A Robust Decentralized Load Frequency Controller for Interconnected Power Systems

A novel design of a robust decentralized load frequency control (LFC) algorithm is proposed for an inter-connected three-area power system, for the purpose of regulating area control error (ACE) in the presence of system uncertainties and external disturbances. The design is based on the concept of active disturbance rejection control (ADRC). Estimating and mitigating the total effect of various uncertainties in real time, ADRC is particularly effective against a wide range of parameter variations, model uncertainties, and large disturbances. Furthermore, with only two tuning parameters, the controller provides a simple and easy-to-use solution to complex engineering problems in practice. Here, an ADRC-based LFC solution is developed for systems with turbines of various types, such as non-reheat, reheat, and hydraulic. The simulation results verified the effectiveness of the ADRC, in comparison with an existing PI-type controller tuned via genetic algorithm linear matrix inequalities (GALMIs). The comparison results show the superiority of the proposed solution. Moreover, the stability and robustness of the closed-loop system is studied using frequency-domain analysis

인공신경망 발전량 예측 불확실성을 고려한 가상발전소 모델예측제어

학위논문(박사) -- 서울대학교대학원 : 공과대학 기계공학부, 2022.2. 차석원.This study presents statistical and control analyses for grid resources to enhance the stability and efficiency on their operations. More specifically, this study focuses on cost-optimal model predictive control for a virtual power plant with the uncertainty in neural network power forecasting. Chapter 2 analyzes the monitoring data of solar photovoltaic power plants (PVs) distributed throughout Korea. Errors within the raw data are categorized according to their causes and symptoms. The effect of typical errors on the statistical analysis is particularly evaluated for a day-ahead hourly PV power forecast study. Chapter 3 addresses a control strategy for an energy storage system (ESS). A virtual power plant or a microgrid with a commercial building load, PV generation, and ESS charge/discharge operation is targeted as a behind-the-meter consumer-generator. Economic dispatch scheduling problem for the ESS is formulated as a mixed-integer linear program. The main goal of the control problem is optimizing the economic benefit under the time-of-use tariff and future uncertainties. Peak control as a regulation ancillary market service can be also applied during the optimization. The resulting control schedule robustly guarantees the economic benefit even under the forecast uncertainties in load power consumption and PV power generation patterns. Chapter 4 presents a more specific case of day-ahead hourly ESS scheduling. An integration of a PV and ESS is considered as a control target. Power transactions between the grid and resources are normally settled according to the time-of-use tariff. Additional incentive is provided with respect to the imbalance between the forecasted-scheduled power and actual dispatch power. This incentive policy stands for the imbalance tariff of a regulation ancillary service market. Accurate forecasting and robust scheduling functions are required for the energy management system to maximize both revenues. The PV power forecast model, which is based on a recurrent neural network, uses a convolutional neural network discriminator to decrease the gap between its open-loop one-step-ahead training and closed-loop multi-step-ahead test dynamics. This generative adversarial network concept for the model training process ensures a stable day-ahead hourly forecast performance. The robust ESS scheduling model handles the remaining forecast error as a box uncertainty set to consider the cost-optimality and cost-robustness of the control schedule. The scheduling model is formulated as a concise mixed-integer linear program to enable fast online optimization with the consideration for both transaction and incentive revenues.