness of the proposed method for increasing backup power during power outages. It is also shown that ICE vehicles can supply residential customers for a reasonable amount of time during a power outage.
Shu Zhang , Tianlei Zang , Wenhai Zhang , Xianyong Xiao
2021, 9(5):1137-1148. DOI: 10.35833/MPCE.2020.000466
Abstract:Secondary earth faults occur frequently in power distribution networks under harsh weather conditions. Owing to its characteristics, a secondary earth fault is typically hidden within the transient of the first fault. Therefore, most researchers tend to focus on a feeder with single fault while disregarding secondary faults. This paper presents a fault feeder identification method that considers secondary earth faults in a non-effectively grounded distribution network. First, the wavelet singular entropy method is used to detect a secondary fault event. This method can identify the moment at which a secondary fault occurs. The zero-sequence current data can be categorized into two fault stages. The first and second fault stages correspond to the first and secondary faults, respectively. Subsequently, a similarity matrix containing the time-frequency transient information of the zero-sequence current at the two fault stages is defined to identify the fault feeders. Finally, to confirm the effectiveness and reliability of the proposed method, we conduct simulation experiments and an adaptability analysis based on an electromagnetic transient program.
Zehuai Liu , Siliang Liu , Qinhao Li , Yongjun Zhang , Wenyang Deng , Lai Zhou
2021, 9(5):1149-1160. DOI: 10.35833/MPCE.2020.000108
Abstract:Due to the lack of support from the main grid, the intermittency of renewable energy sources (RESs) and the fluctuation of load will derive uncertainties to the operation of islanded microgrids (IMGs). It is crucial to allocate appropriate reserve capacity for the economic and reliable operation of IMGs. With the high penetration of RESs, it faces both economic and environmental challenges if we only use spinning reserve for reserve support. To solve these problems, a multi-type reserve scheme for IMGs is proposed according to different operation characteristics of generation, load, and storage. The operation risk due to reserve shortage is modeled by the conditional value-at-risk (CVaR) method. The correlation of input variables is considered for the forecasting error modeling of RES and load, and Latin hypercube sampling (LHS) is adopted to generate the random scenarios of the forecasting error, so as to avoid the dimension disaster caused by conventional large-scale scenario sampling approaches. Furthermore, an optimal day-ahead scheduling model of joint energy and reserve considering risk-based reserve decision is established to coordinate the security and economy of the operation of IMGs. Finally, the comparison of numerical results of different schemes demonstrate the rationality and effectiveness of the proposed scheme and model.
Attique Ur Rehman , Tek Tjing Lie , Brice Vallès , Shafiqur Rahman Tito
2021, 9(5):1161-1171. DOI: 10.35833/MPCE.2020.000741
Abstract:Recent advancement in computational capabilities has accelerated the research and development of non-intrusive load disaggregation. Non-intrusive load monitoring (NILM) offers many promising applications in the context of energy efficiency and conservation. Load classification is a key component of NILM that relies on different artificial intelligence techniques, e.g., machine learning. This study employs different machine learning models for load classification and presents a comprehensive performance evaluation of the employed models along with their comparative analysis. Moreover, this study also analyzes the role of input feature space dimensionality in the context of classification performance. For the above purposes, an event-based NILM methodology is presented and comprehensive digital simulation studies are carried out on a low sampling real-world electricity load acquired from four different households. Based on the presented analysis, it is concluded that the presented methodology yields promising results and the employed machine learning models generalize well for the invisible diverse testing data. The multi-layer perceptron learning model based on the neural network approach emerges as the most promising classifier. Furthermore, it is also noted that it significantly facilitates the classification performance by reducing the input feature space dimensionality.
2021, 9(5):1172-1182. DOI: 10.35833/MPCE.2020.000317
Abstract:Demand response (DR) is a flexible way to improve distributed energy resource scheduling. The innovative contribution of this paper is to include complex contracts in the model, which can accommodate the constraints according to the special expectations of each player. Such contracts are included in the optimization of distributed energy resource scheduling to dispatch DR according to the expectations of consumers. Multi-period DR events are considered. In this way, consumers can specify the limits on the time, power, and remuneration regarding participation in DR events, which has not been considered in the literature. The state of the art treats these aspects separately or uses a statistical approach, without providing consumers with options to combine their preferences regarding different aspects of their flexibility deployment. The model has been validated for 218 consumers using several scenarios and different types of distributed generation, showing that it is possible to increase DR with respect to the preferences of consumers.
