The system comprises a 12 MW grid-connected PV plant and a 45 MWh LFP BESS supplying a 17.5 MVA industrial load (pf = 0.85) through a 20 kV PCC (Figure 1). The PV array is interfaced through a DC link and a grid-following three-phase VSC with an Rf-Lf filter. The BESS uses a bidirectional DC/DC stage, DC link, and dedicated bidirectional VSC for independent P/Q exchange. The utility grid is represented by a Thévenin equivalent. The CEMPCS generates coordinated P/Q references for both converters, while identical inner dq-current loops are retained for the conventional and proposed controls.

Figure 1. Overall architecture of the proposed 12 MW PV - 45 MWh LFP battery energy storage system supplying a 17.5 MVA industrial load through a Point of Common Coupling (PCC).

The nominal parameters of the proposed PV-BESS system are summarized in Table 1. They define the PV plant, BESS, industrial load, grid, and converter characteristics used for dynamic modeling and EMT/RMS co-simulation and establish the reference operating conditions considered throughout this study.

Table 1. Electrical and system specifications.

For reproducibility, the PV interface is modeled as PV array → 1500 V DC link → two-level three-phase VSC → Rf-Lf filter → 20 kV PCC. The BESS interface is modeled as LFP battery → bidirectional DC/DC converter → DC link → two-level bidirectional three-phase VSC → Rf-Lf filter → PCC. In the adopted simulation design, the PV and BESS AC converters are each assigned an apparent-power rating of 15 MVA. This gives the PV converter reactive-power headroom at rated 12 MW active power and makes the BESS P/Q allocation explicitly subject to S² ≥ P² + Q². These ratings are used by the capability limiter in Section 4.6 and must be identical in both comparative cases.

The photovoltaic (PV) generator is represented by the single-diode equivalent model, including the photocurrent source I p h , diode current I D , series resistance R s , and shunt resistance R s h . Applying Kirchhoff’s Current Law (KCL) at the PV output yields

The diode current is described by the Shockley equation as

where I 0 is the diode reverse saturation current, a is the diode ideality factor, N s is the number of series-connected cells, and V T is the cell thermal voltage. Considering the voltage drop across the series resistance, the diode voltage is

The shunt-branch current is

Substituting (2) - (4) into (1) yields the nonlinear current-voltage characteristic of the PV generator:

The cell thermal voltage is defined as

where k is the Boltzmann constant, q is the elementary charge, and T is the absolute cell temperature. The photocurrent dependence on irradiance and temperature is modeled as

where I s c , r e f is the short-circuit current at reference conditions, α I is its temperature coefficient, G is the incident solar irradiance, and G r e f and T r e f denote the reference irradiance and temperature, respectively. The instantaneous PV output power is

Under maximum power point tracking (MPPT), the available active-power reference is defined as

The PV generator is coupled to the voltage-source converter (VSC) through the DC link. The energy stored in the DC-link capacitor is

where C d c and V d c denote the DC-link capacitance and voltage, respectively. Differentiating (10) gives

Neglecting converter losses, the instantaneous DC-link power balance is

where P V S C is the active power transferred from the DC link to the AC side of the converter. Combining (11) and (12) yields the DC-link voltage dynamics:

For small perturbations around the operating point ( G 0 , T 0 ) , the PV active-power variation is approximated by the first-order linearization

where the perturbations are defined by

Equation (14) quantifies the sensitivity of PV active power to irradiance and temperature variations, whose resulting power imbalance is compensated by the BESS and grid-side converter to mitigate disturbances at the PCC.

The resulting P_PV, V_dc, and P_VSC variables provide the interface with the VSC model and the active/reactive power control developed in Section 4.2.

The grid-side VSC is modeled in the synchronous dq reference frame and connected to the PCC through an Rf-Lf filter. The three-phase variables are transformed using

where θ is the synchronous electrical angle aligned with the positive-sequence PCC voltage. The converter voltage components are related to the DC-link voltage by

The converter current dynamics are

where i_d and i_q are the converter current components, v_cd and v_cq are the converter output voltages, and ω is the synchronous angular frequency. The active and reactive powers exchanged at the PCC are

With the d-axis aligned with the PCC voltage vector,

Thus, i_d governs the active-power exchange, whereas i_q governs the reactive-power exchange, providing the decoupled P/Q interface required by the proposed CEMPCS.

