V2G Power Flow Control — MATLAB Simulink
Bidirectional active and reactive power management from EV battery to utility grid using vector-controlled VSI, MOSFET/SiC gate driver hardware circuit, custom inductor and LCL filter design, and SOC-dependent dispatch — all modelled and simulated in MATLAB R2024b / Simulink / Simscape Electrical.
How the Power Flow Control Algorithm Works
The V2G power flow control algorithm operates in the synchronous reference frame (SRF) — a rotating dq coordinate system aligned with the grid voltage vector. This decouples active power (P) from reactive power (Q), allowing independent, precise control of each with simple PI regulators.
- Step 1 — Grid sensing: PT (potential transformer) and Hall-effect current transducers measure Vabc, Iabc at the PCC (point of common coupling).
- Step 2 — SRF-PLL: A software phase-locked loop extracts the grid phase angle θ and frequency f. The PLL bandwidth is 50 Hz to reject harmonic noise while tracking fundamental frequency accurately. In MATLAB, this is implemented using the Three-Phase PLL block (phaselock_threePhase) in Simscape Electrical.
- Step 3 — abc→dq transform: Clarke transform converts Vabc to Vαβ; Park transform using θ from the PLL converts to Vd, Vq. In a grid-aligned reference, Vd = |V| and Vq = 0, confirming synchronisation. The same transforms are applied to Iabc to get id and iq.
- Step 4 — Power calculation: P = 1.5·Vd·id and Q = −1.5·Vd·iq. P_ref comes from the SOC-based dispatch block; Q_ref is set for unity power factor (iq_ref = 0) or for voltage regulation.
- Step 5 — dq PI current control: Two PI controllers independently regulate id and iq. Cross-coupling terms (ωL·iq added to d-axis, −ωL·id added to q-axis) are feed-forwarded to improve dynamic response and eliminate steady-state error at 50 Hz.
- Step 6 — Inverse Park + SPWM: Vd_ref and Vq_ref are transformed back to three-phase Vabc_ref. A triangular carrier at fsw = 20 kHz generates 6 SPWM gate pulses for the three-phase VSI IGBT/SiC bridge.
MOSFET Gate Driver — Key Design Parameters
The gate driver is arguably the most critical component in a V2G bidirectional converter. A poor gate drive leads to excessive switching losses, EMI, and catastrophic failure from parasitic turn-on (shoot-through). The following specifications must be met for 20 kHz SiC operation at 700 V DC bus:
| Parameter | Value | Component / Reason |
|---|---|---|
| Gate drive IC | TLP250H | 2500 V isolation, 2.5 A peak gate current, 50 ns prop. delay |
| Turn-on gate voltage (Vgs+) | +15 V | Full channel inversion for SiC MOSFET (threshold 2–4 V) |
| Turn-off gate voltage (Vgs−) | −5 V | Negative bias prevents Miller-capacitance induced turn-on |
| Turn-on gate resistance (Rg_on) | 10 Ω | Slows dv/dt to < 20 V/ns, reduces EMI |
| Turn-off gate resistance (Rg_off) | 4.7 Ω | Faster turn-off reduces tail current loss |
| Bootstrap capacitor (Cboot) | 100 nF (X7R) | High-side supply charge reservoir, placed <5 mm from VCC pin |
| Deadtime | 200 ns | Set in DSP ePWM module; prevents shoot-through current |
| Desaturation threshold (Vce_sat) | 7 V | Fault tripping at 2× rated current; 1 µs blanking to ignore turn-on transient |
| Miller clamp | BSS316N (N-ch) | Rclamp = 2 Ω, prevents dv/dt induced gate voltage rise above threshold |
| Isolated gate supply | RECOM RPM5.0-1515S | +15/−5 V, 1.5 W, 1500 V isolation per half-bridge channel |
Inductor Design Calculation — Step-by-Step
- Step 1 — Ripple current specification: Allowable inductor current ripple ΔiL = 20% of Irated = 0.20 × 60 A = 12 A peak-to-peak.
- Step 2 — Inductance required: From volt-seconds balance: L = Vin × D × (1−D) / (fsw × ΔiL) = 400 × 0.5 × 0.5 / (20 000 × 12) = 1.0 mH at duty cycle D = 0.5 (worst case).
- Step 3 — Peak current: Ipeak = IL_avg + ΔiL/2 = 60 + 6 = 66 A. Add 15% margin → 75 A peak for saturation check.
