Hierarchical Control of an Islanded AC Micro Grid Using FS-MPC and an EMS

Abstract

Microgrids and distributed energy resources (DERs) are gaining popularity owing to their efficient operation, autonomy, and dependability. Microgrids provide several new opportunities, one of which is the ability to deliver electricity continuously, even in the event of a grid failure. This chapter will first describe the modeling of DER components in a microgrid, with each component using Finite Set-Model Predictive Control (FS-MPC) for controlling the inverters to be robust, to have a fast response, to account for multiple objectives, and to eliminate manual tuning. In addition, droop control will be used to provide a voltage reference for the FS-MPC. The PV-inverter will operate as a grid- forming inverter, while the other inverters will serve as grid-feeding inverters. The proposed inverter models are validated using simulations. The microgrid has been modeled using MATLAB-Simulink software package. A supervisory controller for energy management system of the microgrid to operate in different power flows through the proposed control algorithm has also been designed. The simulation results show the effectiveness and robustness of the proposed controller during dynamic performance and transients, and the developed energy management system algorithm successfully controlled the power flow to ensure continuous power delivery to the load under all circumstances.

1. Introduction

Today’s society needs a dependable supply of electricity to consumers and prosumers, with high power quality. As a result of the continual adoption of novel technologies, the structure of the power grid in many countries is continuously developing, posing difficulties with energy flow changes, capacity limits, and high investment expenditures to update the power grid. For many years, power grids have been digitalized to allow centralized monitoring and administration of the power network, which is a result of the emergence of new technologies [1, 2, 3, 4, 5, 6]. This “smart” digitalized grid has been a reality for the high-voltage section of the power system for a considerable amount of time, and the modernization of the low-voltage distribution sector is also in progress [7, 8, 9]. In the next years, utility grids will depend more and more on renewable energy, and users will reap the benefits of smart technologies such as electric car chargers and smart meters [10, 11, 12, 13].

This gives an opportunity to further digitize the distribution (low-voltage) sector of the grid. One method to do this is by establishing a microgrid. In the event of maintenance or grid failure, microgrids should be able to function independently of the utility grid [14].

Hierarchical control structures consist of a primary control layer that has a quick response in milliseconds, a secondary control layer that is used to reduce steady-state errors and acts in a couple of seconds, and finally, a tertiary control layer that controls the active and reactive energy flow within the microgrid by sending power references either manually by the grid operator or automatically by an Energy Management System (EMS) that balances the net power within the microgrid [1, 2, 3].

Due to the intermittent nature of RES, it is required to incorporate a backup power source such as a battery storage system, and perhaps an additional fuel-based power source, so that the microgrid may continue to run even if the battery is depleted or the maximum discharge current is reached [15, 16, 17].

The authors in [18] proposed a MPC strategy developed in Python to optimize energy production and load management for interactive buildings integrated PV & BESS (battery energy storage system). The forecasting method used in the study involves Weighted Moving Average (WMA) combined with Trigg’s tracking signal and adjustment formulas. This method includes sensitivity parameters and thresholds that allow a stricter or looser approach to be taken in forecasting time series. The proposed method adjusts the forecasted values for the rest of the planning horizon based on the deviation detected between forecasted and real-time series. The adjustment formula of a building’s PV production is different from the adjustment formula of its load since the production of PV is more predictable than the load of a building, especially when it comes to residential loads.

In these research papers [19, 20, 21, 22] the performance of the MPC design procedure for DC-DC and DC-AC converters applied to a PV system was analyzed. The authors in [19] presented a continuous control set MPC designed for a DC-DC buck converter used in a MPPT of a PV module, while in [20] an adaptive MPC for current sensorless MPPT in PV systems was evaluated. The papers [21, 22] address the optimal control problems of a grid-connected PV inverter system MPC-based MPPT method. The steady-state and dynamic performance of the MPC-based system are verified and compared with traditional controllers.

Furthermore, authors in [23] presented an examination of a predictive control method designed to prevent imbalances between the load demand and the generation capacity in an islanded microgrid. The Nonlinear Model Predictive Control (NMPC) is utilized to calculate load shedding and manage energy from batteries within an optimization framework. This results in the establishment of an optimal control problem that integrates all the microgrid’s operating conditions, including load priorities for disconnection, and charging and discharging cycles of batteries. Simulation results of the microgrid’s performance with and without the Microgrid Central Controller (MGCC) were compared. The results demonstrate that the control strategy can improve the reliability of the microgrid when operating in islanded mode, as the control strategy can maintain the voltage and frequency of the microgrid within safe limits and achieve a correct balance between generated power and load demand.

