Modelling and analysis of small signal for multi-machine parallel system based on droop control

Microgrid is a new way to solve current energy problems, such as environmental pollution and resource shortages, for using renewable energy effectively to improve power supply reliability and flexibility. Microgrid inverter has two working modes, on-grid mode and off-grid mode, and seamless transition between the two modes is the key to ensure continuous uninterrupted power supply. The focus of this paper is mainly to achieve the smooth transition from island mode to grid connected mode, to limit the abrupt and transient changes. To achieve this objective, an improved droop control method has been suggested. Voltage-control method based on droop control is used during both on-grid mode and off-grid mode to avoid the forced transition in traditional control strategies. Simulation results are presented using PLECS to validate the seamless transition between the two modes

In an islanded microgrid with multiple distributed generations (DGs), the difference in line impedance may cause local voltage deviation, which leads to a series of problems such as lower power allocation accuracy and bus voltage drop under traditional droop control. In this respect, a method for optimizing the droop control using an improved particle swarm optimization (IPSO) is proposed. Firstly, the microgrid structure and influence of line parameters on traditional droop control strategy is analyzed. Then, an improved particle swarm optimization is proposed. Based on the basic particle swarm optimization (PSO) algorithm, a fuzzy inference system (FIS) is introduced to dynamically adjust the particle swarm optimization, which can effectively improve the global search ability and local search ability of the algorithm. After that, the improved algorithm is applied to the droop controller, simultaneously, the range of stable operation of the system is determined by small signal analysis. Finally, the simulation and experiment results show that the proposed improved droop control strategy can achieve accurate allocation of active and reactive power effectively while maintaining bus voltage and system frequency stability, enhance the dynamic performance and transient stability of the microgrid system.

Droop control is the basic control method for load current sharing in dc microgrid applications. The conventional dc droop control method is realized by linearly reducing the dc output voltage as the output current increases. This method has two limitations. First, with the consideration of line resistance in a droop-controlled dc microgrid, since the output voltage of each converter cannot be exactly the same, the output current sharing accuracy is degraded. Second, the dc-bus voltage deviation increases with the load due to the droop action. In this paper, in order to improve the performance of the dc microgrid operation, a low-bandwidth communication (LBC)-based improved droop control method is proposed. In contrast with the conventional approach, the control system does not require a centralized secondary controller. Instead, it uses local controllers and the LBC network to exchange information between converter units. The droop controller is employed to achieve independent operation, and the average voltage and current controllers are used in each converter to simultaneously enhance the current sharing accuracy and restore the dc bus voltage. All of the controllers are realized locally, and the LBC system is only used for changing the values of the dc voltage and current. Hence, a decentralized control scheme is accomplished. The simulation test based on MATLAB/Simulink and the experimental validation based on a 2 × 2.2 kW prototype were implemented to demonstrate the proposed approach.

Control of Parallel-connected Inverters to Achieve Proportional Load Sharing

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.

PurposeThe model for digitally controlled three-phase pulse width modulation (PWM) boost rectifiers is a sampled data model, which is different from the continuous time domain models presented in previous studies. The controller, which is tuned according to the model in continuous time domain and discretized by approximation methods, may exhibit some unpredictable performances and even result in unstable systems under some extreme situations. Consequently, a small-signal discrete-time model of digitally controlled three-phase PWM boost rectifier is required. The purpose of this paper is to provide a simple but accurate small-signal discrete-time model of digital controlled three-phase PWM boost rectifier, which explains the effect of the sampling period, modulator and time delays on system dynamic and improves the control performance.Design/methodology/approachBased on the Laplace domain analysis and the waveforms of up-down-count modulator, the small signal model of digital pulse width modulation (DPWM) in the Laplace domain is presented. With a combination of state-space average and a discrete-time modeling technique, a simplified large signal discrete time model is developed. With rotation transformation and feed-forward decoupling, the large-signal model is decoupled into a single input single output system with rotation transformation. Then, an integrated small signal model in the Laplace domain is constructed that included the time delay and modulation effect. Implementing the modified z-transform, a small-signal discrete-time model is derived from the integrated small signal model.FindingsIn a digital control system, besides the circuit parameters, the location of pole of open-loop transfer function is also related to system sampling time, affecting the system stability, and the time delay determines the location of the zero of open-loop transfer function, affecting the system dynamic. In addition to the circuit parameters discussed in previous literature, the right half plane (RHP) zero is also determined by the sampling period and the time delay. Furthermore, the corner frequency of the RHP zero is mainly determined by the sampling period.Originality/valueThe model developed in this paper, accounting for the effect of the sampling period, modulator and time delays on the system dynamic, give a sufficient insight into the behavior of the digitally controlled three-phase PWM rectifier. It can also explain the effect of sampling period and control delay time on system dynamic, accurately predict the system stability boundary and determine the oscillation frequency of the current loop in critical stable. The experimental results verify that the model is a simple and accurate control-oriented small-signal discrete-time model for the digitally controlled three-phase PWM boost rectifier.

