# Control of the Hybrid Renewable Energy System with Wind Turbine, Photovoltaic Panels and Battery Energy Storage

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Architectures of Converter Hybrid Renewable Energy Systems

## 3. Mathematical Models of the Main Components of HRES

#### 3.1. Wind Tubine Aerodynamic Model

_{t}produced by the wind turbine can be described with the following Equation [6,18]:

^{2}—area swept by the rotor blades; ρ—air density; λ—tip speed ratio; β—blade pitch angle; C

_{p}—power coefficient of the wind turbine; v

_{w}—wind speed.

_{m}is the mechanical angular speed of the turbine rotor.

_{p}is expressed as a complex dependence on two factors: Tip speed ratio λ and blade pitch angle β. In the literature [6,8,18,19], the approximation of power coefficient C

_{p}by the following equations is introduced:

_{1}to c

_{6}represent coefficients of wind turbine characteristics (c

_{1}= 0.5176, c

_{2}= 116, c

_{3}= 0.4, c

_{4}= 5, c

_{5}= 21, c

_{6}= 0.0068), and β is blade pitch angle expressed in degrees.

_{p}and tip speed ratio λ for different blade pitch angle β is presented in Figure 4.

_{opt}for which the power coefficient C

_{p}reaches its maximum value C

_{pmax}. For the wind system with usual operation of wind turbine at blade pitch angle β = 0 deg, the optimal tip speed ratio is equal to λ

_{opt}=8.1, at which C

_{pmax}= 0.48.

#### 3.2. Model of Permanent Magnet Synchronous Generator

_{sd}, v

_{sq}—dq components of the stator voltage vector; i

_{sd}, i

_{sq}—dq components of the stator current vector; ψ

_{sd}, ψ

_{sq}—dq components of the stator flux vector; ψ

_{PM}—flux established by the permanent magnets ω

_{e}, ω

_{m}—electrical and mechanical angular speed of the PMSG rotor; R

_{s}—stator phase resistance; L

_{d}, L

_{q}—direct and quadrature stator inductances; n

_{p}—number of pole pairs of PMSG.

_{t}—the mechanical torque of wind turbine; T

_{e}—the electromagnetic torque of PMSG; J—the total inertia of the system; B

_{f}—coefficient of viscous friction in WECS mechanical system.

#### 3.3. Mathematical Models of PV Systems

_{ph}in parallel with a diode D and shunt resistor R

_{p}and series resistor R

_{s}[22,23,24].

_{PVc}can be calculated by [25]:

_{o}—the reverse saturation current of diode; V

_{PVc}—the cell output voltage; q—electron charge; A—diode ideality factor; K—Boltzmann’s constant; T—temperature of the PV cell (in K).

_{ph}is proportional to the value of solar irradiation G

_{r}and is linear with respect to the PV cell temperature T:

_{sc}—the short circuit current of PV cell; K

_{i}—the temperature coefficient of the short-circuit current [A/K]; G

_{r}—solar irradiation [W/m

^{2}].

_{PV}of the PV array can be expressed in the form [24,26]:

_{PV}of the PV array can be described by the following equation:

#### 3.4. Mathematical Models of Battery Energy System

_{OC}and a current controlled current source i

_{Bat}. The left circuit is operated as energy balanced circuit and it is used for modelling the capacity and State of Charge (SOC) of the battery. It includes the capacitance C

_{Cap}in parallel with the resistance R

_{Sd}. The capacitance C

_{Cap}represents the overall capacitance of the battery, the resistance R

_{Sd}is used for modeling the process of battery self-discharging. The right circuit is operated as voltage response circuit and it is used for modelling the steady-state and transient behavior of the battery. It includes the controlled voltage source v

_{OC}, series resistance R

_{s}, and two elements connected in series: Resistance R

_{s1}in parallel with capacitance C

_{s1}and resistance R

_{s2}in parallel with capacitance C

_{s2}. The controlled voltage source v

_{OC}represents a voltage open circuit (VOC) of the battery. Series resistance R

_{s}is used for modelling steady-state operation and power losses in the battery. Resistance R

_{s1}with parallel capacitance C

_{s1}represent the circuit for modelling the transients of short time constant, resistance R

_{s2}with parallel capacitance C

_{s2}represent the circuit for modelling the transients of long time constant. It is possible to add more RC networks to the battery model for improving model’s accuracy, but it causes the increase of model complexity. In improved models, a dependence of the network elements on the SOC value was also proposed to achieve higher accuracy [29].