본 논문에서는 전력망 내 에너지자원들의 운영에 있어 안정성과 효율을 향상시키기 위한 통계분석 및 제어분석 방법과 그 결과를 서술한다. 더욱 상세하게는 인공신경망 기반 발전량 예측 결과의 불확정성을 고려한 가상발전소 전력시장 비용 최적화 모델예측제어를 목표로 한다. 제2장에서는 대한민국 전역에 분포한 태양광발전소들의 모니터링 데이터에 대한 분석 결과를 서술한다. 원시 데이터 내에 존재하는 오류들이 목록화되며, 그 원인과 증상에 따라 분류된다. 일반적으로 발생 가능한 데이터 오류들이 통계분석 결과에 미치는 영향을 확인하기 위해, 인공신경망 기반 통계적 태양광발전소 발전량 예측 모델의 성능에 대한 오류 데이터의 영향이 평가된다. 제3장에서는 전력망 내 에너지저장장치에 대한 제어 방법론을 제시한다. 상업용 건물 부하, 태양광발전소 발전, 에너지저장장치 충방전 운전을 포함하는 가상발전소 또는 마이크로그리드가 계량기 후단에 위치한 전력 소비원이자 발전원으로 제시된다. 에너지저장장치를 위한 경제적 급전계획 문제는 혼합정수 선형계획법 형태로 수식화된다. 최적화 목표는 시간대별 요금제하에서 미래 부하와 발전량 예측 불확실성을 고려한 마이크로그리드 경제적 이득 최대화이며, 피크 제어에 대한 목표 역시 보조서비스 형태로 적용 가능하다. 최적화 문제 해결을 통해 도출된 충방전 제어 스케줄은 마이크로그리드 내 부하와 발전량 예측에 대한 불확실성에도 불구하고 경제적 이득을 강건하게 보장할 수 있다. 제4장에서는 특수 조건하에서의 에너지저장장치 하루 전 시간대별 운전 스케줄 도출 방법론을 제시한다. 태양광발전소와 에너지저장장치를 물리적 또는 가상으로 연결한 집합전력자원이 고려된다. 집합전력자원과 전력망 사이의 전력 거래는 일반적인 시간대별 요금제하에서 이루어진다. 전력망 보조서비스에 해당하는 불균형 요금제가 대한민국 전력시장에서의 분산자원 중개사업자 인센티브 제도 형태로 추가 고려된다. 해당 제도 하에서 집합전력자원은 전일 예측 또는 결정된 운전 스케줄과 실제 스케줄 사이의 오차율에 따라 추가적인 인센티브를 부여받을 수 있다. 집합자원을 위한 에너지관리시스템은 시간대별 요금제와 인센티브 각각에 따른 경제적 이득을 최대화하기 위하여 정확한 예측 기능과 강건한 스케줄 도출 기능을 제공한다. 제안되는 RNN 기반 태양광발전소 발전량 예측 모델은 개방회로 형태의 학습 과정과 폐회로 형태의 사용 방식 사이의 차이를 줄이기 위해 CNN 기반 식별기를 적용한다. 모델 학습 과정에 적용되는 이 GAN 개념은 하루 전 도출한 시간대별 운전 스케줄이 안정적이도록 지원한다. 제안되는 에너지저장장치를 위한 강건 스케줄 도출 모델은 남아있는 예측 오차를 박스 형태의 불확실성 집합으로 처리하여, 도출된 제어 스케줄의 경제적 최적성과 강건성을 보장한다. 스케줄 도출 모델은 간결한 혼합정수 선형계획법 형태로 수식화되어 전력 거래 수익과 인센티브 수익 양쪽 모두를 고려한 빠른 실시간 최적화가 가능하다.1 Introduction 1 2 Analysis of Data Errors in the Solar Photovoltaic Power Plant Monitoring System Database 8 2.1 Background 9 2.2 Solar Photovoltaic Power Plants in Korea 11 2.3 Solar Photovoltaic Power Plants for Analysis 14 2.4 Errors in Static Information Data 16 2.4.1 Errors: Missing or Redundant Static Information Data 19 2.4.2 Errors: Incorrect Specification Data 20 2.5 Errors in Monitoring Data 21 2.5.1 Errors: Invalid Peak Power Values 21 2.5.2 Errors: Invalid Units 23 2.5.3 Errors: Conflictions Between Static and Monitoring Data 23 2.5.4 Errors: Garbage or Corrupted Values 24 2.5.5 Errors: Terminations of Daily Monitoring 26 2.5.6 Errors: Long-term Disconnections 27 2.5.7 Errors: Fluctuating Data Transmission Periods 28 2.5.8 Errors: Disharmonious Data Collection Timings 30 2.6 Analyses with Error Data 33 2.6.1 Effect of Incorrect Location Information 38 2.6.2 Effect of Invalid Monitoring Data Values 40 2.6.3 Effect of Missing Monitoring Data 42 2.7 Conclusion 45 2.8 Acknowledgments 47 3 Robust Scheduling of a Microgrid Energy Storage System with Ancillary Service Considerations 48 3.1 Background 49 3.2 System Architecture 52 3.3 Robust MILP Optimization 55 3.3.1 ESS Constraints 55 3.3.2 Non-Robust Approach 56 3.3.3 Intuitive Approach 58 3.3.4 ESS Power Partitioning Approach 60 3.3.5 Combined Constraint Approach 63 3.4 ESS Efficiency Maps 65 3.5 External Working Conditions 68 3.5.1 Peak Control 69 3.5.2 Demand Response 71 3.6 Simulation Results 72 3.6.1 Computation Time 72 3.6.2 Cost Robustness 76 3.6.3 Precise ESS Control 77 3.6.4 External Working Condition 79 3.7 Conclusion 81 3.8 Acknowledgments 82 4 Robust PV-BESS Scheduling for a Grid with Incentive for Forecast Accuracy 83 4.1 Background 84 4.2 PV Power Forecast Model 88 4.2.1 Data Preprocessing 88 4.2.2 RNN-based Sequence Generator 90 4.2.3 CNN-based Sequence Discriminator 93 4.2.4 Training Objectives 94 4.2.5 Training and Validation 96 4.3 Robust BESS Scheduling 98 4.3.1 Power Transaction Revenue 98 4.3.2 Forecast Accuracy Incentive 102 4.4 Results 106 4.4.1 Benchmark Models for PV Power Forecasting 106 4.4.2 Stability of the PV Power Forecast Results 107 4.4.3 Accuracy of the PV Power Forecast Results 109 4.4.4 Incentive Analysis for the PV Power Forecast Results 110 4.4.5 Effect of Input Data Accuracy on Forecast Results 111 4.4.6 Robust BESS Scheduling for the Transaction Revenue 112 4.4.7 Computation Speed of the Scheduling Problems 116 4.4.8 Online Optimization for the Incentive Revenue 117 4.5 Conclusion 119 4.6 Appendix 120 4.6.1 A Toy Example for the Robust Optimization Result 120 4.7 Acknowledgments 121 5 Conclusion 122 Bibliography 125박

