Advanced Control Systems for Grid Connected Inverter Applications
Michael L. McIntyre, Ph.D., PE. Associate Professor, Electrical and Computer Engineering
13th Annual University of Pittsburg - Electric Power Industry Conference
10/15/2018
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Outline • • • • • • •
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Introduction Existing Control Schemes For Grid Connected Inverters Model Based Approach Applications Areas 3 φ and 1φ Grid Connected Inverter Control Solutions Micro-Grid Control Solutions Conclusions
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Introduction • Single and Three Phase Voltage Sources Inverters have a wide range of applications in modern Power Systems – Renewable Integration – Energy Storage – FACTS Devices – Active Rectification
• Low Steady State Error • Transient Performance
– Fast Dynamic Response
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Outline • • • • • • •
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Introduction Existing Control Schemes For Grid Connected Inverters My Approach Applications Areas 3 φ and 1φ Grid Connected Inverter Control Solutions Micro-Grid Control Solutions Conclusions
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Existing Control Schemes • Circuit – Modulation - Control • 1Φ & 3Φ Phase Circuit Topologies – Additional Switching Leg for Three Phase
• Bidirectional Power Flow • Modulation Schemes allow for proper DC Bus Utilization – Unipolar vs. SVM
• Control Real and Reactive Power
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Current Control • Grid current is controlled to regulate Active and Reactive power. – Control Objective 𝑒𝑒𝑃𝑃 ≜ 𝑃𝑃∗ − 𝑃𝑃 & 𝑒𝑒𝑄𝑄 ≜ 𝑄𝑄∗ − 𝑄𝑄
• Focus on Inertia emulations • Standards require grid tied systems to preserve � 𝜔𝜔, 𝜃𝜃). grid quality of voltage waveform (𝑉𝑉, • THDi < 5% for EN61000-3-2 𝑑𝑑𝑑𝑑 𝐿𝐿 + 𝑟𝑟𝑟𝑟 = 𝑉𝑉𝑝𝑝𝑝𝑝𝑝𝑝 − 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 𝑑𝑑𝑑𝑑 6
𝑉𝑉𝑝𝑝𝑝𝑝𝑝𝑝 ≜ 𝐷𝐷𝑉𝑉𝑑𝑑𝑑𝑑−𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙
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Current Control • Use of rotating (αβ) and stationary(dq) reference frames are utilized for single and three phase systems. Feed-Forward Loop
Modulation Scheme
• GI(s) takes various forms
– PI Control: Shortcomings for due poor disturbance rejection and leads to SSE and power factor issues – PR Control: Uses frequency matching to increase controller gain to improve performance.
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Voltage Control • For voltage forming applications, control scheme takes on a cascaded approach
• Inner Current Loop
– Manage and limit output current
• Outer Voltage Loop
– Manage voltage waveform
• Third Loop Determines Grid Parameters 8
� � 𝜔𝜔, – (𝑉𝑉, � 𝜃𝜃)
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Grid Synchronization • Establishing Grid Parameters – Voltage Magnitude – Current Magnitude – Grid Frequency – Grid Phase
� 𝜔𝜔, ̂ (𝑉𝑉, � 𝜃𝜃)
• IEEE 1547 in packs Grid Synchronization Function • Typically implemented with a Feedback System (Observer) known as Phase Locked Loop
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Existing Control Schemes
Example Control Diagram for Renewable Integration with Grid Notice: PR, PLL, and MPPT 10
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Grid Interface Requirements of the PV System • Quality, Safety & Reliability • IEEE 1547 (<= 10 MVA) • Grid Support • FERC Order 661-A (20+ MW wind farms) • Low-voltage ride through (LVRT) capability • Power factor: +/- 0.95 • Reactive power support • Operation Communication • Monitoring (>=250kVA or aggregated) • SCADA (MW-level) • Dispatchability • Required for large DGs 11
• •
UL 1741, 2nd ed., Nov 7, 2005 Clause 46.1.1 - A utility-interactive inverter and interconnection system equipment (ISE) shall comply with IEEE 1547, and IEEE 1547.1. 10/15/2018
Existing Control Schemes Islanding Detection in the Grid-connected PV System
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Existing Control Schemes Supervisory Level Control
>1 min.
Power Input
Power Export
Load Leveling
Secondary Level Control
~1 sec.