_{0}—initial state of battery charge; Q

_{N}—nominal capacity of the battery; i

_{Bat}—the battery current (positive by discharging and negative by charging); it—the charge supplied or drawn by battery; t-time.

_{OC}in series with resistance R

_{in}. The circuit model of battery directly describes the behavior of a battery with using only terminal voltage, open circuit voltage, internal resistance, dis/charge current, and state of charge. This battery model is described by the following equations [29]:

_{OC}

_{0}—no load battery voltage; K—polarization voltage; Q—battery capacity; A—exponential component amplitude; B—time constant inverse; R

_{in}—battery internal resistance.

## 4. Control of Converter Systems of HRES

#### 4.1. Control of DC/DC Converter for PV Array

_{b}, boost inductor L

_{d}, and filter capacitor C

_{d}.

_{PV}and photovoltaic current I

_{PV}. The certain disadvantage of the P&O algorithm is the possibility of power oscillation at the state, when the algorithm is almost reaching the MPP. To avoid power oscillations, the right choice of step size for the next time cycle is very important. In the literature, many other improvements of P&O algorithm are also considered [23,31].

#### 4.2. Control of Bidirectional DC/DC Converter for Battery System

_{a}and S

_{b}, inductor L

_{d}, and filter capacitor C

_{d}. The converter can be treated as the combination of two basic chopper circuits, the step-down chopper and the step-up chopper. The bidirectional DC/DC converter enables the operation in the power mode with charging the battery and the operation in the regenerative mode with discharging the battery. It is obtained by the suitable control system, which generates two control signals for two controlled transistor switches of the converter.

_{Bat}* is calculated as the difference of the current demand of load power P

_{Load}, the wind turbine generated power P

_{WT}, and photovoltaic generated power P

_{PV}. The obtained value of the reference battery power P

_{Bat}* is then divided by battery voltage V

_{Bat}. In this way, the reference battery current I

_{Bat}* is determined. In the control system, the reference battery current I

_{Bat}* is compared with the measured battery current I

_{Bat}. The error signal is given to the PI controller. The reference signal of duty cycle D1 of DC/DC bidirectional converter is determined as the output value from the PI controller. In the realized control system, the additional limited block was introduced in order to protect the battery against the flow of power greater than the maximum allowable power.

#### 4.3. Control of Wind Turbine with MPPT and PMSG with Machine Side Converter

_{opt}. It is realized by controlling the turbine speed in order to follow the optimum speed ω

_{opt}. On the base of Equation (2) and Figure 4, the reference value of rotational speed ω

_{ref}is determined by the choice of optimal tip-speed ratio λ

_{opt}

_{.}The reference rotational speed ω

_{ref}of the wind turbine rotor is equal to an optimal value of the rotational speed ω

_{opt}of the wind turbine rotor, which is specified as follows:

_{opt}, the reference turbine rotational speed ω

_{ref}should be changed proportionally to the current wind speed v

_{w}.

_{ref}is compared with the measured rotational speed ω

_{m}of the turbine rotor. The obtained error signal is given to the PI controller. The output control signal of the speed control loop is the reference signal i

_{sq}* of q-component of stator current vector, which determines the electromagnetic torque of the PMSG.

_{opt}of the wind turbine, at which the maximum power of wind turbine is produced. The reference signal i

_{sq}* of the q-component of stator current vector is generated as the output control signal of the speed control loop. The reference signal i

_{sq}* determines the desired electromagnetic torque of PMSG.