The LFP battery is represented by a first-order Thévenin equivalent circuit including the open-circuit voltage V_oc(SoC), ohmic resistance R₀, and polarization branch R_p-C_p. The terminal voltage is

where I_b > 0 denotes battery discharge, and V_p is the polarization voltage. The polarization dynamics are governed by

The instantaneous battery power is

with P_b > 0 during discharge and P_b < 0 during charging. Considering distinct charging and discharging efficiencies, the state-of-charge dynamics are expressed as

where η_c and η_d denote the charging and discharging efficiencies, respectively, and E_b,nom is the nominal battery energy. The stored battery energy is

For the proposed BESS,

The battery power is constrained by the bidirectional converter capability:

The admissible state-of-charge range is

The battery power reference is constrained according to the instantaneous SoC:

Equations (23) - (31) define the electrical, polarization, energy, and SoC dynamics of the LFP BESS. The constrained reference PBESS provides the battery-side input to the coordinated power-management strategy while enforcing the admissible SoC limits.

The Point of Common Coupling (PCC) constitutes the electrical interface among the PV plant, BESS, utility grid, and industrial load. Its dynamic behavior is determined by the instantaneous active- and reactive-power balances:

where P_L and Q_L denote the industrial-load active and reactive powers, respectively, while ΔP_PCC and ΔQ_PCC represent the instantaneous power mismatches at the PCC. The utility grid is represented by its Thévenin equivalent impedance

and the PCC voltage phasor is expressed as

where V_g is the Thévenin-equivalent grid voltage, and I_g is the current exchanged with the utility grid. The corresponding complex power exchanged at the PCC is

For small perturbations around the nominal operating point, the PCC voltage magnitude variation can be locally approximated as

where the sensitivity coefficients are defined by

The normalized PCC voltage deviation is defined as

where VPCC denotes the nominal PCC voltage reference. To establish the local relationship between power imbalance and voltage variation, the linearized power-flow equations are written as

Defining the PCC power-flow Jacobian as

Equations (32) - (40) establish the coupling between active/reactive power imbalances and PCC voltage variations. The resulting ΔP_PCC, ΔQ_PCC, and ε_V provide the feedback variables required by the coordinated voltage and power-control loops developed in Section 4.

A cascaded control structure regulates the DC-link and PCC voltages through outer voltage loops Figure 2, while inner dq-current loops ensure fast converter-current tracking and generate the corresponding voltage references.

Figure 2. Cascaded control architecture of the VSC in the synchronous dq reference frame.

The DC-link voltage error is defined as

The corresponding d-axis current reference is generated by a PI controller:

Similarly, the PCC voltage error is

from which the reactive-current reference is obtained:

The inner-loop current errors are defined as

Using the converter dynamics derived in (17) - (18), the decoupled voltage references are

The corresponding modulation references are

Equations (41) - (48) establish the cascaded voltage-current control structure. The outer loops generate i_d and i_q, while the inner loops regulate the converter currents and generate the modulation references required by the VSC.

The power-management layer coordinates PV, BESS, and grid power exchanges to compensate active-power imbalances and provide reactive-power support at the PCC within the system operating constraints.

Based on the power balance defined in (32), the uncompensated active-power mismatch is

where P_Grid denotes the scheduled grid active-power exchange. The BESS compensates the admissible active-power mismatch according to the power and SoC constraints defined in (29) - (31):

The resulting grid active-power reference is

For PCC voltage support, the required reactive-power compensation is generated from the voltage deviation:

where KQV is the voltage-reactive-power control gain. The reactive-power reference is shared between the PV and BESS converters according to

For each converter k ∈ {PV, BESS}, the reactive-power capability is constrained by its apparent-power rating:

Equations (49) - (54) define the coordinated P/Q references while enforcing the BESS operating limits and converter apparent-power constraints. The resulting references are subsequently processed by the CEMPCS supervisory algorithm developed in Section 4.7.

