A Grid Frequency Support Control Strategy of the Three Phase Cascaded H-Bridge Based Photovoltaic Generation System

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I. INTRODUCTION
In order to solve global energy crisis and environmental problems, renewable energy sources, especially photovoltaic (PV) generation has been developed rapidly during last decades [1], [2]. With the increased PV generation penetration into the power system, the proportion of conventional synchronous generators has been reduced dramatically. This leads to the weakened power system response to power fluctuations and system faults, bringing potential risks to the grid stability [3].
Different from wind turbines, there are no mechanical rotation devices in the PV generation system. Therefore, The associate editor coordinating the review of this manuscript and approving it for publication was B. Chitti Babu .
no kinetic energies, such as ones stored in the turbine and drive train of wind turbines, can be released to support grid frequency for the PV generation system [4]. In addition, PV cells usually operate at maximum power point tracking (MPPT) mode [5]. When the grid frequency drops, their output active power can't be increased to execute the frequency response control.
To address the abovementioned issue, grid frequency support from the PV generation system has attached wide attention [6]- [9]. The fast output power change of the PV generation system can reduce the power unbalance in the grid, contributing to the improvement of grid frequency dynamic characteristics. Inertia and damping characteristics were emulated with the virtual synchronous generator (VSG) control of the battery energy stored quasi-Z source inverter based PV generation system in [10]. A decentralized VSGbased adaptive coordinated control strategy was proposed for islanding microgrids consisting of PV generation combined with battery energy storages in [11]. Dynamic performances of the system were enhanced. Nevertheless, the inverter output power change was from energy storage devices in the schemes above, resulting in the increased system volume, weight, cost and maintenance workload. The PV cell operation point can be moved from the maximum power point, meaning that it operates at deload mode, and some power is reserved. In terms of control strategies, a predictive PV inverter control method, coupled with a maximum power point estimation method was proposed in [12]. Fast and accurate active power response to a demanding range of grid frequency events was provided. A novel adaptive PV frequency control strategy was proposed to reserve the minimum power for grid frequency support in [13]. Based on a machine learning model trained, system frequency response under various system conditions was predicted, and an adaptive allocation of PV headroom reserves was made. An event-triggering power reserve control for the three phase two-stage PV generation system, consisting of two operation modes, was proposed in [14] to track the maximum power point accurately with fast dynamics or increase output power with reservation. The PV generation system was regulated as an adaptable current source with reserved power for grid frequency support.
In order to connect the medium voltage grid directly, a cascaded H-bridge (CHB) multilevel inverter can be used as the grid-connection interface in the PV generation system. PV strings fulfill the requirement of independent DC sources supplying for the CHB topology [15]. The voltage stress of switching devices is reduced, and the inverter output voltage and current quality is improved [16]. With the direct connection between PV strings and DC-links, DC-DC converters can be eliminated, leading to further reduced system loss and volume, and enhanced efficiency [17]. Few literatures have studied the grid frequency support control of the CHB based PV generation system. An H-bridge inverter, directly connected to a battery is added in a single phase CHB based PV generation system in [18]. Each PV string operates at its maximum power point, and the battery can be easily adopted to snubber the power difference between power demands and system generation. However, increased system output power when supporting grid frequency is still from energy storage devices. A power reserve control strategy was proposed for the single phase CHB converter in [19]. The PV cell with the maximum output power is selected as the reserved cell. When the grid frequency drops, the reserved power is fast released to support grid frequency. Nevertheless, over-modulation risks of H-bridge modules corresponding to other cells are increased. Furthermore, the single phase PV generation system was chosen in both literatures above. In the more common three phase system, the power unbalance between H-bridge modules introduces unbalanced three phase transmission power and grid-connected current. Although the three phase grid-connected current unbalance can be improved with the zero-sequence voltage injection, the balanced three phase grid-connected current can't always be obtained due to the DC-link voltage limit, when the three phase transmission power being unbalanced severely [20]- [22]. Normally, a three phase CHB based PV generation system should be controlled to maximize the solar energy captured. The three phase transmission power is expected to achieve maximum balance during both power reserve and grid frequency support operation. High quality grid-connected current should always be maintained during the operation stages above. This is the main challenge for the CHB based PV generation system at deload mode, compared with common PV generation systems.
Based on the analysis above, a grid frequency support control strategy of the three phase CHB based PV generation system is proposed in this paper. During power reserve operation, the reserved power required is obtained with the coordinated control of all PV strings. The system output power is increased fast according to the grid frequency change when participating in grid frequency support, leading to the improvement of grid frequency dynamic characteristics. Different from common methods that controlling three phase grid-connected current to be balanced after the occurrence of unbalanced three phase transmission power, the main contribution of this paper is proposing a control method to regulate the transmission power between modules to achieve maximum balance. The reserved power is distributed between modules only with the correction of DC-link voltage references. The maximum balance of the transmission power between modules and three phase grid-connected current can be ensured, resulting in the reduced H-bridge inverter over-modulation risk and improved grid-connected current quality. Finally, the effectiveness of the control strategy proposed is validated with both simulation and experimental results.

