Power electronics for renewables, storage and electric vehicles

Solar panels produce direct current at a voltage that varies with sunlight and temperature. Wind turbines produce alternating current at a frequency that varies with wind speed. Batteries store direct current at a voltage that changes with their state of charge. None of these can connect directly to the 60 Hz grid or to each other, and each needs power electronics to extract energy efficiently, control it safely and deliver it in usable form. As the electricity system shifts toward solar, wind, batteries and electric vehicles, a growing share of all electrical energy passes through converters. This lesson looks at the converters in these systems: photovoltaic inverters and maximum power point tracking, wind turbine converters, battery storage and battery management, bidirectional converters, and electric vehicle chargers. Their grid interaction, covered briefly in Lesson 7, is developed further in ELE-490.

Photovoltaic arrays and their characteristics

A photovoltaic (PV) cell behaves like a current source proportional to irradiance in parallel with a diode. Its current-voltage curve is nearly flat at the short-circuit current until the voltage approaches the open-circuit voltage, then falls steeply. Power, the product of voltage and current, therefore has a single maximum, the maximum power point (MPP), at roughly 80 percent of the open-circuit voltage. Modules combine 60 to 144 cells (often as half-cut cells) to give open-circuit voltages of about 40 to 50 V and powers of 400 to 600 W or more.

The MPP moves constantly. Higher irradiance raises the current, and so the power, almost proportionally; higher temperature lowers the voltage, by about 0.3 percent per kelvin for crystalline silicon, so modules produce less on hot days and more on cold, bright ones. Cold weather also raises the open-circuit voltage, which designers must account for when sizing strings so that the inverter's maximum input voltage is never exceeded on the coldest morning. Partial shading of some cells in a string can create several local maxima, because bypass diodes in each module conduct around shaded sections.

Maximum power point tracking

A maximum power point tracker (MPPT), usually a DC-DC stage or the inverter's own control, adjusts the operating voltage of the array to stay at the MPP. The most common algorithm, perturb and observe, changes the operating voltage by a small step, measures whether power increased or decreased, and continues in the same direction if it increased or reverses if it decreased. The operating point therefore oscillates around the MPP by a step or two. Incremental conductance algorithms use the fact that \(dP/dV = 0\) at the MPP, that is, \(dI/dV = -I/V\), to find it more precisely. Under partial shading, trackers periodically sweep the whole voltage range to find the global maximum rather than settling on a local one.

import numpy as np

# Perturb-and-observe maximum power point tracking on a single-diode PV module model
Ns, n, Vt = 72, 1.2, 0.0257
Voc_ref, Isc_ref = 45.0, 10.0
I0 = Isc_ref / (np.exp(Voc_ref / (n * Ns * Vt)) - 1)

def current(V, G):                          # G = irradiance as a fraction of 1000 W/m2
    return max(G * Isc_ref - I0 * (np.exp(V / (n * Ns * Vt)) - 1), 0.0)

def true_mpp(G):
    Vs = np.linspace(0, Voc_ref, 4000)
    P = [v * current(v, G) for v in Vs]
    k = int(np.argmax(P))
    return Vs[k], P[k]

V, step, P_prev, direction = 30.0, 0.5, 0.0, 1
energy, ideal = 0.0, 0.0
for k in range(300):                        # one perturbation every 0.1 s for 30 s
    G = 1.0 if k < 150 else 0.4             # a cloud cuts irradiance to 40% at 15 s
    P = V * current(V, G)
    if P < P_prev:
        direction = -direction              # power fell: reverse the perturbation
    P_prev = P
    energy += P * 0.1
    ideal += true_mpp(G)[1] * 0.1
    if k in (5, 40, 149, 152, 160, 299):
        vm, pm = true_mpp(G)
        print(f"t = {k * 0.1:4.1f} s: G = {G:.1f}, operating {V:5.1f} V, {P:6.1f} W (true MPP {pm:6.1f} W at {vm:4.1f} V)")
    V += direction * step
print(f"tracking efficiency over 30 s: {energy / ideal:.1%}")