Frequency Regulation
Voltage Stability
Primary Level Control
<1 msec.
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Current Control
Voltage Control
Grid Sync.
Island Detection
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Outline • • • • • • •
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Introduction Existing Control Schemes For Grid Connected Inverters Model Based Approach Applications Areas 3 φ and 1φ Grid Connected Inverter Control Solutions Micro-Grid Control Solutions Conclusions
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Model Based Approach • Typical Electromechanical System Electrical Dynamics
u
𝑦𝑦̇ = 𝑔𝑔(𝑥𝑥, 𝑦𝑦, 𝑢𝑢)
Mechanical Dynamics
y
𝑥𝑥̇ = 𝑓𝑓(𝑥𝑥, 𝑦𝑦)
x
• Classical Control Systems Solutions – Linearization of g(x,y,u) and f(x,y) – Apply linear methods u
𝑦𝑦̇ = 𝑔𝑔(𝑥𝑥, 𝑦𝑦, 𝑢𝑢)
y
𝑥𝑥̇ = 𝑓𝑓(𝑥𝑥, 𝑦𝑦)
x
Linear Controller
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Obstacles to Increased Performance System model often contains hard nonlinearities
u
Parameters in the model are usually unknown
u
Actuator dynamics cannot be neglected
u
System states are difficult or costly to measure
u
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𝑦𝑦̇ = 𝒇𝒇(𝑥𝑥, 𝑦𝑦, 𝑢𝑢)
𝑦𝑦̇ =? (𝑥𝑥, 𝑦𝑦, 𝑢𝑢)
sat(u)
y
y
𝑦𝑦̇ = 𝒇𝒇(𝑥𝑥, 𝑦𝑦, 𝑢𝑢)
𝑦𝑦̇ = f(𝑥𝑥, 𝑦𝑦, 𝑢𝑢)
𝑥𝑥̇ = 𝒈𝒈(𝑥𝑥, 𝑦𝑦)
?
𝑥𝑥̇ =? (𝑥𝑥, 𝑦𝑦)
y
𝑥𝑥̇ = 𝒈𝒈(𝑥𝑥, 𝑦𝑦)
𝑥𝑥̇ = g(𝑥𝑥, 𝑦𝑦) 10/15/2018
x
x
x
?
Uncertain Math Model Approach
Research Solution
Advanced Control Design Techniques
Real-time Hardware/Software
• Nonlinear Lyapunov-Based Techniques Provide y u 𝑦𝑦̇ =? (𝑥𝑥, 𝑦𝑦, 𝑢𝑢) – Controllers designed for the full-order nonlinear models Nonlinear Nonlinear Parameter Controller – Adaptive update laws for on-line estimation Estimator of unknown parameters – Observers or filters for state measurement replacement ? u 𝑦𝑦̇ = 𝑔𝑔(𝑥𝑥, 𝑦𝑦, 𝑢𝑢) – Analysis that predicts system performance Nonlinear Nonlinear by providing envelopes for the transient Controller Observer response 17
New Controller/ Observer Solutions
𝑥𝑥̇ =? (𝑥𝑥, 𝑦𝑦)
𝑥𝑥̇ = f(𝑥𝑥, 𝑦𝑦)
x
x
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Control Design/Implementation Cycle Testbed Construction
Interface and Safety Issues
Sensors: Encoders, Force Sensor, Camera Actuators: Motors, Electromagnets, Speakers
Signal Conditioning Power Electronic Interfacing HV/LV Interfacing, Comm.
