Power Tracking Error Research Articles

Coordinating variable refrigerant flow system for effective demand response in commercial buildings

Model Predictive Control (MPC) is extensively utilized for demand response (DR) in commercial buildings. When deploying MPC in real buildings, the model uncertainty is unavoidable, which could come from multiple sources: incorrectly identified values of model parameters, unmeasured disturbances, sensor errors, etc. However, there is a lack of research on the effects of model uncertainty on the performance of MPC for DR events. This study addresses this gap by analyzing the impact of model uncertainty on MPC in coordinating multiple VRF systems in commercial buildings. A virtual testbed was developed to benchmark and evaluate different DR control algorithms. We compared rule-based control (RBC), priority stack-based control (PSBC), and MPC with model uncertainties. This involved assuming normal distributions with various means for biased and unbiased uncertainties and different standard deviations. Our results show that MPC is robust to model uncertainty. For costs saving tasks, when the model uncertainty is unbiased, MPC outperforms the RBC controller with fewer discomfort hours and lower energy costs when the uncertainty of cooling load is below 40 % and 90 %, respectively; when the model uncertainty is biased and increases gradually, MPC can only outperform RBC under small uncertainties of cooling load. For load tracking tasks, when the model uncertainty is unbiased, MPC outperforms PSBC in terms of fewer discomfort hours and lower power tracking error, even with a 100 % uncertainty of cooling load; when the model uncertainty is biased, it exhibits a similar pattern to the unbiased uncertainty. Last, this study compared the computation time and control performance of formulating MPC as integer versus linear programming, demonstrating that linear programming is more suitable for coordinating thermally controllable loads (TCLs) at large-scales due to its faster computation time and good tracking performance. This study provides valuable insights into the effects of model uncertainty on MPC performance in demand response and supports its practical application in commercial buildings.

Adaptive maximum power point tracking based on Kalman filter for hydrogen fuel cell in hybrid unmanned aerial vehicle applications

In this paper, an adaptive real-time estimation method based on Kalman filter is proposed for tracking the maximum power point (MPP) of a hydrogen fuel cell (FC) in hybrid unmanned aerial vehicle (UAV) applications. To achieve the adaptive MPP tracking (MPPT), a mathematical model for the hydrogen FC is established. Then, the recursive least square method is employed to identify the initial values of model parameters. On this basis, the MPP of the hydrogen FC under steady conditions can be derived. Furthermore, the state and observation equations based on Kalman filter are introduced to adaptively estimate the model parameters in real-time. Moreover, the real-time model parameters would be used to optimize the MPP in accordance with the operating conditions such that the adaptive MPPT can be achieved. Finally, various simulations and experiments are conducted to verify the effectiveness and accuracy of the adaptive MPPT for the hydrogen FC in hybrid UAV applications. Results show that the adaptive MPPT can not only track the MPP accurately in real-time, but also reduce the oscillation of the hydrogen FC. Compared with the MPPT methods based on perturb and observe (P&O) and particle swarm optimization (PSO), the maximum power tracking error of the adaptive MPPT can be improved by 2.83% and 1.10%, respectively.

Heteroscedastic Bayesian Optimisation for Active Power Control of Wind Farms*

Active power control of wind farms remains an open challenge due to inherent noise in wind power that arises from uncertain wind speed measurements and plant/model mismatch. To leverage the heteroscedastic nature of the wind power noise, heteroscedastic Bayesian optimisation (BO) is used for active power control of wind farms. BO utilises closed-loop performance data to tune the parameters of a stochastic model predictive controller (SMPC) in a systematic and data-efficient manner. This, in turn, allows for enhancing the closed-loop performance of the controller intended to decrease the power tracking error. A case study with 9 turbines in a 3 × 3 wind farm shows that the heteroscedastic BO approach achieves a reduced closed-loop power tracking error in terms of root-mean-square by 8.89% compared to one that relies on nominal BO and a decrease by 64.99% compared to a nominal model predictive controller (MPC) whose performance is not tuned using closed-loop data and BO.

