© The Author(s), published by EDP Sciences, 2025

Nomenclature

a : Indicator for LVDC power reference

CC: Current-Controlled mode

D_PV, D_W : PV and wind boost duty cycle

K₁, K₂ : Voltage controller arbitrary constants; K₁/K₂ > 0

K_p, K_I : Proportional Integral controller (PI) gains

I_BAT, I_{BAT_Ref} : Battery instantaneous, reference current

I_{BAT_Err} : Battery current error fed to PI controller

I_C, V_AC,ω : AC capacitor current, voltage, frequency

I_GRID, V_GRID : Grid current, voltage exchange with grid

I_INV, V_INV : Interlinking converter (ILC) converter output current and voltage

I_{INV_Ref}, V_{INV_Ref} : ILC reference current and voltage

P_BAT, P_{BAT_Ref} : Battery instantaneous, reference power

P_dc, P_LVDC : Total power demand by DC load, LVDC bus

P_{BAT_Lim} : Battery power limit in passive grid mode

P_{INV_Ref} : Inverter reference power

P_LV48, P_MVDC : Power flow at the DC buses 48 V/380 V

P_PV, P_W : Power generated by distributed energy resources (DERs) PV, wind

Q_{GRID_Ref}, Q_{GRID_Err} : Reactive power reference and error

t, t₀ : Current time instant and step time

S_AC, P_AC, Q_AC : Power demand by the AC load

S_GRID, P_GRID, Q_GRID : Power exchanged with grid

S_ILC, P_ILC, Q_ILC : Apparent power, active power, reactive power exchanged through ILC

S_NET, S_LOSS : System net excess/deficit power, Losses

SW_GRID, SW_PV, SW_W : Status of grid, solar PV and wind DER on/off

SW_BAT : Battery status on/off

SW_LV48, SW_MVDC : On/off status of loads

VC: Voltage-Controlled mode

V_LVDC, V_MVDC : LVDC, MVDC-bus voltages

V_{LVDC_Ref}, V_{MVDC_Ref} : DC buses reference voltages

V_{LVDC_Err}, V_{LVDC_Err}, V_{MVDC_Err} : PI control errors of DC-bus voltages

1 Introduction

1.1 Background

The development of grid-interactive residential Power Control Units (PCUs) is desperately needed in order to integrate Distributed Energy Resources (DERs) and Battery Energy Storage Systems (BESSs). A DC bus arrangement in residential buildings is necessary since a significant portion of household loads these days are of the DC type. The bus arrangement for DC loads is not present in conventional PCUs.

In AC-DC Microgrids (MGs), interconnecting converters make feasible the exchange of energy between the DC and AC grids. If AC-DC grids are interconnected and the AC grid governs the voltage and frequency, there must be a synchronisation of the inverter and the AC grid. The Voltage Source Converter (VSC) should operate in current control mode while the voltage of the interlinking capacitor should be fixed. A number of interlinking converters are introduced, which give rise to a nonlinear system. Advanced control techniques have to be used to take into consideration the nonlinear nature of the system [1].

1.2 Literature review

Installations of Renewable Energy Sources (RESs) in homes have been encouraged by the Government [2]. It is thought that Distributed Renewable Energy Sources (DRESs) could help to meet the rising need for energy. Evidence indicates that renewables have now overtaken hydrocarbons in new power generation facilities, thanks to technological advancements, supportive policy frameworks, and growing environmental consciousness [3]. Achieving synchronised electricity from different mixtures of fossil, nuclear, and green fuels is the goal of hybrid energy resources. There are significant efforts to replace fossil fuels with green energy, so there is a propensity to employ several sources. Nonetheless, these systems improve the overall stability and dependability of energy supply by reducing the intermittency problems that come with individual renewable sources. While wind power can be used even when there is less solar available, solar power produces its most during the day [4]. The energy supply is made more reliable by combining several sources, which lowers the possibility of power outages during changing weather. Furthermore, energy storage technologies used in hybrid systems make it easier to store energy during times of low loads, allowing it to be used during times of increased loads. This improves system efficiency and lowers waste. In semi-urban or rural households with frequent power interruptions, the grid-interactive PCU is advantageous [5]. Most of the Control units lack the DC bus structure, and each DC equipment has its own device for AC rectification [6].

The controllers for power balancing in isolated systems under diverse conditions are proposed [7, 8]. But since the DC link is stabilized rather than rigid, it cannot be used with DC appliances [9]. The development of PCUs for integrating a number of renewable energy sources for single-phase households to fulfil desired functions is not given much attention [10, 11]. For the same reason, conventional PCUs of the grid-connected or islanded types are not accessible over the DC bus. Given the increased usage of DC appliances, having a DC bus layout is advantageous [12]. To lower transients and circulating power flow in the DC system, sophisticated control strategies are required [13]. A quick and precise droop-based controller minimises the circulating current flow, stabilises bus voltages, and lowers losses [14, 15]. Droop control is a traditional control strategy. It does not require communication among participating generators. Droop control offers a seamless transfer from a grid-tied MG to an islanded MG. Though droop control is very helpful, it is not favourable in MG due to a number of issues like voltage control, PQ control, and poor performance.

