Balance Control of SOC for MMC-BESS With Power Fluctuation Suppression, PCC Voltage Regulation, and Harmonic Mitigation in Grid-Connected Wind Farm

With the rapid increase in the penetration rate of renewable energy, the power quality of grid-connected wind farm is deteriorated seriously with power fluctuation and point of common coupling (PCC) voltage instability. The conventional solution is to use the energy storage device and the reactive power compensation apparatus to adjust separately, which complicates the system structure. Besides, an active power filter is needed additionally when harmonic pollution caused by local nonlinear load is serious. To solve these problems, this paper investigates the modular multilevel converter-based battery energy storage system (MMC-BESS), which can realize fluctuating power suppression, PCC voltage regulation, and harmonic mitigation simultaneously in grid-connected wind farm. Firstly, the topology and energy flow of MMC-BESS have been studied. Then, three-layer balance control of the state of charge (SOC) is proposed, which is essential to maintaining the normal operation of the device. Finally, the overall control of MMC-BESS applied in the grid-connected wind farm is given. Plenty of experimental results are obtained from a downscaled MMC-BESS prototype, which validate the effectiveness of the proposed control strategy.


I. INTRODUCTION
Nowadays, due to the depleting of fossil energy, clean and renewable energy such as photovoltaics and wind power has been developed and utilized on a large scale [1], [2]. However, with the penetration rate of renewable energy increasing rapidly, the power quality of the power system is deteriorated seriously by fluctuating power and unstable PCC voltage aroused from renewable power [3], [4].
The associate editor coordinating the review of this manuscript and approving it for publication was Alexander Micallef .
Taking wind power generation as an example, the output power of wind turbines depends on wind speed [5]. Due to the randomness and high uncertainty of wind speed, the output power of wind turbines fluctuates greatly. Besides, with the sudden switching on/off of local loads, the PCC voltage in the grid-connected wind farm is also unstable. Furthermore, the harmonic pollution of local nonlinear loads is another issue that needs to be solved. Currently, the commonly used method in industry is to adjust power fluctuation and PCC voltage through energy storage devices and reactive power compensation equipment separately.
In order to smoothen the output power of the wind farm, supercapacitors and flywheel energy storage devices can be used to achieve power fluctuation suppression [6], [7]. However, their energy storage density is limited, so they become costly in suppressing large-scale power fluctuation. Therefore, the hybrid energy storage device was proposed [8], [9], in which, wind farm power is divided into three parts. The high-frequency part with fast fluctuation is suppressed by supercapacitors, the intermediate-frequency part with slightly smooth fluctuation is suppressed by the batteries, and the low-frequency part with relatively flat fluctuation amplitude is used as the grid-connected power. Thus, the fluctuating power of the wind farm is eventually suppressed by the hybrid energy storage device. Although the methods above overcome the shortcoming of the low power density of a single energy storage device, its coordinated control strategy is more complicated. If the grid-connected wind farm still needs to stabilize the PCC voltage or suppress harmonics at the same time, additional installation of a static var compensator (SVC) or harmonic treatment device is necessary. However, it needs extra expense and makes the system structure more complicated [10].
Compared with the conventional two-level/three-level converters, the multilevel structure is preferable in high voltage and high power applications [11]. The modular multilevel converter (MMC) is a more promising topology than the neutral point clamped (NPC) converter, flying capacitor converter (FCC), and cascaded H-bridge converter (CHB). Because MMC has the advantages of simple control, good modularity, superior scalability, high efficiency, and lower output voltage total harmonic distortion (THD) [12], [13], [14]. When the battery energy storage system (BESS) is combined with MMC, the capability of reactive power compensation of BESS can be expanded. Moreover, it can achieve active and reactive power regulation in one device at the same time. That means it can solve the problems of output power and PCC voltage fluctuation in the wind farm, which tends to have good economic performance compared with adjusting the power fluctuation and PCC voltage through energy storage devices and reactive power compensation equipment separately. Besides, by controlling the output current of the MMC-BESS to mitigate the harmonic current generated by local nonlinear loads, the power quality of the grid-connected wind farm can be further improved.
Since Trintis et al. proposed the modular multilevel converter-based battery energy storage system (MMC-BESS) in 2011 [15], the novel topology has drawn a lot of attention among researchers [16], [17], [18], [19], [20], [21], [22]. Generally, the energy storage unit of MMC has two access methods [17], [18]. The first is that a large quantity of energy storage units is connected to the DC bus in series and parallel [19]. The second is that the energy storage unit is distributed to each submodule directly or through a nonisolated DC/DC converter. The latter is more popular than the former as it has the advantages of flexible control and strong fault tolerance, which is critical in high voltage and large capacity applications [20], [21], [22]. During the operation of MMC-BESS, the state of charge (SOC) of the energy storage unit in each submodule will differ from each other due to the aging degrees of the battery [23]. In order to improve the utilization of battery capacity, the balance control of SOC is indispensable and is a key control technology of MMC-BESS.
This paper investigates the control strategy of MMC-BESS, which can comprehensively realize power fluctuation suppression, PCC voltage regulation, and harmonic mitigation in wind farm. Simultaneously, three-layer balance control of SOC is proposed, which is essential to maintaining the normal operation of MMC-BESS. Compared with the SOC balance control presented in [17] and [18], the three-layer balance control of SOC proposed in this paper is realized by regulating the DC and fundamental component of circulating current directly, reconstructing the modulation wave respectively, which is simple and effective. The rest of this paper is composed of five parts. Section II gives the topology of MMC-BESS and then analyzes the energy flow of the whole device. Section III introduces the three-layer balance control of SOC in detail. The overall control of MMC-BESS including fluctuating power suppression, PCC voltage regulation, and harmonic mitigation in the grid-connected wind farm is illustrated in Section IV. Plenty of experimental results are given subsequently in Section V, which verify the effectiveness of the proposed control strategy. Finally, conclusions are drawn in Section VI.

