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Viet Thanh et al. / IJOCTA, Vol.15, No.4, pp.625-648 (2025)
            transient energy shortages. This process is en-   where I max is selected equal to 1 per unit and
            tirely dependent on the charging and discharging  I   ′ is determined as follows in Equation (22):
                                                               max
            of the battery, controlled by limiting the battery’s
            SOC level. Therefore, the output signal of the                s Z      2
                                                                              |I max|
                                                                                           2
            battery charge controller can be obtained based        I max’ =           |I max | − I d 2  dt  (22)
            on the following conditions in Equation (20):                     0
                                                              3.4. The current controller
                  (
                   i d p ref  if SOC min ≤ SOC ≤ SOC max      The main purpose of the applied current con-
              i d =                                    (20)
                   0       otherwise                          troller in BESS is to regulate reactive and active
                                                              powers. Its structure is demonstrated in Figure 5.
            where the battery charging and discharging op-    From this figure, the I ds and I qs measured currents
            erations are carefully managed to maintain the    at the PCC. The voltage angle at PCC is deter-
            SOC within the optimal range of SOC min and       mined using the phase-locked-loop to calculate I ds
            SOC max . 33  In this study, SOC min and SOC max  and I qs of the d and q reference frame from the
            were selected at 10% and 100%, respectively. 34   abc global reference frame. The error between the
            The I d signal was passed through the current lim-  I d ref and I q ref reference currents from the damp-
            iter to regulate the reference active current in the  ing controller and the I ds and I qs measured cur-
            d axis of I d ref , which is limited by the maximum  rents are passed through the PI controller to cre-
            current value of the absolute. The difference be-  ate the d- and q-axes modulation indexes of m d
            tween the current of I d ref and the current of I d  and m q , respectively, which were the input of the
            is that the feedback signal of ∆I d was considered  PWM.
            the input signal of the active power control loop.
                                                              4. Displayed mathematical equations
                On the contrary, the control strategy based
            on the q-axis is shown in Figure 6 using the re-  4.1. Introduction to test systems
            active power control loop. It is the same as the
            active power control loop; the first-order filter,  The feasibility of the proposed BESS control
            PI controller, and lead-lag controller were con-  method for frequency stability, particularly with
            sidered. The error between the obtained refer-    high levels of renewable energy, was evaluated us-
                                                              ing both the IEEE 39-bus system and the Viet-
            ence reactive power from Equation (19) and the
                                                              namese Tay Nguyen 500/220 kV system. In the
            measured BESS reactive power at PCC is passed
                                                              modified IEEE 39-bus system, as shown in Figure
            through the filter. The error between the output
                                                              7, three synchronous generators at buses 2, 25,
            signal of this filter and the ∆I q signal from the
                                                              29, and 23 were replaced with three solar farms
            charge controller was passed through the PI con-
                                                              (PV1, PV2, and PV3) and one wind farm, with
            troller. The output signal from this PI controller
                                                              rated powers of 250 MW, 1200 MW, 600 MW, and
            was passed through two lag and lead compensa-
                                                              1,000 MW, respectively. Details are provided in
            tions, a washout, and a limiter block, respectively.
                                                              Table 1. For the Vietnamese Tay Nguyen 500/220
            Then, the output signal denoting I q WAS passed
                                                              kV system, depicted in Figure 8, it is projected
            through the current limiter to regulate the refer-
                                                              that by 2025, the total generating capacity in
            ence active current in the q-axis of I d −ref , which
                                                              the area will reach 5521.5 MW. Of this, 4255.5
            is limited by the maximum current value of the
                                                              MW will come from renewable sources, including
            absolute. The difference between the current of
                                                              2435.5 MW from PV and 1820 MW from wind
            I q −ref and the current of I q to be the feedback
                                                              turbine generators. Thus, renewable energy will
            signal of ∆I d was considered the input signal of
            the reactive power control loop.                  account for approximately 77% of the region’s to-
                                                              tal electricity generation.
                The grid input capacity of BESS depends on
            the DC/AC converter capacity. Therefore, the          The models for the PV and WT systems are
                                                                                         26,35,36
            total current on the d- and q-axes must be equal  based on previous studies.         All dynamic
            to the DC/AC converter’s rated value to avoid     models in the system, such as those for the syn-
            overloading it. The limit between the obtained    chronous generators, excitation systems, trans-
                                                              mission lines, and loads, are implemented using
            reference d- and q-axes currents is determined as
                                                              the DIgSILENT PF simulation environment. The
            follows in Equation (21):
                                                              reference response was evaluated through time-
                                                              domain simulations conducted in DIgSILENT PF
                       
                                  R  |I max|
                        I d −ref =      (I d ) dt            2021. The parameters for the IEEE 39-bus system
                                   −|I max|
                                 R |I  ′|              (21)   were sourced from Thanh et al., 37  while the pa-
                        I q −ref =  max  (I q ) dt
                                  −|I   ′|                    rameters for the Vietnamese Tay Nguyen 500/220
                                     max
                                                           634
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