Convex Optimization-Based Control Design for Parallel Grid-Connected Inverters

This paper presents a novel frequency-domain approach toward the control design for parallel grid-connected voltage source inverters (VSIs) with LCL output filters. The proposed method allows the controllers of multiple VSIs to be designed in a single step, and inherently attenuates the resonances introduced by the output filters and coupling effects while guaranteeing stability. Performance specifications such as desired closed-loop bandwidth, decoupling or robustness toward multi-model uncertainty can be specified through frequency-domain constraints. Furthermore, controllers can be designed in a plug-and-play fashion. The designed controllers are equivalent in structure to multi-variable PI controllers with filters. As the control design is based on the frequency response of the system, the algorithm is independent of the model order, which allows the use of large and high-order models. The performance of the method is demonstrated on a relevant example of a low-voltage distribution grid with five VSIs, and the results are validated both in numerical simulation using MATLAB/Simulink as well as in power-hardware-in-the-loop experiments

Stability Analysis of High Voltage Hybrid AC/DC Power Systems

Interest in large-scale integration of power from renewable energy sources (RES) has grown in the last decade as a result of energy policies adopted by governments in an effort to reduce CO2 and greenhouse gas emissions. Both large scale, and distributed solar and wind energy have proliferated the power system and will continue to do so in the future. Thus, large and complex transmission systems are needed for robust, flexible and secure operation of the future power system. Multi-terminal HVDC (MTDC) grids are expected to play an important role in an efficient socio-economic operation of the electric power system by acting as a means for integration of RES, exchange of balancing power, crossborder power market trading, grid reinforcement, etc. As the introduction of MTDC grids will eventually result in a hybrid ac/dc power system, it is necessary to carry out a global analysis that considers the entire hybrid ac/dc power system, which includes both dc and all synchronous areas of the power systems. The main objective of this PhD is to study the stability of hybrid ac/dc power systems, with a particular focus on the ac grids. The work investigates how the dynamic characteristics of ac grids will be affected by the introduction of the MTDC grids and/or by control methods implemented in MTDC converter controllers. Modal analysis, in particular eigenvalues, mode shapes, and participation factors, was used to identify and analyze interactions (dynamic coupling) between different subsystems in a hybrid ac/dc power system. Mode shapes were used to identify electromechanical interactions between generators located in different synchronous areas (asynchronous grids). The inter-grid electromechanical interactions are generally weak but are influenced by dc grid control strategy, controller tuning and damped frequency of electromechanical modes. The source of the interactions is dynamic coupling between ac and dc grids. When several terminals share the duty of dc voltage regulation, as in the case of dc voltage droop control operation mode, the dynamics of the ac grids behind those terminals are coupled to a common dc grid dynamics. This leads to indirect coupling of dynamics of different ac grids through dc grid dynamics. A qualitative analysis of state matrix of a single 2-level converter with and without connection to a detailed ac grid model was used to supplement the findings of the quantitative modal analysis. It was shown that there is a two-way dynamic coupling between ac and dc grids when a converter is operated in constant dc voltage or dc voltage droop control modes, i.e. ac grid dynamics is coupled with dc grid dynamics and dc grid dynamics is coupled with ac grid dynamics. However, there is only a one-way coupling between an ac grid and a dc grid if the converter is operated in constant power control mode. In such cases, the ac grid dynamics is coupled with the dc grid dynamics, but the dc grid dynamics is not coupled with the ac grid dynamics. Decentralized control techniques were used to study interactions between power oscillation damping (POD) controllers on multiple terminals of an MTDC that interconnects several asynchronous ac grids. Interaction between the selected control loops was assessed using dynamic relative gain array and performance relative gain array techniques in the frequency domain. In addition, modal and time domain analyses carried out for the study case supported the findings from the frequency domain analysis. For the study case analyzed, it was found that due to control loop interactions the performance of one of the controllers was augmented, while the performance of the other controller deteriorated. The analyses clearly showed that control loop interaction should be considered while tuning PODs on converters even if they are connected to different grids. Finally, a coordinated control strategy for terminal converters of a dc grid was proposed to address the issue of frequency disturbance in other ac grids when one grid receives frequency support from an offshore wind farm. It was shown that by coordinating converter controllers at the terminals of an offshore wind farm and one ac grid, it is possible to maximize frequency support contribution of the offshore wind farm and avoid disturbance in other ac grids connected to the MTDC. However, the proposed method works when only one ac grid is receiving frequency support and the remaining ac grids are connected MTDC terminals, which are operating in dc droop or constant power control mode. If more than one ac grids are to receive frequency support through MTDC grid, then negative interactions occur when the proposed controller is used. Therefore, in such cases, distributed dc voltage and frequency droop control is the best control option. However, it should be noted that with distributed dc voltage and frequency droop control method, the frequency support comes not only from the wind farm but also from other ac grids behind an MTDC terminal operating in dc voltage droop control mode