A. TOPOLOGY AND MATHEMATICAL MODEL
The main circuit topology of three-phase three-wire MMC-BESS is shown in Fig.1(a), which is composed of two VOLUME 10, 2022 star-connected three-phase half-bridge cascaded converters (HBCC) in anti-parallel. Each phase consists of the upper and lower arm, which is formed through N cascaded submodules separately as shown in Fig.1(b). The upper and lower arm is connected to the midpoint of each pole via the buffer inductor and resistor, then the midpoint of the pole is directly connected to the PCC. As described in Fig.1(c), the SM is the half-bridge structure, including two IGBTs with their antiparallel diodes, and a capacitor connected in parallel on the DC side. At the same time, the energy storage unit which consists of several batteries in series is directly connected to the capacitor in parallel. The output voltage of the AC side of the SM is either equal to its capacitor voltage or zero, depending on the switching states of the two switches. Define the cascaded voltage of N submodules on the upper arm as v jp (j = a, b, c), and the total voltage of the lower arm as v jn . The virtual common DC side voltage is noted as V dc , and the upper and lower arms currents are defined as i jp and i jn (j = a, b, c), respectively. Then denote the output current of the device as i cj , whose positive direction is point to PCC. The PCC voltage is v Tj (j = a, b, c). The buffer inductor is marked as L F and the resistor as R F . i cp_N represents the capacitor current of the N th submodule of the upper arms, whose DC side voltage and AC side voltage are expressed as v bat_cp_N and v cp_N , respectively.
According to [24] and [25], equation (1) describes the external characteristics of MMC-BESS, and equation (2) describes the internal voltage and current characteristics.
e difj (j = a, b, c) represents the differential mode voltage that can be used to control the output current of MMC-BESS. e sumj (j = a, b, c) is denoted as the common mode voltage which can be used to control the circulating current as shown in (2). According to formula (1), the equivalent circuit of MMC-BESS is shown in Fig.2.

