The rapid integration of renewable energy sources into power systems has accelerated the development of advanced energy storage technologies, with the battery energy storage system (BESS) playing a pivotal role in enhancing grid stability and efficiency. Among various configurations, the delta-connected high-voltage transformer-less BESS (D-HVTL-BESS) stands out due to its large unit capacity, high operational efficiency, and fast response, making it an ideal solution for large-scale energy storage power stations. However, a significant challenge in such systems is the presence of low-frequency pulsating currents, primarily the second harmonic current (SHC), which flows through the battery clusters. This phenomenon necessitates large passive filtering networks, leading to increased system cost, volume, and reduced dynamic performance. Therefore, developing effective SHC suppression strategies is crucial to minimize the dependency on passive components and optimize the overall design of the battery energy storage system.
In this context, this article proposes a novel suppression strategy based on third harmonic current injection for the delta-connected high-voltage BESS. The approach aims to adaptively eliminate the SHC by injecting precisely calculated third harmonic currents, thereby reducing the requirements for passive filters without compromising system efficiency. The derivation of SHC expressions under varying power factors and power levels is presented, followed by the design of third harmonic current parameters. The effectiveness of the proposed method is quantitatively evaluated through theoretical analysis and simulation, demonstrating significant reductions in battery current and capacitor voltage ripple rates. The findings highlight the potential of this strategy to enhance the compactness and cost-effectiveness of large-scale battery energy storage systems.
The fundamental structure of a delta-connected high-voltage BESS involves modular multilevel cascaded converters (MMCCs) with H-bridge submodules connected in series per phase. Each submodule integrates a battery cluster through an LC filter to mitigate current harmonics. The system’s operation in a three-phase grid-connected setup introduces inherent power pulsations due to the single-phase power characteristics of the submodules, resulting in SHC in the battery current. This low-frequency ripple adversely affects battery lifespan and state-of-charge (SOC) estimation accuracy, underscoring the need for effective suppression techniques. Traditional methods, such as enlarging passive filters or adding active power converters, increase system complexity and cost, whereas the proposed third harmonic injection offers a control-based solution with minimal hardware modifications.
To analyze the SHC generation mechanism, consider the phase voltages and currents in a symmetric three-phase system. Let the phase voltage \( u_x \) and current \( i_x \) be defined as:
$$ u_x = U_m \cos(\omega t + \theta_x) $$
$$ i_x = I_m \cos(\omega t – \varphi + \theta_x) $$
where \( U_m \) and \( I_m \) are the amplitudes, \( \omega \) is the grid angular frequency, \( \theta_x \) represents the phase angle for phase \( x \) (a, b, c), and \( \varphi \) is the power factor angle. For a delta-connected system, the phase voltage and current are related to the line quantities, leading to expressions for the bridge arm voltage \( u_{bx} \) and current \( i_{bx} \):
$$ u_{bx} = \sqrt{3} U_m \cos\left(\omega t + \theta_x – \frac{\pi}{6}\right) $$
$$ i_{bx} = \frac{\sqrt{3}}{3} I_m \cos\left(\omega t – \varphi – \frac{\pi}{3} + \theta_x\right) $$