Distributed generation in future distribution systems : Dynamic aspects

The objective of this thesis work was to study the stability of a distribution network with several distributed generators (DGs) considering different types of regulators in the DGs and loading conditions. The distribution network under study, Øie \u96 Kvinesdal, is a 57 km long radial feeder. It contains 8 distributed generators; seven synchronous and one induction generator. The largest generator has 10.3 MW rated power and the lowest has 0.25 MW rated power. The first and last generators are located 7.3 km and 45 km away from the 106/22 kV transformer respectively. Four of the synchronous generators are located on the same side branch.Four cases were studied with three different total active power production levels, two medium and one maximum production levels, and two different network loading conditions, high and low load.In each case, five different types of disturbances were created to analyse the dynamic response of the distribution network. The disturbances are synchronous generator disconnection, change in load, change in system voltage, short circuit fault, and disconnection of the 22 kV feeder from the HV network. Five different scenarios of synchronous generator disconnections were studied; disconnecting the largest four one by one and disconnecting the smallest three at the same time. Two different scenarios of load changes were studied. The first one is a step change in load either from high load to low load or from low load to high load depending on the initial loading condition of the network. The second type of change in load is disconnection of loads in one area which account to 66% of the total loads in the system. Change in system voltage was created by a 2.5 % step up on the swing bus voltage. The pre-disturbance linear analysis result showed that controllers connected to the smallest generators have strong relations with the least damped eigenvalues. The case with maximum generation and low loading had very low damped oscillations; as low as 6% damping ratios. Selecting appropriate regulator gain constants plays vital role in the distribution system\u92s small signal stability. There are some eigenvalues with imaginary part as high as 11 Hz. This is due to the low inertia of the distributed generators.The generators in all cases were able to regain synchronism after disturbances caused by disconnection of synchronous generators, change in load and system voltage. This is because the distribution network is connected to a strong high voltage network. But not all studied scenarios had terminal voltage and power factor within the allowed range in their post-disturbance steady state. Depending on settings of reactive power and over voltage relays, and how quickly a new set point is calculated for the excitation system controllers, a cascade of faults may occur. This could lead to instability. Relays were not included in this study.The critical clearing time for the case with maximum production and low load was the shortest because the distribution network had high voltage and the DGs were operating with their rated capacity in the pre-disturbance steady state. The distribution network was not able to reach new steady state, and be able to operate in island mode after disconnection of the feeder from the HV network with the turbine and governor models used

Wind Turbine Model Validation with Measurements

The objective of this work is to validate wind turbine models available in commercial simulation tools with measurements. Results are shown for two turbines located in two different wind farms; wind turbine 1 is a fixed speed turbine with induction generator, and wind turbine 2 is a variable speed turbine with converter-interfaced synchronous generator. Simulated active and reactive power transient responses to voltage dips have been compared to measured responses, as suggested by IEA Wind Annex 21. For the fixed speed turbine quite good agreement between measurement and simulation is obtained. Shaft parameters are seen to have significant influence on the simulated active power response. For the variable speed turbine the active and reactive power responses are to a high degree determined by the power electronics interface and corresponding controllers, and particularly the control strategy applied during voltage dips. Wind turbine manufacturers are generally very restrictive on giving out this type of information, and thus typical configurations and parameters have been used in this work. The agreement between measurement and simulation can to some degree be improved by changing the inverter controller parameters by trialand error, but detailed knowledge on the control of the converter would be required in order to achieve a very good agreement. Copyright © 2012 Published by Elsevier Ltd.publishedVersio

