The output of a PV system fluctuates significantly due to the irregular nature of solar energy due to climatic conditions. The maximum decrease/increase in PV generation on a cloudy or windy day is determined by the wind speed and the size of the PV plant. When clouds are moving quickly, PV output decreases significantly. Thus, the injection of PV energy into a distribution grid creates issues with power quality such as voltage variations, stability deprivation, etc. PV power variations are not severe under normal climate conditions, but severe climate conditions account for 70–90% of all PV power fluctuations (see Figure 2A). It is probable to alleviate these power quality issues by using an efficient ESS (Brahmendra Kumar et al., 2018). In order to smooth out the output of the PV, the BS can be used with RR control. The RR control is a method of limiting the rate of power change from the PV system in order to maintain grid stability. The battery power characteristics are presented in Figure 2B based on RR control. The area around the green line shows the minimum and maximum energy capacity of the battery that is needed to effectively smooth the variation in PV output.

Figure 2C Depicts a block diagram for a basic RR control system. The rate of rise/fall is limited to a maximum RR (r_max ) value denoted as RES-RR. The maximum RR value that can be considered is 10%/min. P b * = P p v , r a m p * − P p v , r a t e d * (1)

The difference between rated PV power ( P p v , r a t e d * ) and ramp-rate power ( P p v , r a m p * ) generates the reference power for the battery ( P b * ). The sign of the generated power determines the charging and discharging conditions of the battery. If the sign is negative, the battery can be charged and vice versa. The P p v , r a m p * is calculated based on the maximum limit rate (r _max). The required ramp-rate power ( P p v , r a m p * ) equation is given below. P p v , r a m p * = r max × P p v , r a t e d * 60 (2)

As illustrated in Figure 3, the EMS control parameters balances power between RES, grid and ESS. This algorithm takes into account the present state of P_pv , P_l , SoC_b , SoC_sc , I_b , and I_sc as input parameters. The algorithm starts with input parameters and secondly, the algorithm considers these variables to decide the operation mode of MG (i.e., RES balances or less or more than the load demand). The BS and SC status of SoCs is analyzed in the third stage, i.e., whether SoC_b and SoC_sc are within or above the SoC_H or SoC_L limits. Finally, different BS and SC reference conditions and preferences are determined by various grid-interactive states that decide the MG-VSC reference, such as grid sharing, grid injection or idle mode, and also by BS and SC charging and discharging, or both charging and discharging, or both being in idle conditions. By limiting SoC_b and SoC_sc to safe levels, this technique considers the ESS’s energy content and limits active involvement to its rating.

The EMS and converter control are shown in Figure 4 as a simplified control scheme for this proposed system. The reference currents for the BS, SC, and MG-VSC converters are generated according to the scheme shown in Figure 5. To generate the error signal, a comparison is made between the actual (i.e., i_pv , i_b , i_sc , i_g ) and reference currents in the current controller. The BS, SC, and RES-based converters rely on the modular signals generated by PI controllers for input. A hysteresis current controller regulates the MG-VSC’s switching pulses.

A constant DC-link voltage maintains system power balance (Neto et al., 2018). A DC-link controller generates a net current (i*_dc ) that is either injected or drawn from the DC-link. A PI controller processes this signal to generate the net current (i ^* _dc ), which is shown in Figure 6. The voltage control loop written in (4) is used to calculate the total current, i_net(t). The HESS and the utility grid must sustain power balance by dividing the i _net into average (i _avg ) and transient (i _trs ) components, respectively. v e ( t ) = v d c * ( t ) − v d c ( t ) (3) i n e t ( t ) = k p v e ( t ) + k i ∫ v e ( t ) (4) i a v g * ( t ) = ( 1 1 + s τ c ) i n e t ( t ) (5) i t r s * ( t ) = ( 1 − 1 1 + s τ c ) i n e t ( t ) (6)

The DC-link power (P _dc ) is taken by, P d c ( t ) = v d c * ( t ) i a v g ( t ) (7) Where k _p and k _i are the PI controller’s proportional and integral components, and τ _c is the low-pass filter time constant. The control structure and power balance at the DC-link are illustrated in Figure 5 and the equation is as follows: P p v ( t ) ± P h e s s ( t ) ± P g ( t ) = P d c l ( t ) + P a c l ( t ) (8) Where P _pv , P _g , P _hess , P _dcl , and P _acl are PV, grid, HESS, DC and AC load powers, respectively.