The output voltage of each bridge arm, \( e_x \), can be expressed as:
$$ e_x = E_m \cos\left(\omega t + \delta + \theta_x – \frac{\pi}{6}\right) $$
where \( E_m \) is the amplitude and \( \delta \) is the phase angle relative to the bridge arm voltage. For a submodule \( SM_{xj} \) in phase \( x \), the DC-side current \( i_{dxj} \) is derived from the product of the modulation index and the bridge arm current. Assuming identical submodule behavior per phase, the DC-side current contains a DC component and a SHC component:
$$ i_{dxj} = I_{dc} + i_{SHC} = \frac{\sqrt{3}}{2} M I_m \cos(\delta + \varphi) + \frac{\sqrt{3}}{2} M I_m \cos\left(2\omega t – \delta – \varphi – \frac{\pi}{3}\right) $$
Here, \( M \) is the modulation index amplitude, and \( I_{dc} \) represents the average DC current. The SHC propagates through the LC filter to the battery current \( i_{bxj} \) and capacitor voltage \( u_{cxj} \), causing ripple. The battery current ripple rate \( \eta_i \) and capacitor voltage ripple rate \( \eta_u \) are defined as:
$$ \eta_i = \frac{\sqrt{3} M I_m}{2 I_{dc} (4\omega^2 LC – 1)} $$
$$ \eta_u = \frac{\sqrt{3} \omega L M I_m}{2 U_b (4\omega^2 LC – 1)} $$
where \( L \) and \( C \) are the filter inductance and capacitance, and \( U_b \) is the battery voltage. To achieve desired ripple rates, the LC parameters can be designed as:
$$ L = \frac{\sqrt{3} U_b \eta_u}{2 \omega M I_m \eta_i \cos(\delta + \varphi)} $$
$$ C = \frac{\sqrt{3} M I_m (1 + \cos(\delta + \varphi))}{4 \omega U_b \eta_i \eta_u} $$
However, large \( L \) and \( C \) values increase system size and cost, motivating the proposed suppression strategy.
The third harmonic current injection method modifies the modulation wave to include a third harmonic component. For a submodule \( SM_{xj} \), the revised modulation wave \( m_{xj3} \) is:
$$ m_{xj3} = m_{xj} + m_3 = M \cos\left(\omega t + \delta – \frac{\pi}{6}\right) + M_3 \cos(3\omega t + \delta_{m3}) $$
where \( M_3 \) and \( \delta_{m3} \) are the amplitude and phase of the third harmonic voltage. The corresponding bridge arm current \( i_{bx3} \) includes a third harmonic current \( i_3 \):
$$ i_{bx3} = i_{bx} + i_3 = \frac{\sqrt{3}}{3} I_m \cos\left(\omega t – \varphi – \frac{\pi}{3} + \theta_x\right) + I_{m3} \cos(3\omega t + \delta_{i3}) $$
The DC-side current \( i_{dxj3} \) after injection is derived as:
$$ i_{dxj3} = m_{xj3} i_{bx3} = I_{dc} + i_{SHC}’ + i_{FHC} + i_{SIXHC} $$
where \( i_{SHC}’ \) is the residual SHC, \( i_{FHC} \) is the fourth harmonic current, and \( i_{SIXHC} \) is the sixth harmonic current. To eliminate the SHC, the third harmonic current parameters are set as:
$$ I_{m3} = \frac{\sqrt{3}}{3} I_m $$
$$ \delta_{i3} = \delta – \varphi – \frac{\pi}{2} \pm \pi $$
This configuration cancels the SHC, reducing the battery current and capacitor voltage ripple. The revised battery current \( i_{bxj3} \) and capacitor voltage \( u_{cxj3} \) are:
$$ i_{bxj3} = I_{dc} \left[1 + \eta_i g_i(\eta_i, t)\right] $$
$$ u_{cxj3} = U_b \left[1 + \eta_u g_u(\eta_i, \eta_u, t)\right] $$
where \( g_i \) and \( g_u \) are functions representing the ripple after injection. The suppression effectiveness is quantified by the reduction ratios \( \kappa_i \) and \( \kappa_u \):
$$ \kappa_i = 1 – \frac{\max|g_i(\eta_i, t)|}{\eta_i} $$
$$ \kappa_u = 1 – \frac{\max|g_u(\eta_i, \eta_u, t)|}{\eta_u} $$
Numerical analysis shows that for \( \eta_i \in (0, 0.2) \) and \( \eta_u \in (0, 0.05) \), \( \kappa_i \geq 0.74 \) and \( \kappa_u \geq 0.5 \), indicating approximately 70% and 50% reduction in battery current and capacitor voltage ripple rates, respectively.
