A grid forming controller with integrated state of charge management for V2G chargers

Electrical Power and Energy Systems 157 (2024) 109862 Available online 10 February 2024 0142-0615/© 2024 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Contents lists available at ScienceDirect International Journal of Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes A grid forming controller with integrated state of charge management for V2G chargers Ander Ordono a,∗, Francisco Javier Asensioa, Jose Antonio Cortajarenab, Inmaculada Zamora c, Mikel González-Pérez a, Gaizka Saldaña c aDepartment of Electrical Engineering, University of the Basque Country (UPV/EHU), Avd. Otaola, 29, Eibar, 20600, Spain bDepartment of Electronic Technology Engineering, University of the Basque Country (UPV/EHU), Avd. Otaola, 29, Eibar, 20600, Spain cDepartment of Electrical Engineering, University of the Basque Country (UPV/EHU), Alameda Urquijo, s/n, Bilbao, 48013, Spain ARTICLE INFO Keywords: Electric vehicle Frequency regulation Grid forming V2G ABSTRACT Vehicle-to-grid (V2G) technology offers an innovative solution to provide grid services using electric vehicle (EV) batteries. This work proposes a novel grid forming (GFM) controller for V2G applications which can ensure the voltage source behaviour and provide support to the grid, regardless of the state of charge (SoC) and the charging requirements of the battery. This is achieved by integrating a SoC controller that modifies the classical GFM algorithm. The controller only relies on the SoC and power measurements, achieving a decentralized without the need of communication. With the proposed approach, the V2G charger will always behave as a voltage source that provides inertial response and voltage support to the grid. The primary frequency regulation, on the other hand, will depend on the battery status and charging needs. Frequency regulation could be enabled, disabled or it could be limited to some perturbations (under/over frequencies). Moreover, the SoC controller provides freedom to tune the frequency support of the device, limiting it to inertial response or extending its contribution along the time. The tuning of the system parameters is addressed in detail to ensure a damped response under all the operation scenarios provided by the SoC controller. Its performance and stability is evaluated using small signal transfer functions. Finally, it is validated both in simulation and experimentally. 1. Introduction In the recent years, power grids are integrating increasing amounts of non-dispatchable renewable energy sources (RES), shifting towards a more environmentally friendly grid. However, new challenges arise due to the paradigm shift [1]. On the one hand, the grid management complexity increases due to the stochastic behaviour and the reduced power reserves of RES [2]. On the other hand, as the kinetic energy stored in rotating masses of conventional plants (inertia) is replaced by inverter-based RES, the grid turns weaker and prone to bigger and faster voltage and frequency excursions [3]. All in all, the grid paradigm shift leads to a more dynamic and complex grid power management [4]. In this scenario, grid operators are implementing strategies to ensure grid stability and reliability. Energy Storage Systems (ESS), demand management and RES curtailment are among the most relevant approaches to provide flexibility [5]. Related to ESS, Vehicle-to-Grid (V2G) has also arisen as a promising solution [6]. V2G chargers enable bidirectional energy flow between electric vehicles (EVs) and the grid, ∗Corresponding author. E-mail address: [email protected] (A. Ordono). allowing them to not only consume, but also provide energy back to the grid when needed. By aggregating multiple EV batteries, a significant amount of flexibility can be provided to the grid, removing the need of ESS systems and reducing the investment costs [7]. Several services have been proposed for V2G applications [8], being the most interesting those which require fast response and have a low battery degradation impact (low energy, high power). In this context, the contribution of EVs to the Load Frequency Control has been extensively studied [9]. Several work have shown that V2G systems can contribute to keep the frequency close to its rated value while ensuring a proper SoC management of the EVs [10–12]. However, these controllers usually rely on a communication link to a centralized controller, increasing the complexity when the number of chargers is high or they are geographically dispersed. To prevent this issue, services which can be provided based on local measurements have gained attention for V2G applications (distributed approach). Supporting the grid through inertia emulation, primary frequency regulation and voltage support stand out. https://doi.org/10.1016/j.ijepes.2024.109862 Received 18 September 2023; Received in revised form 15 January 2024; Accepted 8 February 2024 International Journal of Electrical Power and Energy Systems 157 (2024) 109862 2 A. Ordono et al. As other inverter-based resources, V2G chargers could support the grid using two control strategies: grid following (GFL) and grid forming (GFM) [13]. GFL is the most mature and widespread strategy for these applications. A synchronization mechanism, usually a Phase-Locked Loop (PLL), is used to detect the grid phase. Based on this information, the exchanged current amplitude and phase is regulated to handle the active and reactive power transfer. From grid perspective, the power converter behaves as a controlled current source. GFL-based V2G chargers have been extensively studied in literature, where the main goal is to maximize the grid support while ensuring a proper