It operates in two modes: 1) excess power (EPM: P_H > 0) and (ii) deficit power (DPM: P_H ≤ 0) modes. Two operating modes are considered depending on the availability of RES power generation and system load requirements. The balance equation for EPM and DPM is P_H = P_b + P_sc + P_g = P_dcl + P_acl - P_pv . As illustrated in flowchart Figure 7, the system works in various modes of operation depending on the condition of P_H . As shown in Tables 1A,B, DPM and EPM distinguish four distinct operating modes based on the conditions of the SoC_b and the SoC_sc .

An important part of BS-based devices is the State of charge (SoC), which also improves BS performance. The BS can be protected, overcharging can be prevented, its lifetime can be extended, and the system’s accuracy can be improved with proper SoC calculations (Hosseini et al., 2021). The SoC of BS and SC is calculated using the count-coulomb approach and the resulting equations are given by, S o C b = S o C b i n − 1 3600 C N b ∫ i b d t (9) S o C s c = S o C s c i n − 1 3600 C N s c ∫ i s c d t (10)

The current i(t) is measured and integrated over time to calculate the amount of energy that remains in the battery and SC. SoC helps to analyse battery and SC whether to charge or stop charging. This approach relies on exact measurements of battery and SC current and initial SoC. Where SoC _bin and SoC _scin are the BS and SC initial SoCs, C _Nb , and C _Nsc are the BS and SC nominal capacitances, and i _b and i _sc are the BS and SC currents.

The operational objectives defined for DPM are discussed in the following sections.

State I: Discharging both the BS and SC is necessary if SOC_b > L_b and SOC_sc > L_sc . The BS, SC, and grid settings are set to the following, i b * = ρ . i a v g *         , i s c * = i s c , r *         ,   i g * = ( 1 − ρ ) . i a v g (11)

ρ represents the charging and discharging condition of the BS. Table 2 contains the results of a four-state logic used to determine the value of ρ.

State II: The BS should be idle if SoC _b < L _b and SoC _sc > L _sc . SC provides transient and oscillatory current while the grid meets average power demand. i b * = 0 ,   i s c * = i s c , r *       ,   i g * = i a v g (12)

State III: The SC should be idle if SoC _b > L _b and SoC _sc < L _sc , and the BS is discharged until SoC _b reached L _b to meet the average power demand while the SC is idle or charged from the grid. The grid supplies the required SC and average power demand. i b * = ρ . i a v g *         ,   i s c * = 0 ,   i g * = ( 1 − ρ ) . i a v g + i s c , r (13)

State IV: When SOC _b < L _b and SOC _sc < L _sc , the BS and SC are idle or charged by the utility grid. The grid is able to handle the total difference between generation and load power requirements. i b * = 0 ,   i s c * = 0 ,   i g * = i a v g + i s c , r (14)

In this case, the grid supplies both average and transient power demand.

The battery controller block diagram is presented in Figure 8. The TF of control to inductor current is taken as (Kollimalla et al., 2014), G i , b = V 0 C b s + 2 V 0 R L L b C b s 2 + L b R L s + ( 1 − D b ) 2 (15)

The TF of CCL compensator is as follows: G p i , b = K p b + K i b s (16)

The OLTF of CCL is given by, G O L , b = G p i , b G i , b H b (17)

The Bode plot of the OLTF for the battery is depicted in Figure 9. To develop and optimize the control parameters, the SISO tool is used. The PI controller is calibrated to obtain a PM of 60° at rate of 1.97 krad/s. The calculated D _b , K _pb and K _ib parameters are 0.4, 0.1 and 11, respectively.

The SC controller block diagram is presented in Figure 10. The TF of control to inductor current is taken as (Kollimalla et al., 2014), G i , s c = V 0 C s s + 2 V 0 R L L s C s s 2 + L s R L s + ( 1 − D s c ) 2 (18)

The TF of CCL compensator is as follows: G p i , s c = K p s c + K i s c s (19)

The OLTF of CCL is given by, G O L , s c = G p i , s c G i , s c H s c (20)

The Bode plot of OLTF for SC is depicted in Figure 11. The PI controller is calibrated to obtain a PM of 60° at rate of 6.43 krad/s. The calculated D _s , K _psc and K _isc parameters are 0.6, 0.56 and 120, respectively.