In order to lessen transient oscillations in DC bus voltages, an effective model predictive controller (MPC) based strategy of a photovoltaic (PV)-based DC MG is suggested [16]. Energy storage added to a residential system via the grid improves system reliability and efficiency. An essential consideration when searching for cutting-edge techniques to create hybrid PCUs is fault isolation and detection. The examples of how MGs might help to guarantee the continuous supply to the DC bus system are given in [17, 18]. An imbalance in loads leads to an imbalance in the terminal voltage. The unbalanced load current is shared between DERs, and the output voltage is not affected. In [19], a closed-loop control approach for decentralized paralleling of uneven inverters to share nonlinear and unbalanced loads is proposed.

A number of control techniques, such as Artificial Fish Swarm Algorithm (AFSA), Artificial Neural Network (ANN), and hybrid AFSA-ANN, are suggested in the literature [20]. Li et al. [21] proposed a flexible control strategy for voltage regulation in DC distribution networks using distributed Energy Storage Systems (ESS). It implements a droop control method that works independently at each storage unit at the primary level, distributed optimization at the upper level for efficient, long-term operation and SOC balancing. Kakigano et al. [22] proposed a low voltage bipolar type DC microgrid that can supply super high quality with a three-wire DC distribution line. Microgrid is based on droop control, which enables proportional power sharing among converters without requiring heavy communication.

1.3 Research gap and inspiration

The integration of generating sources and batteries to form a MG involves a huge mathematics and a complex structure. A PCU that enables the microgrid to operate in a stable manner for a wide variation of inputs, like variation in PV power, wind power, variation in state of charge (SOC) of batteries, and variation in loads, is required. It is a challenge to manage imbalances caused by harmonics, an improper voltage profile, synchronizing generating units and load, and fluctuating PV and wind energy behaviours. A MG structure capable of integrating AC as well as DC loads is needed which can function in grid-tied or islanded mode and is proficient in operating in transition mode also, from grid-tied to islanded mode. A PCU of such type is under research, and possibilities of improvement in the PCU structure are being explored.

This article suggests using a multi-terminal grid interactive PCU to integrate solar and wind energy-based system with energy-storage devices in single-phase households. For the purpose of implementing the hybrid microgrid system architecture within the homes, the PCU complexity is decreased, and functionality is increased. During transients, the battery helps to stabilise the DC bus. Applications involving hybrid electric vehicles can benefit from the presence of the DC bus port via PCU. The PCU’s coordinated control may interface with DERs, DC/AC loads, and BESS. In order to maintain grid regulations, the PCU controls the flow of reactive power. The suggested system is verified to be feasible in islanded and grid-connected modes by the simulation results.

1.4 Contributions

1. A microgrid with PV-wind-BESS integrated with a single-phase AC grid is designed.

2. A multi-terminal grid interactive PCU is designed, which integrates PV and wind energy systems with energy-storage devices in single-phase households.

3. PCU involves a Hysteresis Current Controller (HCC) for grid-tied mode of operation and a Sliding Mode Controller (SMC) for islanded mode.

4. The suggested PCU is capable of providing DC bus voltage control and power management for variation in solar PV power, variation in SOC of battery, and variation in loads.

1.5 Future significance

The study of advanced control strategies and hybrid PCUs for renewable-energy-based DC microgrids hold vast future significance across multiple aspects and disciplines, as discussed below:

1.5.1 Engineering and technological advancements

The proposed strategy will lay the groundwork for the development of next-generation PCUs with higher precision, stability, and adaptability. Integration of DC bus structures into household systems will accelerate the adoption of DC appliances, reducing conversion losses and enhancing energy efficiency.

1.5.2 Energy and power systems

Hybrid RES-based microgrids with robust controllers can ensure reliable electricity access in semi-urban and rural areas, where conventional grids remain weak. Large-scale adoption of these techniques can facilitate grid decarbonisation, reducing dependence on fossil fuels. Optimised control of DERs and storage systems will support demand-response management in future smart cities.

1.5.3 Environmental sustainability

Enhanced utilisation of RES with reduced intermittency will accelerate the transition toward net-zero emissions. More efficient systems will minimise energy waste, indirectly reducing the carbon footprint of energy conversion and storage.

1.5.4 Economic and social impact

Cost-effective hybrid PCUs can make RES integration affordable for households and small businesses, leading to energy democratisation. Reliable power in rural areas will promote socio-economic development, enabling digital access, healthcare, and education services that depend on uninterrupted electricity. The optimised load sharing and fault-tolerant systems will reduce outage-related economic losses.

1.5.5 Multidisciplinary applications

Cyber-physical systems: Integration of PCUs with Internet of Things (IoT)-enabled smart meters will pave the way for real-time monitoring and control of microgrids.

Policy and governance: Insights from this research can guide policymakers in designing standardised frameworks for DC microgrid adoption, particularly in developing countries.

Education and research: The multidisciplinary nature of this work creates opportunities for cross-domain collaboration in electrical engineering, computer science, environmental studies, and economics.

1.6 Paper structure

The paper is divided into various sections. Section 2 describes the control algorithm and the multi-terminal residential PCU. Section 3 analyses stability of the system. Section 4 describes the modes of operation of the suggested PCU. Section 5 discusses simulation results. A comparative analysis is given in Section 6. Finally, the conclusion of the work is given in Section 7.

