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# Stability evaluation of a grid-tied hybrid wind/PV farm joined with a hybrid energy-storage system

*Sustainable Environment Research*
**volume 33**, Article number: 21 (2023)

## Abstract

This paper presents the stability-evaluation outcomes of a multimachine power system (MMPS) connected with a large-scale hybrid wind farm (WF) and photovoltaic (PV) farm or hybrid wind/PV farm (HWPF) and a hybrid energy-storage system (HESS) consisting of a vanadium redox flow battery (VRFB) and a supercapacitor (SC). A probability scheme is used to determine the rated power of the proposed HESS, where the capacities of the VRFB-ESS and the SC-ESS are designed to effectively utilize their operating features. The control strategy of the HESS is proposed to reduce the pressure of the VRFB-ESS and smooth the output power fluctuations of the HWPF. The steady-state stability, small-signal stability, dynamic performances, and transient simulations of the studied grid-tied HWPF fed to the MMPS with and without the HESS are achieved. The simulation outcomes show that the proposed HESS can enhance the stability and power-smoothing performance of the HWPF fed to the MMPS.

## 1 Introduction

The huge increase in energy demands and fast shortage of fossil fuels significantly demonstrate the importance of employing alternative power-production schemes. Renewable energy sources (RES) and especially wind/PV-based power-generation systems can be the most practical and effective means to offer the energy demand on the earth. Producing power from RES is not only completely environmentally friendly but also reliable and renewable. Both wind and PV energies can be considered the most mature technology to produce large electric power from RES. Due to the random characteristics of RES, ESS should be effectively used to compensate for the intermittent power-generation features of RES.

Jing et al. [1] reviewed and discussed the developments of the HESS based on battery and SC used in autonomous microgrids while this study also explored both technical complexity and economic sustainability of the microgrid. Manandhar et al. [2] proposed a new control scheme for a PV-based DC grid system using an HESS with battery and SC while the control scheme employed the uncompensated power from the battery to promote the operating characteristics of the overall HESS. Lin et al. [3] proposed an integral droop (ID) to apply to a group of ESSs with high ramp rates while the transient power allocation in the HESS was able to be implemented by coordinating the ID and the traditional V-P droop. Xiao et al. [4] discussed a combined energy-storage mode to meet the ESS requirements for wind power under short-term and long-term modes, where the short-term energy-storage mode was designed to meet fast-changing powers using SCs while the long-term energy-storage mode was scheduled to meet large-scale capacity requirements using a battery based on Li-ion or VRFB. Kollimalla et al. [5] proposed a new control scheme to achieve power-sharing between batteries and SCs to match generation-demand mismatch and control grid voltage. Wang et al. [6] proposed a rule-based power-control algorithm to activate the power dispatch of a utility-scale PV power plant with a HESS according to Australian National Electricity Rules. Li et al. [7] discussed the strategies to conquer the obstacles of real-time simulations of WFs with complicated and high-frequency switching using real-time hardware-in-the-loop while a wind-turbine generator (WTG) using a HESS based on flow battery and SC to smooth wind power was investigated. Wang et al. [8] proposed a HESS consisting of a VRFB and an SC bank for smoothing the fluctuating output power of a 1-MW grid-tied PV power plant while the HESS was designed to minimize the required power rating of the SC bank to only 1/5 of the VRFB rating to avoid the VRFB operating at low power levels by increasing its overall efficiency. Manandhar et al. [9] proposed a new energy management scheme to achieve effective power sharing between different ESSs, faster response DC-link voltage regulation, dynamic power sharing between the battery and the grid based on the battery’s state of charge (SOC), etc. Samosir and Yatim [10] presented a power converter for connecting an ultracapacitor as a secondary ESS to a fuel cell while a bidirectional DC/DC converter was utilized for interfacing the ultracapacitor to the fuel cell. Wee et al. [11] used a statistical method to design a battery/SC-based ESS for a WF by treating the input wind power as random and using a proposed coordinated power flow control scheme for the ESS. Hajizadeh et al. [12] presented the control of hybrid fuel cell/energy-storage distributed generation systems subject to a voltage sag at distribution systems. Tang et al. [13] presented a coordinated optimization control scheme for a HESS based on real-time online analysis of the power spectrum while the developed device was applied to some engineering projects with both simulation and practical applications. Hazra and Bhattacharya [14] proposed a HESS comprising an ultracapacitor and battery for smoothing the oscillating power of a wave-energy conversion system while each component of the proposed HESS was sized to optimize the cost. Pan et al. [15] introduced an integrated control strategy of smoothing power fluctuations and peak shaving based on a HESS with SC and battery while the power fluctuations of the wind/PV/HESS were controlled under constraints by a low-pass filter. Wang and Yue [16] proposed a probabilistic scheme for determining the rated power capacity of a HESS while the scheme allowed for optimization of the performance of the high energy density of the battery and the SC.