_{sd}and i

_{sq}are regulated thorough two inner control loops with PI controllers. In the control system, the method of zero d-axis stator current control is realized, and for this reason, the reference component i

_{sd}* of stator current vector is set to zero value. As a result of this, the stator current vector will be equal only to its q-axis component i

_{sq}. With i

_{sd}= 0, the generator electromagnetic torque is proportional to the q-axis current component i

_{sq}. The stator current reference i

_{sq}* is achieved in the control system by using the operation of the MPPT block. The reference dq-axis components i

_{sd}* and i

_{sq}* of stator current vector are compared with the real current components i

_{sd}and i

_{sq}, obtained from measurement and transformation of real stator phase currents. As the result of the comparison operation, the error control signals are generated and sent to the individual PI controllers. In the control system, the decoupling blocks have also been implemented in order to assure high control performance. The output signal from each decoupling block is added to the output signal of the corresponding controller. In this way, the resultant control signals that form the dq-axis reference components v

_{pd}* and v

_{pq}* of the stator voltage vector are obtained. These reference voltages are then transformed from the rotating d-q-system to the stationary α-β-system, and are sent to the block of Space Vector Modulation (SVM) of the MSC.

#### 4.4. Control of Grid Side Converter

_{g}* is set to zero in order to perform the system operation at the unity power factor. The reference of active grid power p

_{g}* is calculated on the base of multiplication of the measured DC voltage v

_{dc}of the converter and the reference value of grid current vector component i

_{gd}*. The reference value of grid current vector component i

_{gd}* is obtained from the outer control loop. The output signals from the inner PI controllers determine the reference grid voltage vector components v

_{gcd}* and v

_{gcq}* for the control of GSC. After transformation of these reference voltages from rotating d-q-system to the stationary α-β-system, the control signals are obtained, which are sent to the block of SVM of GSC. For the determining the angle θ

_{g}used for the transformation of reference voltages v

_{gcd}* and v

_{gcq}* from d-q-system to the α-β-system, the grid voltages are measured. For the determination of the angle θ

_{g}of grid voltage vector v

_{g}, the PLL method and control circuit have been implemented.

## 5. Energy Management Strategies

#### 5.1. General Conditions of Energy Management

_{min}(about 20%) and the maximum value SOC

_{max}(usually about 80–90%). In addition, in the energy management strategy, it was concluded that during battery charging and discharging processes, the maximum permissible power load of the battery may not be exceeded.

_{WT}—output power of WT and PMSG; P

_{PV}—the power delivered by PV system; P

_{Bat}—the battery power; P

_{Grid}—the grid power; and P

_{Load}—the electrical load power.

_{Grid}in this equation should be omitted.

#### 5.2. Energy Management Strategy for Grid-Connected HRES

_{WT}and the PV power P

_{PV}is treated as the primary supply power, that has the priority in satisfying the load demand over that provided by utility grid. It was assumed, that the energy consumption from the grid should be avoided because it requires additional payment and costs. For this reason, the using of energy from the utility grid is put at the end of the list of priorities.

_{WT}+ P

_{PV}) is greater than the load demand P

_{Load}, the surplus power P

_{Sur}= P

_{WT}+ P

_{PV}− P

_{Load}has the priority in charging the battery with the power P

_{Bat}. The battery can be charged until it will be fully charged. The whole surplus power can be delivered to the grid only in the case when the battery was fully charged P

_{Grid}= P

_{Sur}. Because the battery can be charged only with the limited maximal power P

_{Batmax}, when the surplus power is greater than P

_{Batmax}, then the battery is charging with its maximal power, and only the rest of surplus power is returned to the utility grid P

_{Grid}= P

_{Sur}− P

_{Batmax}.

_{WT}+ P

_{PV}) is lower than the load demand P

_{Load}, then deficit power P

_{Def}= P

_{Load}− (P

_{WT}+ P

_{PV}) will occur in HRES. The battery has the priority, and at discharging is able to deliver the addition to the power demand of the load. However, when the battery is fully discharged, the deficit power must be completely delivered from the grid. Because the battery can be discharged only with the limited maximal power P

_{Batmax}, then when the deficit power is greater than P

_{Batmax}, the battery is used at discharging with maximal power, and the rest of deficit power must be received from the utility grid P

_{Grid}= P

_{Def}− P

_{Batmax}.

