Voltage Stabilization in Microgrids via Quadratic Droop Control

We consider the problem of voltage stability and reactive power balancing in islanded small-scale electrical networks outfitted with DC/AC inverters ("microgrids"). A droop-like voltage feedback controller is proposed which is quadratic in the local voltage magnitude, allowing for the application of circuit-theoretic analysis techniques to the closed-loop system. The operating points of the closed-loop microgrid are in exact correspondence with the solutions of a reduced power flow equation, and we provide explicit solutions and small-signal stability analyses under several static and dynamic load models. Controller optimality is characterized as follows: we show a one-to-one correspondence between the high-voltage equilibrium of the microgrid under quadratic droop control, and the solution of an optimization problem which minimizes a trade-off between reactive power dissipation and voltage deviations. Power sharing performance of the controller is characterized as a function of the controller gains, network topology, and parameters. Perhaps surprisingly, proportional sharing of the total load between inverters is achieved in the low-gain limit, independent of the circuit topology or reactances. All results hold for arbitrary grid topologies, with arbitrary numbers of inverters and loads. Numerical results confirm the robustness of the controller to unmodeled dynamics.Comment: 14 pages, 8 figure

On the Robust Control and Optimization Strategies for Islanded Inverter-Based Microgrids

In recent years, the concept of Microgrids (MGs) has become more popular due to a significant integration of renewable energy sources (RESs) into electric power systems. Microgrids are small-scale power grids consisting of localized grouping of heterogeneous Distributed Generators (DGs), storage systems, and loads. MGs may operate either in autonomous islanded mode or connected to the main power system. Despite the significant benefits of increasing RESs, many new challenges raise in controlling MGs. Hence, a three layered hierarchical architecture consisting of three control loops closed on the DGs dynamics has been introduced for MGs. The inner loop is called Primary Control (PC), and it provides the references for the DG’s DC-AC power converters. In general, the PC is implemented in a decentralized way with the aim to establish, by means of a droop control term, the desired sharing of power among DGs while preserving the MG stability. Then, because of inverterbased DGs have no inertia, a Secondary Control (SC) layer is needed to compensate the frequency and voltage deviations introduced by the PC’s droop control terms. Finally, an operation control is designed to optimize the operation of the MGs by providing power setpoints to the lower control layers. This thesis is mainly devoted to the design of robust distributed secondary frequency and voltage restoration control strategies for AC MGs to avoid central controllers and complexity of communication networks. Different distributed strategies are proposed in this work: (i) Robust Adaptive Distributed SC with Communication delays (ii) Robust Optimal Distributed Voltage SC with Communication Delays and (iii) Distributed Finite-Time SC by Coupled Sliding-Mode Technique. In all three proposed approaches, the problem is addressed in a multi-agent fashion where the generator plays the role of cooperative agents communicating over a network and physically coupled through the power system. The first approach provides an exponentially converging voltage and frequency restoration rate in the presence of both, model uncertainties, and multiple time-varying delays in the DGs’s communications. This approach consist of two terms: 1) a decentralized Integral Sliding Mode Control (ISMC) aimed to enforce each agent (DG) to behaves as reference unperturbed dynamic; 2) an ad-hoc designed distributed protocol aimed to globally, exponentially, achieves the frequency and voltage restoration while fulfilling the power-sharing constraints in spite of the communication delays. The second approach extends the first one by including an optimization algorithm to find the optimal control gains and estimate the corresponding maximum delay tolerated by the controlled system. In the third approach, the problem of voltage and frequency restoration as well as active power sharing are solved in finite-time by exploiting delay-free communications among DGs and considering model uncertainties. In this approach, for DGs with no direct access to their reference values, a finite-time distributed sliding mode estimator is implemented for both secondary frequency and voltage schemes. The estimator determines local estimates of the global reference values of the voltage and frequency for DGs in a finite time and provides this information for the distributed SC schemes. This dissertation also proposes a novel certainty Model Predictive Control (MPC) approach for the operation of islanded MG with very high share of renewable energy sources. To this aim, the conversion losses of storage units are formulated by quadratic functions to reduce the error in storage units state of charge prediction