In order to achieve the flexible and efficient utilization of distributed energy resources, microgrids (MGs) can enhance the self-healing capability of distribution systems. Conventional primary droop control in microgrids exhibits deviations in voltage and frequency and lacks research on voltage–frequency control during network reconfiguration. Therefore, this paper investigates the control strategy of secondary control for voltage and frequency during the process of reconstructing distribution networks to operate in the form of microgrids after faults. Firstly, the mathematical model of three-phase voltage-source inverters with droop control is analyzed. Then, inspired by the generator’s secondary frequency control strategy, an improved secondary control method based on droop control is proposed, and the effectiveness of the improved droop control strategy is verified. Finally, simulation examples of distribution networks with various dynamic boundary topology changes are designed to simulate a relatively stable control result, validating the proposed strategy.

Besides the voltage drop issue by the droop control, dynamic current unbalance due to inertia inconsistency would also happen in multi-parallel energy storage system (ESS) supplied DC charging station. For this, a new multi-phase interleaved-parallel DC converter combined with capacitor-integrated electric spring (C-ES) is developed. And dynamic inertia unified loop and energy-balance-combined dynamic voltage drop compensation control are proposed for this C-ES-combined interleaved-parallel ESS architecture. Dynamic current balance and voltage drop compensation can be simultaneously achieved. In detail, the multi-phase interleaved-parallel structure is taken as the front stage and the C-ES is adopted as the back stage. The working principle is illustrated by analyzing the switching state of the devices one by one. In terms of the control, the dynamic unified inertia loop is designed for the multi-parallel interleaved structure, and the inertia characteristics of each energy unit is reshaped to be consistent and the dynamic current balance can be guaranteed. Thus, the dynamic current balance is achieved by the consistency of physical structure and control performance. Then, an energy-balance-combined dynamic voltage drop compensation control is developed for the C-ES to compensate for both the dynamic and steady-state voltage drop by charging the C-ES. Moreover, the small-signal model is built to reveal the essential mechanism of dynamic current balance and voltage drop compensation. Finally, the effectiveness of C-ES-combined interleaved-parallel ESS architecture on dynamic current balance and voltage drop compensation is validated by simulation and experiment results.

In the three-phase four-wire low-voltage micro grid, three-phase imbalance usually happens because of a large number of single-phase loads. In this situation, the traditional control method cannot effectively control the voltage and frequency stability when the low-voltage micro grid operates in the island mode. According to the characteristics of the three-phase four-wire low-voltage micro grid, this paper designs a single-phase independent control based on the droop control. This paper firstly uses the improved droop control considering that the impedance characteristic of the low voltage micro gird is mainly resistance, and also designs single-phase independent control to ensure the control system have the ability to run under the unbalanced loads. Then this paper designs a two-level control strategy to control the voltage and frequency in the micro grid during the island operation. Finally, a simulation analysis based on the proposed method is used to prove the effectiveness. A micro grid is set up on PSCAD, and verifies the effectiveness of the single-phase control strategy based on the improved droop control. The proposed method can also realize the requirement of the voltage and frequency stability during the island operation. At the same time, the control method proposed in this paper can achieve the control objective under the condition of unbalanced three-phase.

When distributed energy storage units (DESUs) in islanded ac microgrid are controlled by conventional P-f droop control, the state-of-charge (SOC) of DESUs becomes unbalanced due to the inconsistent line impedances and initial SOC. In order to achieve SOC balancing, an improved droop control is presented in this paper. The SOC balancing of DESUs and frequency regulation can be realized by adding a SOC balancing factor to conventional P-f droop control. The advantage of this scheme is that frequency can maintain within the specified range in the process of SOC balancing. Finally, simulation and experimental results in different conditions show the effectiveness of the proposed scheme.