Electronic Compatibility
Mathematical Model
NI Compact RIO/Embedded (encoders, D/A, A/D, digital I/O)
Software Development Matlab/Simulink/RealTime NI-Labview RT PLECS
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PDE-ODE model (flexible systems) ODE model (rigid systems)
Master Thesis Students
Data Acquisition
Real-Time OS, Driver Interface, Data Handling
Physics-Based Models
Control Objective
PhD Students Coding the Control Algorithm
Problem Formulation Tracking, Setpoint Parametric Uncertainty Bounded Disturbance Unmeasurable Signals
Stability Analysis
Control Design
Lyapunov Techniques Simulation Studies Model-Based, Adaptive, Robust 10/15/2018
Outline • • • • • • •
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Introduction Existing Control Schemes For Grid Connected Inverters Model Based Approach Applications Areas 3 φ and 1φ Grid Connected Inverter Control Solutions Micro-Grid Control Solutions Conclusions
10/15/2018
Research Application Areas
Nonlinear Control and Estimation Schemes
Controls for FACTS Devices
Electric Machinery and Drives
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Electrical Energy Systems
Grid Connected Inverters with Loads
Demand Side Management for Smart Grids 10/15/2018
Outline • • • • • • •
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Introduction Existing Control Schemes For Grid Connected Inverters Model Based Approach Applications Areas 3 φ and 1φ Grid Connected Inverter Control Solutions Micro-Grid Control Solutions Conclusions
10/15/2018
3φ Current Control Single-Stage Three-Phase Grid-Connected Photovoltaic Systems with Maximum Power Point Tracking and Active and Reactive Power Control Based on Nonlinear Control Renewable Integrations
Controller 1
Controller 2
Dynamic System Equations Control Signals 𝑑𝑑𝑑𝑑′ (𝑡𝑡) and 𝑑𝑑𝑞𝑞′ (𝑡𝑡):
𝑅𝑅 𝑑𝑑𝑑𝑑′ 1 𝑉𝑉𝑝𝑝𝑝𝑝 − 𝑉𝑉𝑔𝑔𝑔𝑔 𝐼𝐼𝑑𝑑̇ = − 𝐼𝐼𝑑𝑑 + 𝐿𝐿 𝐿𝐿 𝐿𝐿 𝑑𝑑𝑞𝑞′ 𝑅𝑅 1 𝐼𝐼𝑞𝑞̇ = − 𝐼𝐼𝑞𝑞 + 𝑉𝑉𝑝𝑝𝑝𝑝 − 𝑉𝑉𝑔𝑔𝑔𝑔 𝐿𝐿 𝐿𝐿 𝐿𝐿 ′
′
̇ = − 𝑑𝑑𝑑𝑑 𝐼𝐼𝑑𝑑 − 𝑑𝑑𝑞𝑞 𝐼𝐼𝑞𝑞 + 1 𝐼𝐼𝑝𝑝𝑝𝑝 𝑉𝑉𝑝𝑝𝑝𝑝 𝐶𝐶
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𝐶𝐶
𝐶𝐶
𝜔𝜔𝜔𝜔 𝐼𝐼 𝑉𝑉𝑝𝑝𝑝𝑝 𝑞𝑞 𝜔𝜔𝜔𝜔 𝑑𝑑𝑞𝑞′ = 𝑑𝑑𝑞𝑞 − 𝐼𝐼 𝑉𝑉𝑝𝑝𝑝𝑝 𝑑𝑑
𝑑𝑑𝑑𝑑′ = 𝑑𝑑𝑑𝑑 +
P. R. Rivera, M. L. McIntyre, M. Mohebbi, and J. Latham, “Single-Stage Three-Phase Grid-Connected Photovoltaic System with Maximum Power Tracking and Active and Reactive Power Control based on Nonlinear control,” in Proc. of Energy Conversion Congress and Exposition, ECCE, October, 2017, pp. 1-7