The motivation to carry out this study is the growing interest of RES based DG units & ESSs. This chapter is focused on modeling and simulation of an AC microgrid, developed in MATLAB-Simulink environment, which consists of a hydrogen fuel cell, a solar farm, a wind turbine, and a utility grid [24, 25, 26, 27, 28, 29, 30, 31, 32]. Verification by simulations with a hierarchical control structure to operate the AC microgrid in islanded mode has been performed. The primary control mainly consists of FS-MPC, where the solar farm inverter is modeled as a grid-forming inverter [29, 30, 33], and FS-MPC, which was modeled as described in [34, 35, 36, 37, 38], is shown to be highly robust in a variety of different scenarios. The EMS is created to protect the battery’ SOC, and the maximum charging/discharging current from being reached while keeping the power balance stable in the microgrid. The constraints of operating the AC microgrid in islanded operation are the maximum discharging off the battery and fuel cell, and the stochastic RES. The novelty of this research chapter is the use of FS-MPC in the primary control with a new EMS algorithm that is highly robust during islanded operation.

The main contributions of this chapter can be summarized as follows:

1. Modeling and simulation of DER components in an AC Microgrid, including the primary and secondary controllers.

2. The primary controllers are designed to be robust and resilient based on finite-set model predictive control, which is capable of handling sudden changes in the load demand.

3. An algorithm for EMS is developed for managing the energy flow if the microgrid is completely detached from the grid and operating in islanded mode.

4. Various scenarios are developed to test and prove the robustness of the controllers.

The chapter is organized as follows. Section 2 describes the modeling of DER components in the AC microgrid, including the design of the LCL grid inverter filter, while in Section 3 the proposed EMS strategy is described and validated by simulations, using many different scenarios. The conclusion section summarizes the main outcomes of the paper.

2. Modeling of DER components

This section describes how we created and developed detailed models for many microgrid components that make up the proposed microgrid. In the following sections, each component, including equations, parameters, and other design factors, will be thoroughly examined. The MATLAB-Simulink software program is used to implement all simulation models. The various component models are well-known and available in the literature, however the parameters, filter designs, and converter designs have been adjusted and chosen to match the requirements of the proposed microgrid model.

The general structure of the proposed microgrid is displayed in Figure 1. A solar farm, a wind turbine, a lithium-ion battery, a hydrogen fuel cell, and a utility grid are all part of the proposed AC microgrid. The AC microgrid (MG) architecture has been chosen instead of a DC architecture owing to its compatibility with existing infrastructure and greater flexibility in power distribution network. AC MGs are emerging and becoming more attractive structures with integration of RES based DG units and ESSs in order to manage our future energy demands based flexibility, digitalization and energy transition, but also as a viable and reliable solution to the population without access to energy or with poor energy supply to effectively reduce the greenhouse gas emissions. The microgrid requires a battery to handle electrical loads during periods of low renewable energy generation because renewable energy supply is highly variable and depends on the environmental conditions. The microgrid may be confronted with extended periods of low irradiance and low wind speed, potentially resulting in a fully discharged battery. In this instance, if the utility grid is unavailable, a hydrogen-fueled fuel cell can be employed to meet the load demand.

Figure 1.

General structure of the proposed microgrid.

2.1 PV system

Multiple photovoltaic arrays with a combined capacity of 60 kW make up the solar farm. A boost converter is used to boost the DC output of the photovoltaic arrays and keep the PV modules’ generation at its highest level. A three-phase full-bridge inverter is employed because the microgrid’s PCC is a three-phase AC system, and the three-phase square waves from the inverter are subsequently filtered using an LCL filter. Figure 2 illustrates the model [39].

Figure 2.

Model of the PV system [39].

2.1.1 Photovoltaic array

The MATLAB-Simulink special power system library provides the photovoltaic array model/block/subsystem, which we have utilized in the microgrid simulation. It is a five- parameter single-diode model that uses a light-generated current source (I_ph) and a diode current (I_d) to simulate an ideal PV cell with a series resistance (R_s) and a parallel-coupled shunt resistance (R_sh) to simulate a more practical solar cell and more accurately describes the solar cells’ power losses. The one-diode model is one of the most popular models because of the good compromise between simplicity and precision [7, 24, 33, 37, 38, 39].

The I-V characteristic of the solar cell can then be derived by using the single-exponential Shockley equation for the diode, and the resistances to get Eq. (1) [33].

$$I=I_{\mathit{ph}}-I_0\left(e^{\frac{V+R_{s}I}{{\mathit{nV}}_t}}-1\right)-\left(\frac{V+R_{s}I}{R_{\mathit{sh}}}\right)$$E1

where I₀ is the reverse saturation current, n is the ideality factor of the diode, and V_t is the thermal voltage. Eq. (2) describes the light-generated current I_ph which is based on the value of irradiance (G), the cell temperature (T_c), the STC (Standard Test Condition) of the irradiance (G_ref), and cell temperature (T_ref), the temperature coefficient k_i (A/°C), and the short-circuit current at STC (I_sc) [29].