2 Control algorithm and multi-terminal residential PCU

Utilising simple converter-cum controllers increases the industrial market outreach by lowering system complexity and expense. Moreover, it results in a significant decrease in both development and maintenance expenses. The block diagram of the proposed hybrid PCU is shown in Figure 1. The total number of connection ports available in the suggested PCU is displayed in Figure 1. The source ports are 1, 2, and 3; the BESS connection port is 4, and the load ports are 5, 6, and 7. Different ports are connecting the single-phase AC grid (port 1), solar PV DC DER (port 2), wind AC DER (port 3), battery Stack (port 4), 48 V LVDC loads (port 5), 380 V DC loads (port 6), and single-phase, 230 V AC loads (port 7).

Figure 1 Proposed hybrid PCU.

Figure 2 provides detailed information of the proposed PCU. The single-phase (1-ɸ) AC grid is connected at port 1. Solar PV DC DER is connected at port 2. It is connected through a boost converter to the 380 V DC bus. Wind energy DER is connected at port 3. It is connected through a three-phase diode bridge rectifier and a boost converter. BESS is connected through a bidirectional DC-DC converter. 380 V DC grid is connected through an interlinking converter to the single-phase AC grid. If the power supplied by the solar and wind energy sources connected at port 2 and port 3 is surplus, i.e., more than that required by the load and battery charging, then the interlinking converter acts as an inverter, supplying power to the single-phase AC grid. If the power supplied by the solar and wind energy sources is deficient for feeding the load, then the interlinking converter will act as a rectifier, taking power from the single-phase AC grid.

Figure 2 Detailed view of PCU.

Islanded and grid-tied operations are supported by the proposed PCU. The switching state space modelling of the different DC-DC and DC-AC converters is utilised in the suggested PCU [23, 24]. Depending on the user’s preference, the various converters used in the PCU can function in either voltage or current regulated mode. The intended PCU controllers are designed to achieve the DC and AC bus voltage balance and system power management.

2.1 MPPT controllers for wind and solar PV

One benefit of using the Incremental Conductance (IC) approach of Maximum Power Point Tracking (MPPT) in solar PV systems is to reduce computing complexity [25]. Electrical MPPT is another option for wind systems [26, 27]. Xia et al. proposed a new MPPT strategy for Permanent Magnet Synchronous Generator (PMSG)-based wind turbines [26]. It avoids the need for sensors or turbine data while delivering smooth and accurate power tracking. Dalala et al. proposed a simple and effective MPPT technique designed specifically for small-scale wind energy systems [27]. It eliminates the need for wind speed sensors. It is based on the duty cycle adjustment of the DC-DC converter. It tracks the maximum power by measuring only electrical signals (voltage and current). The Perturb and Observe (P&O) algorithm is used for wind MPPT. ΔI/ΔV − I/V slope, determines the converter operating point, and the current (I_PV, I_W) and voltage (V_PV, V_W) are supervised (Fig. 3a). At any given moment t, the duty cycle of the boost converter in PV can be expressed as follows:$$D_{\mathrm{PV}}\left(t\right)={\mathrm{Limit}}_{\mathrm{Min}=0}^{\mathrm{Max}=1}\left[D_{\mathrm{PV}}\left(t-t_0\right)\pm ∆D\right].$$(1)In a similar manner, the wind MPPT can be expressed as D_W(t), the duty cycle of the boost converter in wind.

Figure 3 (a) MPPT controller for solar PV and wind and (b) Low-voltage DC bus voltage controller.

2.2 Low-voltage DC bus voltage controller

It serves as a controller for the low-voltage DC (LVDC) bus voltage. The bus voltage (V_LVDC) is measured and compared with the reference voltage (V_{LVDC_Ref}). The error, V_{LVDC_Err,} balances the LVDC-bus voltages (Fig. 3b). The proportional integral (PI) controller is tuned taking into account extreme power flow. PI controller tuning has been done with the Zeigler-Nichols method:$$V_{{\mathrm{LVDC}}_{\mathrm{ERR}}}=V_{\mathrm{LVDC} \mathrm{Ref}}-V_{\mathrm{LVDC}},$$(2) $$D_{\mathrm{LVDC\_}1}·a+ D_{\mathrm{LVDC\_}2}·\overline{a}=(a-\overline{a})\bullet {\mathrm{Limit}}_{\mathrm{Min}=-1}^{\mathrm{Max}=1}\left(K_{\mathrm{p}}.V_{\mathrm{LVDC\_Err}}+K_{\mathrm{I}}\bullet {\int }_{t-t_0}^t{V}_{\mathrm{LVDC\_Err}} \mathrm{d}t\right).$$(3)

Where, a = 1 if$${\mathrm{Limit}}_{\mathrm{Min}=-1}^{\mathrm{Max}=1}\left(K_p.V_{\mathrm{LVDC\_Err}}+K_I.{\int }_{t-t_0}^t{V}_{\mathrm{LVDC\_Err}}\mathrm{.d}t\right)\ge 0,$$

a = 0, if$${\mathrm{Limit}}_{\mathrm{Min}=-1}^{\mathrm{Max}=1}\left(K_p.V_{\mathrm{LVDC\_Err}}+K_I.{\int }_{t-t_0}^t{V}_{\mathrm{LVDC\_Err}}\mathrm{.d}t\right)\le 0.$$