- Step 4 — Core selection: Choose ETD49 ferrite core (N87 material, µr = 2200). Effective area Ae = 2.11 cm², effective path le = 11.4 cm. Required AL = µ0 × µr × Ae / le without gap = 48 µH/turn² (before gap).
- Step 5 — Air gap: To achieve L = 1 mH with N turns, the gap dominates: lg = µ0 × Ae × N² / L. With N = 28 turns: lg = (4π×10⁻⁷ × 2.11×10⁻⁴ × 784) / 0.001 = 0.208 mm each leg × 2 sides (E-core has two gaps) ≈ 0.42 mm total (0.21 mm each gap face). Practical gap = 1.2 mm (accounting for fringing factor ~2).
- Step 6 — Flux density check: Bpeak = µ0 × N × Ipeak / lg = (4π×10⁻⁷ × 28 × 75) / 0.0012 = 2.2 T — this is wrong without fringing; with effective µe = 200: Bpeak = L × Ipeak / (N × Ae) = 0.001 × 75 / (28 × 2.11×10⁻⁴) = 0.127 T. Well below N87 Bsat = 420 mT at 100°C.
- Step 7 — Wire gauge: J = 4 A/mm² for natural cooling. Wire cross-section = 60/4 = 15 mm². Use 2 × AWG 8 (8.37 mm² each) Litz wire in parallel → 16.7 mm², 28 turns, DCR ≈ 4.8 mΩ, copper loss = 60² × 0.0048 = 17.3 W.
- Step 8 — Core loss: Using Steinmetz equation with N87 Kfe = 0.0044, α = 1.27, β = 2.4; Bac = ΔiL × L / (Ae × N × 2) = 0.027 T; Pcore ≈ 1.8 W at 20 kHz. Total loss = 17.3 + 1.8 = 19.1 W.
dq Current Controller — PI Tuning by Internal Model Control (IMC)
The dq-axis current controller is tuned using the IMC (Internal Model Control) method, which gives a systematic relationship between bandwidth and PI gains. The plant model in the dq frame is a simple R-L circuit: G(s) = 1/(R + sL) where R = 0.1 Ω (filter resistance) and L = 1 mH (LCL filter converter-side inductor).
- Bandwidth selection: Current loop bandwidth ωc = 2π × 1000 rad/s (1 kHz, one decade below switching frequency 20 kHz). Allows 10 switching cycles per fundamental current period for adequate rejection.
- IMC PI gains: Kp = L × ωc = 0.001 × 6283 = 6.28 V/A. Ki = R × ωc = 0.1 × 6283 = 628.3 V·A⁻¹·s⁻¹. In MATLAB Discrete PID block: Kp = 2 (normalised), Ki = 150 (at Ts = 50 µs).
- Cross-coupling compensation: d-axis: Vd_ref = Vd_PI + ωL·iq_feedback. q-axis: Vq_ref = Vq_PI − ωL·id_feedback. This decouples the axes and eliminates steady-state error at 50 Hz.
- Anti-windup: Output saturation at ±Vdc/√3 (maximum modulation) with back-calculation anti-windup (Ka = 1/Kp) prevents integrator wind-up during current limiting.
- DC bus voltage outer loop: Bandwidth ωv = 2π × 50 rad/s (50 Hz, one decade below current loop). Kp_v = 0.2 A/V, Ki_v = 10 A·V⁻¹·s⁻¹. Generates id_ref ≤ Imax.