The reverse saturation current is given by Eq. (2), where the I_sc is the short-circuit current, V_oc is the open-circuit voltage, V_to is the STC thermal voltage, E_g is the energy bandgap of the semiconductor, and the energy bandgap at T = 0 K (E_go) [29].

$$I_0=\frac{I_{\mathit{SC}}{e}^{\left(\frac{E_{\mathit{go}}}{V_{\mathit{\text{to}}}}-\frac{E_g}{V_t}\right)}}{e^{\left(\frac{V_{\mathit{OC}}}{{\mathit{nN}}_S{V}_{\mathit{\text{to}}}}\right)}-1}\cdot {\left(\frac{T_C}{T_{\mathit{ref}}}\right)}^3$$E2

Next, the semiconductors energy bandgap value at any cell temperature (T_c) is described by Eq. (3), where the α_gap, and β_gap are the characteristic parameters of the semiconductor [33, 35].

$$E_g=E_{\mathit{go}}-\frac{a_{\mathit{gap}}{T}_C^2}{b_{\mathit{gap}}+T_C}$$E3

However, several solar cells are connected in series in a photovoltaic module, and some modules may have multiple parallel branches of the series connections. The solar cell equations can be scaled up by representing the number of solar cells connected in series as (N_s) and the number of parallel branches (N_p). The scaling is performed on the module current (I_m = N_pI), module voltage (V_m= N_sV), module series resistance $\left(R_{\mathit{sm}}=\frac{N_s}{N_p}{R}_s\right)$ and module shunt resistance $\left(R_{\mathit{shm}}=\frac{N_s}{N_p}{R}_{\mathit{sh}}\right)$ [29, 32].

Furthermore, by denoting the number of PV modules connected in series by (N_sm) and the number of series strings connected in parallel by (N_pm), the PV modules can be scaled up to create a PV array.

The MPP (Maximum Power Point) of the PV array current (I_mg) and PV array voltage (V_mg) can therefore be characterized using the Eqs. (4) and (5), respectively [33].

$$I_{\mathit{mg}}=N_{\mathit{pm}}\left(\frac{I_{\mathit{mmR}}}{1000}G+\left(\frac{{\mathit{dI}}_{\mathit{scm}}}{\mathit{dT}}\right)\left(T_c-T_{\mathit{ref}}\right)\right)$$E4

$$V_{\mathit{mg}}=N_{\mathit{sm}}\left(N_s{V}_{t}ln\left(1+\frac{\mathit{\text{Iscm}}-I_{\mathit{mg}}}{I_{\mathit{scm}}}\left(e^{\frac{V_{\mathit{ocm}}}{N_s{V}_t}}-1\right)\right)-I_{\mathit{mg}}{R}_{\mathit{sm}}\right)$$E5

Where I_mmg is the rated MPP current of the module at STC, I_scm is the short-circuit current of the module at STC, V_ocm is the open-circuit voltage of the module at STC. The PV- module operating temperature (T_c), can then be found for any irradiance condition, and ambient air temperature (T_air), as shown in Eq. (6). NOCT is the normal operating cell temperature at an irradiance of 800 W/m², and an ambient air temperature of 20°C [33].

$$T_c=T_{\mathit{air}}+\frac{\mathit{\text{NOCT}}-20}{800}G$$E6

It is worth noting that the single-diode model has poor accuracy for extremely low irradiances, but the two-diode model can be utilized to improve accuracy in these cases. The two-diode model, on the other hand, is substantially slower to simulate because it has seven parameters and two exponential components, and the accuracy at low irradiances has no effect on the overall output power.

2.1.2 Boost converter and MPPT

The boost converter is a DC/DC converter that increases the output voltage through active switching. The boost converter contains an input capacitor, an inductor, an IGBT, a diode, and an output capacitor and is built using blocks from the MATLAB-Simulink special power system library. Figure 3 shows the MATLAB-Simulink model.

Figure 3.

MATLAB-Simulink model of the boost converter modeled with blocks from Simscape/SPS library and the MPPPT controller based on a MATLAB function.

When the gate of the IGBT receives a square wave of sufficient magnitude, it conducts (ON state), creating a short circuit between the inductor and the negative input. The inductor on the input side stores energy in the magnetic field, and the current will only pass through the IGBT because the diode, capacitor, and load all have much greater impedances.

