Passivity-Based Power Sharing and Voltage Regulation in DC Microgrids With Unactuated Buses

In dc microgrids, load power sharing and bus voltage regulation are two common control objectives. In this article, a consensus-based algorithm is presented to achieve proportional power sharing and regulation of weighted geometric mean of bus voltages in dc microgrids with ZIP (constant impedance, constant current, and constant power) loads simultaneously. By using the virtue of the Laplacian matrices of undirected connected graphs, a lemma is derived to assist the stability analysis of the dc microgrids. Thus, a sufficient condition that stabilizes the system with ZIP loads is established. In addition, with the help of a distributed voltage regulation error estimator, the tuning of the bus voltages can be realized without the requirement on initial voltage conditions. Through the Lyapunov synthesis, the large-signal stability of the closed-loop system is theoretically ensured for a wide range of load conditions. Finally, simulation studies are performed to validate the merits of the proposed consensus-based algorithm.

In this paper, a novel distributed control algorithm for current sharing and voltage regulation in DC microgrids is proposed. The DC microgrid is composed of several distributed generation units, including buck converters and current loads. The considered model permits an arbitrary network topology and is affected by an unknown load demand and modeling uncertainties. The proposed control strategy exploits a communication network to achieve proportional current sharing using a consensus-like algorithm. Voltage regulation is achieved by constraining the system to a suitable manifold. Two robust control strategies of sliding mode type are developed to reach the desired manifold in a finite time. The proposed control scheme is formally analyzed, proving the achievement of proportional current sharing, while guaranteeing that the weighted average voltage of the microgrid is identical to the weighted average of the voltage references.

The P-V Curve, Q-V Curve, or P-Q-V Curve have been widely used to analyze power system behaviors under varying loading conditions. These curves have been generated under the condition that tire constant P-Q load component of a bus (or a collection of buses) varies, with the constant current load and constant impedance load being kept indeed As such, the physical meaning of these curves can be easily explained. Motivated by the facts that load models have profound impacts on power system behaviors and that the nonlinear load model ZIP-model is popular in modeling nonlinear behaviors of loads, this paper proposes a new class of curves, called ZIP-V curves, to better trace power system steady-state stationary behavior due to load and generation variations. The ZIP-V curves encompass the traditional P-V, Q-V, P-Q-V curves (constant P-Q load), I-V curve (constant current load), Z-V curve (constant impedance load), or generalized curves such as IP-V (constant current and constant power load), ZP-V (constant impedance and constant power load) or IZ-V (constant current and constant impedance load) curve when the values of corresponding components are kept constant. A tool based on the continuation power flow (CPFLOW) method useful for generating the ZIP-V curves is developed and its application to generate ZIP-V curves of a 4561-bus interconnected power system is illustrated.

The increasing penetration of dc distributed energy resources (DERs) and dc loads has motivated the utilization of dc microgrids (MGs). In this paper, a new two-level control scheme is proposed for accurate power sharing and appropriate voltage regulation in dc MGs during islanded operation mode. In the primary control level, a P-\dot V droop method is proposed to eliminate the dependency of power sharing among DERs on line resistances. Since the P V droop deviates the voltage derivative to a nonzero value, a voltage derivative restoration mechanism is adopted in the secondary control level to provide voltage stability. The secondary control level also compensates the voltage deviations by cascading an outer voltage control loop with the inner voltage derivative restoration loop. The secondary control signal is broadcasted to each DER via a unidirectional low-bandwidth communication link. Small signal stability of the proposed scheme is analyzed by studying the locus of the system eigenvalues. To verify the efficacy of the proposed method and compare it with the conventional scheme, real-time simulations in OPAL-RT lab setup are provided.