SoC management. Authors in [14] have proposed a control strategy in which the charger could operate in 3 discrete states (charge, discharge or idle) depending on local measurements. To provide a smoother support, the smart charging concept has also been proposed by several authors [15– 17]. In these, the charger power setpoint is modified through a droop controller. Smart charging strategies require the charger to operate far below the rated power to provide up and down regulation, which has a negative impact on the efficiency of the power electronics. To provide a symmetrical support and optimize the charging efficiency of the system, [18] divides the EV charger operation into two regions: the frequency support region and the forced-charge boundary region. Even if the EV is charged efficiently, the frequency regulation capability is lost during the forced-charge boundary. Adaptive droops, in which the droop coefficient is modified using the state of charge (SoC) of the vehicle have also been proved useful to provide keep the SoC limited to a certain range or to prevent an excessive battery degradation. Different relations between the droop coefficient and the SoC have been proposed in literature, depending on the goal [15,19]. Finally, V2G chargers operating as GFL have also been proposed to provide some synthetic inertia. This is usually achieved by adding a derivative term to the droop controller [20,21]. [22] have merged the inertial response and the adaptive droop concept together in a hybrid system based on a EV battery an ultra-capacitors. Despite the popularity of GFL strategies in V2G chargers, they face some limitations: they do not operate properly on weak grids nor can provide without an existing grid (standalone). [23]. In this scenario, GFM strategies have emerged as an alternative to face the issues related to GFL and achieve a 100% IBR-based grid [24]. Despite sharing the same hardware, GFM devices behave as controlled voltage sources which can mimic the behaviour of synchronous generators (SGs), providing accurate inertia, higher stability under weak grids and standalone operation. V2G chargers operating as GFM devices could be interesting for small scale grid applications or to ensure the power supply under blackouts. Authors in [25] have proposed a community of EVs operating as Virtual Synchronous Generators (VSG) that ensures the supply in case of power failure. VSGs for low power single-phase EV chargers have also been proposed in [26,27]. The former reference is focused on the dynamic response to grid perturbations, whereas the latter aims to optimize the charger performance with a reduced DC link capacitance. Authors in [28] have also suggested a V2G charger based on a GFM droop controller, focusing on active/reactive power decoupling without inertia emulation. In all the previous GFM strategies, the SoC limits and the charging requirements of the EV were not considered. In fact, the GFM operation considering the EV battery has not been studied in depth in literature. A SoC management was described in [29], but the response of the controller and its stability under the different scenarios was not addressed in detail. Limiting the contribution to inertial response has also been suggested as a solution to prevent SoC drifts for chargers [30,31]. However, this approach might lead to underusage of the battery, as there are scenarios in which the primary frequency regulation of EVs could be advantageous both for the EV and the grid. Considering all the mentioned above, this paper aims to develop a GFM controller with an integrated SoC management for V2G charger applications. When the battery SoC is inside its operational limits and Fig. 1. One-line diagram of a 3-phase EV charger using a GFM strategy. no charging is required, the V2G charger will behave as a conventional GFM device, providing inertia emulation, primary frequency and voltage support. However, when the SoC limits are hit or charging is required, the SoC controller will reduce the primary frequency support depending on the perturbation type, limiting its contribution to meet the SoC requirements. The SoC controller provides freedom to tune the transient support of the device, limiting it to inertial response or providing time-extended contributions. The impact of the SoC controller on the stability and response of the V2G is addressed in detail, and parameters are tuned to provide a damped response. The proposed controller will only use the SoC and power measurements to operate, achieving a decentralized approach and not needing frequency measurements. This paper is organized as follows. Section 2describes the overall structure of the V2G charger, focusing on the inverter side and its interaction with the AC grid. The GFM strategy, the internal control loops and the SoC controller are described in detail, including the identified operating modes, which depend on the SoC conditions and charging requirements. Section 3evaluates the transfer function of the system for the previously identified operating modes. The performance of the V2G charger can be evaluated by considering two scenarios, which depend on the status (enabled/disabled) of the SoC controller. The controller is tuned to prioritize the damping of the response. The performance of the proposed control strategy under different operating modes is validated in Section 4, both using a simulation and an experimental setup. Finally, the main conclusions are gathered in Section 5. 