There is no path through the IGBT when it is turned off, and the abrupt drop in current causes the inductor to generate a back EMF with the polarity of the voltage across it during the ON period. As a result, two voltages are generated, one from the supply and the other from the inductor. The current going through the diode is now charging the capacitor and powering the load at the same time. Even if no current passes from the input to the output during the ensuing on-period, the output capacitor will retain charge and continue to power the load [7].

Because the output voltage remains constant in a steady state, the integral of the inductor voltage over one period is zero. Eq. (7) can therefore be used to explain the dynamics in CCM (Continuous Conduction Mode). After that, divide both sides of Eq. (7) with.

T_s and rearrange to get Eq. (8) [7].

$$V_i{t}_{\mathit{on}}+\left(V_i-V_o\right)t_{\mathit{off}}=0$$E7

$$\frac{V_o}{V_i}=\frac{T_s}{t_{\mathit{off}}}=\frac{1}{1-D}$$E8

Where V_i is the input voltage, V_o is the average output voltage, t_on, and t_off are the time the IGBT is switched on, and off during one period respectively, T_s is the switching period, and D is the duty cycle.

We can define the minimal amount of inductance required to function at CCM when choosing the inductor. Eq. (10) may be used to compute the critical inductance value, whereas Eq. (9) can be used to calculate the duty cycle [7].

$$D=1-\frac{V_{\mathit{mpp}}}{V_{o-\mathit{nom}}}$$E9

$$L_c=\frac{V_{\mathit{mpp}}D}{\mathrm{\Delta }{I}_L{f}_{\mathit{sw}}}$$E10

Where V_mpp is the PV-maximum array’s rated voltage at maximum irradiance and lowest ambient temperature. The nominal output voltage is V_oNom, the inductor ripple current is ΔI_L, and the switching frequency is f_sw. Eqs. (11) and (12) may then be used to compute the capacitance required at the input and output [7].

$$C_{\mathit{\text{in}}}=\frac{\mathrm{\Delta }{I}_L}{8\mathrm{\Delta }{V}_{\mathit{pv}}{f}_{\mathit{sw}}}$$E11

$$C_{\mathit{\text{out}}}\ge \frac{V_{o}D}{f_{\mathit{sw}}\mathrm{\Delta }{V}_{o}R}$$E12

2.1.3 MPPT algorithm

To always generate the maximum possible power with the PV array, an MPPT (Maximum Power Point Tracking) algorithm is used [37]. The algorithm that is used in this simulation is called P&O (Perturb & Observe) and its flowchart is visualized in Figure 4. The MPPT generates a voltage reference in the model. The duty cycle for the PWM generation is then produced by feeding the difference between the observed voltage and the voltage reference into a PI controller.

Figure 4.

MATLAB-Simulink MPPT algorithm used for controlling the duty cycle of the boost converter.

2.1.4 Three-phase square-wave inverter

The three-phase full-bridge inverter is a switching transistor-based DC/AC converter. A large-value capacitor is utilized in the DC-link to smooth out the input voltage to the inverter since VSIs (Voltage Source Inverters) depend on a consistent DC source. The square-formed sine wave that the inverter outputs as AC voltage must first be filtered before reaching the PCC [38, 40, 41].

The six IGBTs that make up the three-phase, two-level inverter are split into three at the top that are connected to one of the phase outputs from the positive DC input and three more that are connected to the same output from the negative DC input. To prevent a short circuit, it is crucial that never both of an IGBT’s top and bottom levels conduct at once. Figures 5 and 6 show the three-phase square wave inverter’s basic setup and the voltage for each phase, respectively.

Figure 5.

Basic configuration of the three-phase square wave inverter.

Figure 6.

Three-phase voltages of the three-phase square wave inverter.

2.1.5 LCL filter

For applications that employ a VSI, a filter is necessary to improve the performance of the feedback control and reduce harmonics. There are many different filters that can be utilized, but in this instance an LCL filter is used [27, 28, 37, 38]. The LCL filter offers greater attenuation than using a single high-value inductor. Even at power levels of hundreds of kW, the capacitor and inductor values might be minimal. The current ripple, filter size, and switching ripple attenuation must all be considered while creating an LCL filter for a VSI. Additionally, both the inductor and the capacitor may contribute if the controller is used to regulate reactive power, necessitating damping to prevent resonance The maximum ripple current I_max can be calculated with Eq. (15). In this equation, it is assumed that the maximum peak-to-peak current happens at the inverter modulation factor (m = 0.5). Using Eq. (16), the maximum ripple is set to be 10% of the maximum current [40, 41].