The paradigm shift in electrical power grids and the increased interest towards decentralisation has opened a new window in the design, control and theoretical analysis of small scale power systems, i.e. microgrids, which aim at the integration and utilisation of renewable energy sources, energy storage systems and responsive loads at a local scale. Given their DC nature, DC microgrids have attracted significant interest as they provide a natural interface to the main grid by avoiding additional conversion steps. The aim of this thesis is to design and analyse novel hierarchical control schemes, both at the primary and secondary control level, that guarantee tight voltage regulation, accurate power sharing, current or voltage limitation, and present a straightforward approach towards deriving stability conditions for DC microgrids that incorporate nonlinear loads. As the microgrid configuration is paramount in the theoretical analysis, a rigorous method of computing the admittance matrix is developed that facilitates the stability analysis of DC microgrid systems supplying a constant impedance (Z), constant current (I) or constant power (P) load. This method is particularly useful as it permits the factorisation of the admittance matrix, while separating the singular matrices. In this way, the closed-loop asymptotic stability proof can be more easily approached by isolating the singularities and then, employing straightforward linear algebra tools, such as quadratic eigenvalue problem (QEP) theory, to derive the stability conditions. As stated in the technical specifications of every source, a crucial issue is represented by the ability to protect itself and its interface device (power converter) during faults, transients and unrealistic power demands. That is why current-limiting control is often combined with the primary control, i.e. often droop control, in DC microgrids to ensure the desired unit protection. In this thesis, novel current-limiting droop controllers areformulated for DC microgrids consisting initially of multiple unidirectional DC/DC boost converters and, later on, bidirectional DC/DC boost and three-phase AC/DC converters, that integrate different distributed generation units with the local grid. In contrast to the traditional approaches that use small-signal modelling, here, the accurate nonlinear models of the converter units are taken into account to prove the boundedness and the current-limiting property, by employing Lyapunov methods and the ultimate boundedness theory. Exponential stability at the desired equilibrium point is mathematically guaranteed, and further analysed from a graphical perspective, providing insights of the load’s effect onto the system performance and stability. To address the shortcomings that conventional droop control approaches introduce, i.e. inaccurate power sharing and significant load voltage drop, a DC microgrid architecture that takes into account the power converter dynamics of distributed generation units is deployed under decentralised primary and distributed secondary control scheme, in a hierarchical control framework. At the primary control layer, a novel current-limiting droop control scheme is implemented in a decentralised manner, whereas at the secondary control layer a fully distributed controller that performs a voltage restoration and improves the power sharing is deployed using a nearest-neighbour coupling communication network. By investigating for the first time both the dynamics of the converters with the nonlinear load and the two-layer control, singular perturbation theory is applied to analytically guarantee the stability of the entire DC microgrid. Finally, apart from the desired overcurrent protection, since DC capacitors are customary used at the output of each converter unit to stabilise the output voltage, they also introduce a maximum voltage limit. Hence, as the need for protection against overvoltages has emerged, droop controllers with inherent overvoltage protection are also proposed for parallel and meshed configuration networks. The upper limit of the voltage of each source is rigorously proven using ultimate boundedness theory. Asymptotic stability to the desired equilibrium for the closed-loop system is analytically guaranteed, and detailed conditions are derived to guide the control design. In order to validate the effectiveness of the different control methodologies developed in this thesis, both simulation and experimental testing are performed for each one of the methods, and are also compared with the conventional approaches to highlight their superiority.

The integration of renewable energy sources in DC microgrids presents significant challenges in maintaining stable voltage regulation and efficient power management. Existing control approaches struggle to handle the inherent variability of renewable sources while maintaining optimal system performance. This paper presents an Adaptive Sinh Cosh Optimizer (ASCHO) integrated with cascade Fractional Order Proportional-Integral (FOPI) control to address these challenges. ASCHO enhances the original SCHO algorithm through dynamic parameter updating and improved exploration-exploitation mechanisms. The proposed control system demonstrates significant performance improvements, with ASCHO achieving a fitness value of superior to conventional approaches' values. In practical implementation, the system maintains voltage regulation within ±5V of the reference value and achieves a 70\% reduction in steady-state error (3.15V vs 10.39V) compared to SCHO. The method was extensively validated through 23 benchmark functions comprising unimodal, multimodal, and fixed-dimension multimodal functions, with ASCHO outperforming other algorithms in 17 functions. Comprehensive testing validates the system's robustness under varying solar irradiance, wind speed, and load demands. The results demonstrate faster rise times (0.00208s vs 0.00209s) and improved power management capabilities, while maintaining battery state of charge variations within 0.003%. The successful implementation establishes ASCHO as an effective solution to optimize DC microgrid control systems with high penetration of renewable energy.

In these lecture notes, we delve into the models of the most commonly used DC-DC power converters: namely, the buck converter and the boost converter. Furthermore, we derive models for a DC microgrid consisiting of multiple buck and/or boost converters interconnected via (dynamic) resistive-inductive power lines and supplying the so-called ZIP loads, which are characterized by the parallel combination of constant impedance (Z), current (I), and power (P) load components. Furthermore, we introduce the primary control objectives in DC microgrids, focusing on voltage regulation and current sharing. Finally, we explore the most advanced control techniques to achieve these objectives. Importantly, these lecture notes are not intended to advocate total replacement of Alternating Current (AC) power systems with their Direct Current (DC) counterparts, but rather aim to offer a balanced perspective between them, acknowledging the historical dominance of AC power systems while underscoring the contemporary relevance of DC microgrids, which, with their inherent advantages, represent a viable complement to the existing infrastructure, fostering innovation and resilience in modern power networks.

In this work, we present a novel consensus-based secondary control scheme for current sharing and voltage balancing in DC microgrids, composed of distributed generation units, dynamic RLC lines, and nonlinear ZIE (constant impedance, constant current, and exponential) loads. Situated atop a primary voltage control layer, our secondary controllers have a distributed structure, and utilize information exchanged over a communication network to compute necessary control actions. Besides showing that the desired objectives are always attained in steady state, we deduce sufficient conditions for the existence and uniqueness of an equilibrium point for constant power loads -- E loads with zero exponent. Our control design hinges only on the local parameters of the generation units, facilitating plug-and-play operations. We provide a voltage stability analysis, and illustrate the performance and robustness of our designs via simulations. All results hold for arbitrary, albeit connected, microgrid and communication network topologies.