Analysis And Mitigation Of The Impacts Of Delays In Control Of Power Systems With Renewable Energy Sources

ABSTRACT Analysis and Mitigation of the Impacts of Delays in Control of Power Systems with Renewable Energy Sources by Chang Fu Apr. 2019 Advisor : Dr. Caisheng Wang Major : Electrical and Computer Engineering Degree : Doctor of Philosophy With the integration of renewable resources, electric vehicles and other uncertain resources into power grid, varieties of control topology and algorithms have been proposed to increase the stability and reliability of the operation system. Load modeling is an critical part in such analysis since it significantly impacts the accuracy of the simulation in power system, as well as stability and reliability analysis. Traditional power system composite load model parameter identification problems can be essentially ascribed to optimization problems, and the identied parameters are point estimations subject to dierent constraints. These conventional point estimation based composite load modeling approaches suer from disturbances and noises and provide limited information of the system dynamics. In this thesis, a statistic (Bayesian Estimation) based distribution estimation approach is proposed for composite load models, including static (ZIP) and dynamic (Induction Motor) parts, by implementing Gibbs sampling. The proposed method provides a distribution estimation of coecients for load models and is robust to measurement errors. The overvoltage issue is another urgent issues need to be addressed, especially in a high PV penetration level system. Various approaches including the real power control through photovoltaic (PV) inverters have been proposed to mitigate such impact, however, most of the existing methods did not include communication delays in the control loop. Communication delays, short or long, are inevitable in the PV voltage regulation loop and can not only deteriorate the system performance with undesired voltage quality but also cause system instability. In this thesis, a method is presented to convert the overvoltage control problem via PV inverters for multiple PVs into a problem of single-input-single-output (SISO) systems. The method can handle multiple PVs and dierent communication delays. The impact of communication delays is also systematically analyzed and the maximum tolerable delay is rigorously obtained. Dierent from linear matrix inequality (LMI) techniques that have been extensively studied in handling systems with communication delays, the proposed method gives the necessary and sucient condition for obtaining a controller and the design procedure is explicitly and constructively given in the paper. The effectiveness of the proposed method is veried by simulation studies on a distribution feeder and the widely-used 33-bus distribution test system. The similar design strategy can be utilized to mitigate delay impacts in Load frequency control (LFC) as well. LFC has been considered as one of the most important frequency regulation mechanisms in modern power system. One of the inevitable problems involved in LFC over a wide area is communication delay. In this thesis, an alternative design method is proposed to devise delay compensators for LFC in one or multiple control areas. For one-area LFC, a sucient and necessary condition is given for designing a delay compensator. For multiarea LFC with area control errors (ACEs), it is demonstrated that each control area can have its delay controller designed as that in a one-area system if the index of coupling among the areas is below the threshold value determined by the small gain theorem. Effectiveness of the proposed method is veried by simulation studies on LFCs with communication delays in one and multiple interconnected areas with and without time-varying delays, respectively

Analysis And Mitigation Of The Impacts Of Delays In Control Of Power Systems With Renewable Energy Sources