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Single-Stage Three-Phase Grid-Connected Photovoltaic …….. Objectives
A single-stage three-phase grid-connected PV system with Lyapunov-based nonlinear control is proposed: To achieve MPOP regardless of atmospheric conditions To control the Active, Reactive Power, & Unity Power factor on the grid side. Control Development The objective is to design 𝑑𝑑𝑑𝑑′ (𝑡𝑡) and 𝑑𝑑𝑞𝑞′ (𝑡𝑡) such that:
𝐼𝐼𝑑𝑑 (𝑡𝑡) → 𝐼𝐼𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 (𝑡𝑡) and 𝐼𝐼𝑞𝑞 𝑡𝑡 → 𝐼𝐼𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞 𝑡𝑡 as t → ∞
thus controlling the Active, Reactive Power & Unity Power factor on the grid side. The control law must also ensure that 𝑉𝑉𝑝𝑝𝑝𝑝 (𝑡𝑡) → 𝑉𝑉𝑟𝑟𝑟𝑟𝑟𝑟 (𝑡𝑡) as 𝑡𝑡 → ∞ to achieve MPPT. 𝐿𝐿 𝑅𝑅 1 ̇ −𝐾𝐾𝑑𝑑 𝑒𝑒𝑑𝑑 + 𝐼𝐼𝑑𝑑 + 𝑉𝑉𝑔𝑔𝑔𝑔 + 𝐼𝐼𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑉𝑉𝑝𝑝𝑝𝑝 𝐿𝐿 𝐿𝐿 𝐿𝐿 𝑅𝑅 ̇ 𝑑𝑑𝑞𝑞′ = −𝐾𝐾𝑞𝑞 𝑒𝑒𝑞𝑞 + 𝐼𝐼𝑞𝑞 + 𝐼𝐼𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞 𝑉𝑉𝑝𝑝𝑝𝑝 𝐿𝐿
𝑑𝑑𝑑𝑑′ =
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𝑉𝑉𝑝𝑝𝑝𝑝 𝐼𝐼𝑝𝑝𝑝𝑝 𝐶𝐶 𝑉𝑉𝑝𝑝𝑝𝑝 𝐶𝐶 𝑉𝑉𝑝𝑝𝑝𝑝 𝑉𝑉̇ + − 𝐼𝐼𝑑𝑑 𝐿𝐿𝐼𝐼𝑑𝑑 𝐿𝐿 𝐼𝐼𝑑𝑑 𝐿𝐿 𝐼𝐼𝑑𝑑 𝑟𝑟𝑟𝑟𝑟𝑟 𝐼𝐼𝑞𝑞 𝑅𝑅 𝐼𝐼𝑞𝑞2 𝑅𝑅 1 ̇ − 𝐼𝐼𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞 − +𝐾𝐾𝑑𝑑 𝑒𝑒𝑑𝑑 − 𝐼𝐼𝑑𝑑 − 𝑉𝑉𝑔𝑔𝑔𝑔 𝐼𝐼𝑑𝑑 𝐿𝐿 𝐼𝐼𝑑𝑑 𝐿𝐿 𝐿𝐿
̇ 𝐼𝐼𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 = 𝐾𝐾𝑞𝑞 𝑒𝑒𝑞𝑞
𝐼𝐼𝑞𝑞
+ 𝐾𝐾𝑣𝑣 𝑒𝑒𝑣𝑣
P. R. Rivera, M. L. McIntyre, M. Mohebbi, and J. Latham, “Single-Stage Three-Phase Grid-Connected Photovoltaic System with Maximum Power Tracking and Active and Reactive Power Control based on Nonlinear control,” in Proc. of Energy Conversion Congress and Exposition, ECCE, October, 2017, pp. 1-7
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Single-Stage Three-Phase Grid-Connected Photovoltaic …….. Instantaneous Circuit Simulation
Fig. 6 PV and Ideal Power
Fig. 12 Grid voltage and current
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Fig. 13 Transient response of the grid current at t=0.4 seconds
Fig. 10 𝐼𝐼𝑑𝑑 , 𝐼𝐼𝑞𝑞 , and references current
Fig. 16 Active and Reactive power of the grid
P. R. Rivera, M. L. McIntyre, M. Mohebbi, and J. Latham, “Single-Stage Three-Phase Grid-Connected Photovoltaic System with Maximum Power Tracking and Active and Reactive Power Control based on Nonlinear control,” in Proc. of Energy Conversion Congress and Exposition, ECCE, October, 2017, pp. 1-7