Robust Cadence and Power Tracking on a Switched FES Cycle With an Unknown Electromechanical Delay

Functional electrical stimulation (FES) is commonly used to facilitate cycling tasks for people with lower-limb movement disorders. In this work, FES and motor controllers are designed to track a desired power and cadence, respectively, and a Lyapunov-based switched systems analysis is performed to guarantee uniformly ultimately bounded power tracking and global exponential cadence tracking for a switched, delayed, nonlinear, and uncertain FES-cycling system. A unique challenge in this problem is that there is an unknown time-varying input delay to produce force, and a different unknown time-varying residual input delay where force is still produced after stimulation is removed. These delays impact the dwell-time conditions that dictate stimulation timing, and if not properly accounted for can lead to undesired effects such as antagonistic muscles exerting force at the same time or potential instabilities. The proposed controllers were validated by experimental analysis of four participants with neurological conditions (NCs) and five able-bodied participants, and yielded average power and cadence tracking errors of 0.01 ± 0.09 W and −0.05 ± 0.65 revolutions per minute (RPM), respectively, for the able-bodied participants and 0.01 ± 1.11 W and −0.07 ± 1.17 RPM, respectively, for the participants with NCs.

A hierarchical dispatch strategy of hybrid energy storage system in internet data center with model predictive control

The internet data center (IDC) can improve the stability of power system and increase the utilization of uninterruptible power supply (UPS) with battery energy storage system (BESS) and hydrogen fuel cell (HFC) by participating in dispatch operations. This paper proposes a hierarchical dispatch strategy assisted by model predictive control (MPC) for UPS in IDC including available energy analysis, the upper-level power system dispatch strategy and the lower-level IDC dispatch strategy. The data security can be ensured through available energy analysis based on load forecasting information of IDC. Then, the upper-level dispatch model aims at increasing the utilization of UPS and the revenue of IDC via minimizing the total generation cost. Meanwhile, the lower-level dispatch method with MPC reallocates the upper-level dispatch instructions between BESS and HFC by balancing power tracking error and the state of charge of BESS. Finally, the effectiveness of the strategy is verified by several experiments in MATLAB platform. Numerical results show that the proposed strategy increases the utilization rate of the UPS by about 85% and the revenue by about ¥5950, and the SOC fluctuation is reduced to 12%-19%.

Robust H2-Optimal TS Fuzzy Controller Design for a Wind Energy Conversion System

In this paper, robust optimal control of an uncertain wind energy conversion system (WECS), described by a Takagi–Sugeno fuzzy model, is proposed to guarantee the maximum power trajectory tracking (MPTT). The design of the fuzzy optimal control is based on a quadratic criterion related to the maximum power tracking error. The proposed fuzzy controller allows to regulate the rectified direct current (DC) voltage of the variable-speed wind turbine by adjusting the duty cycle of a boost converter. Linear matrix inequality (LMI) conditions, ensuring the optimal H2 tracking error, are proposed for the controller gain design. Simulation as well as experimental tests are performed for efficiency evaluation of the established MPPT fuzzy control scheme under variable wind speed conditions.

Study of a virtual-impedance of the capacitor-series inverter for wider accurate power control range

A droop control method with virtual-impedance for capacitor-series inverter (CSI) is studied in this paper. Compared with the traditional inverters, CSI has more merits in low-cost reactive power compensation. Therefore, it may a promising solution in a microgrid (MG) to reduce the loss and improve the reactive power compensation, harmonics damping abilities. A control strategy based on the droop-curve is wide-spread in the MG system to achieve inverter’s regulation. However, the inherent flaw of droop control narrowed the accurate power output range to a very small scope, which will influence the application of CSI. The control loop which can emulate the impedance, called virtual impedance, is developed to realize wider precise power transfer. Additionally, the principles of the virtual-impedance are presented in the paper as well, by evaluating the margins of power control, transient performance, and stability of the inverter. Some tests on the experiment prototype are conducted, results indicated the proposed method is effective to extend accurate power control range, and power tracking error can be reduced to 0.5% from 17%.