ABSTRACT Analysis and Mitigation of the Impacts of Delays in Control of Power Systems with Renewable Energy Sources by Chang Fu Apr. 2019 Advisor : Dr. Caisheng Wang Major : Electrical and Computer Engineering Degree : Doctor of Philosophy With the integration of renewable resources, electric vehicles and other uncertain resources into power grid, varieties of control topology and algorithms have been proposed to increase the stability and reliability of the operation system. Load modeling is an critical part in such analysis since it significantly impacts the accuracy of the simulation in power system, as well as stability and reliability analysis. Traditional power system composite load model parameter identification problems can be essentially ascribed to optimization problems, and the identied parameters are point estimations subject to dierent constraints. These conventional point estimation based composite load modeling approaches suer from disturbances and noises and provide limited information of the system dynamics. In this thesis, a statistic (Bayesian Estimation) based distribution estimation approach is proposed for composite load models, including static (ZIP) and dynamic (Induction Motor) parts, by implementing Gibbs sampling. The proposed method provides a distribution estimation of coecients for load models and is robust to measurement errors. The overvoltage issue is another urgent issues need to be addressed, especially in a high PV penetration level system. Various approaches including the real power control through photovoltaic (PV) inverters have been proposed to mitigate such impact, however, most of the existing methods did not include communication delays in the control loop. Communication delays, short or long, are inevitable in the PV voltage regulation loop and can not only deteriorate the system performance with undesired voltage quality but also cause system instability. In this thesis, a method is presented to convert the overvoltage control problem via PV inverters for multiple PVs into a problem of single-input-single-output (SISO) systems. The method can handle multiple PVs and dierent communication delays. The impact of communication delays is also systematically analyzed and the maximum tolerable delay is rigorously obtained. Dierent from linear matrix inequality (LMI) techniques that have been extensively studied in handling systems with communication delays, the proposed method gives the necessary and sucient condition for obtaining a controller and the design procedure is explicitly and constructively given in the paper. The effectiveness of the proposed method is veried by simulation studies on a distribution feeder and the widely-used 33-bus distribution test system. The similar design strategy can be utilized to mitigate delay impacts in Load frequency control (LFC) as well. LFC has been considered as one of the most important frequency regulation mechanisms in modern power system. One of the inevitable problems involved in LFC over a wide area is communication delay. In this thesis, an alternative design method is proposed to devise delay compensators for LFC in one or multiple control areas. For one-area LFC, a sucient and necessary condition is given for designing a delay compensator. For multiarea LFC with area control errors (ACEs), it is demonstrated that each control area can have its delay controller designed as that in a one-area system if the index of coupling among the areas is below the threshold value determined by the small gain theorem. Effectiveness of the proposed method is veried by simulation studies on LFCs with communication delays in one and multiple interconnected areas with and without time-varying delays, respectively

Stability analysis and robust control of power networks in stochastic environment

The modern power grid is moving towards a cleaner form of energy, renewable energy to meet the ever-increasing demand and new technologies are being installed in the power network to monitor and maintain a stable operation. Further, the interactions in the network are not anymore localized but take place over a system, and the control centers are located remotely, thus involving control of network components over communication channels. Further, given the rapid integration of wind energy, it is essential to study the impact of wind variability on the system stability and frequency regulation. Hence, we model the unreliable and intermittent nature of wind energy with stochastic uncertainty. Moreover, the phasor measurement unit (PMU) data from the power network is transmitted to the control center over communication channels, and it is susceptible to inherent communication channel uncertainties, cyber attacks, and hence, the data at the receiving end cannot be accurate. In this work, we model these communication channels with stochastic uncertainties to study the impact of stochastic uncertainty on the stability and wide area control of power network. The challenging aspect of the stability analysis of stochastic power network is that the stochastic uncertainty appears multiplicative as well as additive in the system dynamics. The notion of mean square exponential stability is considered to study the properties of stochastic power network expressed as a networked control system (NCS) with stochastic uncertainty. We develop, necessary and sufficient conditions for mean square exponential stability which are shown in terms of the input-output property of deterministic or nominal system dynamics captured by the mean square system norm and variance of the channel uncertainty. For a particular case of single input channel uncertainty, we also prove a fundamental limitation result that arises in the mean square exponential stabilization of the continuous-time linear system. Overall, the theoretical contributions in this work generalize the existing results on stability analysis from discrete-time linear systems to continuous-time linear systems with multiplicative uncertainty. The stability results can also be interpreted as a small gain theorem for continuous-time stochastic systems. Linear Matrix Inequalities (LMI)-based optimization formulation is provided for the computation of mean square system norm for stability analysis and controller synthesis. An IEEE 68 bus system is considered, and the fragility of the decentralized load-side primary frequency controller with uncertain wind is shown. The critical variance value is shown to decrease with the increase in the cost of the controllable loads and with the rise in penetration of wind farms. Next, we model the power network with detailed higher order differential equations for synchronous generator (SG), wind turbine generator (WTG). The network power flow equations are expressed as algebraic equations. The resultant system is described by a detailed higher order nonlinear differential-algebraic model. It is shown that the uncertainty in the wind speed appears multiplicative in the system dynamics. Stochastic stability of such systems is characterized based on the developed results on mean square exponential stability. In particular, we study the stochastic small signal stability of the resultant system and characterize the critical variance in wind speeds, beyond which the grid dynamics becomes mean square unstable. The power fluctuations in the demand side and intermittent generation (from renewables) cause frequency excursions from the nominal value. In this context, we consider the controllable loads which can vary their power to achieve frequency regulation based on the frequency feedback from the network. Two different load-side frequency controller strategies, decentralized and distributed frequency controllers are studied in the presence of stochastic wind. Finally, the time-domain simulations on an IEEE 39 bus system (by replacing some of the traditional SGs with WTG) are shown using the wind speeds modeled as stochastic as well as actual wind speeds obtained from the wind farm located near Ames, Iowa. It can be seen that, with an increase in the penetration of wind generation in the network, the network turns mean square unstable. Furthermore, we capture the mean square unstable behavior of the power network with increased penetration of renewables using the statistics of actual wind analytically and complement them through linear and nonlinear time domain simulations. Finally, we analyze the vulnerability of communication channel to stochastic uncertainty on an IEEE 39 bus system and design a wide area controller that is robust to various sources of uncertainties that arise in the communication channels. Further, the PMU measurements and wide area control inputs are rank ordered based on their criticality