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Nonlinear Control for Single-Stage, Single-Phase GridConnected Photovoltaic Systems Objectives
A single-stage Single-phase grid-connected PV system with Lyapunov-based nonlinear control is proposed: To achieve MPOP regardless of atmospheric conditions To control the Active, Reactive Power, & Unity Power factor on the grid side. Minimize Double Line Frequency Ripple through Control Trajectory Development 𝑑𝑑𝑖𝑖𝑎𝑎 = −𝑅𝑅𝑖𝑖𝑎𝑎 + 𝑑𝑑𝑑𝑑𝑝𝑝𝑝𝑝 − 𝑣𝑣𝑔𝑔𝑔𝑔 𝐿𝐿 𝑑𝑑𝑑𝑑 𝑑𝑑𝑉𝑉𝑝𝑝𝑝𝑝
𝐶𝐶 𝑑𝑑𝑑𝑑 = 𝐼𝐼𝑝𝑝𝑝𝑝 − 𝑑𝑑𝑖𝑖𝑎𝑎 +
𝑉𝑉𝑔𝑔𝑔𝑔 𝐼𝐼𝑎𝑎𝑎𝑎 2𝑉𝑉𝑝𝑝𝑝𝑝
Natural Reference Frame
𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
1 ̇ −𝐾𝐾𝑑𝑑 𝑒𝑒𝑑𝑑 + 𝑅𝑅𝐼𝐼𝑑𝑑 + 𝑉𝑉𝑔𝑔𝑔𝑔 + 𝐿𝐿𝐼𝐼𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑉𝑉𝑝𝑝𝑝𝑝 1 ̇ 𝑑𝑑𝑞𝑞′ = −𝐾𝐾𝑞𝑞 𝑒𝑒𝑞𝑞 + 𝑅𝑅𝐼𝐼𝑞𝑞 + 𝐿𝐿𝐼𝐼𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞 𝑉𝑉𝑝𝑝𝑝𝑝 𝑑𝑑𝑑𝑑′ =
dq Reference Frame
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P. R. Rivera, M. L. McIntyre, M. Mohebbi, and J. Latham, “ Nonlinear Control for Single-Stage, SinglePhase Grid-Connected Photovoltaic Systems,” in Proc. of Control and Modelling for Power Electronics, COMPEL, July, 2017.
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Nonlinear Control for Single-Stage, Single-Phase….. Instantaneous Circuit Simulation
Fig. 11 𝐼𝐼𝑑𝑑 , 𝐼𝐼𝑞𝑞 , and references current
Fig. 7 PV and Ideal Power
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Fig. 13 Grid voltage and current
P. R. Rivera, M. L. McIntyre, M. Mohebbi, and J. Latham, “ Nonlinear Control for Single-Stage, Single-Phase Grid-Connected Photovoltaic Systems,” in Proc. of Control and Modelling for Power Electronics, COMPEL, July, 2017.
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Current Control For Three-Phase Inverter in the Presence of Unknown Grid Parameters Control Objective Design 𝐷𝐷𝛾𝛾 𝑡𝑡 and 𝐷𝐷𝛿𝛿 𝑡𝑡 to force 𝐼𝐼𝛾𝛾 𝑡𝑡 and 𝐼𝐼𝛿𝛿 𝑡𝑡 to follow their respective reference currents 𝐼𝐼𝛾𝛾∗ 𝑡𝑡 and 𝐼𝐼𝛿𝛿∗ 𝑡𝑡 in the presence of the unknown grid parameters: 𝑉𝑉𝑔𝑔 , 𝜔𝜔 and 𝜃𝜃 𝑡𝑡 . An observer will also be developed for 𝜃𝜃̂ 𝑡𝑡 . It is to be noted that through the Lyapunov analysis we can prove the grid phase estimation angle 𝜃𝜃� 𝑡𝑡 → 0 as 𝑡𝑡 → ∞, hence after convergence 𝐼𝐼𝛾𝛾∗ 𝑡𝑡 = 𝐼𝐼𝑑𝑑∗ 𝑡𝑡 and 𝐼𝐼𝛿𝛿∗ 𝑡𝑡 = 𝐼𝐼𝑞𝑞∗ 𝑡𝑡 . 𝐿𝐿