A. TOPOLOGY OF THE CHB BASED PV GENERATION SYSTEM
The topology of the three phase CHB based PV generation system with Star-connection is shown in Fig. 1. An H-bridge inverter is connected to a PV string directly to form an H-bridge module. n H-bridge modules are cascaded in each phase. C and L are the DC-link filter capacitance and grid side filter inductance, respectively. I PVxj and V dcxj are the output current and DC-link voltage of the PV string in the jth H-bridge module in Phase x (x = A, B, C, j = 1, 2, . . . , n). v x and i x are the three phase grid voltage and grid-connected current, respectively. With the three level voltage obtained from each H-bridge module, 2n + 1 level system output voltage expressed below can be achieved.  where m xj is the modulation index of each H-bridge module.
According to the Kirchhoff law, the relationship between system output voltage and current is: When the output power decreases in some phase due to partial shading, accumulated dust, and so on, unbalanced three phase transmission power can introduce unbalanced three phase grid-connected current. Zero sequence voltage injection methods such as fundamental frequency zero-sequence injection, weighted min-max zero-sequence injection, double 1/6 three harmonic injection, optimal zero-sequence injection can be applied to achieve balanced three phase grid-connected current output in the case of unbalanced three phase transmission power [23]. However, due to DC-link voltage limit, only the power unbalance below 20% can be handled even with the optimal zerosequence voltage injection method with the best balancing capability [24]. Therefore, to address the three phase gridconnected current unbalance issue, it is essential to control all PV string output power to achieve maximum balance.

B. ANALYSIS ON STABLE DELOAD OPERATION AREA
One P-V characteristic curve of a PV string is shown in Fig. 2. The PV string output power ranges from 0 to P mpp , the maximum output power corresponding to the maximum power point. Therefore, the power reserve can be achieved by changing its operation point from the maximum power point. During grid frequency support, the reserved power is released with the increased PV string output power by changing its operation point. There are two voltages corresponding to every power point except the maximum one. On the left of the maximum power point, the relationship between the PV string voltage V dc and its output power P pv is expressed as dP PV /dV dc > 0. On the right side, it is expressed as dP PV /dV dc < 0. The PV string operation area should be selected at deload mode for its stable operation.
The PV string output power is expressed in equation (4) according to the power flow relationship on both sides of the DC-link capacitor.
P out is the H-bridge module output power. P c is the capacitor charging or discharging power. After the linearization of any operation point (V 0 , P 0 ) on the operation curve, equation (5) can be obtained.
The eigenvalue is: The system can operate stably only when all eigenvalues of its characteristic equation are negative real numbers or conjugate complex numbers with negative real parts. Therefore, the PV string should be controlled to operate on the right of the maximum power point at deload mode.

III. OVERALL CONTROL OF THE THREE PHASE CHB BASED PV GENERATION SYSTEM
The overall control diagram of the three phase CHB based PV generation system is shown in Fig. 3  from the grid. Since the AC signal zero steady error can be obtained with a proportional resonant (PR) regulator, it is chosen to achieve the closed-loop current control in the αβ coordination system. Therefore, complex coordination transformation and decoupled control can be avoided, leading to improved system dynamic characteristics. The angle used in the coordination transformation is obtained based on the grid voltage measured with a phase locked loop (PLL). A feedforward voltage compensator is implemented by adding the filter inductance voltage reference from the PR regulator to the grid voltage components in the αβ coordination system to avoid high transient current during grid voltage sags [17].
Each H-bridge inverter voltage reference is calculated by dividing v * x by n, which is the number of cascaded modules in one phase. In order to maintain stable system operation with different transmission power between modules, H-bridge inverter voltage references should be modified. Since the sum of all 3n DC-link voltages has been controlled to track its reference in the outer voltage loop, 3n-1 voltages are selected at random and controlled to track their corresponding references, resulting in the closed-loop control of all DC-link voltages. Take the first H-bridge inverter in Phase A as an example, a PI regulator is used to calculate the amplitude of its compensation voltage with the error between V * dca1 and V dcfa1 . The compensation voltage v a1 is obtained by multiplying the unit sine signal with the same phase as the output current in Phase A. The H-bridge inverter final output voltage reference is calculated by adding v a1 to v * a /n. Similarly, all other selected H-bridge inverter output voltage references are obtained. The compensation control is not executed for the unselected H-bridge module, in other words, its compensation voltage is set 0. At last, phase-shifted sinusoidal pulse width modulation (PS-SPWM) is used to generate gate signals of all 3n H-bridge inverters.
Power reserve and grid frequency support can be achieved only by modifying each DC-link voltage reference, meaning that adding V dca1 to the original voltage reference in Fig. 3. Therefore, the consistency of the control strategy can be ensured. The selection of modified H-bridge modules and the modification value calculation will be illustrated in detail below.

