Research on the overvoltage suppression strategy of single-phase photovoltaic grid-connected systems based on FCS-MPDPC

For the overvoltage problem brought by the access of high-penetration photovoltaic power plants to the low-voltage distribution network, this paper chooses to deal with it by using the reactive power regulation capability of photovoltaic power plant inverters, which reduces the equipment investment in distribution line voltage regulation. Based on the reactive power regulation theory of the inverter, a finite set model predictive direct power control method is proposed by constructing a virtual voltage vector, taking a single-phase cascaded 2H bridge grid-connected inverter as an example, to realize independent control of active and reactive power. By setting different power reference values, the inverter can be made to have two functions: grid-connected per-unit power factor and reactive power control during overvoltage. Finally, the two modes of inverter operation are verified by Simulink simulation, and the verification by example shows that the method can limit the grid-connected voltage deviation to within 7% and meet the requirements of grid-connected regulations.


Introduction
With the "double carbon" strategy, China ushers in a critical period of power system energy transition.Solving the optimal EDP (Energy Dispatch Problem) can not only achieve the sustainable development of the power system but also maximize the benefits.At present, the proportion of PV power plants connected to the distribution network is getting higher and higher, and the derived overvoltage problem of grid connection has seriously limited the grid connection capacity of PV power plants [1][2][3].In recent years, the use of inverters for reactive voltage control has been studied by many scholars as the most cost-effective voltage regulation method.The Literature [4] analyzed in detail the three stages of inverter participation in voltage regulation according to the inverter capacity.In the Literature [5], three modes of overvoltage suppression, undervoltage suppression, and optimization of network loss and power factor are proposed by means of inverter reactive power control.
In recent years, FCS-MPC (Finite Control Set Model Predictive Control) has been widely used in the control of converters [6].The Literature [7] applied FCS-MPC to a three-phase multilevel cascaded H-bridge inverter to solve the problem of steady-state errors at low sampling frequencies and when the parameters in the predictive model do not match those of the actual system.Inspired by the DTC (Direct Torque Control) method in motor control, the DPC (Direct Power Control) method can achieve separate control for instantaneous active power and reactive power, respectively [8].In the Literature [9], a virtual motor-based DPC control strategy for grid-connected PV inverters is proposed to eliminate the effect of grid frequency fluctuations on the instantaneous power calculation.
In this paper, the FCS-MPDPC (Finite Control Set Model Predictive Direct Power Control) method is proposed for a single-phase cascaded 2H-bridge grid-connected inverter as an example, and by designing different power reference values, the unit power factor grid-connected and reactive power of the inverter is achieved at a voltage to solve the overvoltage problem.Its control strategy has a simple structure and can directly receive power commands from the dispatch center.The distribution network dispatch center can directly issue reactive power control commands to the inverter according to the real-time overvoltage situation of the line and coordinate the distribution of the system reactive power regulation quantity acting on the inverter to make the distribution network voltage return to the normal limit value.

Calculation of system reactive power regulation ( pv Q )
The grid-connected equivalent circuit of a distributed PV plant is shown in Figure 1  When the PV plant output active power PV P is small, and the grid-connected network voltage k U has not crossed the limit, the inverter works in MPPT mode, using a unit power factor grid connection, The PV grid-connected network voltage k U is [4]: When the PV power plant output active power PV P is too large and the local load on the line is small, the line tide reverses and the grid network voltage k U crosses the limit, then reactive voltage control is used to send reactive power through the inverter for voltage regulation, and the grid network crossed voltage is restored to the normal limit 2) is the amount of reactive power regulation emitted by the PV inverter, which is calculated from Equations ( 1) and ( 2 A single-phase cascaded 2H-bridge inverter grid-connected model is shown in Figure 2, where ( 1,2) dci U i  is the DC-side input voltage (assuming equal DC-side voltages), L is the filter inductor, R is the line equivalent resistance, s i is the output grid-connected current, u is the inverter output voltage, and e is the single-phase grid voltage.
Since the two switches of the same bridge arm of the cascaded 2H bridge inverter cannot be on at the same time, define "1" as the switch of the upper bridge arm is on and the switch of the lower bridge arm is off; define "0" as the switch of the lower bridge arm is on and the switch of the upper bridge arm is off.The switch combination, inverter output voltage, and grid-connected current of the inverter are as follows: Table 1.Inverter output voltage, switching combination, and virtual voltage vector.
Serial Number To realize the independent control of active and reactive components, for the single-phase system, it is necessary to construct a virtual quadrature component with u as the  axis and establish the  coordinate system virtual voltage vectors u  and u  in the two-phase stationary coordinate system control is performed.For the single-phase cascaded 2H-bridge inverter, there are 5 levels and 16 switch combinations.Eliminating some of the redundant switch combinations, the output voltage, switch combinations, and virtual voltage vector of the single-phase cascaded 2H-bridge inverter are shown in Table 1.