Risk-Averse Model Predictive Operation Control of Islanded Microgrids

In this paper we present a risk-averse model predictive control (MPC) scheme for the operation of islanded microgrids with very high share of renewable energy sources. The proposed scheme mitigates the effect of errors in the determination of the probability distribution of renewable infeed and load. This allows to use less complex and less accurate forecasting methods and to formulate low-dimensional scenario-based optimisation problems which are suitable for control applications. Additionally, the designer may trade performance for safety by interpolating between the conventional stochastic and worst-case MPC formulations. The presented risk-averse MPC problem is formulated as a mixed-integer quadratically-constrained quadratic problem and its favourable characteristics are demonstrated in a case study. This includes a sensitivity analysis that illustrates the robustness to load and renewable power prediction errors

Fault Detection for Grid-Forming Inverters in Islanded Droop-Controlled AC Microgrids

In this paper, we develop an observer-based fault detection mechanism for grid-forming inverters operating in islanded droop-controlled AC microgrids. The detection scheme uses linear matrix inequalities as constraints with $\mathcal{H}_{-}/\mathcal{H}_{\infty}$ optimization to achieve sensitivity to faults and robustness against disturbances or parametric uncertainties. We explore a nonlinear inverter model formulation based on the less-restrictive one-sided Lipschitz and quadratic inner-boundedness conditions instead of the state-of-the-art formulation based on the Lipschitz condition. In this sense, we aim to overcome the sensitivity of observer-based schemes to the Lipschitz constant. The relation between these two formulations for fault detection is analyzed theoretically. We find the deterministic matrix expressions of different internal faults, including busbar, actuator, and inverter bridge faults. The performance of the proposed detection method is tested on an islanded AC microgrid with four grid-forming inverters and compared against the state-of-the-art nonlinear detection based on the Lipschitz condition. Most importantly, this method requires no additional sensors, a crucial advantage over many proposed solutions in the literature.Comment: 10 pages, 6 figure

Distributed MPC for coordinated energy efficiency utilization in microgrid systems

To improve the renewable energy utilization of distributed microgrid systems, this paper presents an optimal distributed model predictive control strategy to coordinate energy management among microgrid systems. In particular, through information exchange among systems, each microgrid in the network, which includes renewable generation, storage systems, and some controllable loads, can maintain its own systemwide supply and demand balance. With our mechanism, the closed-loop stability of the distributed microgrid systems can be guaranteed. In addition, we provide evaluation criteria of renewable energy utilization to validate our proposed method. Simulations show that the supply demand balance in each microgrid is achieved while, at the same time, the system operation cost is reduced, which demonstrates the effectiveness and efficiency of our proposed policy.Accepted manuscrip

Distributed Control Strategies for Microgrids: An Overview

There is an increasing interest and research effort focused on the analysis, design and implementation of distributed control systems for AC, DC and hybrid AC/DC microgrids. It is claimed that distributed controllers have several advantages over centralised control schemes, e.g., improved reliability, flexibility, controllability, black start operation, robustness to failure in the communication links, etc. In this work, an overview of the state-of-the-art of distributed cooperative control systems for isolated microgrids is presented. Protocols for cooperative control such as linear consensus, heterogeneous consensus and finite-time consensus are discussed and reviewed in this paper. Distributed cooperative algorithms for primary and secondary control systems, including (among others issues) virtual impedance, synthetic inertia, droop-free control, stability analysis, imbalance sharing, total harmonic distortion regulation, are also reviewed and discussed in this survey. Tertiary control systems, e.g., for economic dispatch of electric energy, based on cooperative control approaches, are also addressed in this work. This review also highlights existing issues, research challenges and future trends in distributed cooperative control of microgrids and their future applications

A Novel Stochastic Predictive Stabilizer for DC Microgrids Feeding CPLs

In this work, a novel nonlinear approach is proposed for the stabilization of microgrids (MGs) with constant power loads (CPLs). The proposed method is constructed based on the incorporation of a pseudo-extended Kalman filter (EKF) into stochastic nonlinear model predictive control (MPC). In order to achieve high-performance and optimal control in dc MGs, estimating the instantaneous power flow of the uncertain CPLs and the available power units is essential. Thus, by utilizing the advantages of the stochastic MPC and the pseudo-EKF, an effective control solution for the stabilization of dc islanded MGs with CPLs is established. This technique develops a constrained controller for practical application to handle the states and control input constraints explicitly; furthermore, as it estimates the current by using the pseudo-EKF, it is a current-senseless approach. As noisy measurements are taken into account for the state estimation, it leads to a less conservative control action rather than the classical robust MPC, whereas it guarantees the global asymptotic stability in the presence of noisy measurements and parameter uncertainty. To validate the performance of the proposed controller, the attained results are compared with state-of-the-art controllers. Furthermore, the implementability of the proposed method is validated using real-time simulations on dSPACE hardware