The overall control strategy for the battery energy storage system incorporates the SHC suppression technique within a dq-frame current control loop. The grid-side currents and voltages are transformed to dq components:
$$ i_d = I_m \cos(\omega t – \varphi – \theta) $$
$$ i_q = I_m \sin(\omega t – \varphi – \theta) $$
$$ u_d = U_m \cos(\omega t + \theta) $$
$$ u_q = U_m \sin(\omega t + \theta) $$
The phase angle \( \delta \) and current amplitude \( I_m \) are computed as:
$$ \delta = \tan^{-1}\left(\frac{e_q}{e_d}\right) $$
$$ I_m = \sqrt{i_d^2 + i_q^2} $$
The third harmonic voltage \( e_3 \) is generated as \( e_3 = 3\omega L I_{m3} \cos(3\omega t + \delta_{i3}) \) and added to the fundamental modulation signals. The resultant signals are divided by the number of submodules per phase \( N \) and used in carrier-based pulse-width modulation (PWM). This approach integrates seamlessly with existing controls, avoiding additional hardware.
To validate the proposed strategy, a simulation model of a 35 kV/30 MW/60 MWh delta-connected high-voltage BESS was developed in PSCAD/EMTDC. Key parameters are summarized in Table 1.
| Parameter | Symbol | Value |
|---|---|---|
| Grid Phase Voltage Peak | \( U_{m0} \) | 28.57 kV |
| Rated Power | \( P_0 \) | 30 MW |
| Grid Frequency | \( f_{g0} \) | 50 Hz |
| Submodules per Phase | \( N \) | 80 |
| AC-Side Inductance | \( L_g \) | 13 mH |
| DC-Side Inductance | \( L \) | 1.04 mH |
| DC-Link Capacitance | \( C \) | 14.53 mF |
| Battery Voltage | \( U_b \) | 0.92 kV |
| Battery Current | \( I_b \) | 0.14 kA |
Simulations were conducted for both discharge and charge modes. In discharge mode, without third harmonic injection, the battery current and capacitor voltage ripple rates were 19.95% and 2.02%, respectively. After injection, these reduced to 5.61% and 1.19%, demonstrating the strategy’s efficacy. Similarly, in charge mode, ripple rates decreased from 19.08% and 1.73% to 5.58% and 0.85%. Comparative analysis with enlarged passive filters showed that achieving similar suppression would require increasing \( L \) and \( C \) by over 100% and 75%, respectively, highlighting the volume and cost savings of the proposed method.
System efficiency was evaluated considering losses in H-bridge IGBTs and battery internal resistance. The total loss per submodule includes conduction loss \( P_{cond} \), switching loss \( P_{sw} \), and battery loss \( P_L \). For an IGBT module, conduction loss is calculated as:
$$ P_{cond} = \frac{1}{2\pi} \int_0^{\pi} v_{CE}(t) i_C(t) \tau(t) dt $$
and switching loss as:
$$ P_{sw} = f_{sw} \sum_{n=1}^{f_{sw}} \left( E_{sw(on)} + E_{sw(off)} \right) $$
Battery loss due to ripple is:
$$ P_L = I_{dc}^2 r_b + \frac{1}{2} I_{dc}^2 \eta_i^2 r_b $$
After third harmonic injection, battery loss reduces by approximately 2.1%, while IGBT losses increase slightly. Overall system efficiency decreases marginally from 98.97% to 98.72%, indicating a minimal impact on performance while achieving significant ripple suppression.
In conclusion, the third harmonic current injection strategy effectively suppresses low-frequency pulsating currents in delta-connected high-voltage battery energy storage systems. By deriving precise SHC expressions and designing adaptive third harmonic parameters, the method reduces battery current and capacitor voltage ripple rates by about 70% and 50%, respectively, without substantial efficiency loss. This approach lowers the demand for passive filters, enhancing system compactness and cost-effectiveness, and is particularly beneficial for large-scale BESS applications. Future work could focus on real-time implementation and optimization under dynamic grid conditions.