$$I_{\max }=\frac{P_n\sqrt{2}}{3V_{\mathit{ph}}}$$E13

$$\mathrm{\Delta }{I}_{Lmax}=0.1I_{\max }$$E14

With this information, the inverter side inductance L₁, the grid side inductance L₂, and the capacitance C_f can be calculated by using Eqs. (17), (18), and (19). The capacitors can be connected either in Δ or Y configuration. The equations below are for Y connection, while for Δ connection the resulting value from Eq. (19) is divided by 3 and the same goes for the damping resistor g_f [37].

$$L_1=\frac{V_{\mathit{dc}}}{6f_{\mathit{sw}}\mathrm{\Delta }{I}_{Lmax}}$$E15

$$L_2=\frac{\sqrt{\frac{1}{k_a^2}}+1}{C_f{f}_{\mathit{sw}}^2}$$E16

$$C_f=x\cdot C_b$$E17

where k_a is the attenuation factor, and x is the maximum power factor variation as seen by the grid. Next, the resonant frequency and damping resistor can be calculated by using Eqs. (20), (21) [40, 41].

$${\omega }_{\mathit{res}}=\sqrt{\frac{L_1+L_2}{L_1{L}_2{C}_f}}$$E18

$$R_f=\frac{1}{3{\omega }_{\mathit{res}}{C}_f}$$E19

It is important that the resonant frequency is kept between the limits in Eq. (22) [40, 41].

$$10f_g<f_{\mathit{res}}<0.5f_{\mathit{sw}}$$E20

All the parameters that have been used for the model can be seen in Table 1.

fg	Grid Frequency	50 Hz
fsw	Switching Frequency	10 kHz
Pn	Nominal Power	60 kW
Vg	Phase Grid Voltage	230 V
Vdc	DC-Link Voltage	700 V
x	Maximum Power Variation	20%
kα	Attenuation Factor	20%
L1	Inverter Side Inductor	1.4 mH
L2	Grid Side Inductor	0.374 mH
Cf	Capacitor Filter	160 μF
Rf	Damping Resistor	0.4528

Table 1.

Parameter for the LCL filter.

2.2 Wind farm

The wind farm consists of a synchronous machine, which is driven by a wind turbine coupled with a diode rectifier and a boost converter that is used to increase the DC-link voltage. A full-bridge inverter is then used to convert the DC power back to three-phase AC. After that, an LCL filter is employed to remove harmonics and smooth out the square waves coming from the inverter. The model is drawn from the MATLAB-Simulink Simscape/special power systems package, where the parameters are designed to satisfy the microgrid requirements [42].

2.2.1 Wind turbine

The wind turbine is modeled using the wind speed V_w, the pitch angle β, and the rotor speed ω_t as input parameters. The equations used for modeling the wind turbine are shown below in Eqs. (23), and the Simulink block model is shown in Figure 7. The mechanical system is based on the equation of motion that is displayed in Eq. (24) [43].

Figure 7.

The MATLAB-Simulink block model of a wind turbine.

$$P_m=\frac{1}{2}\rho {\mathit{Av}}_w^3{C}_p\left(\lambda ,\beta \right)$$E21

$$T_{\mathit{\text{mech}}}-T_{\mathit{\text{elec}}}=I\frac{\mathit{d\omega }}{\mathit{dt}}$$E22

2.2.2 Synchronous machine

The synchronous machine model has been taken from the specialized power system library and represents the dynamics of the stator, field, and damper windings. It is modeled in the dq-reference frame and is based on Eqs. (25)–(33) [6, 44].

$$V_d=-i_d{R}_s-{\mathit{\omega \psi }}_q+\frac{d{\psi }_d}{\mathit{dt}}$$E23

$$V_q=-i_q{R}_s-{\mathit{\omega \psi }}_d+\frac{d{\psi }_q}{\mathit{dt}}$$E24

$$V_0=-i_0{R}_0+\frac{d{\psi }_0}{\mathit{dt}}$$E25

$${\mathit{V}}_{\mathit{fd}}=V_{\mathit{fd}}=\frac{d{\psi }_{\mathit{fd}}}{\mathit{dt}}+r_{\mathit{fd}}{i}_{\mathit{fd}}$$E26

$$\frac{d{\psi }_{\mathit{kd}}}{\mathit{dt}}+R_{\mathit{kd}}{i}_{\mathit{kd}}=0$$E27

$$\frac{d{\psi }_{\mathit{kq}1}}{\mathit{dt}}+R_{\mathit{kq}1}{i}_{\mathit{kq}1}=0$$E28