B. ENERGY FLOW IN MMC-BESS
Assuming that the modulation wave of the lower arms is msin(ωt + θ j ) (j = a, b, c), which is inverse to that of the upper arms. The initial phase angle of each phase is θ a = 0, Under phase-shifted carrier pulse width modulation (PSC-PWM), the total voltage of the upper and lower arms can be expressed by (3), which are both composed of DC and fundamental components.
Since the batteries are connected to the capacitor in parallel directly, the DC side voltage of the submodule is relatively stable. Therefore, the second harmonic component of the AC side current is neglected, which can be expressed by (4) where ϕ j represents the phase angle of the fundamental component of the output current, and γ j stands for the phase angle of the fundamental component of the circulating current.
The power of the upper arm, lower arm, and whole phase, marked as P jp , P jn , and P j (j = a, b, c), is obtained by multiplying (3) and (4), which can be expressed as It can be seen from (5) that the power of each phase P j is affected by the DC component of circulating current I cir_dc and the output current of the device I cj . By regulating I cir_dc , P j can be changed. The power of the arms P jp or P jn is affected by the DC and fundamental component of the circulating current (i.e., I cir_dc and I cir_50Hz ) and the output current of the device I cj . However, I cir_50Hz has the opposite effect on P jp and P jn , which means it can be controlled to regulate the power between the upper and lower arm without changing the phase power P j . The analysis above shows that the circulating current may change the energy flow between different phases as well as between the upper and lower arm. Hence, the SOC balance between different phases, between the upper and lower arm can be achieved by controlling the circulating current.

III. THREE-LAYER BALANCE CONTROL OF SOC
When MMC-BESS is put into operation and the output power of each submodule is the same, the difference in SOC value between batteries may gradually become larger due to the slight difference between batteries.
The coulomb counting method can be used to estimate the SOC of battery, which is shown as where SOC(0) is the initial SOC value of the battery and Q max represents the maximum charge of the battery.
As shown in (7), SOC jp , SOC jn , and SOC j are defined as the average SOC value between submodules in the upper arm, lower arm, and whole phase j (j = a, b, c), respectively. SOC abc is the average SOC value of the entire device. The proposed three-layer balance control strategy of SOC for MMC-BESS is illustrated in Fig.3.

A. SOC BALANCE CONTROL BETWEEN DIFFERENT POLES
According to the previous analysis, the energy between different phases can be distributed to achieve the SOC balance by controlling the DC component of the circulating current I cir_dc . Hence, the first layer balance control between different poles is shown in Fig.3(a). In Fig.3(a), the average SOC value of each phase is subtracted from the average SOC value of the whole system, then the error is amplified by the proportional controller to obtain the reference of the DC circulating current. Meanwhile, the circulating current is passed through a low-pass filter (LPF) to obtain the feedback value of the DC circulating current. Then the error between the reference and feedback value is sent to the PI controller to obtain the modulation wave V j_cir_dc , which can realize the SOC balance control between different poles.

B. SOC BALANCE CONTROL BETWEEN UPPER AND LOWER ARM IN THE SAME POLE
By controlling the fundamental component of the circulating current I cir_50Hz , the energy between the upper and lower arm in the same pole can be distributed to realize the SOC balance between them without changing the total energy of the pole. The control scheme is illustrated in Fig.3 If the fundamental component of the circulating current is positive, the upper arm transfers energy to the lower arm, and vice versa. Therefore, the difference in the average SOC value between the upper and lower arm is amplified by the proportional controller, and the result is used as the amplitude of the fundamental component of the circulating current reference, whose phase is consistent with the PCC voltage. Then the error between the reference and feedback value is adjusted by the proportional resonant (PR) regulator to obtain the modulation wave V j_cir_50Hz . Thus, the SOC balance between the upper and lower arm in the same pole can be achieved. The PR regulator is applied to extract the fundamental component of the circulating current, so its resonant frequency is designed at 50Hz.