Build the power prediction model and the objective function
To achieve independent control of active and reactive power, the SOGI (Second Order Generalized Integrator) transform is used to decompose the single-phase sinusoidal signals of grid voltage e and grid current s i into two-phase orthogonal sinusoidal signals, where e and s i can be obtained using voltage sensors and current sensors.
Firstly, the single-phase grid-connected system is converted into the  coordinate system, that is, the coordinate transformation of Equation ( 6), and then the mathematical model of the current of the single-phase cascaded 2H bridge inverter in the  coordinate system is: where u  , s i  and e  are the  components of the inverter output voltage, grid-connected current and grid voltage, respectively; u  , s i  and e  are the  components of the inverter output voltage, grid-connected current and grid voltage respectively.
Based on the single-phase instantaneous power theory, the active and reactive power of the inverter in the  coordinate system can be expressed as: e

i e i P e i e i Q
Taking derivatives for both sides of Equation ( 8), substituting Equation (7), and using forward Eulerian discretization, the power prediction model of the inverter in the  coordinate system is obtained as: The basic control objective is to minimize the error between the power prediction value and the reference value, that is, the actual power value stably tracks the reference value, and the variance function is introduced to establish the cost function as: According to Equations ( 9) and ( 10), the magnitude of the objective function ( ) J k is directly related to the inverter output voltage u ; that is, it is directly related to inverter switch sequence where vp K and vl K are the proportional and integral regulation gains of the voltage outer loop.Based on the above derivation process, the FCS-MPDPC control structure block diagram of a single-phase grid-connected inverter in the coordinate system is shown in Figure 3.The SOGI method is used to construct the orthogonal components of grid voltage and current, and the power at the next moment is predicted by using the prediction model.By setting different reference values, the switch combination with the minimum objective function is selected to act at the next moment.The functions of grid-connected unit power factor and reactive voltage control are realized.The flow chart of the FCS-MPDPC grid-connected overvoltage suppression strategy is shown in Figure 4.

Simulation analysis
To verify the control strategy in this paper, a single-phase cascaded 2H-bridge inverter grid-connected simulation model is built in Matlab/Simulink software, and the simulation parameters are shown in Table 2.

Unit power factor grid connection
The simulation time is set to 1 s, and the active power reference ref P is 2 kW at the beginning, which is raised to 3 kW after 0.5 s, and the reactive power reference ref Q is always 0 var.The simulation results are shown in Figure 5.
From Figure 5, it can be seen that the FCS-MPDPC control strategy can realize the unit power factor grid-connected mode, and the system dynamic response is fast when the active power changes abruptly, and the reactive power is always kept as 0var, which realizes the decoupling control of active power and reactive power.

Inverter reactive power control in case of overvoltage
The simulation time is set to 1 s, the active power reference value ref P is set to 2 kW at the beginning and 3 kW after 0.5 s, the reactive power reference value ref Q is set to -3000 var at the beginning and - 2000 var after 0.5 s, the simulation results are shown in Figure 6.
From Figure 6, it can be seen that the FCS-MPDPC control strategy can realize the inverter to output active power and reactive power at the same time, and when the active power reference value and reactive power reference value change abruptly, the dynamic response of the system is fast and can complete the fast action of the set power.

Instance validation
The voltage of the grid connection point of a PV power plant in a certain area is monitored, and the monitoring data are processed and analysed.Due to the losses in the transmission process of the distribution line, in order to ensure that the line voltage is near the rated value, the voltage of the parallel network is generally set 5% higher than the rated line voltage [10], then set the nominal voltage of the low-voltage distribution line to 231V, and calculate the voltage deviation, when % 7% V   , overvoltage phenomenon occurs at the grid-tied point.
As can be seen from Figure 7, during the time from 9:00 to 17:30, the overvoltage phenomenon occurs at the grid connection point of the PV plant, which seriously affects the power consumption experience of local customers.When a certain amount of reactive power is output by the FCS-MPDPC control strategy, the voltage at the grid connection point is restored to the normal range, which confirms the feasibility of the proposed control strategy.

Conclusions
In order to solve the overvoltage problem of the parallel network brought by the integration of highpenetration PV power plants into the low-voltage distribution network, this paper proposes an FCS-MPDPC method for direct control of the inverter, which effectively limits the voltage deviation % V  to within 7% by setting the reference value ref Q with a reasonable allocation of the system reactive power regulation amount pv Q .The advantages of this method are: (1) Compared with the use of reactive power compensation devices, on-load regulating transformers, and other voltage regulation devices, it reduces the investment in equipment and achieves the solution of overvoltage problems at the source.
(2) Compared with the traditional voltage and current double closed-loop control, FCS-MPDPC does not need PWM modulation and complex PI parameter setting, and the control structure is simple, which can realize a fast control response to power and effectively solve the problem of overvoltage.
, and there are n nodes in the figure.where the PV plant is connected to distribution network node k , k U is the grid- connected voltage, S U is the distribution network voltage, PV PV +j P Q is the active and reactive power injected into the grid by the PV plant, +j k k P Q is the power consumed by the local load, +j k k R X is the line and transformer equivalent impedance, impedance from node 0 to node k .

Figure 1 .
Figure 1.Equivalent circuit of distributed photovoltaic power plant grid-connected.
ref Q : when the distribution network parallel network voltage not crossed the limit, that is, 1when the distribution network parallel network voltage has crossed the limit, that is, 1.1 .e pu  , ref Q is set using Equation (3).

Figure 5 .
Figure 5. FCS-MPDPC power simulation waveform in unit power factor mode.