2.3 Charge controller for BESS

In islanded mode, the BESS maintains system power balance and adjusts the medium voltage DC (MVDC) bus voltage (V_MVDC = V_{MVDC_Ref}). In passive grid feeding mode, the utility grid is still operating, but power is transferred to ESS first (ESS limits engaged). The interlinking converter, also known as a bidirectional DC/AC converter, exchanges electricity with the grid only when there is a surplus or shortage of power in the system. In equations (6)–(7), the ESS power references are defined. It is dependent upon the ESS and the grid connection state. In grid-forming mode, the battery cannot be disconnected.$$V_{{\mathrm{MVDC}}_{\mathrm{ERR}}}=V_{\mathrm{MVDC} \mathrm{Ref}}-V_{\mathrm{MVDC}},$$(4) $$S_{\mathrm{NET}}=K_p·V_{\mathrm{MVDC\_Err}}+K_I·{\int }_{t-t_0}^t{V}_{\mathrm{MVDC\_Err}}·\mathrm{d}t,$$(5) $$I_{\mathrm{BAT\_Ref}}= \frac{P_{\mathrm{BAT\_Ref}}}{V_{\mathrm{BAT}}},$$(6) $$I_{\mathrm{BAT\_Err}}= \frac{P_{\mathrm{BAT}\mathrm{\_}\mathrm{Ref}}}{V_{\mathrm{BAT}}}-I_{\mathrm{BAT}}.$$(7)

2.4 Bidirectional DC-AC ILC controller

The circuit of the bidirectional DC-AC converter is shown in Figure 4. The state matrices of the bidirectional DC-AC converter can be derived by applying KVL and KCL in Figure 5, under different operating modes (grid-connected and islanded modes).

Figure 4 Circuit diagram of single-phase bidirectional DC-AC converter.

Figure 5 Circuit diagram to derive the state space analysis of single-phase bidirectional DC-AC converter.

In Figures 4 and 5, S₁ V₁ and V₂ are the voltages across inductor L; I_L is converter output current; I_S is the current exchange with grid in current controlled mode; C₁ is the DC bus capacitance; C₂ is the AC side filter capacitance; R₁ and R₂ + s L₂ is the equivalent MG load seen on DC and AC sides, respectively. Further, S₁ = 1, 0, –1 represents the positive, zero, and negative inverter output voltages.

The state space model for the bidirectional DC-AC converter is given by equation (8). Output, Y_O/P of the converter is given by equation (9). In current-controlled operation, I_L is the parameter to be controlled; and in voltage-controlled operation, V₂ is the controlled parameter. Hence, I_L and V₂ are chosen as the state variables.

A state space vector represents the behaviour of a dynamic system using a set of first-order differential equations. It typically has the form $\dot{x}\left(t\right)=A\left(x\right)t+\mathrm{Bu}\left(t\right)$ and y(t) = Cx(t) + Du(t). Where, x(t) is a vector of state variables, u(t) is a vector of inputs, and A, B, C, and D are matrices that describe the system dynamics.$$\left[\begin{array}{c}{\overline{\dot{I}}}_L\\ {\dot{V}}_2\end{array}\right]=\left[\begin{array}{cc}0& -\frac{\left(Y-\overline{Y}\right)}{L}\\ \frac{\left(Y-\overline{Y}\right)}{C_2}& \frac{1}{C_2}·\frac{1}{\left(R_2+s{L}_2\right)}\end{array}\right]\left[\begin{array}{c}{I}_L\\ V_2\end{array}\right]+\left[\begin{array}{c}\frac{S_1·\left(Y-\overline{Y}\right)}{L}\\ 0\end{array}\right]V_1+\left[\begin{array}{c}0\\ -\frac{\left(Y-\overline{Y}\right)}{C_2}\end{array}\right]I_s·\mathrm{CC}$$(8) $$Y_{\mathrm{O}/\mathrm{P}}=\left[\begin{array}{cc}\left(Y-\overline{Y}\right)·\mathrm{CC}& \overline{\mathrm{CC}}\end{array}\right]\left[\begin{array}{c}{I}_L\\ V_2\end{array}\right]$$(9)

Bi-directional DC-AC converter operates in inverting, or rectifying mode, based on the power scenario of the DC and AC sides. The controller can operate in either grid current control mode or islanded voltage control mode. The AC side of the converter comprises an LC filter, along with equivalent AC side impedance, R₂ + sL₂, connected in parallel with the grid, feeding a current I_S. Negative values of I_S show that the power is drawn from the utility grid and the converter operates in rectification mode. The individual state space models for the bidirectional DC-AC converter operating in either current-controlled or voltage-controlled modes could be obtained from equations (8) and (9) by substituting the following values.