2021, 9(5):1183-1192. DOI: 10.35833/MPCE.2019.000258
Abstract:In a grid-integrated photovoltaic system (GIPVS), there exist issues such as surplus active power and inadequate performance of maximum power point tracking (MPPT). A surplus active power causes the overvoltage problem at the point of common coupling in low- or medium-voltage grid during the peak hours of power generation. Additionally, the inadequate performance of the MPPT algorithm results in power loss due to high settling time during the sudden change of irradiance. Therefore, to solve the surplus power problem, the curtailment of active power is suggested with improved MPPT algorithm under variable irradiance conditions. In this paper, a derated power generation mode (DPGM) control strategy is presented for the curtailment of active power. Additionally, a drift-free (named as modified) perturb and observe (P&O) technique is also proposed to improve the performance of the MPPT algorithm. Consequently, the DPGM control scheme with the intermediate boost converter shaves the surplus active power during the peak hours of power generation. Furthermore, the modified MPPT algorithm deals with the fluctuation of irradiance during non-peak hours. Thus, the proposed control scheme delivers in a more efficient system during the peak hours of power generation. In addition, it reduces the power loss and settling time during the change of irradiance for non-peak hours. Based on the proposed control scheme, a 30 kW system has been simulated in MATLAB/Simulink using Simpower tools under different environmental conditions.
Samaa Fawzy , Mohammed Saeed , Abdelfattah Eladl , Magdi El-Saadawi
2021, 9(5):1193-1204. DOI: 10.35833/MPCE.2019.000170
Abstract:This paper presents an adaptive control system using model predictive control for a biogas-fueled power system. The control scheme is derived from an anaerobic digestion model that includes the concentration of biodegradable volatile solid in the reactor, the concentration of volatile solid in influent, the concentration of acidogens, and the concentration of methanogens. All these concentrations are the state variables of model predictive control. The whole biogas-fueled power system has been modeled, implemented, and tested in MATLAB/Simulink environment. To validate the performance of the proposed controller, different operation conditions are studied and analyzed. The simulation results prove the effectiveness and the applicability of the proposed control system under different operating conditions.
Huayanran Zhou , Yihong Zhou , Junjie Hu , Guangya Yang , Dongliang Xie , Yusheng Xue , Lars Nordström
2021, 9(5):1205-1216. DOI: 10.35833/MPCE.2020.000501
Abstract:As typical prosumers, commercial buildings equipped with electric vehicle (EV) charging piles and solar photovoltaic panels require an effective energy management method. However, the conventional optimization-model-based building energy management system faces significant challenges regarding prediction and calculation in online execution. To address this issue, a long short-term memory (LSTM) recurrent neural network (RNN) based machine learning algorithm is proposed in this paper to schedule the charging and discharging of numerous EVs in commercial-building prosumers. Under the proposed system control structure, the LSTM algorithm can be separated into offline and online stages. At the offline stage, the LSTM is used to map states (inputs) to decisions (outputs) based on the network training. At the online stage, once the current state is input, the LSTM can quickly generate a solution without any additional prediction. A preliminary data processing rule and an additional output filtering procedure are designed to improve the decision performance of LSTM network. The simulation results demonstrate that the LSTM algorithm can generate near-optimal solutions in milliseconds and significantly reduce the prediction and calculation pressures compared with the conventional optimization algorithm.
Jianshe Feng , Xiaodong Jia , Haoshu Cai , Feng Zhu , Xiang Li , Jay Lee
2021, 9(5):1217-1226. DOI: 10.35833/MPCE.2019.000142
Abstract:Accurate battery capacity prediction is important to ensure reliable battery operation and reduce the cost. However, the complex nature of battery degradation and the presence of capacity regeneration phenomenon render the prediction task very challenging. To address this problem, this paper proposes a novel and efficient algorithm to predict the battery capacity trajectory in a multi-cell setting. The proposed method is a new variant of Gaussian process regression (GPR) model, and it utilizes similar trajectories in the historical data to enhance the prediction of desired capacity trajectory. More importantly, the proposed method adds no extra computation cost to the standard GPR. To demonstrate the effectiveness of the proposed method, validation tests on two different battery datasets are implemented in the case studies. The prediction results and the computation cost are carefully benchmarked with cutting-edge GPR approaches for battery capacity prediction.
Chenjia Feng , Chengcheng Shao , Xifan Wang , Life
2021, 9(5):1227-1232. DOI: 10.35833/MPCE.2019.000212
Abstract:Economic dispatch (ED) aims to minimize the generation cost subject to power balance constraints. It is extensively used in power system operation and planning. ED problem as well as other problems with the same formulation are named as ED-type problems in this letter and a fast solution method is provided. The proposed method is achieved by solving a series of relaxed problems. With a closed-form solution for the relaxed ED-type problems, it is demonstrated that the proposed method consumes far less computing time and memory space than the off-the-shelf solvers and other quadratic programming (QP) methods. Finally, the effectiveness and computational efficiency of the proposed method are verified by the case studies, which shows the great potential in power system planning and operation.
Guanzhong Wang , Zhiyi Li , Feng Zhang , Ping Ju , Hao Wu , Changsen Feng
2021, 9(5):1233-1236. DOI: 10.35833/MPCE.2019.000106
Abstract:In this letter, a new formulation of Lebesgue integration is used to evaluate the probabilistic static security of power system operation with uncertain renewable energy generation. The risk of power flow solutions violating any pre-defined operation security limits is obtained by integrating a semi-algebraic set composed of polynomials. With the high-order moments of historical data of renewable energy generation, the integration is reformulated as a generalized moment problem which is then relaxed to a semi-definite program (SDP). Finally, the effectiveness of the proposed method is verified by numerical examples.
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