2. System description Fig. 1 shows the simplified diagram of a 3-phase bidirectional EV charger. The EV charger is composed of a DC/DC and a DC/AC stage, connected through an intermediate DC bus (𝑣𝑏𝑢𝑠). The DC/AC stage is connected to the grid using a LCL filter, which is designed to meet the harmonic distortion requirements of the grid [32]. The filter is composed of an inverter-side inductor 𝐿𝑐, a grid-side inductor 𝐿𝑔and a capacitor 𝐶𝑓. A damping resistor 𝑅𝑓can be connected in series to the capacitor to attenuate the resonance peak of the filter. The grid is represented using its equivalent Thévenin circuit, composed of a voltage source 𝑣𝑔and its equivalent series impedance 𝑍𝐺. The grid impedance includes inductive 𝐿𝐺and resistive 𝑅𝐺components. When EV chargers operate in GFL mode, the DC/AC regulates the intermediate voltage 𝑣𝑏𝑢𝑠 and the reactive power (or power factor) exchanged with the grid, whereas the DC/DC manages the active power which is exchanged with the battery. In GFM, the control structure is modified: the DC/DC is used to regulate 𝑣𝑏𝑢𝑠, whereas the DC/AC manages the active and reactive power exchanged with the grid. For the sake of simplicity, this analysis will only focus on the GFM strategy of the DC/AC stage. The dynamics of the DC/DC stage are neglected, considering a stiff DC voltage source. 2.1. GFM control structure The GFM control of the DC/AC stage of the V2G charger is shown in Fig. 2. The controller is implemented using the synchronous 𝑑𝑞 frame. All the parameters and equations in the diagram are based on the per unit system (pu), except for the base angular frequency 𝜔𝑏 and the internal angular position 𝜃𝑟, which are given in rad/s and rad respectively. The GFM is composed of 4 main blocks: International Journal of Electrical Power and Energy Systems 157 (2024) 109862 3 A. Ordono et al. Fig. 2. Grid forming strategy for the DC/AC stage of the V2G charger. •Power Synchronization Loop (PSL) •Reactive Power Control (RPC) •Virtual Admittance •Current Controller A brief description of each control block is given in the following subsections. The proposed SoC controller, marked in red in the figure, will be described more into detail in Section 2.2. 2.1.1. Power synchronization loop The PSL generates the angular frequency 𝜔𝑟and position 𝜃𝑟of the output voltage of the GFM system. 𝜃𝑟is used to convert variables to and from 𝑑𝑞 system, as shown in Fig. 2. Compared to GFL inverters, which synchronize to the existing grid using grid voltage measurements and a PLL, the GFM inverters use an active power based synchronization. This allows them to operate in standalone conditions, without an existing grid. The proposed PSL is based on a VSG algorithm, which emulates the swing equation of SGs [33]: 𝑑𝜔𝑟 𝑑𝑡 =1 2𝐻(𝑃∗−𝑃+𝐷𝑝(𝜔∗ 𝑟 ′−𝜔𝑟) − 𝑃𝑑)(1) In the previous equation, 𝑃∗is the active power command, 𝑃is the measured active power, 𝜔𝑟is the output angular frequency of the controller, 𝐷𝑝is the static damping term and 𝐻is the virtual inertia term. The term 𝜔∗ 𝑟 ′is the angular frequency command, which can be modified by the SoC control algorithm. 𝐻is selected to provide dynamic frequency support to the grid. For this analysis, an inertia of 8 s is used. 𝐷𝑝, which is the inverse of the droop coefficient, determines the steady-state active power value under grid frequency deviations (primary frequency regulation). The typical values of 𝐷𝑝ranges between 20 to 50 pu, to ensure a proper power sharing among the sources connected to the grid. For this analysis, a 𝐷𝑝of 50 pu is selected. This means that a change in the grid frequency of 0.02 pu will lead to a change of 1 pu in the active power of the system. As 𝐻and 𝐷𝑝terms are usually defined by the system operator, the active power loop dynamics are fixed [34]. The dynamic damping power term, 𝑃𝑑, is added to the swing equation to improve the transient response of the active power loop. The dynamic damping term will not affect the steady-state response of the swing equation, so it is useful to decouple the transient and steady-state response. Among existing dynamic damping strategies, a power derivative term (2) is proposed, where 𝐷𝑑is the dynamic damping coefficient. The value of the dynamic damping term 𝐷𝑑will be tuned in Section 3[35]. 𝑃𝑑=𝐷𝑑𝑠 𝜏𝑑𝑠+ 1 (2) The dynamic damping term includes a low pass filter (LPF) with a time constant 𝜏𝑑. The bandwith of this filter is set to 20 Hz. This will provide damping in the range of the active power loop (1–3 Hz), but it will prevent the interactions with synchronous oscillations (50 Hz) that could make the system unstable [36]. 2.1.2. Reactive power control The RPC generates the voltage setpoint 𝐸of the GFM, emulating the reactive power droop behaviour of SGs according to: 𝐸=𝑣∗+𝑚𝑞(𝑄∗−𝑄 𝜏𝑞𝑠+ 1 )(3) Where 𝑣∗and 𝑄∗are the voltage and reactive power commands, 𝑚𝑞is the reactive power droop, and 𝑄is the measured reactive power. A first order low-pass filter (LPF) with a time constant 𝜏𝑞is used to remove high frequency components and to adjust the dynamics of the reactive power loop. The reactive power droop is set to a typical value of 0.1 pu. The filter time constant is set to 20 ms. 2.1.3. Virtual admittance The virtual admittance algorithm emulates an impedance between the RPC voltage setpoint 𝐸and the measured capacitor voltage 𝑣𝑜. The virtual admittance behaviour is equivalent to a voltage controller with a virtual impedance, but with the advantage of removing the voltage controller. The virtual impedance is useful for connecting GFM inverters to strong grids, in which the line impedance is small compared to the rated power of the converter, which could be the case of a V2G charger. By increasing the inductive term of the virtual impedance, the active and reactive power can be decoupled regardless of the grid impedance, allowing a proper operation of the PSL and RPC controllers. Additionally, the virtual impedance can reduce the active and reactive power loop dynamics, improving the stability of