C. SOC BALANCE CONTROL BETWEEN SUB-MODULES IN THE SAME ARM
Since the submodules in the same arm are connected in series, the energy distribution of these submodules cannot be realized by controlling the circulating current. At this time, reconstructing the modulation wave of each submodule is proposed. As shown in Fig.3(c), the average SOC value between the arm and individual submodule is sent to the proportional controller. Then the result is judged by the Judge function, which is shown in Fig.4(a), to get the modulation factor k jp_i/jn_g of the submodule. In this way, the modulation wave of each submodule in the same arm is reconstructed, which means the energy of each submodule can be distributed. Hence, the SOC balance control between submodules in the same arm can be realized. At this time, on the basis of the balance control in the first two layers, the SOC balance of all submodules can be realized.
The Judge function is employed to extend the working time of the submodule with a relatively small SOC value in the case of charging by amplifying the modulation wave, which means that it can be charged more. Similarly, the working time of VOLUME 10, 2022 the submodule with a larger SOC value will be increased in the case of discharging to make it discharge more. More importantly, the method above does not change the equivalent output voltage waveform of the arm. When the SOC value of SM 2 is bigger than that of SM 1 and MMC-BESS is charging, the basic principle of reconstructing the modulation wave of PSC-PWM is illustrated in Fig.4(b). As shown in Fig.4(b), when the condition of k 1 v ref_cp > v c1 > v ref_cp is true, SM 2 is forced to output low level while the final equivalent output voltage of the arm is the same as when both submodules are modulated by v ref_cp . In this way, the SOC of each submodule can be balanced while the harmonics of the equivalent output voltage of the arm are not increasing.

IV. IMPROVEMENT OF POWER QUALITY IN GRID-CONNECTED WIND FARM BY MMC-BESS A. PCC VOLTAGE AND REACTIVE POWER
As shown in Fig.5(a), a simplified diagram of the gridconnected wind farm is given. The active power output by the wind farm is greatly determined by wind speed, which has great volatility and randomness. Besides, the sudden change of local load or severe short-circuit fault will cause the PCC voltage to be over/under voltage. Moreover, due to local nonlinear loads, harmonic pollution will occur if it is not treated effectively. Therefore, the power quality in the gridconnected wind farm faces great challenges. In this paper, it is proposed to install MMC-BESS at PCC in parallel near the wind farm to improve the power quality of the system as shown in Fig.5(a).
In order to analyze the characteristic of PCC voltage, the wind farm and MMC-BESS in Fig.5(a) can be considered as a part of the load connected to the grid. Meanwhile, the transformer turns ratio is assumed to be 1:1 and the equivalent resistance of the transmission line is ignored. In this way, the relationship between active power, PCC voltage, and load can be described by (8).
In Eq. (8), V S is the ideal grid voltage. V T , X , and Z L represent the PCC voltage, line impedance, and load impedance, respectively. P stands for the active power of the whole system, whose power factor angle is ϕ.
Supposing the load is a pure resistor, the maximum active power is given in (9) when the norm of load impedance is equal to the norm of line impedance.
If the characteristic of load changes, the equations P/P max and V T /V S can be derived as follows According to (10), by changing the load power factor, the P-V characteristic nose curve of the system can be obtained, which is shown in Fig.5(b). As can be seen from Fig.5(b), the maximum active power varies with the load power factor. The system needs to work in the interval above the critical point.
For resistive-capacitive loads, the maximum active power absorbed by loads is higher than that of purely resistive loads, and the PCC voltage is higher than the grid voltage. If the load appears resistive-inductive, the maximum active power absorbed by loads is lower than that of purely resistive loads situation, and the PCC voltage is lower than the grid voltage. The inductive or capacitive loads will decrease or increase the PCC voltage, deteriorating the power quality of the system.

B. FLUCTUATING POWER SUPPRESSION
Supposed the local load is ignored, the power flow of the gridconnected wind farm can be calculated as P g represents the active power absorbed by the grid. P wf is denoted as the active power generated by the wind farm. P mb is expressed as the active power of MMC-BESS, and P f is indicated as the active power loss of the entire system which can be neglected for the reason of a small amount. The fluctuating active power generated by the wind farm, which varies with wind speed, will weaken the system's stability. Hence, it needs to be smoothed. Since the high-frequency part of the wind farm power is the main suppression target, a first-order low pass filter (LPF) can be used to design the fluctuating power suppression strategy, which is illustrated in Fig.6. The active power output by the wind farm is filtered through a first-order LPF to obtain the expected active power, which is subtracted from the input of the filter to obtain the active power reference P * mb of MMC-BESS. Then multiply P * mb by 2/3 and 1/V Td to get the active current reference I * d of MMC-BESS. By controlling the active current, MMC-BESS can output active power to counteract the fluctuating power of the wind farm, realizing power fluctuation suppression. Consequently, the grid can obtain relatively stable active power. In Fig.6, τ = 1/2πf L , and f L is the cut-off frequency of the LPF.