Robust H8 design for resonant control in a CVCF inverter application over load uncertainties

CVCF (constant voltage, constant frequency) inverters are electronic devices used to supply AC loads from DC storage elements such as batteries or photovoltaic cells. These devices are used to feed different kinds of loads; this uncertainty requires that the controller fulfills robust stability conditions while keeping required performance. To address this, a robust H8 design is proposed based on resonant control to track a pure sinusoidal voltage signal and to reject the most common harmonic signals in a wide range of loads. The design is based on the definition of performance bounds in error signal and weighting functions for covering most uncertainty ranges in loads. Experimentally, the H8 controller achieves high-quality output voltage signal with a total harmonic distortion less than 2%Peer ReviewedPostprint (published version

Commitment and Dispatch of Heat and Power Units via Affinely Adjustable Robust Optimization

The joint management of heat and power systems is believed to be key to the integration of renewables into energy systems with a large penetration of district heating. Determining the day-ahead unit commitment and production schedules for these systems is an optimization problem subject to uncertainty stemming from the unpredictability of demand and prices for heat and electricity. Furthermore, owing to the dynamic features of production and heat storage units as well as to the length and granularity of the optimization horizon (e.g., one whole day with hourly resolution), this problem is in essence a multi-stage one. We propose a formulation based on robust optimization where recourse decisions are approximated as linear or piecewise-linear functions of the uncertain parameters. This approach allows for a rigorous modeling of the uncertainty in multi-stage decision-making without compromising computational tractability. We perform an extensive numerical study based on data from the Copenhagen area in Denmark, which highlights important features of the proposed model. Firstly, we illustrate commitment and dispatch choices that increase conservativeness in the robust optimization approach. Secondly, we appraise the gain obtained by switching from linear to piecewise-linear decision rules within robust optimization. Furthermore, we give directions for selecting the parameters defining the uncertainty set (size, budget) and assess the resulting trade-off between average profit and conservativeness of the solution. Finally, we perform a thorough comparison with competing models based on deterministic optimization and stochastic programming.Comment: 31 page

Adaptive Robust Optimization with Dynamic Uncertainty Sets for Multi-Period Economic Dispatch under Significant Wind

The exceptional benefits of wind power as an environmentally responsible renewable energy resource have led to an increasing penetration of wind energy in today's power systems. This trend has started to reshape the paradigms of power system operations, as dealing with uncertainty caused by the highly intermittent and uncertain wind power becomes a significant issue. Motivated by this, we present a new framework using adaptive robust optimization for the economic dispatch of power systems with high level of wind penetration. In particular, we propose an adaptive robust optimization model for multi-period economic dispatch, and introduce the concept of dynamic uncertainty sets and methods to construct such sets to model temporal and spatial correlations of uncertainty. We also develop a simulation platform which combines the proposed robust economic dispatch model with statistical prediction tools in a rolling horizon framework. We have conducted extensive computational experiments on this platform using real wind data. The results are promising and demonstrate the benefits of our approach in terms of cost and reliability over existing robust optimization models as well as recent look-ahead dispatch models.Comment: Accepted for publication at IEEE Transactions on Power System