1. Inverter current controlled mode: Y = 1, $\overline{Y}$= 0; CC = 1, $\overline{\mathrm{CC}}=0$

2. Rectifier current controlled mode: Y = 0, $\overline{Y}$ = 1; CC = 1, $\overline{\mathrm{CC}}=0$

3. Inverter voltage controlled mode: Y = 1, $\overline{Y}$ = 0; CC = 0, $\overline{\mathrm{CC}}=1$.

4. Rectifier voltage controlled mode: Y = 0, $\overline{Y}$ = 1; CC = 0, $\overline{\mathrm{CC}}=1$.

The AC loads are supplied with power by ILC; if surplus power is available on the DC side, otherwise, power is drawn from the utility grid. Reactive power exchanged with grid, Q_GRID ~ 0. The Q_{GRID_Err} is minimized by varying the phase shift between V_INV and I_INV, ϴ_INV, as given in equation (10).$$Q_{\mathrm{GRIDErr}}=\left\{{\mathrm{Mean}}_{\mathrm{freq}=50\mathrm{Hz}}\left[\left|V_{\mathrm{INV}}\right|·\left|I_{\mathrm{INV}}\right|·\sin \left(\mathrm{\angle }{V}_{\mathrm{INV}}-\mathrm{\angle }{I}_{\mathrm{INV}}\right)t\right]\right\}-Q_{\mathrm{GRID}\mathrm{\_}\mathrm{Ref}},$$(10) $$V_{\mathrm{INV\_Ref}}=1.414·\frac{P_{\mathrm{INV} \mathrm{Ref}}}{{\mathrm{RMS}}_{\mathrm{freq}=50\mathrm{Hz}}\left[V_{\mathrm{INV}}\right]}\mathrm{.sin}\left[\mathrm{wt}-\left(K_p·Q_{\mathrm{GRID\_Err} }+ K_I·{\int }_{t-t0}^t{Q}_{\mathrm{GRID\_Err}}·\mathrm{d}t\right)\right].$$(11)

Where, V_INV, I_INV are the ILC AC side parameters. Hysteresis Current Control (HCC) error, I_{INV_ERR} generates ILC control pulses in grid feeding mode, equation (12). In grid-forming mode, ILC operates in voltage control (VC) mode, ensuring constant AC bus voltage. Capacitor current, I_C, and voltage V_INV are controlled for a constant AC voltage. Here, K₁ and K₂ are the constants, such that K₁, K₂ > 0. Hysteresis voltage control error, V_{INV_ERR}, equation (13), generates an ILC pulse in this mode, where, V_{TRIANGULAR_Ref} is the carrier; C_AC is the AC capacitor. Proposed controllers are stable under source and load variations.

2.4.1 Hysteresis Current Control (HCC)

Figure 6 shows the block diagram of the HCC strategy. The switching logic pulses for the power converter’s semiconductor switches are obtained by passing the generated current error through a hysteresis band logic generator. Within a designated hysteresis band (±h), the generated actual converter current tracks the reference signal while the switching logic signal generates the necessary bipolar output voltage. The switching state does not change as long as the error stays inside the hysteresis band. Every time the current error passes the upper or lower hysteresis band, the switching states shift. The DC link voltage, system variables, hysteresis band, and controller sampling frequency affect the hysteresis current control method’s switching frequency. Higher hysteresis band limits result in lower switching frequencies and, hence, lower switching losses. Current error I_{INV_Err} produces ILC control pulses in grid-connected mode as given by equation (12) based on hysteresis current control.$$I_{{\mathrm{INV}}_{\mathrm{ERR}}}=I_{\mathrm{INVRef}}-I_{\mathrm{INV}.}$$(12)

Figure 6 HCC strategy.

Figure 7 SMC strategy.

Figure 8 Interlinking converter control.

2.4.2 Sliding Mode Control (SMC)

The capacitor voltage and current flowing through it are the parameters that are looked after and controlled in the SMC technique. In this control method, the reference inverter inductor current is compared with the actual current, and similarly, the reference inverter capacitor voltage is compared with the actual voltage. These pulses are added and compared to a triangular carrier wave and are sent to a hysteresis band generator to obtain the switching logic pulses for the semiconductor switches of the power converter. Equation (13) gives the equation for voltage error, V_INVERR, when the grid is disconnected based on SMC.$$V_{\mathrm{INVERR}}=K_1\left(V_{\mathrm{INVRef}}-V_{\mathrm{INV}}\right)+K_2\left\{C_{\mathrm{AC}}.\frac{\mathrm{d}\left(V_{\mathrm{INVRef}}\right)}{\mathrm{d}t}-I_{\mathrm{c}}\right\}-V_{\mathrm{TRIRef}}$$(13)

3 Stability analysis

Routh-Hurwitz (RH) and Lyapunov’s stability criteria are used to check the system stability as detailed below:

3.1 RH criterion

Adjusting the terms of equation (13) $$K_1\left(V_{\mathrm{INVREF}}-V_{\mathrm{INV}}\right)+K_2\left\{C_{\mathrm{AC}}·\frac{\mathrm{d}}{\mathrm{d}t}\left(V_{\mathrm{INVREF}}\right)-I_c\right\}-V_{\mathrm{TRIREF}}-V_{\mathrm{INVERR}}=0.$$(14)

Differentiating on both sides$$K_1.\frac{\mathrm{d}}{\mathrm{d}t}\left(V_{\mathrm{INVREF}}-V_{\mathrm{INV}}\right)+K_2.\left[C_{\mathrm{AC}}.\frac{{\mathrm{d}}^2}{{\mathrm{d}t}^2}\left(V_{\mathrm{INVREF}}\right)-\frac{\mathrm{d}{I}_c}{\mathrm{d}t}\right]+\frac{\mathrm{d}}{\mathrm{d}t}(-V_{\mathrm{INVERR}}-V_{\mathrm{TRIREF}})=0.$$(15)