C. PCC VOLTAGE REGULATION
If considering the local loads, sudden changes in the load will cause PCC voltage fluctuations. According to the P-V characteristic nose curve shown in Fig.5(b), PCC voltage can be regulated to a specified range by controlling MMC-BESS to inject a certain amount of reactive power into the grid.
As shown in Fig.7, the PCC voltage is detected and sent to the synchronous rotating coordinate firstly, whose d-axis is defined to be coaxial with the three-phase equivalent electromotive force. Then, after the equal amplitude coordinate transformation, the d-axis component of the voltage represents the amplitude of phase voltage of PCC, which is subtracted with the reference of the rated amplitude of PCC voltage. Subsequently, the error is regulated by the PI controller to obtain the reference of the q-axis current of MMC-BESS. By controlling the corresponding reactive current, MMC-BESS can inject required reactive power into the grid, realizing over/under voltage regulation.

D. HARMONIC MITIGATION
As shown in Fig.5(a), since local loads in the grid-connected wind farm usually consist of nonlinear loads, it is necessary to suppress harmonic currents generated by the nonlinear loads to avoid harmonic pollution. Compared with installing a harmonic suppression device at PCC additionally, using MMC-BESS for harmonic mitigation is a more economical solution.
In order to achieve harmonic suppression, it is essential to extract the desired harmonics i * Lk from the nonlinear load current i L . Among the various selective extraction methods, Recursive Discrete Fourier Transform (RDFT) is the most preferred one due to its low computational burden and fast dynamic time [26], which can be expressed as where K m is the maximum harmonic order to be concerned. A k and B k are the cosine and sine amplitudes of k th harmonic. ω 1 is the fundamental angular frequency of the grid. n is the present instant with the discrete cycle τ . N is the number of sampling points in each fundamental cycle T 1 , therefore Based on RDFT, Fig.8 shows the harmonic extraction strategy in the grid-connected wind farm. As can be seen from Fig.8(b), harmonic reference i * Lhαβ is the sum of desired harmonics i * Lk , which are selectively extracted from load current i L by RDFT k as shown in Fig.8(a). Then, through αβ/dq coordinate transformation, the harmonic reference in the dq frame can be obtained, which are marked as i * Lh_d and i * Lh_q . Finally, by the current controller in the dq frame, MMC-BESS can output currents with the same magnitude and direction as the harmonic currents, realizing harmonic mitigation in the grid-connected wind farm.
The overall control architecture of MMC-BESS for the grid-connected wind farm is shown in Fig.9, which includes VOLUME 10, 2022  fluctuating power suppression, PCC voltage regulation, harmonic mitigation, and the three-layer balance control of SOC. First, in the synchronous rotating coordinate, the parallel-connected PI controller and repetitive controller (RC) are adopted to track the reference of active currents, reactive currents, and harmonic currents which are obtained from fluctuating power suppression, PCC voltage regulation, and harmonic mitigation control strategy, respectively. Then, due to the coupling of the d, q axis current caused by the connected inductance, the state variable feedback cross-decoupling of the d, q axis current is carried out. The PCC voltage feedforward is also adopted to improve the dynamic performance of the system. Next, through dq/abc coordinate transformation, the output voltage reference v ref in the three-phase stationary coordinate can be obtained. Finally, in order to achieve SOC balance of all submodules, superimposing the modulation reference V j_cir_dc and V j_cir_50Hz on the original reference v ref , and multiplying the result by the proportional coefficient k jp_i/jn_g , the final modulation waves are obtained. Through PSC-PWM, the drive signals are finally got.