t =  0.5 s: G = 1.0, operating  32.5 V,  323.8 W (true MPP  364.4 W at 38.5 V)
t =  4.0 s: G = 1.0, operating  38.0 V,  363.8 W (true MPP  364.4 W at 38.5 V)
t = 14.9 s: G = 1.0, operating  38.5 V,  364.4 W (true MPP  364.4 W at 38.5 V)
t = 15.2 s: G = 0.4, operating  38.0 V,  135.8 W (true MPP  138.1 W at 36.6 V)
t = 16.0 s: G = 0.4, operating  36.0 V,  137.7 W (true MPP  138.1 W at 36.6 V)
t = 29.9 s: G = 0.4, operating  36.5 V,  138.1 W (true MPP  138.1 W at 36.6 V)
tracking efficiency over 30 s: 99.3%

Starting away from the MPP, the tracker reaches it within a few seconds and then oscillates within a step of it. When a cloud cuts the irradiance to 40 percent, the MPP voltage drops slightly and the tracker follows. Over 30 seconds it captures more than 99 percent of the available energy. Faster changes in irradiance, such as broken clouds, can confuse a simple tracker, because a change in power caused by irradiance is mistaken for the result of its own perturbation; practical algorithms use adaptive step sizes and checks to avoid this. Modern inverters achieve tracking efficiencies above 99 percent.

PV inverter architectures

Several architectures connect PV arrays to the grid, each with trade-offs between cost, efficiency, tolerance of shading and safety:

In the US, PV installations follow NEC Article 690, inverters are listed to UL 1741 with grid-support functions tested to IEEE 1547.1, and grid connection follows IEEE 1547 and the utility's requirements. NEC 690.12 requires rapid shutdown of PV conductors on buildings, which reduces voltages within the array boundary to safe levels within 30 seconds and has driven the adoption of module-level electronics.

Wind turbine converters

Wind turbines turn at speeds that vary with the wind, and operate most efficiently when the rotor speed is adjusted in proportion to wind speed so that the blade tips move at an optimum ratio to the wind. Variable speed requires power electronics. Two arrangements dominate. In the doubly fed induction generator (DFIG), the stator connects directly to the grid and a back-to-back converter feeds the rotor windings through slip rings; because only the slip power passes through the converter, it needs to be rated at only about 30 percent of the turbine rating. In full-converter turbines, used in most new large turbines and almost all offshore turbines, all the generator's output, often from a permanent magnet synchronous generator, passes through a converter rated for the full power. The full converter decouples the generator completely from the grid, which simplifies meeting grid requirements during faults and allows grid-forming control.

Battery storage and battery management

Battery energy storage systems, from home units of a few kilowatt-hours to grid installations of hundreds of megawatt-hours, use bidirectional inverters, often called power conversion systems, to charge from and discharge to the grid. Their battery packs consist of many lithium-ion cells in series and parallel, and a battery management system (BMS) is essential:

• It measures every cell's voltage and temperature and the pack current, and estimates state of charge and state of health.
• It protects the cells by opening contactors if any cell goes outside its safe voltage, current or temperature limits, the first line of defense against the thermal runaway described in DCE-440.
• It balances cells, because small differences in capacity and self-discharge make cells in series drift apart; without balancing, the weakest cell would limit the whole pack. Passive balancing bleeds energy from the highest cells through resistors; active balancing transfers it to lower cells with small converters.

Lithium-ion cells are charged with a constant current until they reach a maximum voltage (about 4.2 V for common nickel-based chemistries and 3.65 V for lithium iron phosphate), then at constant voltage while the current tapers off. The constant-voltage phase is needed because the cell's internal resistance makes its terminal voltage higher than its open-circuit voltage during charging.