Design and control of a new power conditioning system based on superconducting magnetic energy storage

Superconducting magnetic energy storage (SMES) is characteristic as high power capacity and quick response time, which can be widely applied in power grid to suppress rapid power fluctuation, and improve transient stability. But the traditional power conditioning system (PCS) of SMES, which handle the power transfer between the superconducting magnet and AC power grid, will induce high frequency overvoltage on the magnet, which may lead to the rapid aging of the coil and the decrease of its service life. In this paper, a new circuit scheme of PCS is proposed, and GaN power semiconductor is adopted to increase switching frequency and power density. Then, the model predictive control (MPC) method based on the new scheme is proposed. And the software implementation process for MPC is optimized to reduce the implementation of MPC algorithm time. Finally, simulation and experiment show that the new PCS can not only solve the overvoltage problem of superconducting magnet from the source but also reduce the power tracking error of the superconducting energy storage system. By these software optimization measures, the MPC algorithm can be finished within 10 μs, and the portability and response speed of SMES can be significantly improved to make SMES used in more situations.

Deadbeat prediction direct power control of Vienna rectifier under unbalanced three-phase Voltage

There are many control strategies for Vienna rectifiers, but most of them are carried out when the power grid is balanced. In the case of unbalanced power grids, this paper proposes a deadbeat predictive direct power control to reduce the ripple problem of negative sequence current and active power. The strategy meets the minimum power tracking error as the control target to calculate the desired AC side voltage vector, and introduces space vector pulse width modulation to form a closed loop control system. Under unbalanced grid conditions, this strategy can also effectively extract the positive and negative sequence components of the grid voltage and current to form power compensation to suppress the negative sequence components of the current, thereby reducing the current harmonic content. And carry the Vienna rectifier simulation on MATLAB/Simulink for verification.

Multivector Model Predictive Power Control for Grid Connected Converters in Renewable Power Plants

Model-based predictive power control (MPPC) is a well-known and useful technique for control of electric drives and renewable energy generation systems. However, this strategy relies on the knowledge of accurate system models and parameter values, and would otherwise lead to tracking errors in applications because of inevitable parameter uncertainties. Also, step delays in MPPC implementations have to be compensated to eliminate errors. This article proposes a predictive control application to control active and reactive powers exchanged between the grid and the grid side converter (GSC) interfacing renewable energy sources such as wind farms or photovoltaic. The proposed MPPC minimizes the power tracking error based on a proposed cost function and the control system output is the voltage reference for the electronic converter that is converted into switching pulses by the modulation stage. The proposed control strategy is designed to eliminate tracking errors and has fixed switching frequency while featuring a fast-dynamic response, low current THD, and low computational burden. The method has been evaluated using MATLAB/Simulink environment and an experimental 5-kW grid-connected voltage source converter. Finally, the proposed MPPC method has been critically compared to the previous MPPC approaches.

Model Predictive Power Control of Grid-Connected Quasi Single-Stage Converters for High-Efficiency Low-Voltage ESS Integration

The grid-connected quasi-single-stage converter (QSSC) provides a direct power flow path from low-voltage (LV) energy storage systems (ESS) to ac–dc converters, resulting in reduced power conversion stage for high-efficiency ESS integration. However, due to the dc-link voltage ratio between the two ports varies with the ESS state of charge, the voltage vectors in the ac side are unevenly distributed in the QSSC. This nonlinearity brings some challenges in control and modulation design for the ac–dc part of QSSC. In this article, a virtual two-level converter model considering the two ports as a single dc source is proposed, and model predictive power control (MPPC) based on the virtual two-level model is proposed to enhance the grid current performance. The duty cycle of each phase is calculated based on the active and reactive power tracking error minimization in the two-level converter frame, and the duty cycle for each switching pair is obtained by minimizing the power processed by the dc–dc converter. In this way, the complicated implementation of MPPC for a three-level converter is avoided, and the controller design of the QSSC can be simplified. The effectiveness of the proposed virtual two-level converter model and MPPC method are verified with experimental results.

Real‐time distributed economic dispatch scheme of grid‐connected microgrid considering cyberattacks

Cyber security of microgrids attracts increasing attention since the relatively open communication network of the microgrids is vulnerable to hacker attacks. This study proposes a real-time distributed economic dispatch scheme for the grid-connected microgrid against the cyberattacks. Firstly, a virtual leader agent is placed at the point of common coupling to measure the real-time power tracking error for achieving the power supply–demand balance, and then the optimal solution of the economic dispatch model is solved by the consensus algorithm of the multi-agent system theory. Subsequently, a set of detection algorithms is designed for each generator to determine whether its neighbouring generators suffer from the cyberattacks. The attacked generator is gradually marginalised from the communication network through updating the weight in the communication adjacency matrix based on its reputation value, thereby the impact of the attacked generator on the whole system is reduced greatly. Finally, the numerical simulations are carried out to verify the effectiveness of the proposed cyberattack-resilient distributed economic dispatch scheme.