#### 5.3. Energy Management Strategy for Stand-Alone HRES

_{WT}+ P

_{PV}) is greater than the load demand P

_{Load}, the surplus power P

_{Sur}will charge the battery when the condition is fulfilled P

_{Sur}≤ P

_{Batmax}. The battery can be charged until it will be fully charged. After the battery is fully charged or P

_{Sur}> P

_{Batmax}, the excess power P

_{Sur}cannot be stored, and because of this, it should be limited. It can be obtained by decreasing the generation of renewable energy by throwing control systems from keeping operation at maximum power points or simply by switching off selected sources of renewable energy generation. Excess power can be also dumped in some additional energy loads specially connected to the system in this case.

_{WT}+ P

_{PV}) is lower than the load demand P

_{Load}, than there will be deficit power P

_{Def}in HRES. The battery will be discharged in order to reduce or compensate for the power deficit. This state is possible only in the determined period of time because of the limited battery capacitance. The battery capacitance should be designed for the projected period of no energy production or a reduced value of generated energy. It is also recommended to divide the used power loads into critical loads, which cannot be turned off and into non-critical ones, which can be turned off when the amount of generated energy in the system is insufficient. Another possible solution in this case is to use an additional energy source, e.g., an electric generator system driven by an internal combustion engine.

## 6. Simulation Results

- Data and parameters of the wind turbine system: Rated power, P
_{WT}= 20 kW; rotor radius, R = 4.4 m. - Data and parameters of PMSG generator: Rated power, P
_{e}= 20 kW; stator resistance, R_{s}= 0.1764 Ω; stator dq-axis inductances, L_{d}, L_{q}= 4.48 mH; rated speed, n_{s}= 211 rpm. - Data and parameters of PV array: Rated power, P
_{PV}= 12 kW; number of panels in series, N_{s}= 5; number of parallel strings, N_{p}= 10; open circuit voltage, V_{oc}= 59.26 V; short circuit current, I_{sc}= 5.09 A. - Data and parameters of battery system: Rated capacity, C
_{Bat}= 75 Ah; single module voltage, V_{Bat}= 12 V; number of modules in series, N_{Bs}= 25; rated voltage of battery, V_{Bat}= 12 V × 25 = 300 V; rated power of battery, P_{Bat}= 5 kW.

_{opt}= ω

_{ref}and measured angular speed ω

_{m}of the wind turbine rotor and the rotor of PMSG are presented. The performed studies confirm, that the waveform of turbine angular speed ω

_{m}is accurately adjusted to the waveform of optimal referenced speed ω

_{opt}. The applied MPPT algorithm ensures the determination of the reference speed ω

_{opt}. For these assumed conditions of realization of MPPT, the wind turbine should be in the operation at a constant optimal value of tip speed ratio λ

_{opt}and at a constant maximum value of turbine power coefficient C

_{pmax}. The obtained courses of tip speed ratio λ and turbine power coefficient C

_{p}at various wind speeds have been presented in Figure 18 and in Figure 19, respectively. On the base of these figures, the proper operation of MPPT algorithm of the wind turbine can be confirmed. Even, if there are large changes of wind speeds, the optimal and constant values of tip speed ratio λ and power coefficient C

_{p}have been reached.

_{sd}, i

_{sq}of stator current vector of PMSG have been presented in Figure 20. On the base of these courses, it can be stated that the component i

_{sd}of stator current vector is almost exactly set by the control system to zero value i

_{sd}= 0. This condition is optimal and required for the proper operation of PMSG and for RFOC control of PMSG. On the base of the course, it can be stated that the component i

_{sq}of stator current vector is changing according to the waveforms of wind speed variations. The component i

_{sq}is responsible for the generation of electromagnetic torque T

_{e}of the PMSG generator.

_{e}of PMSG generator and mechanical torque T

_{t}of wind turbine have been presented in Figure 21. On the base of comparison with Figure 20, it can be confirmed that at RFOC control, the electromagnetic torque T

_{e}of PMSG generator is proportional to the stator current vector component i

_{sq}.

_{gd}, i

_{gq}of grid current vector for GSC have been presented in Figure 22. The component i

_{gd}represents the flow of the active power at the AC side of GSC. The power flow between the grid and the GSC converter can be bidirectional: Power can be transferred from the grid to the GSC or delivered from the GSC converter to the grid. At i

_{gd}> 0, the active power is transferred to the GSC and at i

_{gd}< 0 the active power is delivered to the grid. At i

_{gq}= 0, the reactive power is equal to zero, and the optimal operation of unity grid power factor is obtained. These conditions are properly met by the GSC control system, as shown in the Figure 22.