# 1. Constant-current, constant-voltage charging of a lithium-ion cell (simple model)
Q = 5.0                                   # Ah
R = 0.03                                  # ohm internal resistance
def ocv(soc):
    return 3.0 + 1.05 * soc + 0.15 * soc ** 0.5        # simplified open-circuit voltage, V

soc, t, dt = 0.1, 0.0, 1.0
I_cc, V_max, I_end = 1.0 * Q, 4.2, Q / 20            # 1C charge, 4.2 V limit, stop at C/20
t80 = None
while True:
    I = I_cc
    if ocv(soc) + I * R > V_max:                      # constant-voltage phase: current set by headroom
        I = (V_max - ocv(soc)) / R
    if I < I_end:
        break
    soc += I * dt / 3600 / Q
    t += dt
    if t80 is None and soc >= 0.8:
        t80 = t
print(f"cell 10% to 80%: {t80 / 60:.0f} min; to full (C/20 cut-off): {t / 60:.0f} min, final SOC {soc:.1%}")

# 2. Electric vehicle charging time for a 75 kWh pack from 10% to 80%
pack = 75.0
def dc_power(soc):                        # kW: flat at 150 kW to 50%, then tapering to 60 kW at 80%
    return 150.0 if soc < 0.5 else 150.0 - 90.0 * (soc - 0.5) / 0.3
soc, t = 0.10, 0.0
while soc < 0.80:
    p = dc_power(soc) * 0.92              # 92% of charger output reaches the battery
    soc += p / 3600 / pack
    t += 1
print(f"DC fast charge 10% to 80%: {t / 60:.0f} min")
for name, kw in (("Level 2, 7.2 kW", 7.2), ("Level 2, 11.5 kW", 11.5)):
    print(f"{name}: {0.7 * pack / (kw * 0.9):.1f} h for 10% to 80%")

cell 10% to 80%: 42 min; to full (C/20 cut-off): 70 min, final SOC 99.3%
DC fast charge 10% to 80%: 28 min
Level 2, 7.2 kW: 8.1 h for 10% to 80%
Level 2, 11.5 kW: 5.1 h for 10% to 80%

The cell reaches 80 percent in about 40 minutes at a 1C rate, but needs about half an hour more to reach full charge, because the current tapers in the constant-voltage phase. The same pattern explains why electric vehicle fast charging is usually quoted from 10 to 80 percent: the last 20 percent takes much longer, because the vehicle limits charging power as the cells fill to protect them.

Bidirectional converters

Storage, vehicle-to-grid systems and DC microgrids need converters that can move power in either direction. A non-isolated bidirectional buck-boost converter uses two switches in a half-bridge: operated one way it bucks from a high-voltage bus to a battery; operated the other way it boosts from the battery to the bus. Where isolation is needed, the dual active bridge (DAB) has become the standard topology. It consists of two full bridges, each driving one side of a high-frequency transformer, with a series inductance (often the transformer's leakage inductance). Each bridge produces a square wave, and power flows from the leading bridge to the lagging one according to the phase shift \(\varphi\) between them:

where \(V_2'\) is the second bridge's voltage referred to the primary, \(f\) the switching frequency and \(L\) the series inductance. Reversing the phase shift reverses the power flow. The DAB achieves zero-voltage switching over a wide range, giving high efficiency at high frequency.

Electric vehicle charging

Electric vehicles are charged in three ways:

• Level 1 (120 V outlets, about 1.4 to 1.9 kW) and Level 2 (208 or 240 V, typically 7 to 19 kW) supply AC to the vehicle's onboard charger, a converter built into the car, usually consisting of a power factor correction stage followed by an isolated DC-DC converter such as an LLC or dual active bridge.
• DC fast charging, from about 50 kW to 350 kW or more, uses an offboard charger in the station that delivers DC directly to the battery. Stations contain rectifiers with active front ends and isolated DC-DC modules, often stacked in parallel and shared among several dispensers.

In North America, vehicles use either the Combined Charging System (CCS1), built on the SAE J1772 AC connector, or the North American Charging Standard connector developed by Tesla, standardized as SAE J3400 in 2024, which most automakers announced they would adopt from 2025. Vehicles with 800 V battery architectures charge faster at the same current, and require chargers able to supply the higher voltage. Fast charging stations are significant loads for the distribution system, which has led to sites that combine chargers with battery storage to limit peak demand.

Bidirectional charging, in which a vehicle supplies power to a home (vehicle-to-home) or to the grid (vehicle-to-grid), turns electric vehicles into distributed storage. It requires bidirectional converters, either in the vehicle or in the charger, interconnection approval as with any generating source, and agreements on how battery wear is compensated.