Let,$$V_{\mathrm{INVREF}}-V_{\mathrm{INV}}=V_1,$$(16)and$${-V}_{\mathrm{INVERR}}-V_{\mathrm{TRIREF}}=V_2.$$(17)

Putting equations (16) and (17) in equation (15), equation (18) is obtained.$$K_1·\frac{\mathrm{d}{V}_1}{\mathrm{d}t}+K_2\left[C_{\mathrm{AC}}.\frac{{\mathrm{d}}^2}{{\mathrm{d}t}^2}\left(V_{\mathrm{INVREF}}\right)-\frac{\mathrm{d}{I}_c}{\mathrm{d}t}\right]+\frac{\mathrm{d}{V}_2}{\mathrm{d}t}=0.$$(18) $$\left[I_c^{\mathrm{\prime }}=-\frac{\mathrm{d}{I}_c}{\mathrm{d}t}\right].$$(19)

Taking Laplace transform on both sides$$K_1·s·V_1\left(s\right)+K_2\left(s^2·C_{\mathrm{AC}}·V_{\mathrm{INVREF}}+{\mathrm{I\text{'}}}_c\left(s\right)\right)+s·V_2\left(s\right)=0$$(20)

Applying RH criterion$$\begin{array}{ccc}{s}^2& K_2·C_{\mathrm{AC}}·V_{\mathrm{INVREF}}& K_2·{\mathrm{I\text{'}}}_c\left(s\right)\\ s^1& K_1·V_1\left(s\right)+V_2\left(s\right)& \\ s^0& K_2·{\mathrm{I\text{'}}}_c\left(s\right)& \end{array},$$ $$K_2·C_{\mathrm{AC}}·V_{\mathrm{INVREF}}>0,$$ $$K_1·V_1\left(s\right)+V_2\left(s\right)>0,$$ $$K_2·{\mathrm{I\text{'}}}_c\left(s\right)>0.$$

All coefficients are positive. Hence, the system is stable.

3.2 Lyapunov’s stability criterion

Adjusting the terms of equation (13) $$\frac{\mathrm{d}\left(V_{\mathrm{INVREF}}\right)}{\mathrm{d}t}=\frac{\left(V_{\mathrm{INVERR}}+V_{\mathrm{TRIREF}}\right)-K_1\left(V_{\mathrm{INVREF}}-V_{\mathrm{INV}}\right)+I_c}{K_2·C_{\mathrm{AC}}}=F\left(X\right),$$(21) $$\dot{V}\left(X\right)={\left(\nabla V\right)}^T·F\left(X\right)=\left[\begin{array}{cc}\frac{\partial V}{\partial X_1}& \frac{\partial V}{\partial X_2}\end{array}\right] {\left[\begin{array}{cc}{F}_1\left(X\right)& F_2\left(X\right)\end{array}\right]}^T,$$(22) $$F\left(X\right)=F\left(V_{\mathrm{INV}}\right)=\left(V_{\mathrm{INVERR}}+V_{\mathrm{TRIREF}}\right)-K_1\left(V_{\mathrm{INVREF}}-V_{\mathrm{INV}}\right)+I_c.$$(23)

Let,$$V=K_3·{V^2}_{\mathrm{INV}}+K_4·{V^2}_{\mathrm{INVREF}},$$(24) $$\frac{\partial V}{{\partial V}_{\mathrm{INV}}}=2K_3·V_{\mathrm{INV},}$$(25) $$\frac{\partial V}{{\partial V}_{\mathrm{INVREF}}}=2K_4·V_{\mathrm{INVREF}},$$(26) $$\dot{V}\left(X\right)=\left[\begin{array}{cc}{2K}_3·V_{\mathrm{INV}}& {2K}_4·V_{\mathrm{INVREF}}\end{array}\right]{\left[\begin{array}{cc}{V}_{\mathrm{INVERR}}+V_{\mathrm{TRIREF}}+I_c& -\left(V_{\mathrm{INVREF}}-V_{\mathrm{INV}}\right)\end{array}\right]}^{\mathrm{T}}<0,$$(27) $$\dot{V}\left(X\right)<0.$$

Hence, the system is stable.

Figure 9 shows the flowchart for the operation of PCU. When the system is ON, check the operation status i.e., if the grid is operative, if yes, check whether the battery is operating or not. If the grid and battery both are operating, it is called passive grid feeding mode (Case 1). If the battery is not operating, it is called active grid feeding mode (Case 2). If the grid is not operating, it is called grid-forming mode (Case 3). For Case 1, check if S_NET > 0; if yes, check whether S_NET > P_{BAT_Limit}, if yes feed to the grid and battery both, if not, feed to the battery. If S_NET < 0, check if S_NET < P_BATLimit. If yes, draw power from the grid and the Battery. If No, draw power from Battery only. For Case 2, check if S_NET > 0, if yes, feed power to the grid; if no, draw power from the grid. Sense system parameters. For Case 3, check if S_NET > 0; if yes, feed power to the battery, if no draw power from the Battery. Check whether SOC is in the limit? If yes, resume normal operation; if no, sense system parameters.

Figure 9 Flowchart for operation of PCU [1].