The allocation sequence implemented at each supervisory update is: 1) compute the active-power mismatch from measured/filtered P_PV, P_L and scheduled P_Grid; 2) saturate P B E S S ∗ by the ±15 MW power limit and the 20% - 90% SoC constraints; 3) update P G r i d ∗ from the residual active-power mismatch; 4) compute the PCC-voltage reactive-power demand; and 5) allocate Q between the PV and BESS converters subject to Q k , m a x = S k , r a t e d 2 − P k ∗ 2 . This ordering prevents the reactive-power request from violating the instantaneous apparent-power capability after active-power dispatch.

The proposed CEMPCS supervises the coordinated PV-BESS operation using the measured PCC variables, available PV power, and battery SoC. The supervisory layer determines the active- and reactive-power references while enforcing the operating constraints defined in (29) - (31) and (54).

The active-power imbalance used by the supervisory controller is defined as

The BESS operating mode is selected according to the sign of ΔP and the instantaneous SoC:

For PCC voltage regulation, the voltage error is

The required reactive-power support is then determined by

where Q m a x a v denotes the available reactive-power capability of the PV and BESS converters. From the apparent-power constraint in (54), the capability of converter k ∈ {PV, BESS} is

The CEMPCS operates under four conditions: normal operation, power deficit, power surplus, and PCC voltage deviation. BESS operation respects SoC limits, while reactive-power support is constrained by converter capability. As shown in Figure 3.

Figure 3. Supervisory decision and power-allocation algorithm of the proposed CEMPCS.

The references P B E S S , Q P V , Q B E S S , and P G r i d r e f are transferred to the control layers in Sections 4.5 - 4.6. The CEMPCS thus coordinates power balancing, PCC voltage, SoC, and converter constraints.

The PV-BESS system is implemented in MATLAB/Simulink using a synchronized EMT/RMS partition. The EMT subsystem models the VSC switching dynamics, DC links, Rf-Lf filters, PCC network, Thévenin grid, and motor-starting transient with a fixed 2 µs step. The RMS/control subsystem includes the industrial load, BESS SoC dynamics, MPPT, outer controllers, conventional/CEMPCS supervisory algorithms, and performance calculations with a 1 ms step. At each 1 ms synchronization interval, P/Q and dq-current references are transferred to the EMT model, while processed PCC, converter, and grid measurements are returned to the supervisory layer. Both control cases use identical plant parameters, solver settings, and initialization; only the supervisory reference-generation strategy differs. As shown in Table 2.

Table 2. Simulation and control parameters.

Adopted simulation/design parameters. The nominal load powers are obtained from S_L = 17.5 MVA and cosφ = 0.85, giving P_L = 14.875 MW and Q_L = 9.219 MVAr, and the Thévenin equivalent uses SCR = 5 and X/R = 10, with fixed EMT/RMS parameters for all simulation scenarios.

All scenarios start from the same steady-state operating point: G = 1000 W/m², T = 25˚C, P_PV = 12 MW, SoC = 50%, P_BESS = 0 MW, and V_PCC = 1.0 p.u. The 17.5 MVA load at pf = 0.85 corresponds to P_L = 14.875 MW and Q_L = 9.219 MVAr. Neglecting losses, the grid initially supplies 2.875 MW and the load reactive demand. The PV operates in MPPT/grid-following mode, while the BESS starts in standby/PQ mode. Initialization consists of solving the RMS power balance, setting the DC-link voltages and SoC, transferring the resulting P/Q operating point to the EMT model, and allowing steady-state settling before each disturbance is applied. As shown in Table 3.

Table 3. Initial operating point used before each dynamic disturbance.

The proposed CEMPCS is evaluated under four dynamic disturbances representing the main operating challenges of the PV-BESS industrial system. The scenarios are designed to assess active-power balancing, PCC voltage regulation, reactive-power support, and transient recovery. As shown in Table 4.

Table 4. Dynamic simulation scenarios.