The TF of VCL is taken as (Kollimalla et al., 2014), G i , V = R L ( 1 − D s ) ( 1 − L s R L ( 1 − D s ) 2 s ) 2 + R C s s (21)

The TF of VCL compensator is as follows: G p i , V = K p V + K i V s (22)

The OLTF of VCL is given by, G C L , s c = G p i , s c G i , s c 1 + G p i , s c G i , s c H s c (23) G O L , s c = G p i , V G C L , s c G i , V H V (24)

The Bode plot of the OLTF for the voltage controller is depicted in Figure 12. The PI controller is calibrated to obtain a PM of 60° at rate of 0.2 krad/s. The calculated D _s , K _pV and K _iV parameters are 0.6, 0.23 and 15, respectively.

The scale of the figures presented in Figures 17, 18, 19, the X-axis represents the time per division (s/div) and the Y-axis represents the current (A/div), voltage (V/div), and power (W/div) values ​​per division. Figures 17A–H illustrates the performance of the EMS during EPM operation. In this mode, the generation exceeds load demand by a predetermined margin.

The PV current profile shown in Figure 17Aa. The response battery and SC current profiles are presented in Figure 17Ab,c. At time t ₁ , SoC _b and SoC _sc are lower than H. Changes are made to the DC load at time t ₁ = 1s in Figure 17Bb, which results in a voltage deviation in the DC link. In this state, charge the BS and SC to their rated charging capacity and the SoC will attain its maximum value. The grid provides the required P _avg to sustain a stable DC link voltage in Figure 17Ba. The SC device provides transient power.

When SoC _b reaches H _b at time t ₂ , i _b equals zero. The SC is charged at its rated current in this state because the SoC _sc is still less than the H _sc . The SC is charged with a part of the surplus power, and the remaining surplus power being fed back into the grid.

At time t ₃ , when SoC _sc reaches H _sc , i _sc equals zero. After that, the BS is charged at its rated current until H _b is reached. The grid utilizes both transient and average power to sustain a stable DC link voltage during this condition in Figure 17Ba.

The At time t ₄ , i _acl has increased in Figure 17Ca. At this point, SoC _sc is equal to H _sc and SoC _b is lower than H _b . As a result, the charging current i _b is constant and the transient power is delivered by the SC. The response of grid and VSC currents is illustrated in Figures 17Cb,c.

At time t ₅ , SOC _b and SOC _sc are higher than H. In this state, the grid is able to stabilize the DC link voltage. The generation meets the total demand and surplus power is fed back into the grid. The i _g and v _g operate at unity power factor under all operating conditions. Figures 17D–G show the constant AC load, VSC, grid currents and various power results of PV, BS, SC, VSC, grid, DC and AC loads. Figures 17Ha-c show the inverter, AC load, grid currents, and grid voltage, respectively.

In this case, the i _pv is less than the load demand, resulting in a P _H < 0 and the PV current profile shown in Figure 18Aa remains constant. The SOC _b and SOC _sc thresholds are changed to observe the system behavior under extreme conditions. Hence, the controller and the proposed EMS can be studied under extreme operating circumstances.

Condition I: The P _deficit shared by BS with the grid power until SoC _b < L. The DC load is being changed from R = 50Ω–25 Ω at t ₁ in Figure 18Bb. As i _b increases slowly in Figure 18Ab, the SC adjusts to the rapidly changing DC load power depicted in Figure 18Ac. Therefore, V _dc is quickly regulated in Figure 18Ba and i _b changes smoothly as shown in Figure 18Ab.

Condition II: In this case, the SOC _b is reduced. As a result, the grid supply deals with the active power demand under steady state, where the SC pack absorbs a transient change in power at t = t₂. Therefore, i_vsc achieves a smooth change at instant t₂ in Figure 18Cb. The grid current response is shown in Figure 18Cc.

Condition III: SOC _b is greater than L _b and SOC _sc is less than L _sc . The BS and grid supply handle the deficit load power until SoC _b < L.