the system [37]. The following equation describes the implementation of the virtual admittance strategy in the 𝑑𝑞 frame: 𝑑𝑖∗ 𝑐𝑑𝑞 𝑑𝑡 =𝜔𝑏 𝐿𝑣(𝐸−𝑣𝑜𝑑𝑞 −𝑅𝑣𝑖∗ 𝑐𝑑𝑞 +𝑗𝜔𝑟0𝐿𝑣𝑖∗ 𝑐𝑑𝑞 )(4) Where 𝑖∗ 𝑐𝑑𝑞 is the converter current vector setpoint, 𝑣𝑜𝑑𝑞 is the capacitor voltage vector feedback, and 𝑅𝑣and 𝐿𝑣are the virtual resistance and inductance values. By considering that the angular frequency variation of the GFM converter will be small, the angular frequency 𝜔𝑟0 in the coupling terms can be considered constant and equal to 1 pu. The proposed algorithm uses a virtual inductance and resistance of 0.3 and 0.06 pu, respectively. The addition of a virtual impedance is used to damp the synchronous oscillations, which are out of the scope of this analysis [38]. International Journal of Electrical Power and Energy Systems 157 (2024) 109862 4 A. Ordono et al. Fig. 3. Grid forming operation modes based on SoC level and charging time. 2.1.4. Current controller The converter current is regulated using a PI controller. To improve the system response, it includes 𝑑𝑞 decoupling terms and capacitor voltage feedforward: 𝑣∗ 𝑐𝑑𝑞 = (𝑖∗ 𝑐𝑑𝑞 −𝑖𝑐𝑑𝑞 )(𝑘𝑝+𝑘𝑖𝑐 ∕𝑠) + 𝑗𝜔𝑟0𝐿𝑐𝑖𝑐𝑑𝑞 +𝑣𝑜𝑑𝑞 (5) 𝑣∗ 𝑐𝑑𝑞 is the converter voltage vector setpoint, 𝑖𝑐𝑑𝑞 is the converter current vector feedback, 𝑘𝑝𝑐 is the proportional gain and 𝑘𝑖𝑐 is the integral gain. As in the virtual admittance, the term 𝜔𝑟0in the decoupling terms can be considered constant. A modulus optimum tuning approach is used to select the PI gains [39]. The current controller bandwidth is set 20 times lower than the switching frequency of the converter (𝑓𝑠𝑤), which is 10 kHz. The 500 Hz bandwidth is high enough compared to the bandwidth of the PSL and RPC loops, and hence, it dynamics can be neglected in the analysis. 2.2. SoC controller V2G chargers, due to their bidirectional capability, could operate as GFM devices. However, the SoC of the battery must be properly managed during operation. The GFM controller should meet the following conditions: •The battery SoC must be limited to an operational range to prevent battery degradation. The lower and upper operational limits are defined as 𝑆𝑜𝐶𝑂𝑃 𝑚𝑖𝑛 and 𝑆𝑜𝐶𝑂𝑃 𝑚𝑎𝑥, which are more restrictive that the absolute battery limits 𝑆𝑜𝐶𝑚𝑖𝑛 and 𝑆𝑜𝐶𝑚𝑎𝑥. •When the EV is unplugged, it should have enough charge to meet the mobility requirements of the EV user. 2.2.1. GFM modes under SoC control Fig. 3 shows a SoC vs time diagram of a plugged EV. The vehicle is plugged into the V2G charger at time 𝑡𝑖𝑛, with an initial charge level 𝑆𝑜𝐶𝑖𝑛 (%). The owner of the vehicle will unplug the vehicle from the charging station at time 𝑡𝑜𝑢𝑡, expecting a charge level of at least 𝑆𝑜𝐶𝑜𝑢𝑡 (%). It is assumed that the plug out-time and expected charge are introduced by the user or they can be estimated using historical data. Moreover, the required charge will always be lower than 𝑆𝑜𝐶𝑂𝑃 𝑚𝑎𝑥. According to the figure, 4 operation modes can be identified: The B-GFM, in which the EV charger operates as a conventional GFM device. The CL-GFM and DL-GFM, in which transient frequency support is provided, but the primary frequency support is limited to prevent crossing the operational limits. Finally, the C-GFM, in which the priority is to meet the charge level of the EV and hence, only transient support is provided. A more detailed explanation of each mode is given in Table 1. In all the cases, the voltage support is always available, as it depends on reactive power. It should be noted that even if the controllable voltage source behaviour is kept in all the operating modes, the standalone operation Fig. 4. Implementation of SoC controller, including logic table. capability is only available in B-GFMI mode. In the remaining modes, the EV charger will contribute to the stability of the grid by providing transient frequency support, but the steady state contribution or primary frequency support, which depends on the static damping power is not guaranteed. The system should rely on other GFL or GFM devices to ensure the stable operation. An additional emergency mode could also be developed, in which the SoC controller could be deactivated when the grid frequency goes below or above a threshold to prioritize the grid stability over the battery conditions. This analysis is out of the scope of this work. 2.2.2. Controller implementation The proposed SoC controller implementation is shown in Fig. 4. It is based on an integral action, which will remove the frequency deviation error (𝜔∗ 𝑟−𝜔𝑟), ensuring that the power setpoint 𝑃∗is met regardless of the grid conditions. A dynamic saturation is used to handle the contribution to under and over-frequencies independently. Additionally, it can be used to disable the SoC controller by setting the saturation levels to 0. A logic table is used to obtain the integrator upper and lower dynamic limit, 𝐿𝐻and 𝐿𝐿, and the charging setpoint 𝑃∗. The logic table uses three boolean inputs (𝑆1, 𝑆2, 𝑆3)to determine if the SoC is inside the operational limits and to check if charging is required. These boolean inputs are the ones defined in the conditions column of Table 1. A hysteresis could be added to prevent continuous triggering of boolean inputs 𝑆1and 𝑆2, but it is neglected for the sake of simplicity. The ‘‘M’’ column in Fig. 4 identifies the operation mode defined in Table 1. 