V. EXPERIMENTAL VALIDATION
In order to verify the correctness of the proposed control strategy, a three-phase three-wire downscaled laboratory prototype of MMC-BESS is built as shown in Fig.10, whose experimental parameters are given in Table. 1. Each arm consists of two submodules and thus the device has twelve submodules in total.  At first, V l and E SM are set to 20V and 24V respectively when SOC balance control, fluctuating power suppression, and PCC voltage regulation were implemented by MMC-BESS. At this time, the DC side of each submodule is connected with two 12V/100Ah lead-acid batteries in series, which is shown in Fig.10(b). Then, in order to verify the feasibility of the proposed harmonic mitigation strategy further, the DC side of each submodule is connected with their DC-link capacitor only since the number of lead-acid batteries is limited in the laboratory. Accordingly, V l and E SM are increased to 60V and 72V respectively. It should be noted here that the DC side voltage of each submodule can be conveniently adjusted by changing the number or voltage rating of batteries in practical applications. Similarly, the phase-to-phase voltage can be adjusted by the voltage regulator easily in the laboratory.
Under laboratory conditions, the short-term fluctuating active power of the simulated wind farm is directly generated through the MATLAB random function. As shown in Table.1, load A and load B are switched on/off to simulate under/over voltage in the grid-connected wind farm. A typical threephase bridge diode rectifier (Load D) is chosen as a nonlinear load, whose DC side is connected with a 3 resistor and 0.5mH inductor in series. After applying PSC-PWM, the equivalent switching frequency of the device is 4kHz while the switching frequency of a single submodule is 1kHz. Therefore, the prototype only suppresses the 5 th , 7 th , and 11 th harmonics selectively when the harmonic mitigation strategy was implemented by the prototype due to the limitation of the equivalent switching frequency.