_{dc}in the common DC link of the considered system of converters. It can be stated that the course of instantaneous voltage v

_{dc}is kept practically on the constant level despite variations of wind speeds and changes of the power flows in the system. This is a confirmation of the high accuracy and quick operation of the control system.

_{PV}= 0) and the load power consumption P

_{Load}is high. Because the power of the wind system is smaller than the demand of load power (P

_{WT}< P

_{Load}), the power shortage is supplemented by the battery, which operates at the rated power output in the discharging mode (P

_{Bat}> 0). Despite these conditions, there is still a power shortage, which can only be eliminated by taking additional power from the grid (P

_{Grid}> 0).

_{PV}> 0), the wind system is in operation (P

_{WT}> 0), and the load power consumption P

_{Load}is high. Because the sum of the power of the wind system and the power of the PV system is greater or equal to the load power (P

_{WT}+ P

_{PV}≥ P

_{Load}), there is no need to take power from the grid (P

_{Grid}= 0). In the time intervals, when there is a surplus of generator and PV power over the load power, the battery works in the charging mode, i.e., with power consumption (P

_{Bat}< 0). The system operation in this state is similar to the operation of the stand-alone system.

_{PV}> 0), the wind system is in operation (P

_{WT}> 0), and the load power consumption P

_{Load}is small or equal to zero. Because the sum of the power of the wind system and the power of the PV system is greater than the demanded load power (P

_{WT}+ P

_{PV}> P

_{Load}), the part of surplus of generator and PV power over the load power is used for charging the battery with rated power (P

_{Bat}< 0). The remaining part of the surplus power is the power recovered to the grid (P

_{Grid}< 0).

_{Bat}> 0).

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**The detailed converter scheme of HRES with common DC bus and with Wind Energy Conversion Systems (WECS), Photovoltaic (PV), and Battery Energy Storage (BES) system.

**Figure 4.**Curves of power coefficient C

_{p}for different values of tip speed ratio λ and blade pitch angle β.

**Figure 6.**Computed current (

**a**) and power characteristics (

**b**) for the PV array at different levels of irradiation and fixed module temperature.

**Figure 7.**The electric equivalent circuits for batteries: (

**a**) Dynamic model with 2 RC networks (Runtime-based model); (

**b**) nonlinear circuit model (Shepherd’s model).

**Figure 13.**Control diagram of Rotor Field Oriented Control for Permanent Magnet Synchronous Generator (PMSG) with MSC.

**Figure 14.**The detailed scheme of Grid Side Converter (GSC) with applied Direct Power Control-Space Vector Modulation (DPC-SVM) control.

**Figure 17.**Waveforms of reference speed ω

_{opt}and the actual angular speed ω

_{m}of wind turbine and PMSG.

**Figure 21.**The courses of electromagnetic torque T

_{e}(with reverse sign) of PMSG and mechanical torque T

_{t}of wind turbine.

**Figure 24.**The courses of: Wind turbine and generator output power P

_{WT,}photovoltaic power P

_{PV,}battery power P

_{Ba}

_{t}, grid power P

_{Grid}, and load power P

_{Load}.

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**MDPI and ACS Style**

Gajewski, P.; Pieńkowski, K.
Control of the Hybrid Renewable Energy System with Wind Turbine, Photovoltaic Panels and Battery Energy Storage. *Energies* **2021**, *14*, 1595.
https://doi.org/10.3390/en14061595

**AMA Style**

Gajewski P, Pieńkowski K.
Control of the Hybrid Renewable Energy System with Wind Turbine, Photovoltaic Panels and Battery Energy Storage. *Energies*. 2021; 14(6):1595.
https://doi.org/10.3390/en14061595

**Chicago/Turabian Style**

Gajewski, Piotr, and Krzysztof Pieńkowski.
2021. "Control of the Hybrid Renewable Energy System with Wind Turbine, Photovoltaic Panels and Battery Energy Storage" *Energies* 14, no. 6: 1595.
https://doi.org/10.3390/en14061595