Linear Quadratic Gaussian Design in a Grid-Connected and Islanded Microgrid System for Stability Enrichment ^†

Abstract

This paper proposes a Linear Quadratic Gaussian (LQG) control design for a grid-connected and Islanded mode Microgrid composed of a single-network feeding and forming converter with one local load. The LQG controller was designed for two different Microgrid modes: Grid-connected mode and islanded mode. A separate LQG controller was designed for each mode and a comparative analysis was made. The LQG controller was designed using the State-Space variables determined by linearizing the model. The controller consists of the optimal gain ‘K’, optimal Linear Quadratic Regulator (LQR), and the Kalman Filter. In both Microgrid modes, the LQG eliminates disturbance and noise in the system and makes the system optimally controlled. The Microgrid system also consists of another control system that comprises the subsequent control subsystem, i.e., Alpha–Beta control, Power and Current loop, and Space Vector Modulation. The steady-state response of the Microgrid system, noise, and disturbance present in Grid-connected and islanded modes was rectified by the LQG controller. The design environment used for developing the Microgrid and LQG controller was the MATLAB/Simulink platform. The effective simulations have permitted and determined results that convey the optimal control and stable performance of the proposed system.

1. Introduction

In the electricity generation, transmission, and distribution industry, the development of recent technologies was taken in various stages up to the current scenario. The entire infrastructure is commonly referred to as “electrical power systems”. At the start of the 20th century, the electrical environment was progressing towards the combination of already-existing power generation competitors, which were usually closer to the end consumers, into large-scale state-sanctioned monopolies. A wider move towards a standardized infrastructure and increase in the reliability of services was considered to be the main impact on technological development. The implementation of recent technologies within the generation units instigated the development path in the electrical engineering field. This technology development enhanced the computing network in electrical power systems and made it smarter, efficient, reliable, and eco-friendly [1]. Due to the increase in load demand and pressure for environmentally friendly power generation technologies, the stability between the generation and distribution of power began to be taken into consideration. Modern projects related to the concepts of sustainable power and smart cities depend on grids with more low-capacity distributed generation systems being installed [2].

The main type of small-scale generation system has a typical capacity of less than 50 MW and is installed nearer to the end consumer facilities. The power generation system acts independently of the Central Load Dispatcher, most probably linked to renewable energy sources, including wind turbines and solar photovoltaic panel-powered systems. The main scope for this distributed generation system is the formation of a locally connected generation, distribution, and consumption electrical power system. The essential parameters for distributed generation units are as follows: Energy storage devices and load, effectively handled with a single controllable unit with specific electrical boundaries connecting the main grid. This design mechanism is considered a Microgrid. The Microgrid reduces the environmental impact and also enhances the local area reliability. It also reduces the risk involved with its less capital-intensive infrastructure [3,4]. Microgrid systems are mainly characterized as flexible and intelligent. This configuration is commonly classified according to the level of integration with the main grid. These classifications are termed operating modes, and they can either be temporary conditions of the grids are selected by design [5,6].

Microgrids can be essentially classified as either grid-connected or islanded Microgrids. In this grid-connected mode, the energy importing and exporting process is carried out from the power utility grid for the Microgrid operation, and it ensures energy and power control flow balance. The grid is supported through an array of ancillary services. This ancillary service involved voltage and frequency control regulation. Based on load and generation conditions, another functionality is also considered [7]. The Microgrids are consistently interlinked to the power utility grid; when there is an excess of energy in the Microgrid, it is sent to the main grid, and if there is any energy defect found in the Microgrid then the energy is supplied by the utility grid since the Microgrid must be self-sufficiently designed [8]. This operating mode mainly considers the power utility grid to regulate the network voltage amplitude, frequency, and phase at the point of common coupling; this corresponds to the Microgrid and the main grid, which are electrically connected.

When the converter systems are electronically coupled to the distributed energy sources connected to one or more loads, they will normally act as voltage followers in the grid-connected mode. They are commonly known as network-feeding. The network—feeding systems are permanently synchronized with the main grid and are aligned to operate proportionally as current sources when the power electronic converters are constrained to network-feeding [9]. In network-forming, power converters can be used for control purposes, and their work is equivalent to the voltage sources.

2. Microgrid Mode

In this Microgrid design, two operating modes are considered, namely, a grid-connected mode that is interlinked with the utility grid, and an islanded mode which refers to an autonomous operation. They are described in the below sections.

2.1. Grid-Connected Mode

The grid-connected Microgrid was operated with a network-feeding converter and one load connected to it. The voltage amplitude, frequency, and phase are defined from the utility grid. Additionally, the Microgrid control methods were used to control the active and reactive power, which was achieved by adjusting the modulating signal from the control subsystem as shown in Figure 1.