When the power grid impedance mutates, the output power of the grid-connected photovoltaic power generation system controlled by drooping will become very unstable. To solve this problem, an improved droop control algorithm based on network impedance detection is proposed. Taking photovoltaic grid-connected power generation system as the research object, the influence of power grid impedance on traditional droop control is firstly expounded by introducing power grid impedance value into traditional droop control. Then the method of real-time network impedance extraction is introduced. Furthermore, according to the bandwidth and phase angle constraints of the equivalent output impedance phase frequency characteristics of the photovoltaic grid-connected inverter, the controller parameters are updated in real time to achieve the purpose of adaptive network impedance mutation. Finally, the proposed method is tested and verified by real-time simulation in the loop respectively. The results show that the proposed method is correct.

The energy management optimization and DC voltage stability are the main challenges when loads surging and renewable energy sources (RESs) fluctuations occur in the medium-voltage DC distribution system (MVDC-DS). To solve these issues, this paper proposes a dual-time scale energy management method based on improved droop control for the MVDC-DS. Firstly, a ±10 kV three-terminal hybrid modular multilevel converter (MMC)-based ring MVDC-DS with DC fault ride-through capability is constructed, which including electric vehicle charging stations, energy storage systems, multiple loads and RESs. Secondly, the droop control adopted by the hybrid MMC is improved by exp-function to achieve higher power quality. On this basis, a dual-time scale energy management method is proposed to minimize the electricity purchasing cost. The reference power of each controllable unit is optimized in the long time scale, and the parameters of improved droop control are optimized in the short time scale. Finally, a case study is conducted on the ±10 kV three-terminal hybrid MMC-based ring MVDC-DS, and the results indicate that the proposed method can improve the economy and power quality of system, and help to realize the normal system operation under different conditions.

In this paper, a virtual inertia and damping control (VIDC) strategy is proposed to enable bidirectional DC (bi-DC) converter to dampen the voltage oscillation, using the energy stored in energy storage system (ESS) to emulate the inertia of DC microgrid (DC-MG) without modifications of system hardware. Both inertia part and damping part are modelled in the VIDC regulator, by analogizing with DC machine. Droop control is introduced to achieve multi-parallel operation of ESS. Further, its small signal model is established and the dynamic characteristic of the DC bus voltage during power fluctuation is analyzed. A 2nd-order equivalent model is introduced to simplify the parameters design. By analyzing the control performance indices, the VIDC parameters are optimized. At last, based on the principle of equivalent machine, an inertia matching method of the multi-parallel bi-DC converters is proposed. The simulation results verify that ESS, by acting as a synthetic inertia, can improve the voltage dynamic characteristics and stability in islanded DC-MG. Compared with other control methods, it has better control effect.

In recent researches on inverter-based distributed generators, disadvantages of traditional grid-connected current control, such as no grid-forming ability and lack of inertia, have been pointed out. As a result, novel control methods like droop control and virtual synchronous generator (VSG) have been proposed. In both methods, droop characteristics are used to control active and reactive power, and the only difference between them is that VSG has virtual inertia with the emulation of swing equation, whereas droop control has no inertia. In this paper, dynamic characteristics of both control methods are studied, in both stand-alone mode and synchronous-generator-connected mode, to understand the differences caused by swing equation. Small-signal models are built to compare transient responses of frequency during a small loading transition, and state-space models are built to analyze oscillation of output active power. Effects of delays in both controls are also studied, and an inertial droop control method is proposed based on the comparison. The results are verified by simulations and experiments. It is suggested that VSG control and proposed inertial droop control inherits the advantages of droop control, and in addition, provides inertia support for the system.

Distributed cooperative control methods are widely used in the islanded microgrid control system. To solve the deviation of frequency and voltage caused by the droop control, it is necessary to recovery the frequency and voltage to the rated value using a secondary control strategy. However, the traditional communication method relies on the continuous periodic one, which makes the communication burden of the islanded microgrid system heavy and conflicts with the actual operation of the power grid. Using the secondary recovery control method based on the distributed event-triggered method, we conserve communication resources by reducing the number of transmissions of sampled data and achieving the recovery control of the frequency and voltage and the original proportional sharing of active power. In addition, we analyze the stability of the distributed event-triggered strategy and build a microgrid system with MATLAB/Simulink to verify the effectiveness of the control method. Furthermore, we compare with a traditional periodic communication system and demonstrate the superiority of our distributed event-triggered approach.