$$\frac{d{\psi }_{\mathit{kq}2}}{\mathit{dt}}+R_{\mathit{kq}2}{i}_{\mathit{kq}2}=0$$E29

$$\left[\begin{array}{l}{\psi }_d\\ {\psi }_{\mathit{kd}}\\ {\psi }_{\mathit{fd}}\end{array}\right]=\left[\begin{array}{ccc}{L}_{\mathit{md}}+L_f& L_{\mathit{md}}& L_{\mathit{md}}\\ L_{\mathit{md}}& L_{\mathit{lkd}}+L_{f1d}+L_{\mathit{md}}& L_{f1d}+L_{\mathit{md}}\\ L_{\mathit{md}}& L_{f1d}+L_{\mathit{md}}& L_{\mathit{fd}}+L_{f1d}+L_{\mathit{md}}\end{array}\right]\left[\begin{array}{c}-i_d\\ i_{\mathit{kq}1}\\ i_{\mathit{kq}2}\end{array}\right]$$E30

$$\left[\begin{array}{l}{\psi }_q\\ {\psi }_{\mathit{kq}1}\\ {\psi }_{\mathit{kq}2}\end{array}\right]=\left[\begin{array}{ccc}{L}_{\mathit{mq}}+L_f& L_{\mathit{mq}}& L_{\mathit{mq}}\\ L_{\mathit{mq}}& L_{\mathit{mq}}+L_{\mathit{kq}1}& L_{\mathit{mq}}\\ L_{\mathit{mq}}& L_{\mathit{mq}}& L_{\mathit{mq}}+L_{\mathit{kq}2}\end{array}\right]\left[\begin{array}{c}-i_d\\ i_{\mathit{kd}}\\ i_{\mathit{fd}}\end{array}\right]$$E31

All the nomenclatures of the parameters in the equations can be found in [44].

2.2.3 Back-to-Back boost converter

A library from MathWorks’ current collection was also used to select the back-to-back boost converter. It is a part of the library’s specialized power systems block for wind turbine subsystems. Figure 8 depicts the model. Three-phase AC from the synchronous machine is fed into the back-to-back boost converters, which are then transformed into DC by a diode bridge (rectifier). The voltage is subsequently increased by the boost converter; for further information on the boost converter, see Section 2.1.1. The three-phase square wave inverter, which is discussed in Section 2.1.3, is then given the stepped-up DC voltage.

Figure 8.

The MATLAB-Simulink model of the back-to-back converter with DC-DC boost converter in DC-link.

2.3 Energy storage system

It is crucial to have the ability to store energy during periods of high-power generation and use it during periods of low generation since the renewable energy sources in the microgrid are very intermittent and dependent on the environment. Additionally, the ESS (Energy Storage System) can be utilized to peak-shave, trade with the grid, and enhance the microgrid’s dependability and power quality. It is made up of an L-filter, a three-phase square wave inverter, and a lithium-ion battery bank as illustrated in Figure 9. The Simulink model of the ESS is displayed in Figure 10.

Figure 9.

Circuit diagram of the bidirectional grid converter.

Figure 10.

The MATLAB-Simulink model of the battery storage system.

2.4 Lithium-ion battery

Eq. (34) describes the discharging process of the lithium-ion battery, while Eq. (35) describes the charging process of the battery [28].

$$f_1\left(\mathit{it},i^{\ast },i\right)=E_0-K\frac{Q}{Q-\mathit{it}}{i}^{\ast }-K\frac{Q}{Q-\mathit{it}}\mathit{it}+{\mathit{Ae}}^{-B.\mathit{it}}$$E32

$$f_2\left(\mathit{it},i^{\ast },i\right)=E_0-K\frac{Q}{\mathit{it}+0.1Q}{i}^{\ast }-K\frac{Q}{Q-\mathit{it}}\mathit{it}+{\mathit{Ae}}^{-B.\mathit{it}}$$E33

Where E₀ is the constant voltage, K is the polarization constant (V/Ah), i^∗ is the low- frequency current dynamics, i is the battery current, it is the extracted capacity in Ah, Q is the maximum battery capacity, A is the exponential voltage, and B is the exponential capacity (Figure 11).

Figure 11.

Discharge characteristics of the battery storage model at different currents.

2.5 Hydrogen fuel cell

The backup power source is present so that the microgrid can continue to operate in islanded mode even when the energy storage system’s state of charge (SOC) is low. The backup power source in this microgrid is a hydrogen fuel cell. The fuel cell is modeled as a dependent voltage source with a series internal resistance and internal diode as displayed in the equivalent electric circuit as depicted in Figure 12. The inverter used with the fuel cell is the same as the one used with the battery illustrated in Figure 9 and it also uses the same control architecture.