A. SOC BALANCE CONTROL
For simplification, (13) is used to calculate the SOC value of each submodule, where V omax = 27V is the maximum open-circuit voltage of the battery, and V omin = 18V is the minimum open-circuit voltage of the battery. The initial SOC of the energy storage unit at all layers can be calculated by (7) and (13), and the results are shown in Table.2. Under ideal equilibrium conditions, the expected SOC value of energy storage units at all layers is 66.67%, and the expected standard deviation of SOC of all submodules is 0. It can be calculated from Table.2 that before SOC balance control is implemented, the average SOC value of the first layer which is among the three phases is 49.54%. The average SOC values of the second layer which is between upper and lower arms in the same phase are 40.33%, 59.67%, and 48.61%, respectively. The average SOC value of all submodules also known as the third layer is 49.54%, whose standard deviation is 23.55. It can be seen that without the three-layer balance control, the SOC of the energy storage unit at all layers is far from the expected value. Simultaneously, the standard deviation of the submodules is large, and the SOC distribution is relatively scattered.
The active power reference of MMC-BESS is set to 110W, while the reactive current reference is set to 0. Thus the MMC-BESS is charging when assuming the positive direction of the grid-connected current is from PCC to MMC-BESS. Fig.11 shows the result when the three-layer balance control is employed during charging. First, the experiment of SOC balance control between different poles is carried out. It can be seen in Table.2 that at the beginning, the average value of SOC in each phase is (SOC b = 59.67%) > (SOC c = 48.61%) > (SOC a = 40.33%). The current waveforms of the energy storage unit in the upper arms are illustrated in Fig.11(a). After the first layer balance control strategy is employed, a positive DC current appears in phase A and phase C whose average SOC values are relatively smaller. While a negative DC current appears in phase B whose average SOC value is larger than phase A and phase C before balance control.
Before balance control, the average currents of the upper arms in each phase are calculated as 0.23A, 0.45A, and 0.03A. After implementing the first layer balance control VOLUME 10, 2022 strategy, the average currents are 0.58A, −0.37A, and 0.34A. According to the change of average currents of each phase, it can be seen that positive DC circulating currents occur in phase A and phase C whose initial average SOC values are smaller, while a negative DC circulating current has occurred in phase B whose initial average SOC value is higher. Thus the energy is transferred from phase B to phase A and phase C, which proves the effectiveness of the SOC balance control between different poles.
Second, the experiment of SOC balance control between upper and lower arms in the same pole is carried out. It can be seen in Table.2 that, at the initial time, the SOC average value of the two submodules of the upper and lower arms in phase C is (SOC cn = 63.33%) > (SOC cp = 33.89%). On the basis of the first layer control, the second layer control is employed. The waveform of the energy storage unit current is shown in Fig.11(b), which was observed from the upper and lower arm submodules in phase C. It can be seen that the envelope of i cp_1 changes significantly while that of i cn_1 remains basically the same after implementing the balance control.
In Fig.11(b), the submodules' DC currents of the upper and lower arm in phase C are calculated as 0.26A, 0.38A, and the RMS values of the fundamental current are 1.47A and 1.7A respectively. After employing the second layer balance control strategy, the DC currents are 0.35A, 0.32A, and the RMS values of the fundamental currents are 1.84A and 1.52A respectively. As MMC-BESS is charging, the RMS value of the fundamental current in the upper arm increases after the second layer balance control strategy is employed while that in the lower arm decreases, indicating that the fundamental circulating current is negative at this time and the energy of lower arm flows into the upper arm. At the same time, the average value of the submodules' current in the upper arm becomes larger, which means its charging power also becomes larger. While the lower arm is just the opposite. That also indicates the energy of the lower arm is transferred to the upper arm, which proves the effectiveness of the SOC balance control between the upper and lower arms in the same pole.
Finally, the experiment of SOC balance control between submodules in the same arm is carried out. As seen in Table.2, it can be known that the SOC values of the two submodules in the upper arm in phase C are (SOC cp_1 = 4.44%) < (SOC cp_2 = 63.33%). Based on the first and second layer balance control, the third layer control is employed. The current waveforms of the two submodules' energy storage units in the upper arm of phase C are obtained and shown in Fig.11(c). From Fig.11(c), it can be seen that the current duty ratio of SM 1 , which has a smaller SOC value than SM 2 before the third layer balance control, has increased, while the current duty ratio of SM 2 has decreased.
Before and after the third layer balance control strategy was implemented, the average current values of SM 1 and SM 2 changed from 0.1226A and 0.1705A to 0.2595A and 0.132A respectively, indicating that the charging power of SM 1 increased while the charging power of SM 2 decreased.
The energy in the arm is transferred from SM 2 to SM 1 , which proves the utility of SOC balance control between submodules in the same arm. From the results listed in Table.2, the radar chart of the SOC values of the energy storage units at all layers before and after employing the three-layer balance control can be obtained, which is illustrated in Fig.12. The radar chart of the SOC values of different poles is shown in Fig.12(a), whose average value is 64.72%, which increases 130% compared with the initial value. Fig.12(b) represents the radar chart of the SOC values of the upper and lower arms in the same pole, whose average values are 64.23%, 65.59%, and 64.36% respectively, which increases 159%, 109%, and 132% respectively compared with the initial. Fig.12(c) expresses the radar chart of the SOC values of three-phase twelve submodules, and the average SOC of all submodules is 64.72%, which is an increase of 130% compared with the initial, and the standard deviation is 2.45, which is a decrease of 961%. It can be seen from Fig.12 that the implementation of three-layer balance control makes the SOC of each energy storage unit close to the expected value, which means the equilibrium effect is good. The standard deviation of SOC values is decreased, proving that the proposed control strategy is effective.

B. FLUCTUATING POWER SUPPRESSION
Assuming that the short-term grid-connected fluctuating power of the wind farm is given in Fig.13(a), which is also the high-frequency part of the wind farm's active power. The rated active power output by the wind farm is 200W, and the maximum fluctuating power in Fig.13(a) exceeds 50W, which is 0.25 p.u. Obviously, it is beyond the value of 0.1 p.u. specified by the standard [27].  For the convenience of analysis, P wf is directly inverted as the output active power reference P mb * of MMC-BESS. The local load in Fig.5(a) is not considered, and the line inductor is 0.5mH to simulate the grid-connected wind farm. Fig.14(a) shows the dynamic waveform of line voltage v ab and phase current i cb when employing fluctuating power suppression strategy and Fig.14(b) is a partially enlarged waveform of Fig.14(a). From Fig.14(b), we can see that i cb leads/lags v ab 30 • and 150 • . Since the positive direction of the current is pointing to the PCC, it means MMC-BESS absorbs/emits active power to suppress fluctuating power output by the wind farm. The calculated instantaneous power P mb of MMC-BESS is shown in Fig.13(b), P wf and P mb are added to obtain the wind farm's fluctuating power after suppression. From Fig.13(c), it can be seen that MMC-BESS can smoothen the fluctuating power output by the wind farm quickly, and achieve peak-shaving and valley-filling of fluctuating power. The maximum fluctuating power within 1min in Fig.13(c) is 10W, i.e., 0.05 p.u., which is less than 0.1 p.u. and meets the standard.