Condition IV: Both SoC_b and SoC_sc are low in this condition. As a result, the grid provides the necessary power to sustain the V_dc at a stable level. In Figure 18Ca, the AC load increases at times t ₂ and t ₃ . The SoC _sc is now lower than L _sc . As a result, i _sc becomes zero. The i _b gradually rises as the grid contributes to compensating the P _deficit in the system and SC provides the transient change in power. Figures 18D–G show the constant AC load, grid, VSC currents and various power results of PV, BS, SC, VSC, grid, DC and AC loads. show the various power results of PV, BS, SC, VSC, grid, DC, and AC loads. Figure 18H shows the grid current and voltage, which are sinusoidal in nature.

Figure 19A depicts the proposed EMS dynamic performance in various operating modes based on variations in RES power. Figure 19Aa illustrates the high-gain RES converter with emulated RES current pattern applied to determine the feasibility of the proposed scheme. The i _pv reduces the load demand between instants t ₀ and t ₇ . Hence, the system works in DPM, sharing the available power between the BS and the utility grid. During the t ₇ and t ₈ instants, i _pv exceeded the load demand. So, the system operates on EPM, and ESDs are charged with surplus power. Again, the i _pv is lower than the load demand ranges from t ₈ to t ₁₅ . Thus, the system runs on DPM as shown in Figure 19A. The smooth changes in i _b , i_g , and i_vsc that occur during the mode transition are depicted in Figures 19Ab,Cb,Cc.

The power sharing between the seamless transfer operation modes is summarized in Table 4. Where CM: charging mode, DM: discharging mode, CG: charging from the grid, SL: load sharing, respectively. The results show that the high-power-density SC pack and its effective control of the DC link voltage significantly reduce the dynamics of the DC link voltage. The BS lifespan can be extended due to the reduced current stress due to reduced DC link voltage dynamics with the proposed EMS.

As the DC load varies at t ₁ in Figure 19Bb, the PV generation also varies as illustrated in Figure 19Aa. At time t ₁ , BS switches from a -1.2 A charging mode to +2.2 A discharging mode in response to varying load demand as shown in Figure 19Ab. As depicted in Figure 19Ac, the SC absorbs the transient power generated by the load and PV variation during the step change in load demand, thereby reducing BS stress. The i _b gradually increases to compensate for the loss of low-frequency power. Hence, the BS endures less stress and the DC grid remains stable in Figure 19Ba. As can be seen in Figures 19D,E, the system dynamically switches between modes in response to the availability of RES power and current load conditions. The SC packs supply/absorb the transient power surges caused by rapid variations in RES and/or load, and the surplus average power generated in the DC link is utilised to charge ESDs or to inject into the utility grid, depending on the SoC of ESDs. The proposed EMS power quality features are illustrated in Figure 19F for various operating modes. When the VSC is not connected, i_g has both fundamental and harmonic load current components. The nonlinear component of the AC load increases at t ₁ in Figure 19Ca and Figure 19Fa. A DC-AC inverter compensates for the non-linear component of an AC load. In addition to compensating current harmonics and reactive power, the VSC delivers and absorbs real power to and from the utility grid in Figure 19Fb. Therefore, i _g in Figure 19Fc remains constant and the voltage and current of the AC grid are in phase. As a result, grid voltage and current are maintained with UPF. Figure 20A presents the harmonic spectra of i _L and i _g . A total harmonic distortion (THD) of 13.38% is measured on the current drawn by the non-linear load, while the current drawn by the grid is sinusoidal with a THD of 2.14% within the tolerances set by the IEEE-519 standard.

As illustrated at time t ₁ in Figure 19Ba, the results are used to analyse the voltage overshoot and the settling time that occurs with a step change in load demand. The voltage overshoot equation is as follows: M P = Δ V d c V d c × 100 (25)

Figure 20B shows the change in voltage measured between V ₁ and V ₂ and the recovery time of voltage is measured between t ₁ and t ₂ . The performance of the proposed system with the existing methods is presented in Table 5. Table 5 includes the peak overshoot (M _p ), recovery time (T _r ) of voltage, and grid THD compared to existing methods. Based on Table 5, the voltage overshoot is less and the DC link voltage requires less time to stabilise compared to the methods proposed in (Sathishkumar et al., 2012), (Manandhar et al., 2019), and (Tummuru et al., 2015b) techniques. Therefore, the proposed EMS provides less time to compute and has lower THD than existing methods.