IV. CALCULATION OF DC-LINK VOLTAGE REFERENCE MODIFICATION DURING POWER RESERVE AND GRID FREQUENCY SUPPORT A. RESERVED POWER CALCULATION
During power reserve operation, three phase CHB based PV generation system reserved power P res (t) can be calculated according to [25]. During grid frequency support operation, the increased output power reference P s (t) is shown below based on the grid frequency measured.
k and J are the active power droop coefficient and moment of inertia, respectively. ω g (t) and ω 0 are the grid frequency and its rated value, respectively. During grid frequency support operation, the system reserved power reference is calculated in equation (8) according to P s (t) obtained above and P res (t 0 ), which is its initial value at the beginning moment of grid frequency support t 0 . P res (t) = P res (t) , Power reserve P res (t 0 ) − P s (t) , Grid frequency support (8)

B. SELECTION OF POWER RESERVE UNITS AND DISTRIBUTION OF RESERVED POWER
In order to achieve the transmission power balance between H-bridge modules during power reserve and grid frequency support, a power distribution control method is proposed to track the reserved power reference P res (t). MPPT control is executed at some interval, such as 10 min, to obtain the maximum available output power of all PV strings. Based on the power obtained, PV strings at deload mode are selected, and the output power reference P * is calculated according to the flow chart shown in Fig. 4   reducing the corresponding PV string output power from P[i] to P[i + 1]. According to the reserved power reference P res (t) in equation (8), the minimum m value satisfying inequality (9) is calculated, and the result is saved to a variable s. The corresponding PV strings are selected as the power reserve units.
m is an integer between 1 and 3n-1, and s is the number of modules at deload mode. If inequality (9) can't be satisfied even when m = 3n-1, all PV strings should operate at deload mode. For example, it is assumed that all PV string maximum available output power is shown in Fig. 5. Inequality (9) is satisfied when m = 3, and the three PV strings, whose maximum available output power corresponding to P [1], P [2] and P [3], are controlled to operate at deload mode. The other PV strings still operate at MPPT mode. Then, output power references of the selected modules at deload mode are calculated. When some PV strings operate at deload mode, their output power references are same. When all PV strings operate at deload mode, all output power references are same. The output power reference P * of the modules at deload mode is:

C. MODIFICATION OF DC-LINK VOLTAGE REFERENCES
According to the calculated output power reference P * , the closed-loop power control is executed for the modules selected. PI regulators are used to calculate DC-link voltage modification values. For example, if the PV string corresponding to the first H-bridge module in Phase A operates at deload mode in Fig. 6, its closed-loop power control is enabled. The DC-link voltage modification value V dca1 is calculated with a PI regulator, whose input is the error between the actual output power P a1 and its reference P * . Then, V dca1 is added to V mppa1 , corresponding to the module maximum power point voltage, to obtain the final DC-link voltage reference. At last, the PV string operates on the right of the maximum power point in Fig. 2, and the output power is P * . It should be noted that the three phase CHB based PV generation system with the proposed control strategy still can contribute to the improvement of grid frequency dynamic characteristics when the grid frequency increases. Furthermore, the maximum balance of the transmission power between modules and three phase grid-connected current can still be maintained.