C. PCC VOLTAGE REGULATION
As shown in Fig.5(a), the local load which is composed of Load A and Load B in the laboratory is considered, and the line inductor is 6mH. Then the load is switched on and off to simulate the PCC voltage fluctuation of the grid-connected wind farm.
First, the waveforms of v ab and i ca when PCC voltage drops are illustrated in Fig.15(a). As shown in Fig.15(a), only Load A is turned on during t 0 , and the PCC line voltage is kept near the rated value through the voltage regulator. When load B is turned on during t 1 , the PCC line voltage decreases 10.6% from 1.0 p.u. to 0.894 p.u. Then the MMC-BESS is put into operation. And the PCC voltage is adjusted during t 3 , where the MMC-BESS works under capacitive conditions, and the PCC line voltage returns to 0.998 p.u., which means that the under-voltage is only 0.2%. Fig.15(b) shows the enlarged waveforms of PCC under-voltage adjustment. Since the positive direction of the compensation current points to the PCC, v ab leads i ca 122 • , indicating that MMC-BESS is controlled as a capacitor to support PCC voltage.
Secondly, the waveforms of v ab and i ca are illustrated in Fig.15(c) when the PCC voltage rises. Load A and load B are turned on at the same time during t 0 , and the PCC line voltage is maintained near the rated value through the voltage regulator. When load B is turned off during t 1 , the PCC line voltage increases 13.0% from 1.0 p.u. to 1.13 p.u. Then the MMC-BESS is put into operation, and the PCC voltage is adjusted during t 3 , where the MMC-BESS works under inductive conditions and the PCC line voltage return to 1.004 p.u., which means that the over-voltage is 0.4%. Fig.15(d) shows the enlarged waveforms of PCC over-voltage adjustment, v ab lags i ca 63 • , indicating that the MMC-BESS is controlled as an inductor to reduce the PCC voltage.
It can be seen that MMC-BESS can adjust the PCC voltage well whether over/under voltage so that the PCC voltage fluctuation range is limited within the standard value, which meets the requirements of the standard [28]. The PCC voltage will decrease if the inductive load turns on, and it will rise if the load turns off, while the capacitive load will be the opposite. Through the proposed PCC voltage regulation strategy illustrated above, the MMC-BESS is controlled as a capacitor or inductor, and the PCC voltage fluctuation range can be limited to ±5% of the rated value.

D. HARMONIC MITIGATION
Both Load C and Load D are turned on to simulate harmonic pollution in the grid-connected wind farm, whose parameters are listed in Table.1. As shown in Fig.16(a), the load currents i L is distorted severely and the THD of i La is 14.8%. Before the harmonic mitigation control strategy is implemented, the grid currents i s is equal to i L . Therefore, the THD of i sa is also 14.8%, which cannot meet the limits of the IEEE std.519-2014 [29].
The results of applying the proposed harmonic mitigation strategy with the prototype are shown in Fig.16(c) and (d).
As mentioned before, due to the limitation of equivalent switching frequency, the prototype only suppresses the 5 th , 7 th , and 11 th harmonics selectively. It can be seen from Fig.16(c) that after applying the harmonic mitigation strategy by the prototype, the waveform of grid currents i s is almost sinusoidal. The THD of i sa is reduced from 14.8% to 4.0%, which can meet the standard [29].
The dynamic waveform of harmonic mitigation is shown in Fig.17. Both Load C and Load D are turned on at t 1 . With the proposed harmonic mitigation strategy, the prototype outputs harmonic suppression currents quickly to keep grid currents sinusoidal. Hence, through the proposed harmonic mitigation strategy by MMC-BESS, the harmonic pollution in the gridconnected wind farm can be alleviated, and the power quality can be further improved.