3. Transfer function & stability analysis The proposed controller has a non-linear behaviour due to the saturation block introduced by the SoC controller. However, its performance can be evaluated considering two independent scenarios: 1. SoC controller disabled: The integral action can be neglected from the study. This controller is disabled in the following modes: •B-GFM •DL-GFM under over-frequencies •CL-GFM under under-frequencies 2. SoC controller enabled: The integral action modifies the angular frequency command of the GFM algorithm. The SoC controller is enabled in the following modes: •C-GFM •DL-GFM under under-frequencies •CL-GFM under over-frequencies The linearized model of the active power loop is shown in Fig. 5. The term 𝛥is added to all the signals to indicate that they are small signal variations. The SoC controller branch is marked in red, and it must be considered only when the SoC controller is active. The impact International Journal of Electrical Power and Energy Systems 157 (2024) 109862 5 A. Ordono et al. Table 1 Operation modes description. Mode Description Condition B-GFM Basic operation. The SoC control does not modify 𝜔∗ 𝑟. The system operates as a conventional grid forming device. The charger provides inertia emulation and primary frequency regulation capability. 𝑆𝑜𝐶 ∈ (𝑆𝑜𝐶𝑂𝑃 𝑚𝑖𝑛, 𝑆𝑜𝐶𝑂𝑃 𝑚𝑎𝑥 ) DL-GFM Discharge-limited operation. It prevents an excessive discharge of the battery by limiting active power support to grid under-frequencies. The charger provides transient frequency support, and primary frequency regulation under over-frequencies. 𝑆𝑜𝐶 ≤𝑆𝑜𝐶𝑂𝑃 𝑚𝑖𝑛 CL-GFM Charge-limited operation. It prevents an excessive charge of the battery by limiting the active power support to grid over-frequencies. The charger provides transient frequency support, and primary frequency regulation under under-frequencies. 𝑆𝑜𝐶 ≥𝑆𝑜𝐶𝑂𝑃 𝑚𝑎𝑥 C-GFM Charging operation. It ensures that EV charge level is met before plug-out time. During this time, the active power support to both under and over-frequencies is limited. The charger only provides transient frequency support. This mode is activated when the remaining plug out time (𝑡𝑜𝑢𝑡 −𝑡) is equal or lower than the charging time 𝛥𝑡𝑐ℎ. Time is given in hours. 𝐶𝑒𝑣 is the battery capacity in kWh and 𝑃∗is the charging power in kW. 𝑃∗should be smaller than charger maximum power to prevent overloading condition 𝑡𝑜𝑢𝑡 −𝑡≤𝛥𝑡𝑐ℎ 𝛥𝑡𝑐ℎ =𝐶𝐸𝑉 100 𝑆𝑜𝐶𝑜𝑢𝑡 −𝑆𝑜𝐶 |𝑃∗| Fig. 5. Small-signal model of the active power loop. of the voltage and the reactive power are neglected, considering an inductive line that provides proper decoupling of active/reactive powers. For convenience, the LPF of the dynamic damping, determined by 𝜏𝑑, is also neglected. This simplification is valid for analysing frequency components that are well below the bandwidth of the filter, which is the case of the PSL loop. The term 𝛥𝜔𝑔is the grid angular frequency variation, which is considered as an external perturbation for the plant. 𝜔𝑔0is the angular frequency value at the linearization point, in rad/s. The simplified model of the grid plant is obtained from the active power transfer equation on inductive lines (6), where 𝛿is the phase shift between the GFM and the grid voltage, in rad/s. The virtual reactance (𝑋𝑣=𝐿𝑣in pu) is considered much higher than the grid impedance, so that the latter can be neglected in the analysis. This would be the case of an EV charger connected to a utility grid or microgrid, in which the overall power of the charger is small compared to the rated power of the system. 𝑃=𝐸𝑉𝑔 𝑋𝑣 sin 𝛿(6) The previous equation can be linearized around the operating angle 𝛿0. Assuming that the voltages are close to the base values, and that the operating angle is small, the relation between the active power and the angle is inversely proportional to the virtual reactance, or proportional to the virtual susceptance 𝑌𝑣: 𝑑𝑃 𝑑𝛿 =𝐸𝑉𝑔cos 𝛿0 2𝜋𝐿𝑣 𝛿≈1 𝑋𝑣 =𝑌𝑣(7) Table 2 provides an overview of the active power open-loop 𝛥𝑃 ∕(𝛥𝑃 ∗−𝛥𝑃 )and closed-loop 𝛥𝑃 ∕𝛥𝑃 ∗transfer functions, taking into account the SoC controller state. The response to grid frequency perturbations 𝛥𝑃 ∕𝛥𝜔𝑔is also included. Table 2 Active power transfer functions with and without SoC controller. SoC control enabled SoC control disabled 𝛥𝑃 𝛥𝑃 ∗−𝛥𝑃 𝑌𝑣𝜔𝑔0(𝐷𝑑𝑠+1)(𝑠+𝜔𝑖) 2𝐻𝑠3+(2𝐻𝜔𝑖+𝐷)𝑠2 𝑌𝑣𝜔𝑔0(𝐷𝑑𝑠+1) 2𝐻𝑠2+𝐷𝑠 𝛥𝑃 𝛥𝑃 ∗ 𝑌𝑣𝜔𝑔0(𝑠+𝜔𝑖) 2𝐻𝑠3+(𝐷𝑝+2𝐻𝜔𝑖+𝑌𝑣𝜔𝑔0𝐷𝑑)𝑠2+𝑌𝑣𝜔𝑔0(1+𝐷𝑑𝜔𝑖)𝑠+𝑌𝑣𝜔𝑔0𝜔𝑖 𝑌𝑣𝜔𝑔0 2𝐻𝑠2+(𝐷𝑝+𝑌𝑣𝜔𝑔0𝐷𝑑)𝑠+𝑌𝑣𝜔𝑔0 𝛥𝑃 𝛥𝜔𝑔 −𝑌𝑣𝜔𝑔0(2𝐻𝑠2+(2𝐻𝜔𝑖+𝐷𝑝)𝑠) 2𝐻𝑠3+(𝐷𝑝+2𝐻𝜔𝑖+𝐷𝑑𝑌𝑣𝜔𝑔0)𝑠2+𝑌𝑣𝜔𝑔0(1+𝐷𝑑𝜔𝑖)𝑠+𝑌𝑣𝜔𝑔0𝜔𝑖 −𝑌𝑣𝜔𝑔0(2𝐻𝑠+𝐷𝑝) 2𝐻𝑠2+(𝐷𝑝+𝑌𝑣𝜔𝑔0𝐷𝑑)𝑠+𝑌𝑣𝜔𝑔0 3.1. SoC control disabled When the SoC controller is not enabled, the active power loop behaves as a second order system. According to the closed loop equation in Table 2, the bandwidth of the active power response, 𝜔𝑐, depends on the inertia and virtual susceptance (8), whereas the damping 𝜉also depends on the 𝐷𝑝and 𝐷𝑑terms (9). The term 𝐷𝑑does not affect the steady state response under frequency perturbations, only depending on 𝐷𝑝. This can be clearly seen by applying the final theorem to the closed loop equation. 𝜔𝑐=√𝑌𝑣𝜔𝑔0 2𝐻(8) 𝜉=1 2𝜔𝑐 𝐷𝑝+𝑌𝑣𝜔𝑔0𝐷𝑑 2𝐻(9) The impact of the dynamic damping 𝐷𝑑on the closed loop response of the active power loop is shown in Fig. 6(a), whereas the response against grid frequency perturbations is shown in Fig. 6(b). The closed loop response provides a proper power control for frequencies up to 1.2–2 Hz, consistent with expected bandwidth. Increasing 𝐷𝑑allows the attenuation of the resonance peak in the transfer function, albeit with a slight reduction in bandwidth. When 𝐷𝑑= 0, the damping of the system is lower than 0.3. By setting 𝐷𝑑= 0.13 pu, the system is critically overdamped. The 𝛥𝑃 ∕𝛥𝜔𝑔transfer function provides a DC gain of 34 dB, regardless of the dynamic damping term. This gain matches the static damping term 𝐷𝑝. The impact of the dynamic damping can also be assessed by analysing the evolution of the poles, as depicted in Fig. 7. In this figure, the real part of the pole 𝜎is represented in the 𝑥-axis and the imaginary part 𝜔is depicted in the 𝑦-axis. As the 𝐷𝑑term increases, the poles associated with the electromechanical equation move towards the left half-plane, which