The Microgrid active power and current value can be obtained in the desired range by including Microgrid control methods. Here, the Microgrid control system output signals are given to the half-bridge converter circuit to control the active and reactive power. A constant DC voltage of 800 V is connected to the full-bridge converter circuit [10].

2.2. Islanded Mode

This islanded Microgrid operation mode is not connected with the utility grid. It is an off-grid representation with an inverter operating as the voltage source. This also includes one local load of voltage in the range of 230 V [10]. The inner current loop and outer voltage loop in the Microgrid control system are used to determine the desired active and reactive power. The active and reactive power were obtained similarly to the grid-connected Microgrid system. Finally, the results were compared in a simulation. For both the grid-connected Microgrid and islanded Microgrid, the same control loops were considered.

3. Linear Quadratic Controller Design

For the above-designed grid-connected and islanded mode Microgrid system, a Linear Quadratic Control was designed to enhance the stability.

In the control theory environment, the LQG control algorithm is fundamental for optimal control problems. LQG concerns linear systems and acts against the noise reduction in the system, for which the Kalman filter algorithm is implemented. This LQG control includes modern state-space techniques to design control and regulator algorithms. This technique regulates performance and control of the system. The state-space model includes the linearized system matrix (A, B, C, D) and (x, u) as the system states and inputs. Here, the state space matrix (A, B, C, D) was obtained by linearizing the Microgrid system using the MATLAB linearization method. The grid-connected and islanded Microgrids were linearized separately to define the separate LQG controllers. Here, the controller gain K was designed at the beginning, based on the LQR method. The free parameters Q and R, representing the loop gain and state estimation respectively, were implemented by the Kalman filter [11].

The main contribution of the Kalman filter is to estimate variables optimally that cannot be measured directly, even though indirect measurement is available. This filter is also used to determine the best estimation of states by combining information from multiple sensors in the presence of noise.

In this LQG framework, the Kalman filter was implemented to eliminate the noise present in the system initially due to the power electronic circuits and also by injecting noise to the system externally.

The LQG control leads the system to an optimal and guaranteed closed-loop stability performance. The LQG control framework for grid-connected and islanded mode Microgrid systems is given in Figure 2. In this LQG framework, the input signal is injected with white noise. The Kalman filter included in the controller eliminates the noise level present in the signal, and the signal will feed into the first order transfer function and the controller increases the K value, which acts to improve the signal stability to the desired range. This is considered to be the feedback response from the controller. The free parameters Q and R have an important role in determining the controller gain K. By tuning the free parameters, the stable response of the controller gain can be determined successfully. The LQG control framework was designed separately for grid-connected and islanded mode Microgrids by linearizing each mode to obtain a state-space model. The effective simulation results for the grid-connected mode, islanded mode, and LQG Controller response are shown in the below section.

4. Simulation Results

Grid-Connected Mode

The active and reactive power of the grid-connected system were plotted, and the values were found to be 7020 watts for active power and 0 VAr (Volt-ampere reactive). The elaborated plot shows the disturbance found in the active power, which is given by the red line; it has the variation of 0.4 watts of active power, as shown in Figure 3a. The white noise was injected to the active power (P) of the grid-connected mode. After the noise injection to active power with the internal disturbance present in the system, the power fluctuation range became higher (i.e., from 7003.5 to 7004.6 watts) during the time period from 9.3 to 9.4 s. Furthermore, the fluctuation continued until 10 s with an even higher range; it attained a maximum of 7004.9 at 9.82 s. This variation in the active power occurs due to the internal disturbance due the power electronic circuits, and also because of the external injection of white noise to the system.

The active power with internal disturbance and external noise, as in Figure 3b, was given as input to the proposed LQG controller, and the LQG response is represented in Figure 4. From this plot, it is well understood that the LQG with a Kalman filter can give a stable response by effectively reducing the disturbance and noise signal. The LQG response is smooth without any overshoot in the signal, and it reaches 7000-watt power at the time period of 3.8 s.

5. Conclusions

This proposed method includes a Linear Quadratic Gaussian (LQG) control algorithm implemented for grid-connected and islanded mode Microgrid systems to reduce the internal disturbance and external injected noise. This LQG algorithm achieves a highly stable performance against disturbance and noise. The proposed LQG also includes a Kalman filter and a Linear Quadratic Regulator (LQR) for noise reduction and to attain higher loop gain. This method experimented with the active power from grid-connected and islanded Microgrid system and controller leads a better performance by reducing the disturbance range and attains a stable response to the system. This experiment was successfully executed in the MATLAB (R19a)/Simulink environment. Further, this work can be extended to design robust controllers like H-infinity and H₂ norm [12] for comparative analysis of the various controller response.