Figure 12.

Equivalent circuit diagram of the fuel cell.

3. Development and testing of an energy management system (EMS) algorithm

3.1 The proposed EMS algorithm

The suggested approach for controlling the energy flow is depicted in a flowchart in Figure 13. The suggested EMS additionally considers the battery limitations, which state that the battery should never be charged below or above the limits (SOC), nor should the maximum charging or discharging current, denoted by P_bat,max, be exceeded. The algorithm was created using a MATLAB function. Following the validation of the SOC restrictions, the algorithm checks to see if the microgrid is generating more energy than the load is using; if so, the battery is charged in accordance with the restrictions. If the generation is lower than the load, the battery must discharge, or if the SOC is low, the fuel cell must be engaged.

Figure 13.

Flow-chart block diagram of the EMS algorithm.

3.2 Testing scenarios and results

A number of scenarios were developed to test the effectiveness and dependability of the suggested EMS in the islanded mode. The results are presented in Figures 14 and 15, and a summary of these situations is provided in the Table 2. Intially, the load reference were set to 10 kW, and the wind and PV reference were increased to generate the full power. This creates an unbalance as the generation is much larger than the load and since the battery can only absorb 50 kW, the generated power had to be limited to by disabling the MPPT and reducing the PV power reference. That is exactly what the EMS did as it can be seen that the MPPT was disabled shortly after 0 and the PV power was limited while making sure that the battery is charging with a maximum power of 50 kW and the load is kept stable at 10 kW. Next, a step in the load active power reference was applied from 10 to 50 kW and at the same instant, a step in the reactive power was also applied from 0 to 44 kVAR, making the load power factor 0.75 lagging. The controller responds appropiately by increasing the PV power reference to meet the load demand while keeping the battery charging at 50 kW. The reactive power demand is also met by the battery controller. After that, a step in the load reactive power was applied from 44 to −44 kVAR which changes the power factor from lagging to leading and the battery also was able to absorb the reactive power without any issues. At 4 seconds, the reactive power was reset to 0 and another step in the active power was applied from 50 to 100 kW to test the system at full load. Since the load is now much higher, the EMS enabled the MPPT to ensure taking the maximum power of 60 kW available from the PV. The remaining power came from the wind and any excess power was used to charge the battery. Finally, at 6 seconds, the generation was reduced evem further to test the scenario where the load is higher than the generation. A step in the irradiance from 1000 to 100 W/m² was applied to the PV and a similar step in the wind speed was applied from 15 to 8 m/s. As the wind power generation was gradually reducing, the EMS sent control commands to the battery to supply the remaining power and the battery started discharging up to −50 kW, once the battery reached its maximum discharging power, the fuel cell had to be enabled to supply the remaining load power and that is what happened at around 7 seconds. From there on, all the microgrid sources were working in tandem to keep the load power at 100 kW while the EMS adjusted the fuel cell reference based on the power generated by the wind and PV system. These scenarios clearly illustrate that the proposed energy management system is robust and can succesfully control the microgrid under various conditions.

Figure 14.

Active and reactive power of different components in the microgrid under loads steps.

Figure 15.

Three-phase voltage, power, frequency, and RMS value of the load under different scenarios. (a) 10 to 50 kW load step at 2 seconds. (b) 44 to −44 kVAR step at 3 seconds. (c) 50 to 100 kW step at 4 seconds. (d) 1000 to 100 W/m2 at 6 seconds.

Scenario Time	Description
At 2 seconds	Step change in the active power reference from 10 to 50 kW and in the reactive power from 0 to 44 kVAR
At 3 seconds	Step change in the reactive power reference from 44 to – 44 kVAR
At 4 seconds	Step change in the active power reference from 50 to 100 kW and in
At 6 seconds	Step change in the irradiance from 1000 to 100 W/m2 and in the

Table 2.

Summary of the scenarios tested with energy management system in islanded.

The wind and solar references were initially maximized to produce the maximum electricity with the load reference set at 10 kW. Due to the imbalance caused by the generation being significantly greater than the load and the battery’s ability to store only 50 kW of power, the generated power has to be constrained by turning off the MPPT and lowering the PV power reference. The MPPT was disabled shortly after zero, and the PV power was limited to ensure that the battery was charging with a maximum power of 50 kW and the load was maintained at 10 kW. This is exactly what the EMS performed.

The load’s active power reference was then increased from 10 to 50 kW, and at the same time, the load’s reactive power was increased from 0 to 44 kVAR, resulting in a load power factor of 0.75 lagging. In order to fulfill the load requirement, the controller increases the PV power reference as necessary, keeping the battery charging at 50 kW. The battery controller also satisfies the demand for reactive power. The power factor was then changed from lagging to leading by applying a step in the reactive power of the load from 44 to −44 kVAR, and the battery was able to absorb the reactive power without any problems.