V. SIMULATION ANALYSIS
A three phase CHB based PV generation system simulation model is built in Matlab/Simulink to verify the effectiveness of the control strategy proposed. The 1Soltech 1STH-215-P PV cell model in the Simulink library is used. Each PV string is composed of 32 × 8 cells, and the rated power is 55 kW with the temperature 25 • and illumination 1000 W/m 2 . The grid is modeled with a synchronous generator including an excitation regulator and a speed governor. The system main parameters are shown in Tab. 1. The ambient temperature is kept constant, 25 • . Firstly, all PV strings operate at MPPT mode. The power reserve control is executed at 1 s. The reserved power is set 10% of the system output power. At 2 s, a 150 kW load is connected to the grid. The three phase CHB based PV generation system is controlled to support grid frequency with the control strategy proposed. Different illuminations are set for some PV strings to emulate their deload operation, and all PV strings deload operation, respectively.

A. SOME PV STRINGS OPERATING AT DELOAD MODE
The illumination corresponding to the jth H-bridge module in Phase x is expressed as S xj . The illumination is set below: S a1 = 700 W/m 2 , S a2 = 900 W/m 2 , S a3 = 970 W/m 2 , S b1 = 800 W/m 2 , S b2 = 950 W/m 2 , S b3 = 1000 W/m 2 , S c1 = 750 W/m 2 , S c2 = 850 W/m 2 , S c3 = 1000 W/m 2 . Simulation results are shown in Fig. 7, in which each DClink voltage shown in (a), PV string output power shown in (b), the sum of all PV strings output power shown in (c), grid frequency shown in (d), and grid-connected current shown in (e). It can be observed that each PV string operates at its maximum power point individually with the MPPT control before 1 s, leading to the maximum system output power. All PV strings except the ones corresponding to Module a1, b1, and c1 whose operation modes remain unchanged, are selected as power reserve units. Power reserve with 10% system output power is achieved by increasing their terminal voltages. More power losses occur for the modules with more output power when operating at MPPT mode. The transmission power unbalance between H-bridge modules is reduced. The power loss in each PV string depends on its maximum available output power difference and system reserved power demand. The connection of the load leads to the dropping of the grid frequency from 2 s. Based on the power calculation in equation (8), the reserved power has been distributed between H-bridge modules with the control strategy proposed during grid frequency support. At last, the PV string corresponding to Module c2 operates at MPPT mode again, and the output power of the rest five PV strings at deload mode is increased to the same value. The whole system output power is increased fast from 390 kW to  and damping are enhanced, and the obvious improvement of grid frequency dynamic characteristics is achieved. When the control method in [19] is used in the same condition, each PV string output power and grid-connected current are shown in Fig. 8. Since only Module c3 with maximum output power at MPPT mode is selected as the power reserve unit, its dramatically reduced output power exacerbates the power unbalance between H-bridge modules during power reserve operation. This results in the occurrence of the overmodulation in the modules with more output power, and the distortion and unbalance of three phase grid-connected current are caused. By contrast, the power balance between modules is maintained, and the over-modulation and current distortion are avoided with the control strategy proposed in this paper. The system three phase grid-connected current has always been kept balanced.

B. ALL PV STRINGS OPERATING AT DELOAD MODE
The illumination is set 1000 W/m 2 for all PV strings except the three ones whose settings are below: S a1 = 900 W/m 2 , S b2 = 950 W/m 2 , S c2 = 900 W/m 2 . Simulation results are shown in Fig. 9. Due to the reduced difference between PV string maximum available output power, even though all PV strings are controlled to reduce output power to the value corresponding to the maximum available output power of Module a1 and c2 (minimum value among all modules at MPPT mode), 10% power reserve can still not be satisfied. Therefore, all PV strings are controlled to operate at deload mode. The reserved power requirement is fulfilled, and the transmission power between modules is balanced totally. At last, all PV strings are controlled to increase the output power fast to response to the grid frequency dropping. The minimum grid frequency is increased from 49.75 Hz to 49.81 Hz, and the balanced transmission power and grid-connected current have been maintained.