𝐼𝐼𝛾𝛾̇ 𝐷𝐷𝛾𝛾 = 𝑉𝑉𝑑𝑑𝑑𝑑 − 𝑅𝑅 𝐷𝐷𝛿𝛿 �̇ 𝐼𝐼𝛿𝛿̇ 𝜃𝜃𝐿𝐿
1 𝐷𝐷𝛾𝛾 ≜ 𝐷𝐷𝛿𝛿 𝑉𝑉𝑑𝑑𝑑𝑑
𝑅𝑅 �̇ 𝜃𝜃𝐿𝐿 𝑡𝑡
𝐼𝐼𝛾𝛾 �̇ � −𝜃𝜃𝐿𝐿 − 𝑉𝑉𝑔𝑔 cos 𝜃𝜃 𝐼𝐼𝛿𝛿 sin 𝜃𝜃� 𝑅𝑅
𝐼𝐼̃𝛾𝛾 𝐼𝐼𝛾𝛾 �̇ 𝑉𝑉� −𝜃𝜃𝐿𝐿 + 𝑔𝑔 + 𝑘𝑘1 𝐼𝐼𝛿𝛿 𝐼𝐼̃𝛿𝛿 0 𝑅𝑅
� + 𝑘𝑘1 + 1 𝐼𝐼̃𝛿𝛿 𝜃𝜃� ≜ 𝐿𝐿𝐼𝐼̃𝛿𝛿 + � 𝜔𝜔 𝑡𝑡0
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𝑡𝑡
𝜔𝜔 � ≜ 𝑘𝑘𝜔𝜔 𝐿𝐿𝐼𝐼̃𝛿𝛿 + 𝑘𝑘1 � 𝐼𝐼̃𝛿𝛿 𝑡𝑡0
𝑉𝑉�𝑔𝑔̇ ≜ 𝑘𝑘𝑉𝑉 𝐼𝐼̃𝛾𝛾
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Current Control For Three-Phase Inverter …… Instantaneous Circuit Simulation
Figure 2: Current Tracking for Trial 1
Figure 5: Current Tracking for Trial 2
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Figure 3: Grid Parameter Estimation for Trial 1
Figure 4: Control Signals in Both Frames for Trial 1
Figure 6: Grid Parameter Estimation for Trial 2
Figure 7: Control Signals in Both Frames for Trial 2
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Outline • • • • • • •
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Introduction Existing Control Schemes For Grid Connected Inverters Model Based Approach Applications Areas 3 φ and 1φ Grid Connected Inverter Control Solutions Micro-Grid Control Solutions Conclusions
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Micro-Grid Application
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Control Objectives • Grid-Connected Inverter Systems with LC filter: 1. Simultaneously: Inject clean current (Low THD) to the grid. Regulate the output voltage to track a reference voltage. 2. Unity power factor at the grid side. 3. Ensure seamless transition between grid-connected and standalone modes. Maintain consistent control system structure
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Backstepping Control for Grid-Connected SinglePhase Inverter Utilizing Variable Structure Observer Control Objective :to maintain low THD of the local load voltage 𝑉𝑉𝑜𝑜 (𝑡𝑡) regardless of the type of load and achieve the reference output voltage 𝑉𝑉𝑜𝑜 𝑟𝑟𝑟𝑟𝑟𝑟 𝑡𝑡 , hence 𝑉𝑉𝑜𝑜 𝑡𝑡 → 𝑉𝑉𝑜𝑜 𝑟𝑟𝑟𝑟𝑟𝑟 𝑡𝑡 as 𝑡𝑡 → ∞. The stability analysis 𝑡𝑡 . Also, the current control objective is exchanging clean current with the will prove 𝑉𝑉�𝑜𝑜 𝑡𝑡 → 𝑉𝑉𝑜𝑜 𝑟𝑟𝑟𝑟𝑟𝑟
grid by regulating the grid current 𝐼𝐼2 𝑡𝑡 to a reference current 𝐼𝐼2𝑟𝑟𝑟𝑟𝑟𝑟 𝑡𝑡 , hence 𝐼𝐼2 𝑡𝑡 → 𝐼𝐼2𝑟𝑟𝑟𝑟𝑟𝑟 𝑡𝑡 as 𝑡𝑡 → ∞.