%% V2G Power Flow Control — Initialisation Script % Projectsatbangalore.com | IEEE 2026 | V2G Power Flow Control MATLAB % Run before opening the Simulink model (.slx) %% — System parameters — clear; clc; Vbat = 400; % Battery nominal voltage [V] Vdc = 700; % DC bus voltage [V] Vgrid_L = 230; % Grid line-neutral rms [V] fgrid = 50; % Grid frequency [Hz] omega = 2*pi*fgrid; % Angular frequency [rad/s] Prated = 22000; % Rated V2G power [W] %% — LCL Filter — L1 = 1e-3; % Converter-side inductor [H] L2 = 0.5e-3; % Grid-side inductor [H] Cf = 10e-6; % Filter capacitor [F] Rd = 1.5; % Damping resistor [Ω] f_res = 1/(2*pi) * sqrt((L1+L2)/(L1*L2*Cf)); % Resonance freq. [Hz] fprintf('LCL resonance frequency: %.1f Hz\n', f_res); %% — Bidirectional DC-DC Inductor — Lb = 1e-3; % Boost inductor [H] Cin = 470e-6; % Input capacitor [F] Cdc = 1000e-6; % DC bus capacitor [F] fsw_dc = 20e3; % DC-DC switching frequency [Hz] D = (Vdc - Vbat) / Vdc; % Duty cycle ≈ 0.43 %% — SRF-PLL Parameters — Kp_pll = 100; % PLL proportional gain Ki_pll = 4000; % PLL integral gain Ts = 50e-6; % Simulation time step [s] (1/fsw) %% — dq Current Controller (IMC tuning) — wc_I = 2*pi*1000; % Current loop bandwidth [rad/s] Rfilter = 0.1; % Filter winding resistance [Ω] Kp_id = L1 * wc_I; % d-axis Kp = 6.28 V/A Ki_id = Rfilter * wc_I;% d-axis Ki = 628 V/A/s Kp_iq = Kp_id; % q-axis same (symmetric plant) Ki_iq = Ki_id; fprintf('d-axis PI: Kp=%.3f, Ki=%.1f\n', Kp_id, Ki_id); %% — DC Voltage Outer Loop — wc_V = 2*pi*50; % Voltage loop bandwidth [rad/s] Kp_vdc = Cdc * wc_V; % Voltage Kp = 0.314 A/V Ki_vdc = 10; % Voltage Ki [A/V/s] Imax = Prated / (1.5 * Vgrid_L * sqrt(2)); % Max d-axis current %% — SOC Dispatch Table — SOC_V2G_min = 30; % Minimum SOC for V2G discharge [%] SOC_G2V_max = 90; % Maximum SOC for G2V charging [%] f_deadband = 0.2; % Frequency deadband [Hz] (±0.2 Hz) droop_R = 0.04; % Droop coefficient (4% per Hz deviation) %% — Power Reference (from droop + SOC) — % Pref = -(1/R_droop) * delta_f (Hz deviation from 50 Hz) % Positive = V2G injection; Negative = G2V charging disp('Parameters loaded. Open V2G_PowerFlow_Control.slx');
%% V2G Power Flow Control — THD and Harmonic Analysis % Run after simulation: collects Iabc from 'To Workspace' block if ~exist('Iabc', 'var') error('Run simulation first — Iabc workspace variable not found.'); end t = Iabc.time; ia = Iabc.signals.values(:,1); Fs = 1/(t(2)-t(1)); % Sampling frequency t0 = 0.1; % Skip first 100 ms transient idx = t >= t0; ia_s = ia(idx); %% FFT N = length(ia_s); Y = fft(ia_s) / N; f = (0:N/2) * Fs / N; amp = 2*abs(Y(1:N/2+1)); amp(1) = amp(1)/2; % DC component %% THD Calculation fund_idx = round(50 * N/Fs) + 1; I1 = amp(fund_idx); % Fundamental (50 Hz) harm_idx = round((100:50:5000) * N/Fs) + 1; harm_idx = harm_idx(harm_idx <= length(amp)); THD = 100 * sqrt(sum(amp(harm_idx).^2)) / I1; fprintf('Grid Current THD: %.2f%% (IEEE 519-2022 limit: 5%%)\n', THD); %% Plot spectrum figure; stem(f(1:200), amp(1:200), 'filled', 'Color', [0.85 0.47 0.04]); title(sprintf('V2G Grid Current Harmonic Spectrum — THD = %.2f%%', THD)); xlabel('Frequency (Hz)'); ylabel('Amplitude (A)'); xlim([0 5000]); grid on;
LCL Filter Design Equations and Procedure
The LCL filter provides superior high-frequency attenuation (−60 dB/decade above resonance) compared to an L-filter (−20 dB/decade), allowing a smaller and lighter magnetic component while meeting IEEE 519-2022 THD < 5% for grid-connected EV chargers.