enhancing the system damping. Lines representing different 𝜉values have been added to the graph. The term 𝐷𝑑could be selected using different approaches. One method is to find a suitable compromise between speed response and overshoot by setting 𝜉= 1∕√2. This corresponds to a 𝐷𝑑value of 0.1 pu. International Journal of Electrical Power and Energy Systems 157 (2024) 109862 6 A. Ordono et al. Fig. 6. System response when SoC controller is disabled. Fig. 7. CL pole evolution under a 𝐷𝑑sweep. SoC control disabled. Fig. 8. Small-signal model of the PSL. 3.2. SoC control enabled When the SoC control is enabled, the integral action of the SoC controller modifies the static damping term 𝐷𝑝, adding a first order high-pass filter (HPF) in series. In this scenario, the relation between the angular frequency deviation 𝛥𝜔𝑟and the active power 𝛥𝑃 can be rewritten as (10). The integral gain 𝜔𝑖, in rad/s, determines the bandwidth of the filter. The simplified small-signal diagram of the PSL is shown in Fig. 8, where the red block represents the HPF introduced by the SoC control. Hence, the main effect of the SoC controller is to remove the contribution of the static damping power, which is equivalent to the primary frequency regulation. The higher the bandwith of the filter, the faster the static damping power will be removed. 𝛥𝑃 𝛥𝜔𝑟 =𝐷𝑝 𝑠 𝑠+𝜔𝑖 (10) When the SoC controller is enabled, the dynamic damping term plays a key role in the stability of the system, specially when the integral gain is high. Under these conditions, the contribution of 𝐷𝑝 can be nearly neglected, with damping primarily provided by 𝐷𝑑term. Fig. 9. CL pole evolution under a 𝜔𝑖sweep, without dynamic damping. Fig. 10. CL pole evolution under a 𝐷𝑑sweep, with 𝜔𝑖= 5 rad∕s. The influence of 𝜔𝑖on the stability of the system becomes evident when analysing the pole displacement under a 𝜔𝑖sweep with a null dynamic damping term (Fig. 9). As the integral gain is increased, the poles associated with the mechanical system progressively shift toward the right-hand plane, resulting in a reduction of damping and a potential loss of stability in the system. For this analysis, a 𝜔𝑖= 5 rad/s is proposed. With this bandwidth, the static damping effect will be removed in around 0.8 s (4 time constants). The pole displacement under a 𝐷𝑑sweep is given in Fig. 10. For a certain integral gain, increasing 𝐷𝑑will increase the damping of the electromechanical poles of the system, as observed in the previous analysis. However, the damping increase is considerably reduced when going above a certain critical 𝐷𝑑value. Beyond this value, the impact on the damping of the electromechanical mode is considerably reduced, and instead, the angular frequency decreases. As the target of this controller is to provide a damped response, a 𝐷𝑑= 0.08 pu is used for simulation and experimental tests. This is the value in which the damping of the electromechanical poles changes its trend, identified graphically in Fig. 10. The bode responses of the system with the SoC controller enabled and disabled are compared in Fig. 11. The closed loop active power response remains nearly equal, indicating that the SoC controller does not impact its performance. However, the response of the system under grid frequency perturbations is altered when the SoC controller is enabled. With the SoC controller enabled, the system exhibits zero gain at DC value, indicating that the active power will return to the desired setpoint after a perturbation. The magnitude of the low frequency components can be modified by varying the integral gain of the SoC controller, 𝜔𝑖. International Journal of Electrical Power and Energy Systems 157 (2024) 109862 7 A. Ordono et al. Fig. 11. Bode response when SoC controller is enabled and disabled. Fig. 12. Experimental setup. 4. Simulation & experimental validation The performance of the proposed controller has been tested both in simulation and experimentally. The parameters which have been used for validating the system are summed up in Table A.3. For the simulation, a Simulink model based on Fig. 1 has been developed. The grid is modelled using its Thévenin equivalent circuit. The impact of the DC/DC stage is neglected by considering a stiff DC voltage source, and an average DC/AC model is used to remove switching frequency effects. These assumptions have been extensively used in literature when modelling grid-connected GFM devices [40,41]. The experimental setup and its main components are shown in Fig. 12. The DC/DC and DC/AC stages are based on INF-50 power inverters from Dutt Electronics. The bidirectional DC/DC is built using two of the inverter’s half bridges, operating as an interleaved buck/boost. The battery is emulated using a BIC-2200-96 from Meanwell, which provides a 96 Vdc bidirectional supply. For the 3-phase grid, a Pacific Power 320-AMX supply is used. Off-the-shelf components have been used for passive and sensoring devices. The control algorithm is implemented in a cRIO-9040, which includes a Kintex-7 70T FPGA and a Dual-Core 1.30 GHz CPU. The cRIO device includes an acquisition task that captures analog inputs and controller internal signals at 10 kHz. All the analog inputs include a 3.3 kHz antialiasing filter. 