Torque and cadence tracking in functional electrical stimulation induced cycling using passivity-based spatial repetitive learning control

Due to the inherent periodic nature of cycling tasks, iterative and repetitive learning controllers are well motivated for rehabilitative cycling. Motorized functional electrical stimulation induced cycling is a rehabilitation treatment where multiple lower-limb muscle groups are activated jointly with an electric motor to achieve cycling objectives such as speed (cadence) and torque tracking. This paper examines torque tracking accomplished by the stimulation of six lower-limb muscles via a novel spatial repetitive learning control and cadence regulation by an electric motor using a sliding-mode controller. A desired torque trajectory is constructed based on the rider’s kinematic efficiency, which is a function of the crank position. The learning controller takes advantage of the periodicity of the desired torque trajectory to provide a feedforward input to the stimulated muscles. A passivity-based analysis is developed to ensure stability of the torque and cadence closed-loop error systems. The muscle learning and electric motor controllers were implemented in real-time during cycling experiments on five able-bodied individuals and three participants with movement disorders. The combined average cadence tracking error was 0.01±1.20 RPM for a 50 RPM trajectory and the combined average power tracking error was 1.78±1.25 W for a peak power of 10 W.

Virtual Flux Predictive Direct Power Control of Five-level T-type Multi-terminal VSC-HVDC System

This paper proposes a Virtual Flux Predictive Direct Power Control (PDPC) for a five-level T-type multi-terminal Voltage Source Converter High Voltage Direct Current (VSC-HVDC) transmission system. The proposed PDPC scheme is based on the computation of the average voltage vector using a virtual flux predictive control algorithm, which allows the cancellation of active and reactive power tracking errors at each sampling period. The active and reactive power can be estimated based on the virtual flux vector that makes AC line voltage sensors not necessary. A constant converter switching frequency is achieved by employing a multilevel space vector modulation, which ensures the balance of the DC capacitor voltages of the five-level t-type converters as well. Simulation results validate the efficiency of the proposed control law, and they are compared with those given by a traditional direct power control. These results exhibit excellent transient responses during range of operating conditions.

A novel Lyapunov stable higher order B-spline online adaptive control paradigm of photovoltaic systems

In this paper, research on the control of photovoltaic (PV) using a novel higher order B-spline online adaptive neuro-fuzzy paradigm considering high external uncertainties in weather and load demand is presented. We optimize the existing neuro-fuzzy technique by incorporating third order B-spline membership functions in its antecedent part, which we solve using an on-line learning gradient-decent back propagation method. We fit the system parameters online through adaptive fuzzy rules extracted from the maximum power point tracking (MPPT) error and its derivative. Unlike many existing neuro-fuzzy techniques, our method addresses the trapping in local minima. The proposed controller is demonstrated to be stable using Lyapunov stability analysis. The performance of our control philosophy is checked in terms of output power tracking, efficiency, and MPPT error. Finally, we validate via simulation the high robustness and the self-adaptation ability of the proposed method over other existing traditional and intelligent techniques.

Power-tracking control for cross-flow turbines

For economic reasons, above a certain water speed, it is desirable for current turbines to maintain a constant power output. This requires a control strategy to shed power. Here, such a strategy is evaluated through simulation and laboratory experiment for a helically bladed turbine with four blades and a straight-bladed turbine with two blades. These are contrasting cases because hydrodynamic torque produced by the straight-bladed turbine has a substantially more azimuthal phase variability than the helically bladed turbine. For practical implementation, a control algorithm is desired that requires only a time-average characteristic performance curve and estimates of angular velocity and control torque. Additionally, the transition between power maximizing and power tracking regimes should be smooth and automatic. The controller can be further constrained to only apply a resistive torque to the turbine. A control strategy satisfying these constraints is shown experimentally to achieve these objectives for both types of turbines at a variety of power set points. The power-tracking error (<3%) is primarily at the blade passage frequency for the straight-bladed turbine and at the rate of turbine rotation for the helical turbine. While partially a consequence of how the generator drive is tuned, comparison to simulation indicates that perfect power-tracking is not generally possible even under ideal conditions for a fixed-pitch, cross-flow turbine using purely resistive torque control.