This chapter is concerned with load sharing and voltage regulation in DC microgrids. In order to address this issue, a multi-objective optimization problem with tunable weighting coefficients is first formulated for DC microgrids. Second, a distributed control scheme, which only requires local communications among neighbors, is proposed to solve the optimization problem. It is shown that, the proposed distributed control scheme has remarkable advantages in improving reliability and scalability of microgrids.

Robust PMU Placement in Branch Switching Power Networks for Minimum Variance State Estimation

This paper studies the effect of Power System Stabilizers in damping of low frequency oscillations in a multi-machine power system with different load combinations. Various load models considered are constant impedance load, mixture of constant impedance and constant current load and mixture of constant impedance and constant power load. For this, a linearized model of multi-machine power system was developed. After forming state matrix, Eigen value analysis was carried out to find out low frequency local and inter-area modes of oscillations. For the optimal placement of PSS, participation factor analysis was carried out. The generator with highest participation factor is considered best candidate for the placement of PSSs. This analysis is carried out for two area (4-machines, 14 bus system) and multi area (16 machines, 68 bus, NY-NETS) system. The performance of PSSs in damping both local and inter-area modes of oscillations was found to be satisfactory.

Static load which is known for three different characteristics i.e. constant power, constant current and constant impedance shows a different voltage profile because both of their real power and reactive power vary differently as the voltage varies except for constant power. This paper will analyze the impact of each load characteristic individually and also as combination on voltage stability of an IEEE 34 Bus Distribution System by increasing the load demand, and also transient analysis i.e. creating a single phase-to-ground fault i.e. on phase a and balanced three phase fault. The most suitable load to study the voltage stability is also proposed. It was found that, with constant power loads, the reactive power demand increases significantly when load real power and reactive power increases by 25%. Constant current loads and combination loads, on the other hand, the reactive power demand increases but only slightly and the demand is even lesser when with constant impedance loads. However, as the load real power and reactive power increases by 50%, constant power loads causes voltage collapse whilst constant current loads and combination loads turn out to be the next in the order followed by constant impedance loads. In transient analysis, during the single phase fault, with combination loads, phase b voltage increases drastically but only small increment observed in phase c voltage. During the three phase fault, phase b voltage is slightly higher than phase c voltage followed by phase a voltage. As comparison to combination loads, constant power loads causes lesser three phase voltages. After the fault was cleared, a smooth voltage waveform obtained in the period of retaining back to the same pre-fault voltage, however, distortions in the voltage recovering waveform seen when dynamic load included in the system. Constant power load is found to be the suitable load to study the voltage stability.

The inaccessibility of energy to remote communities is a great concern due to economical and feasibility constraints in the conventional electrification approach. The reliable, efficient, autonomous, and sustainable solar driven system having the potential to overcome challenges of expansion of conventional utility grid. The solar PV-based distributed generation could address these issues significantly as the cost is declined. The low-voltage DC-microgrid (DCMG) is a prominent solution to achieve autonomy in generation, cost-effectiveness, efficiency, and reliability. This article brings forward an arrangement of a PV-fed two-stage DC/DC conversion stage with battery storage. This provides better control over MPPT and voltage regulation in DCMG. Also, capable of handling uncertainties in source due to weather intermittency and load. The system performance is analyzed in MATLAB/ Simulink under different irradiance and load conditions. The simulation results describe the effectiveness of the proposed system.

In this letter we propose a new distributed control scheme, achieving current sharing and average voltage regulation in direct current (dc) microgrids. The considered dc microgrid is composed of several distributed generation units (DGUs) interconnected through resistive-inductive power lines. Each DGU includes a generic energy source that supplies a local current load through a dc-dc buck converter. The proposed distributed control scheme achieves current sharing and average voltage regulation, independently of the initial condition of the controlled microgrid. Moreover, the proposed solution requires only measurements of the generated currents, and is independent of the microgrid parameters and the topology of the used communication network, facilitating plug-and-play capabilities. Global convergence to a desired steady state is proven and simulations indicate a good performance.

Advancements in power conversion efficiency and the growing prevalence of DC loads worldwide have underscored the importance of DC microgrids in modern energy systems. Addressing the challenges of power-sharing and voltage stability in these DC microgrids has been a prominent research focus. Sliding mode control (SMC) has demonstrated remarkable performance in various power electronic converter applications. This paper proposes the integration of universal droop control (UDC) with SMC to facilitate distributed energy resource interfacing and power-sharing control in DC microgrids. Compared to traditional Proportional-Integral (PI) control, the proposed control approach exhibits superior dynamic response characteristics. The UDC is strategically incorporated prior to the SMC and establishes limits on voltage variation and maximum power drawn from the DC–DC converters within the microgrid. A dynamic model of the DC–DC converter is developed as the initial stage, focusing on voltage regulation at the DC link through nonlinear control laws tailored for Distributed Generation (DG)-based converters. The UDC ensures voltage stability in the DC microgrid by imposing predetermined power constraints on the DGs. Comparative evaluations, involving different load scenarios, have been conducted to assess the performance of the proposed UDC-based SMC control in comparison to the PI control-based system. The results demonstrate the superior efficiency of the UDC-based SMC control in handling dynamic load changes. Furthermore, a practical test of the proposed controller has been conducted using a hardware prototype of a DC microgrid.