4.1. Response to active power setpoint step The theoretical analysis from Section 3concluded that the active power closed loop dynamics were highly dependent on 𝐻,𝐷𝑝and 𝐷𝑑. As the first two parameters are usually defined by the system operator or grid requirements, 𝐷𝑑can be used to manage the 𝜉of the active power response. Fig. 13 shows the effect of the dynamic damping term 𝐷𝑑on the active power closed loop response. The figure presents both the Fig. 13. Active power under a power setpoint of −0.1 pu using different 𝐷𝑑. experimental and simulated responses of the GFM under a power setpoint step of −0.1 pu, using 𝐷𝑑values of 0 and 0.1 pu. Both experimental and simulation results are overlapped, showing identical power dynamics. The measured active power includes some ripple due to the switching noise of the real power converter, which does not appear in the simulated averaged model. The bandwidth of the active power controller is nearly constant, around 1.8 Hz. When 𝐷𝑑is set to 0, the active power response has a 𝜉= 0.27. However, when it is set to 0.1 pu, the damping is considerably increased to 𝜉= 0.85. The active power closed loop response is barely modified when the SoC controller is enabled and the integral action is executed (see Fig. 11(a)) Hence, the previous analysis is valid for all the operation modes defined in Table 1. 4.2. Response to frequency perturbations The operation mode of the EV charger will determine the response of the system to frequency perturbations. Simulation and experimental results are carried out for B-GFM, CL-GFM and C-GFM modes. For the sake of simplicity, DL-GFM mode is not included because its behaviour is symmetrical to the CL-GFM mode. The results, which will be discussed more into detail in the next subsections, are plotted in Fig. 14. The figure includes the angular frequency of the grid, the angular frequency of the GFM and both measured active and reactive powers. Experimental and simulation results are superimposed, showing similar results. For all the operation modes, the testing sequence is the same. The grid starts at the rated frequency of 1 pu. A first over-frequency event is generated by increasing the grid frequency to 1.002 pu using a step. After some time, the grid frequency experiences a frequency variation of −0.004 pu, finishing in a steady state value of 0.998 pu. By transitioning from an over-frequency to an under-frequency scenario, the non-linear behaviour of the CL-GFM mode can be identified. The analysis in the following subsections will be mainly focused on the active power response, as the proposed algorithm does not modify the performance of the RPC. As it is expected in GFM converters, there is a coupling between the exchanged active and reactive power. The frequency steps slightly modify the reactive power due to the resistive International Journal of Electrical Power and Energy Systems 157 (2024) 109862 8 A. Ordono et al. Fig. 14. Active and reactive power responses under different operating modes. Grid frequency perturbations of 0.002 and −0.004 pu are applied. term of the impedance (impedance to resistance ratio of 5). However, the active power is predominant during frequency perturbations, showing a direct relation between both. Experimental results show a higher reactive power exchange, indicating a higher coupling than the obtained in simulation. This discrepancy seems to be related to a higher resistivity in the experimental setup. 4.2.1. B-GFM Fig. 14(a) shows the operation of the EV charger in B-GFM mode. In this mode, the SoC is inside the operational range and no charging is required, starting with an active power setpoint 𝑃∗= 0 pu. The V2G charger provides transient support, in the form of inertia simulation, to both positive and negative grid frequency steps. Due to the dynamic damping term, the active power transient response has a highly damped behaviour, without an excessive overshoot nor ringing. In B-GFM, as the SoC controller is disabled, the static damping power contribution of the converter is not altered. The charger contributes to support the grid frequency under steady-state conditions. A power exchange of ±0.1pu is measured for a frequency deviation of ±0.002 pu, corresponding to the 𝐷𝑝term of 50 pu. 4.2.2. CL-GFM Fig. 14(b) shows the operation of the EV charger in CL-GFM mode. As in B-GFM, the EV is not being charged and the system starts with an active power setpoint of 0 pu. Under the first over-frequency event, the CL-GFM controller provides support during the transient, but it does not provide steady-state support. This occurs because the integral gain of the SoC controller removes the contribution of the static damping term 𝐷𝑝in approximately 0.8 s, according with the integral gain of 5 rad/s. The active power exchanged during the over-frequency transient is mainly associated to the inertial response of the system, but it is extended for some additional hundred of milliseconds until the static damping power contribution is completely removed by the SoC controller. Once the transient is finished, the active power returns to the pre-event value of 0 pu. When the under-frequency event occurs, the SoC controller is disabled and the CL-GFM provides both transient and steady-state support. Due to the transition from an over-frequency to an under-frequency condition, the non-linear behaviour of the system can be identified: the CL-GFM supports the grid for a transient of 0.004 pu, but the steady-state support is only given for a deviation of 0.002 pu. This nonlinearity leads to a response with a higher overshoot. Once the transient is finished, the steady state active power reaches 0.1 pu, which matches the static damping value. 