𝐿𝐿𝑓𝑓 𝐼𝐼1̇ = 𝑉𝑉𝑑𝑑𝑑𝑑 𝐷𝐷 + 𝑑𝑑0 − 𝑉𝑉𝑜𝑜
𝐶𝐶𝑓𝑓 𝑉𝑉𝑜𝑜̇ = 𝐼𝐼1 − 𝐼𝐼2 − 𝐼𝐼𝑜𝑜
𝐿𝐿𝑔𝑔 𝐼𝐼2̇ = 𝑉𝑉𝑜𝑜 − 𝑉𝑉𝑔𝑔
𝑉𝑉𝑜𝑜̈ =
1 𝑉𝑉 𝐷𝐷 + 𝑑𝑑0 − 𝑉𝑉𝑜𝑜 + 𝐿𝐿𝑓𝑓 𝐶𝐶𝑓𝑓 𝑑𝑑𝑑𝑑 1 1 (𝑉𝑉 𝑔𝑔 − 𝑉𝑉𝑜𝑜 ) − 𝐼𝐼𝑜𝑜̇ 𝐿𝐿𝑔𝑔 𝐶𝐶𝑓𝑓 𝐶𝐶𝑓𝑓
𝐷𝐷 ≜
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𝐿𝐿𝑓𝑓 𝐶𝐶𝑓𝑓 𝐾𝐾𝑔𝑔 1 𝐼𝐼2𝑟𝑟𝑟𝑟𝑟𝑟 + 𝐾𝐾𝑔𝑔 𝐼𝐼2̈ 𝑟𝑟𝑟𝑟𝑟𝑟 − {𝐿𝐿𝑔𝑔 ⃛ 𝑉𝑉𝑔𝑔 − 𝑉𝑉𝑜𝑜 + 𝜔𝜔𝑉𝑉𝑚𝑚 𝑐𝑐𝑐𝑐𝑐𝑐 𝜃𝜃 − 𝑉𝑉�𝑜𝑜̇ + 𝑑𝑑̂ − 𝜔𝜔2 𝑉𝑉𝑚𝑚 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + 𝑑𝑑̂̇ 𝑉𝑉𝑑𝑑𝑑𝑑 𝐿𝐿𝑔𝑔 𝐿𝐿𝑔𝑔 𝐶𝐶𝑓𝑓 2 −𝐾𝐾1𝑐𝑐 𝑒𝑒 − (𝑘𝑘1 𝑘𝑘2 + 1)𝑉𝑉�𝑜𝑜 − 𝑘𝑘3 𝑠𝑠𝑠𝑠𝑠𝑠 𝑉𝑉�𝑜𝑜 + 𝐾𝐾2𝑐𝑐 𝑝𝑝� + 𝑒𝑒} − 𝑑𝑑̂ 0 𝑜𝑜
𝑜𝑜
0
Moath, Alqatamin, M. L. McIntyre, Joseph Latham, “Backstepping Control for Grid-Connected Single-Phase Inverter Utilizing Variable Structure Observer,” American Control Conference (ACC2019), Under Review.
10/15/2018
Backstepping Control for Grid-Connected SinglePhase Inverter Utilizing Variable Structure Observer
Tracking response of the output voltage for nonlinear local load.
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Current tracking response during seamless transfer between SA and GC modes.
Output voltage response during seamless transfer between SA and GC modes.
Tracking response of the grid current under nonlinear local load.
System response to show unity power factor under nonlinear load.
Moath, Alqatamin, M. L. McIntyre, Joseph Latham, “Backstepping Control for Grid-Connected Single-Phase Inverter Utilizing Variable Structure Observer,” American Control Conference (ACC2019), Under Review.
10/15/2018
Other Relevant Works Control Systems for FACTS Devices • Moath, Alqatamin, M. L. McIntyre, “' 'Nonlinear Adaptive Control for Power System with Static VAR Compensator,” The 3rd IEEE Workshop on the Electronic Grid (EGRID2018), Charleston, SC, USA, to appear. • Moath, Alqatamin, M. L. McIntyre, Joseph Latham, P. Rivera, N. Hawkins “Nonlinear Adaptive Control Design for Power System with STATCOM Device,” American Control Conference (ACC2018), Milwaukie, Wisconsin, USA.
Active Power Buffering • Joseph Latham, M. L. McIntyre, “A Novel Controller for Power Decoupling in a Single-Phase Grid-Tied Inverter Using a Boost Converter,” The 44th Annual Conference of the IEEE Industrial Electronics Society (IECON2018), Washington DC, USA. 34
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Outline • • • • • • •
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Introduction Existing Control Schemes For Grid Connected Inverters Model Based Approach Applications Areas 3 φ and 1φ Grid Connected Inverter Control Solutions Micro-Grid Control Solutions Conclusions
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Conclusion • Grid connected inverter based systems are a critical component in the power system • Primary-Level control schemes assume linearity with little to no disturbances • Advanced control schemes can compensate for unmolded, nonlinearity, uncertainty, and disturbances • Move away from cascaded approaches • Creating a faster, more accurate controllable system • Benefit from Model-Based Approaches – Observers, Fault Detections, Identification, Abatement, others……
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