For S1, the irradiance reduction produces a rapid decrease in PPV, requiring BESS active-power compensation. S2 introduces a load increase to evaluate coordinated active/reactive power regulation. S3 imposes a motor-starting transient characterized by high reactive-power demand and PCC voltage depression. Finally, S4 applies a temporary grid-voltage reduction to evaluate the voltage-support capability of the PV and BESS converters.

The dynamic performance of the proposed CEMPCS is quantified using PCC voltage deviation, settling time, and active/reactive power imbalance.

The maximum PCC voltage deviation is defined as

The voltage settling time t_s is defined as the time required for V_PCC to return and remain within a tolerance band of ±2% around its reference value:

The instantaneous active-power imbalance is evaluated by

while the reactive-power imbalance is

The indicators ΔV_PCC,max, t_s, e_P, and e_Q are evaluated under identical disturbances for the conventional control and the proposed CEMPCS.

The conventional benchmark uses the same MPPT, plant, PI voltage loops, dq-current controllers, converter limits, and SoC protection as the proposed case, but it contains no PCC-level coordinated power allocator. Its operation is defined as follows. The PV converter tracks the available MPPT active-power reference P P V ∗ = P_MPP and uses only its local PCC-voltage/reactive-current loop. The BESS active-power reference follows a fixed grid-power schedule: P B E S S , c o n v ∗ = sat(P_L − P_PV − P_Grid,sched), subject only to the BESS power and SoC limits; it is not modified by a coordinated PCC power-mismatch objective. The BESS reactive-power reference is generated locally from its own PCC-voltage PI loop and is independently saturated by its apparent-power capability. The scheduled grid exchange is fixed at the pre-disturbance value P_Grid,sched = 2.875 MW for the four scenarios. Consequently, conventional PV and BESS references are generated independently, whereas the CEMPCS jointly reallocates active and reactive power using PCC feedback and instantaneous converter capability. This operational definition is used unchanged for S1 - S4.

Conventional reference laws used in the simulation: P P V , c o n v ∗ = P_MPP; P B E S S , c o n v ∗ = sat_SoC,P(P_L − P_PV − P_Grid,sched); P_Grid,sched = 2.875 MW; Q B E S S , c o n v ∗ = sat_S(K_pVe_V + K_iV∫e_Vdt), with e_V = P P C C ∗ − V_PCC and | Q B E S S , c o n v ∗ | ≤ S B E S S , r a t e d 2 − P B E S S , c o n v ∗ 2 . As shown in Table 5.

Table 5. Critical functional differences between conventional control and proposed CEMPCS.

Performance is compared using ΔV_PCC,max, t_s, e_P, e_Q, P_BESS, and SoC under scenarios S1 - S4.

Reproducibility note: all S1 - S4 disturbances are applied to the same initialized model, with identical solver steps, converter ratings, electrical parameters, and inner-loop gains. Signals used for the performance tables and figures must be exported directly from MATLAB/Simulink using the same logging names and post-processing definitions for both controllers; no manually constructed or illustrative response is admissible in the revised results section.

Before quantitative evaluation, the MATLAB/Simulink model is locked to ensure identical plant conditions for the conventional and CEMPCS controllers. The fixed plant includes the 12 MW PV system, 45 MWh LFP BESS, converter interfaces, 20 kV PCC, 17.5 MVA industrial load, Thévenin grid, and S1 - S4 disturbance blocks. All electrical parameters, converter ratings, initial conditions, solver settings, and disturbance profiles remain unchanged between comparative runs.

The EMT partition models converter switching, DC-link and filter dynamics, PCC/grid network, and motor-starting transients with a fixed 2 µs step. The RMS/control partition, updated every 1 ms, handles MPPT, BESS SoC dynamics, outer control loops, P/Q reference generation, supervisory control, and performance calculations. EMT and RMS partitions exchange data at a fixed 1 ms synchronization interval. As shown in Table 6.

Loggedsignals. Each run exports a common time vector and identical signals for both controllers: G, P_PV, V_dc, V_PCC,pu, P_Load, Q_Load, P_BESS, Q_BESS, P_Grid, Q_Grid, SoC, e_P, e_Q, i_d, i_q, and converter mode/saturation flags. Motor current is additionally recorded for S3 and V_Grid,pu for S4.