4 Modes of operation of PCU

$$S_{\mathrm{GEN}}=P_{\mathrm{GEN}}=P_{\mathrm{PV}}+P_{\mathrm{W}}.$$(28)

Total Power generated is equal to the power generated by PVs and wind energy.$$S_{\mathrm{Load}}=P_{\mathrm{Load}}+j{Q}_{\mathrm{Load}}=P_{\mathrm{LVDC}}+P_{\mathrm{MVDC}}+\left[P_{\mathrm{AC}}+j·Q_{\mathrm{AC}}\right].$$(29)

Active power absorbed by load is the power absorbed by the load on the LVDC bus, MVDC bus, or AC bus. Reactive power absorbed by the load is the power absorbed by the load on the AC bus.$$S_{\mathrm{NET}}=S_{\mathrm{GEN}}-S_{\mathrm{LOAD}}=S_{\mathrm{GRID}}+S_{\mathrm{BAT}}+S_{\mathrm{LOSS}}.$$(30)

Net power, S_NET, is the power obtained after subtracting power consumed by loads from total generated power, which is the power fed by the AC grid, plus power absorbed or generated by the battery, plus power loss in resistances. Equation (31) could be obtained from equation (30).$$S_{\mathrm{GRID}}=P_{\mathrm{GRID}}+j{Q}_{\mathrm{GRID}}=S_{\mathrm{NET}}-S_{\mathrm{BAT}}-S_{\mathrm{LOSS}}.$$(31)

Total power in the interlinking converter is given by the power produced by the grid and the power absorbed by the AC load.$$S_{\mathrm{ILC}}=S_{\mathrm{GRID}}+S_{\mathrm{AC}}.$$(32)

4.1 Case I: Passive grid feeding mode

Mode I: Power produced by DERs > Power absorbed by load: Battery operates in buck mode. The interlinking converter acts as an inverter in current control mode, and power exchange with the grid takes place if the battery power flow limits are crossed.

Mode II: Power produced by distributed energy sources < Power absorbed by load: Battery discharges and operates in boost mode. The operation of the interlinking converter depends on the power requirement in AC or DC loads. Power is fetched from grid, if battery power flow limits are crossed.

4.2 Case II: Active grid feeding mode

Mode III: Power produced by DERs > Power absorbed by load: Interlinking converter works as an inverter in current control mode, feeding AC load and grid.

Mode IV: Power produced by distributed energy sources < Power absorbed by load: Scarce active power is drawn from the grid and converter as rectifier or inverter, depending on DC power quotient P_dc. Interlinking converter supplies the reactive power demanded by the AC load.

4.3 Case III: Islanded mode

Mode V: Power produced by DERs > Power absorbed by load: Battery charges with no power limits. Battery operates in buck mode and interlinking converter operates as an inverter in voltage control mode.

Mode VI: Power produced by DERs < Power absorbed by load: Battery discharges and operates in boost mode. Interlinking converter operates as an inverter in voltage control mode.

5 Simulation results and discussion

Table 1 indicates the system parameters. The results of the operation of the proposed PCU of the system are given in the following modes:

5.1 Case 1: Passive grid feeding mode

In this mode, distributed energy sources of the grid are active, the battery is connected, with its limits active. In Figures 10a and 10b, from t = 0–1 s, wind power is kept constant at 12 m/s. Wind power input changes to 9 m/s at t = 2 s. From t = 0–3 s, solar irradiation is kept constant at 1000 W/m²; the irradiation is changed to 600 W/m² from t = 4–6 s. Temperature is 25 °C from t = 0–1 s, it is changed from 25 °C to 20 °C from t = 1–6 s.

Figure 10 Case 1: (a) Wind power, (b) PV power (c) Pac, Qac, (d) Pdc, (e) ILC P, Pgrid, (f) Battery voltage, SOC%, Battery current, (g) Battery power, (h) Iinv, (i) MVDC voltage, and (j) LVDC voltage.

During t = 0–1 s, S_NET is high, battery charges upto P_{ESS_Lim}. Excess power on the DC side is supplied to the AC load and grid (P_GRID > 0). At t = 1 s, the DC load increases, and wind power decreases. So, during t = 1–3 s, the power exchanged with the grid falls to zero. (P_GRID ≈ 0). Interlinking converter operates in inverting mode, both AC and DC loads are fed by the DERs, and the battery is in charging mode. At t = 3 s, PV power decreases, so during t = 3–4 s, the battery starts discharging, ILC current remains constant and both AC and DC loads are fed by DERs and battery. At t = 4 s, the DC load is increased, so during t = 4–5 s, the battery discharges with increased current, ILC current remains constant, both AC and DC loads are fed by the battery and DERs. At t = 5 s, the AC load is increased, so during t = 5–6 s, the battery discharges with greater current and supply power. AC load draws power from the current-controlled ILC and the grid.