Using Decentralized Control Techniques for Interaction Analysis in Hybrid AC/DC Grids

One of the ancillary services that can be provided by Multi-terminal Direct Current (MTDC) grid to connected ac grids is power oscillation damping (POD). However, using PODs at multiple terminals of an MTDC grid results in multi-loop, multi-variable control system. Such control systems inherently have control loop interactions challenge, which can result in reduced performance of one or more controllers. This entails that PODs installed at multiple converter terminals to damp oscillations in respective ac grids could be affected due to unfavorable interactions among the controllers. Thus, compromising the stability of the connected ac grids. This paper presents analyses of interaction between multiple POD controllers installed on MTDC. For a three-terminal study system, insights on interactions between POD controllers at two different converter terminals of an MTDC are obtained using relative gain array and performance relative gain array measures.Using Decentralized Control Techniques for Interaction Analysis in Hybrid AC/DC GridsacceptedVersio

Avoiding AC/DC grid interaction in MMC based MTDC Systems

In this paper, the interaction between ac and dc grids is studied for two types of MMC control structures; conventional and non-conventional control structures. Linear analysis methods that are based mode shapes and participation factors are used to identify dynamic interaction in a hybrid ac-dc power system. The analysis uses as a test system a three terminal Modular Multilevel Converter (MMC) based Multi-terminal High Voltage DC (MTDC) grid connecting three multi-machine asynchronous ac grids. The results show that there is some dynamic interaction between ac and dc grids under conventional MMC converter control structure, while the non-conventional MMC converter control structure decouples the ac and dc side of the MMC converter, thus avoiding interaction between the ac and dc grids

Dynamic interactions between asynchronous grids interconnected through an MTDC system

The large-scale integration of renewable energy sources in the power system, combined with the need for an increased transmission capacity has led to a growing interest in multi-terminal high voltage dc (MTDC) grids. In the future, these grids will be integrated with different existing asynchronous ac grids, eventually resulting in hybrid AC/DC power systems. This paper investigates interactions between asynchronous ac grids in a hybrid AC/DC power system. In the study, a symmetrical monopolar ±400kV four-terminal VSC-based MTDC grid connected to three different multi-machine ac systems is modelled in DIgSILENT PowerFactory. One of the ac grids has four generators while the others have two generators each. Governor and automatic voltage controllers are included for each generator so as to capture the complete generator dynamics. DC cables are modelled as PI models with lumped parameters. All dc grid terminal converters are operating in dc droop and reactive power control modes. A small signal analysis is carried out in the test system to investigate interactions between asynchronous ac grids. From the modal analysis of the poorly damped eigenvalues, it is shown that speed state variables of all generators in the study system are observable in these modes; indicating dynamic interactions between generators located in asynchronous ac grids. The change in the level of these dynamic interactions is studied for different time responses of the MTDC terminal converter controllers. It is found that faster and slower converter control response times lead to lower and higher interactions between the asynchronous ac grids, respectively. Results from a time domain simulation of the study system for a fault in one of the ac grids support the findings of the small signal analysis. The study results show that dynamic coupling exists between ac grids across dc grids and that the level of interaction is influenced by the converter controller settings.status: publishe

Frequency Quality in the Nordic Power System: Wind Variability, Hydro Power Pump Storage and Usage of HVDC Links

This work investigates the effect that variable power production from offshore wind farms in the North Sea will have together with the use of pumped storage facilities at hydropower stations in Norway, on the Nordic frequency. Two different pumped storage cases are investigated for a power exchange situation between Norway and Continental Europe, which illustrates the effect of wind power variability. The performance of primary and secondary controllers to restore frequency quality is analyzed