To test the system at maximum load, the reactive power was reset to 0 at 4 seconds and another step in the active power was applied from 50 to 100 kW. Due to the increased load, the MPPT was enabled to use the full 60 kW of available PV power thanks to the EMS. Wind provided the remaining energy, and any extra was used to recharge the batteries. To test the condition where the demand is more than the generation, the generation was further decreased at 6 seconds. The PV received a step-down in irradiance from 1000 to 100 W/m² and a comparable step-down in wind speed from 15 to 8 m/s.

The fuel cell had to be enabled in order to supply the remaining load power, which occurred at roughly 7 seconds as the wind power generation rapidly decreased. The EMS had issued control commands to the battery to deliver the remaining power, and the battery began depleting up to −50 kW. The EMS controlled the fuel cell reference depending on the electricity produced by the wind and PV systems, all the microgrid sources continued to cooperate to maintain the load power at 100 kW. These examples unmistakably show how reliable the energy management system is and how successfully it can operate the microgrid under diverse circumstances.

Following that, the battery’s SOC constraints were evaluated using the scenarios depicted in Figure 16. Figure 17(a) shows a zoomed-in plot of the voltage, frequency, and load consumption at 3 seconds when the controller determined the SOC to be above the limits at 3 s, the battery immediately stopped charging, and the PV could no longer operate at the maximum power point and was given a corresponding reference so the power balance in the microgrid was met. The load is increased to 100 kW at 5 seconds, and the PV irradiance is decreased to 500 W/m². To accommodate the significant increase in load demand, this should cause the battery to begin discharging.

Figure 16.

Active and reactive power of different components in the microgrid to test SOC limiting to protect the battery.

Figure 17.

Three-phase voltage, power, frequency, and RMS value of the load under different scenarios. (a) SOC saturation at 90%. (b) 50 to 100 kW step at seconds. (c) SOC saturation at 10%.

After 8 seconds, the battery starts to deplete until it hits 10%, at which point the EMS sends a command to stop discharging the battery. When this occurs, the EMS responds by igniting the fuel cell to start supplying power right away. In Figure 17(c) the voltage, frequency, and load consumption charts are zoomed in. This demonstrates how the EMS can safeguard the battery from overcharging and over-discharging, demonstrating how it accomplishes some of the goals of a BMS (Battery Management System).

4. Conclusion

In summary, this chapter explored the modeling and simulation of microgrid components, including PV system, wind turbine system, battery storage and fuel cell system. The control architecture, developed for the primary control of these components, was based on model predictive control. An energy management system algorithm was successfully designed and developed to control the power flow and to ensure continuous power delivery to the load under all circumstances. The algorithm was tested on a variety of scenarios and proved its robustness and flexibility. When the generation exceeds the load demand and the battery cannot absorb all the excess power, the EMS would disable the MPPT to limit the generation from the solar cell to protect the battery. If the load demand exceeds the generation, the EMS uses the battery to make up for the difference and if the battery power is not sufficient, the fuel cell is activated to provide the rest of the power. Moreover, SOC- based protection scheme was also implemented to ensure that the battery state of charge remains within acceptable limits which increase the lifetime of the battery.

5. Future work

The simulation of the EMS algorithm presented in this paper provides a promising proof- of-concept for its effectiveness in managing electrical energy in a microgrid. However, there are several avenues for further exploration and improvement. One important step for the validation of the EMS algorithm would be to test it on real hardware, such as a Hardware-in-the-Loop (HIL) platform. This would enable us to evaluate the algorithm’s performance in a realistic setting, which includes the various noise and uncertainties that can arise in the physical world. Moreover, we could measure the real-time performance of the algorithm and compare it with the simulation results.

Another potential area for future work is to add new equipment to the microgrid and reconfigure the algorithm accordingly. The EMS algorithm was designed to work with a specific set of components, and its performance may be affected by the addition or removal of equipment. Hence, future expansion of the microgrid may require a readjustment of the algorithm to ensure its optimal operation.

Finally, the implementation of the EMS algorithm presented in this paper was focused on a single microgrid. However, in practice, multiple microgrids can be interconnected to form a larger network, and the EMS algorithm must be adapted to this scenario. Future work could explore the development of a hierarchical control scheme that manages multiple microgrids simultaneously.

Conflict of interest

The authors declare no conflict of interest.

Funding

This research was partial funded by the EEA and Norway grant/project DOITSMARTER, contract no 2022/337335.