In Figures 10c and 10d, variation in AC (P_ac, Q_ac) and DC (P_dc) load powers are shown. The AC load is increased at t = 5 s. DC load is increased at t = 1 s and t = 4 s. In Figure 10e, variation in ILC power (P_ILC), Pgrid is shown. Power exchanged by the interlinking converter is almost constant from t = 0–5 s, as the battery and DERs are supplying power to the AC and DC loads. It increases at t = 5 s as the AC load increases. Power exchanged with the grid is almost zero from t = 0–5 s, from t = 5–6 s the grid supplies power to the AC load, as AC load is increased. Figure 10f shows the variation of SOC%, battery current, and battery voltage with variation in loads and fluctuating DERs. Figure 10g shows the variation in battery power. From t = 0–3 s, battery power is positive, i.e., battery is charging. From t = 3–6 s, the battery starts discharging, so battery power is negative. I_inv (ILC current) is shown in Figure 10i. ILC current increases at t = 5 s to supply the increased AC load. Figures 10j–10k shows MVDC and LVDC bus voltages are stable under variable input conditions and load conditions also.

5.2 Case 2: Active grid feeding mode

For this case, DERs – Operative; Grid – Operative; Battery – Not operative. Source and load variations are the same as in Case 1. From t = 0–1 s, the DC side power is in excess, which is supplied to the AC side through an interlinking converter working as an inverter in current control mode to supply the AC load and remaining to the grid. The reactive power demand for the AC load is supplied by ILC only. At t = 1 s, the DC load is increased, solar power input increases, so from t = 1–3 s, power exchanged through the interlinking converter and thus grid decreases (Fig. 11a). At t = 3 s, solar power input decreases, so power exchanged through the interlinking converter decreases, current through the interlinking converter also decreases, and power is taken from the grid, so P_grid is negative, i.e., AC load is supplied from the grid. At t = 4 s, the DC load further decreases, and the power in DERs is insufficient to feed the DC load, so power is taken from the grid to feed the DC loads too. So the interlinking converter starts operating in rectifying mode, and the current through it increases. At t = 5 s, the AC load is increased, so the power exchanged with the grid increases.

Figure 11 Case 2: (a) ILC P, Pgrid, (b) Iinv, (c) MVDC voltage, and (d) LVDC voltage.

5.3 Case 3: Islanded mode

In islanded mode, the grid is disconnected, and the BESS operates (no limits). Energy produced from wind/PV sources and load conditions are the same. Figures 12a and 12b shows the variation in battery current, voltage, SOC%, and battery power. The battery operates in charging mode from t = 0–3 s, so the battery power is positive. From t = 3–6 s, the battery operates in discharging mode, so battery power is negative.

Figure 12 Case 3: (a) Battery SOC (%), Battery current, Battery voltage, (b) Battery power, (c) PILC, Pgrid, (d) MVDC voltage, and (e) LVDC voltage.

Figures 12c, variation in power exchanged through the interlinking converter and grid. From t = 0–5 s, the power exchanged through the interlinking converter is almost constant; it increases from t = 5–6 s due to increase in the AC load. The interlinking converter operates in voltage-controlled inverting mode. Power exchanged through grid is nil from t = 0–6 s, Figures 12e and 12f show that MVDC voltage and LVDC voltage are stable under variable input and load conditions, also.

6 Comparative performance analysis

To analyse the superiority of the proposed method, the proposed PCU is compared to the existing strategies. The settling time, voltage deviation, Total Harmonic Distortion (THD), power efficiency, response time, and voltage fluctuation are given in Table 2. It is observed from Table 2 that the proposed PCU produces better results as compared to the control technique used in [21] and [22]. With the proposed method, the values of THD%, settling time, voltage deviation, response time, and voltage fluctuation are minimum while the power efficiency is maximum.

7 Conclusion

The PV system and wind system are integrated with BESS and a single-phase AC source to form a hybrid microgrid, which is able to supply single-phase, 230 V loads and 380 V, 48 V DC loads. A PCU based on HCC and SMC is suggested for effective power management in the system. The configured system can function in every scenario with the help of HCC and SM controllers. The BESS provides a rigid bus voltage control while managing transient power smoothly over extended working hours. The BESS is used to regulate the grid power when it is in grid feeding mode. The three-phase AC source can also be integrated with the DERs and BESS to supply three-phase loads, single-phase loads, and DC loads. Additionally, the proposed method is better than the existing methods.

References

All Tables

All Figures

	Figure 1 Proposed hybrid PCU.
In the text

	Figure 2 Detailed view of PCU.
In the text

	Figure 3 (a) MPPT controller for solar PV and wind and (b) Low-voltage DC bus voltage controller.
In the text

	Figure 4 Circuit diagram of single-phase bidirectional DC-AC converter.
In the text

	Figure 5 Circuit diagram to derive the state space analysis of single-phase bidirectional DC-AC converter.
In the text

	Figure 6 HCC strategy.
In the text

	Figure 7 SMC strategy.
In the text

	Figure 8 Interlinking converter control.
In the text

	Figure 9 Flowchart for operation of PCU [1].
In the text

	Figure 10 Case 1: (a) Wind power, (b) PV power (c) Pac, Qac, (d) Pdc, (e) ILC P, Pgrid, (f) Battery voltage, SOC%, Battery current, (g) Battery power, (h) Iinv, (i) MVDC voltage, and (j) LVDC voltage.
In the text

	Figure 11 Case 2: (a) ILC P, Pgrid, (b) Iinv, (c) MVDC voltage, and (d) LVDC voltage.
In the text

	Figure 12 Case 3: (a) Battery SOC (%), Battery current, Battery voltage, (b) Battery power, (c) PILC, Pgrid, (d) MVDC voltage, and (e) LVDC voltage.
In the text