VI. EXPERIMENTAL VALIDATION
A 10 kW three phase CHB based PV generation system experimental platform shown in Fig. 10 is also built to validate the control strategy proposed. There are three modules in each phase. Each module includes two back-toback IGBT power cells (PM25RL1A120). One power cell is controlled as an active rectifier to emulate power output characteristics of the PV string. Two bridges arms in the other one are used to form an H-bridge inverter. Three H-bridge inverters in one phase are cascaded as a CHB inverter. The nine active rectifiers are fed by the nine secondary side windings of an isolation transformer. The transformer is connected to an input voltage regulator. The cascaded H-bridge inverter is coupled with grid by the other voltage regulator, which also provides the galvanic isolation. Four DSP (TMS320F28335) + FPGA (XC3S400-PQG208EGQ) control boards are used to implement the control algorithm and generate the PWM signals. Three active rectifiers in one phase and all H-bridge inverters are controlled by one control board, respectively [16]. The main parameters are shown in Tab. 2.
At First, all PV strings are emulated to operate at MPPT mode. All DC-link voltages are controlled to be 50 V. The RMS value of the rectifier input three phase current of the first module in Phase C is set 3.07 A to emulate the output power of the PV string corresponding to Module c1 being 130 W. The corresponding RMS values of the other eight modules are all set 2.36 A to emulate the output power being 100 W. Then, the system deload operation is emulated. The reserved power is set 10% of the output power, 93 W. Each module input current is used to reflect its transmission power in this paper.
With the reserved power distribution method proposed in this paper, the input current of Module b1 and c1, gridconnected current in Phase B and C and DC-link voltage corresponding to Module b1 and c1 are shown in Fig. 11. RMS values of all nine rectifiers input three phase current are all 2.19 A during power reserve operation. The reserved power requirement is fulfilled successfully. Furthermore, the transmission power balance between modules and balanced three phase grid-connected current output are achieved. The oscillation with 100 Hz of double grid frequency is observed. The average voltage is increased from 50 V to about 57.1 V and 51.8 V, respectively to emulate the PV strings deload operation, and the stable DC-link voltage is kept successfully.
When the control method in [19] is used in the same condition, the input current of Module b1 and c1 and grid-connected current in Phase B and C are shown in Fig. 12. The reserved power is achieved only with the deload operation of Module c1, with maximum transmission power during MPPT operation. Therefore, its transmission power is reduced to 37 W, and the RMS value of the corresponding rectifier input three phase current is reduced to 0.9 A. The output power of the other eight modules is kept constant. Although the reserved power requirement is fulfilled, the transmission power difference between Module c1 and the other modules is large, leading to the unbalanced three phase grid-connected current. The effectiveness and advantage of the control strategy proposed have been validated.
At last, the system output power is controlled to increase 60 W fast to emulate the grid frequency support control. The input current of Module b1 and c1, the grid-connected current in Phase B and C and DC-link voltage corresponding to Module b1 and c1 are shown in Fig. 13. It can be observed that the rapid increase of the system output power is achieved with the decrease in DC-link voltages. At the same time, the transmission power and three phase grid-connected current are kept balanced with the control strategy proposed.
Overall, from the simulation results and experimental results above, the effectiveness of the proposed grid frequency support control strategy of the three phase CHB based PV generation system has been validated. During power reserve operation, the reserved power requirement is fulfilled. Furthermore, the maximum balance of PV strings output power between modules with the coordinated control of their operation points is achieved. Once the grid frequency dropping is detected, the grid frequency dynamic characteristic improvement is achieved with the release of the reserved power. The transmission power balance can still be maintained, leading to maximum and balanced three phase grid-connected current output.
If partial shading occurs, the power balance control between modules during both power reserve and grid frequency support can still be achieved after updating each PV string maximum available output power next cycle. This means that the control strategy proposed is still valid. Before the power updating, the control performance of the power balance will be affected due to the error between the PV string maximum available output power used and its actual value. However, it can be improved by reducing time interval of the MPPT control to accelerate the power updating.

VII. CONCLUSION
A grid frequency support control strategy of the three phase CHB based PV generation system is proposed in this paper to maintain its stable operation at MPPT, deload and grid frequency support modes. During MPPT operation, each PV string maximum power output and the system maximum power output are achieved by regulating each DC-link voltage reference. The reserved power requirement is fulfilled by changing the PV string operation point. When the grid frequency drops, the reserved power is released to improve grid frequency dynamic characteristics. To address the power unbalance issue between H-bridge modules, the coordinated control of all PV strings is achieved only by modifying DC-link voltage references. Maximum transmission power balance between H-bridge modules and balanced three phase grid-connected current are obtained. The H-bridge module over-modulation risk is reduced, and the consistency of the control strategy has been ensured. The simulation and experimental results validate that the grid frequency has been supported effectively, and the three phase grid-connected current has always been balanced with the control strategy proposed.
The PV string output power only depends on the temperature and illumination in the model built. The model modification to emulate the partial shading condition accurately, tests with actual PV cells on the experimental platform, and the deep analysis of the control parameter's influence on the system stability will be the topics of future papers.