| Component | Value | Design Equation / Constraint |
|---|---|---|
| L1 (converter-side) | 1.0 mH | ΔiL ≤ 20% Irated → L1 ≥ Vdc·D(1−D)/(fsw·ΔiL) = 0.875 mH, rounded to 1 mH |
| Cf (filter capacitor) | 10 µF | Reactive power ≤ 5% rated: Cf ≤ 0.05·Irated/(ωgrid·Vphase) = 13.8 µF; choose 10 µF X2 MKP |
| L2 (grid-side) | 0.5 mH | Ratio r = L2/L1 = 0.5; L2 ≥ L1/(2·r_max+1) = L1/5; choose 0.5 mH |
| Rd (passive damping) | 1.5 Ω | Rd = 1/(3·ωres·Cf) = 1/(3×9600π×10µF) = 1.1 Ω, choose 1.5 Ω |
| Resonance frequency | 3.86 kHz | fres = (1/2π)·√[(L1+L2)/(L1·L2·Cf)] must be: 10·fg < fres < fsw/2 |
| Attenuation at fsw | −62 dB | |H(jωsw)| = 1/|1−(ωsw/ωres)²| · 1/(L1+L2)Cf·ωsw²; harmonic current ratio i2/i1 < 0.3% |
| Total inductance Ltot | 1.5 mH | L1 + L2; defines voltage drop across filter: ΔV = ω·Ltot·Irated = 47.1 V (9% of 500 V) |
Power Dispatch Algorithm — State Transitions
The SOC-based V2G/G2V mode selector runs as a Stateflow chart in Simulink, evaluated every 10 ms. It reads the grid frequency deviation Δf, current SOC, and grid voltage amplitude. The power reference Pref is computed from a frequency droop characteristic with SOC-weighted derating.
- State 1 — IDLE: |Δf| < 0.2 Hz. No power exchange. Maintains DC bus at 700 V. Transitions to V2G if Δf < −0.2 Hz and SOC > 30%, or to G2V if Δf > +0.2 Hz and SOC < 90%.
- State 2 — V2G DISCHARGE: Grid under-frequency (f < 49.8 Hz) detected. Pref = (−1/Rdroop) × Δf × SOC_factor, where SOC_factor = (SOC − 30%)/(90% − 30%). At SOC = 60%, SOC_factor = 0.5, so Pref = 50% of Pmax = 11 kW. Exit if SOC < 25% (emergency reserve) or Δf > 0.1 Hz.
- State 3 — G2V CHARGE: Grid over-frequency (f > 50.2 Hz) or off-peak tariff signal received. Pref = (1/Rdroop) × Δf × (1 − SOC_factor). Exit if SOC > 88% or Δf < −0.1 Hz.
- State 4 — FAULT: MOSFET overcurrent, DC bus overvoltage (>750 V), battery overtemperature (>45°C) or grid voltage sag (<0.85 pu). Disables all gate pulses, closes contactors. Latched until manual reset via CAN message.
- Droop coefficient: Rdroop = 0.04 (4% droop). At Δf = −0.5 Hz, Pref = 0.5/0.04 = 12.5 kW > Pmax — so Pref is clamped to Pmax = 22 kW. The SOC derating prevents deep discharge below the 20% buffer for EV driving range.
Grid Current Ia (A)
Three-phase sinusoidal grid current after LCL filter. Fundamental at 50 Hz, THD < 3%, amplitude 63.7 A peak (22 kW at 230 V). Reverses polarity cleanly during G2V→V2G transition within 2 cycles.
DC Bus Voltage Vdc (V)
Regulated to 700 V with <1% steady-state ripple (7 V). Transient dip of <30 V (4%) during mode switch from IDLE to full V2G, recovering within 40 ms. Overshoot <5% during step load change.
Inductor Current iL (A)
Triangular ripple at 20 kHz superimposed on 60 A DC component. ΔiL = 12 A pp as designed. Current waveform reverses average during G2V charging mode — verified in Simulink Scope with cursors.
Active Power P (kW)
Calculated from P = 1.5·Vd·id in dq frame. Steps from 0 to +22 kW (V2G) in 40 ms, to −22 kW (G2V) in 45 ms. Steady-state error <0.5% at all operating points. Matches Pref from SOC dispatch.
Battery SOC (%)
Ramps from 80% to 30% over 1-hour V2G discharge at 22 kW (simulated in Simulink with 100× speed-up scaling). Coulomb-counting SOC matches actual Simscape Battery block SOC within ±0.5%.
MOSFET Gate Signals
Six SPWM gate pulses (S1–S6) at 20 kHz. 200 ns dead-time visible between complementary switch pairs. Gate voltage swings between +15 V and −5 V as designed. No shoot-through observed in DESAT monitor signal.