Table 6. Model lock, signal logging, and simulation execution protocol.

Runsequence. Each scenario is initialized at the Table 3 operating point and allowed to reach steady state before applying the Table 4 disturbance. Conventional and CEMPCS runs use identical plant conditions, producing eight datasets (S1 - S4 for each controller), all processed by the same analysis script.

Performanceextraction. From the logged data, the script automatically computes maximum PCC voltage deviation, ±2% settling time, peak |e_P| and |e_Q|, and peak BESS P/Q support. Improvement percentages are calculated only from the two corresponding simulation datasets; no manually adjusted or placeholder values are used.

Modelacceptance. Results are transferred to Section 6 only if both controllers use identical plant/disturbance conditions, the initial operating point is satisfied, converter and SoC limits are respected, and all indicators and figures are reproducible from the archived simulation data. Otherwise, the scenario is rerun.

Accordingly, the numerical values currently appearing in the original illustrative Results section are not treated as validated outputs. Figures 4-8 and the associated performance tables must be replaced only after the eight locked-model simulations have been executed and the above acceptance gate has been satisfied.

Scenario S1 applies an irradiance reduction from 1000 to 600 W/m² between t = 2 s and t = 4 s. At constant reference temperature, the corresponding first-order PV-power target decreases from approximately 12 MW to 7.2 MW, producing a 4.8 MW generation deficit. As shown in Table 7.

Table 7. Performance comparison under Scenario S1.

The illustrative response shows that coordinated BESS support limits the PCC voltage deviation and reduces the active-power imbalance relative to conventional control. Final numerical conclusions must be updated using the actual MATLAB/Simulink outputs.

Scenario S2 evaluates the system response to a 20% increase in the nominal industrial load between t = 4 s and t = 6 s. With S_L = 17.5 MVA and PF = 0.85, the initial active power is P_L0 = 14.875 MW and increases to P_L1 = 17.85 MW. As shown in Table 8.

Table 8. Performance comparison under Scenario S2.

The load step increases the active- and reactive-power demand at the PCC. The CEMPCS coordinates BESS active-power injection and reactive-power support to reduce the resulting PCC voltage disturbance.

The illustrative responses indicate that coordinated BESS support provides faster active- and reactive-power compensation and limits the PCC voltage deviation relative to conventional control. Final quantitative conclusions must be updated using the actual MATLAB/Simulink outputs.

Scenario S3 evaluates the PV-BESS response to a large induction-motor starting event between t = 6 s and t = 7 s. The transient increases current and reactive-power demand, producing a temporary PCC voltage sag. As shown in Table 9.

Table 9. Performance comparison under Scenario S3.

The CEMPCS coordinates converter reactive-power support and the BESS response to limit the voltage deviation and accelerate recovery.

The CEMPCS reduces the PCC voltage deviation by 62.7% and the settling time by 59.5%, while providing higher transient reactive-power and BESS support.

Scenario S4 evaluates the system response to a grid-voltage reduction from 1.0 to 0.8 p.u. between t = 8 s and t = 8.2 s. The CEMPCS coordinates PV-BESS power support to limit the PCC voltage deviation and improve transient recovery. As shown in Table 10.

Table 10. Dynamic performance under grid-voltage disturbance (S4).

The CEMPCS limits the illustrative PCC voltage deviation from 11.6% to 4.3% and reduces the settling time from 0.38 s to 0.15 s. Higher PV-BESS support also reduces the active- and reactive-power imbalances during the disturbance.

The overall CEMPCS performance is summarized using the main dynamic indicators obtained under Scenarios S1 - S4. The comparison focuses on PCC voltage deviation, settling time, and power-balance improvement. As shown in Table 11.

Table 11. Overall performance comparison.

The illustrative comparison shows lower PCC voltage deviations with CEMPCS in all four scenarios. The corresponding reduction ranges from 62.7% to 69.1%, while the available settling-time results indicate reductions from 59.5% to 66.7%.