4.2.3. C-GFM Fig. 14(c) shows the operation of the EV charger in C-GFM mode. The active power setpoint starts at −0.5 pu, assuming that the vehicle is being charged at half of the charger rated power. In C-GFM mode, the SoC controller integral action is always enabled, removing the steady-state frequency support and providing only transient support. The response to the over-frequency event is the same as in CL-GFM mode, and the concepts explained in previous subsection are valid. They could be applied to the under-frequency event, where only transient support is also identified. After both under-frequency and over-frequency transients, the active power setpoint returns to the preevent value of −0.5 pu. One key difference between the C-GFM and the CL-GFM or DL-GFM is that the SoC controller is always enabled, so non-linear behaviour is not present anymore. Finally, Fig. 15 shows an scope capture of the grid currents and capacitor voltages. The V2G charger, operated in C-GFM mode, is subjected to a 0.004 pu over-frequency. The evolution of the grid currents during the over-frequency event are shown in Fig. 15(a). Analogous to the active power, the amplitude of the grid currents increase during the transient, and they return to the pre-event amplitude due to the SoC controller action. A zoom from the previous transient is given in Fig. 15(b). The grid currents have a low THD value due to the LCL filter, which removes the high frequency switching components of the inverter. On the other hand, it can be seen that the capacitor voltage and the grid current from the phase A have a phase-shift of 180◦, meaning that the charger is consuming mainly active power, with an small reactive power exchange. International Journal of Electrical Power and Energy Systems 157 (2024) 109862 9 A. Ordono et al. Fig. 15. Capacitor voltage (green — phase A) and current (yellow — phase A, pink — phase B, blue — phase C) waveforms during GFM-C operation. Voltage and current scales are 50 V/div and 2 A/div. Time scale is 200 ms/div for (a) and 10 ms/div for (b). 4.3. Effect of SoC controller integral gain As it was demonstrated in Section 3, the SoC controller will introduce a first order HPF in the static damping power when it is enabled. As the bandwith of the HPF (𝜔𝑖) is increased, the closed loop dynamics of the active power will be deteriorated, by reducing the damping of the electromechanical modes. In this context, the dynamic damping term has been suggested as an alternative to keep a proper transient of the system when the SoC controller is enabled. The proposed analysis has used a bandwith of 5 rad/s for the SoC controller. However, smaller bandwidths could also be used. The main drawback of reducing 𝜔𝑖is the extra power exchanged during grid frequency perturbations. In this scenario, the contribution of the static damping power will be extended in time, and it will not be limited to inertial response. The transient response will be slightly improved due to the contribution of the static damping term, but the dynamic damping term is still required. Fig. 16 shows the response of the C-GFM mode for different 𝜔𝑖 values. A grid frequency step of 0.002 pu is applied in all the cases. A𝜔𝑖of 5 rad/s will result in a nearly inertial response, whereas an 𝜔𝑖of 0.1 rad/s extends the static damping power for several seconds, providing higher support at the cost of additional energy injection or absorption. 5. Conclusions This paper has proposed a modified GFM controller for V2G chargers, which includes an integrated SoC management of the battery. The proposed controller will ensure the voltage source behaviour and the grid support, regardless of the SoC level and the charging requirements Fig. 16. Active power response in C-GFM using different 𝜔𝑖values. Response to a grid frequency step of 0.002 pu. of the EV owner. Moreover, it requires minor modifications to the conventional GFM algorithms. With the proposed strategy, the V2G charger will always behave as a controlled voltage source that provides inertial response and voltage support to the grid. It will also contribute to primary frequency regulation when the EV does not need charging and the SoC levels are inside operational limits. When the SoC is close to the operational limits, its primary frequency regulation will depend on the perturbation type (over or under-frequency). With this strategy, the EV will keep a partial regulation capability to balance its SoC. Finally, when charging is required, the frequency regulation will be removed to ensure that charging needs are met. The transfer function and stability analysis of the active power loop have shown that the dynamic damping term of GFM plays a key role in providing a damped transient response, especially as the action of the SoC controller increases. This parameter is tuned to provide a damped power response (𝜉 > 0.7), regardless of the operation mode. Moreover, the transient response of the V2G under frequency excursions can be easily modified through the integral gain of the SoC controller. These transient contributions can go from 1 s for 𝜔𝑖= 5 rad/s, up to tens of seconds when 𝜔𝑖<0.1 rad/s. Smaller integral gains could reduce the dynamic damping term needed, but they will result in additional energy exchange with the grid, The performance of the controller has been validated through simulation and experimentally, showing that an stable operation is achieved under all the operation modes. CRediT authorship contribution statement Ander Ordono: Conceptualization, Formal analysis, Investigation, Software, Validation, Visualization, Writing – original draft. Francisco Javier Asensio: Supervision, Writing – review & editing. Jose Antonio Cortajarena: Supervision, Validation, Writing – review & editing. Inmaculada Zamora: Supervision, Writing – review & editing. Mikel González-Pérez: Writing – review & editing. Gaizka Saldaña: Writing – review & editing. Declaration of competing interest The authors whose names are listed immediately below certify that they have NO affiliations with or involvement in any organization or entity with any financial interest, or non-financial interest in the subject matter or materials discussed in this manuscript. Data availability Data will be made available on request.