Receding Horizon Optimization of Wind Farm Active Power Distribution with Power Tracking Error and Transmission Loss

In this paper, a receding-horizon optimization strategy is introduced to optimize the wind farm active power distribution with power tracking error and transmission loss. Based on the wind farm transmission connections, a wind farm can be divided into clusters, in which the wind turbine generator systems connected to one booster station can be taken as one cluster, and different clusters connected from booster stations to the farm-level main transformer output the electric power to the grid. Thus, in the proposed strategy, the power tracking characteristic of the wind turbine generator system is modeled as a first-order system to quantify the power tracking error during the power tracking dynamic process, where the power transmission losses from wind turbine generator systems to booster stations are also modeled and considered in the optimization. The proposed strategy is applied to distribute the active power set-point within a cluster while the clusters’ set-point still follows the conventional strategy of the wind farm. Simulation results show significant improvement for both optimization targets of the proposed strategy.

Predictive Approach for Power Quality Improvement Based Direct Power Control

The extensive use of non-linear loads in industry becomes increasingly a serious problem that affects the quality of energy delivered to customers. Therefore, the shunt active power filter (SAPF) has emerged as an important industrial tool to eliminate induced harmonic currents and compensating of reactive power. This paper proposes an improved control configuration for SAPF based on a modern technique called predictive direct power control (Predictive-DPC). The principle of this control is based on the direct regulation of the instantaneous active and reactive powers to guarantee a good energy quality on the grid side. For this purpose the appropriate average voltage vector which cancels power tracking errors is calculated by a simple predictive model at the bigining of each control period. This type of control includes various features such as the lack of look up table (LUTs) and closed current loops and the constant switching frequency is achieved through the use of PWM modulation. The results of the simulation process show a high performance in the steady and transient state function for predictive-DPC control that might be a reasonable alternative to conventional DPC in the field of active power filtering.

Multi-Level Energy Management System for Real-Time Scheduling of DC Microgrids With Multiple Slack Terminals

Multi-level energy management system (EMS) is proposed for dc microgrids operations to ensure system reliability, power quality, speed of response, and control accuracy in this paper. System distributed control is scheduled as the primary control. Battery energy storages (BESs) operate in voltage regulation mode with droop control for power sharing. However, bus voltage deviation and power tracking error due to line impedance are the main drawbacks of distributed control. To enhance the system power quality and control accuracy, bus voltage restoration and power sharing compensation are implemented in secondary control. Economic dispatch based on comparison of system units' marginal operation costs is carried out in tertiary control to minimize the system operation cost. Detailed elaboration has been derived to quantify BES utilization cost due to the cumulated lifetime degradation. In case of communication failure, system operation can still be retained with primary control without operating mode change so that to enhance system reliability. A lab scale dc microgrid is developed for the verification of the proposed multi-level EMS and relevant control techniques.

Multilevel Energy Management System for Hybridization of Energy Storages in DC Microgrids

Hybridization of energy storages (ESs) with different ramp rates helps minimization of system bus voltage variation and extension of ESs lifetime in dc microgrids. Hybrid ES system (HESS) control is normally realized with centralized coordination. In this paper, HESS distributed control, which is independent of the communication link, is proposed to enhance system reliability. All ESs are configured as slack terminals to regulate system bus voltage with droop control. System net power decomposition and ESs power sharing are realized with localized low-pass filter (LPF) applied to ESs with low-ramp rates. The relationship between LPF cut-off frequency and ES ramp rate is elaborated in detail. However, bus voltage deviation and power tracking errors are the main drawbacks of HESS distributed control. Multilevel energy management system (EMS) is thus proposed to enhance system control accuracy. HESS distributed control is scheduled as the primary control. Bus voltage restoration and power sharing compensation are applied in secondary control to eliminate the voltage deviation and power tracking errors, respectively. In tertiary control, autonomous state of charge (SoC) recovery is implemented to limit SoC variation of ES with high-ramp rate. A lab-scale dc microgrid is developed to verify the proposed multilevel EMS for HESS control.