This paper’s contribution is to propose a scheme to design the rated powers for the VRFB and the SC of the proposed HESS to effectively stabilize the MMPS connected with a large-scale HWPF. The organization of this paper is listed below. Section 2 describes the system configuration and the associated mathematical models and/or equations of each subsystem. Section 3 depicts the design of the rated powers for the VRFB and the SC of the proposed HESS. Section 4 demonstrates the calculated eigenvalues and root-loci plots for small-signal stability analysis of the studied system. Section 5 illustrates dynamic and transient time-domain simulations of the studied system under variable wind speeds and solar irradiations as well as sudden trips of PV farm and WF. The important specific conclusions are depicted in Section 6.

## 2 Architecture of the studied system and mathematical models

Figure 1 shows the one-line architecture of the studied system, where the HWPF of rated 100 MW consists of an equivalently aggregated PV farm of rated 25 MW and an equivalently aggregated WF based on a permanent-magnet synchronous generator (PMSG) of rated 75 MW. The common DC link of rated 1200 V is connected to the WF, the PV farm, an equivalently aggregated DC load, and a HESS through an equivalently aggregated AC/DC voltage-source converter (VSC), an equivalently aggregated DC/DC boost converter, an equivalently aggregated DC/DC buck converter, and two equivalently aggregated bidirectional DC/DC converter, respectively. The common DC link of rated 1200 V is also connected to Bus 4 of the 14-bus MMPS [17] through an equivalently aggregated bidirectional DC/AC voltage-source inverter (VSI), two step-up power transformers, and a power cable. Bus 4 shown in Fig. 1 can be treated as the point of common coupling (PCC) where the HWPF is linked to the MMPS. This paper refers to the models of the 1200-V DC link, the PV array with the DC/DC boost converter, the SC bank with the bidirectional DC/DC converter, and other subsystems shown in [18] to develop a new system architecture shown in Fig. 1 with the HWPF, the HESS, the MMPS, etc.

Bus 4 shown in Fig. 1 is a very important bus to accept large power fluctuations generated from the HWPF of rated 100 MW. Such large time-varying injected power into Bus 4 can cause large voltage variations on Bus 4 and neighboring buses. Hence, the proposed HESS in this paper is used to effectively mitigate and smooth such power fluctuations injected into Bus 4.

### 2.1 Controls of the AC/DC VSC of the WF

The control block diagram of the equivalently aggregated AC/DC VSC of the WF based on PMSG is illustrated in Fig. 2. The major goal of this control block diagram is that the WF can capture available maximum power from variable wind speeds. To achieve this purpose, the optimal torque control algorithm [18, 20, 21] of the wind PMSG can be embedded in the control program of the AC/DC VSC. The cut-in, rated, and cut-out wind speeds of the wind turbine of the WF are appropriately chosen as 4, 12, and 24 m s^{−1}, respectively.

### 2.2 Models of the PV farm and its DC/DC boost converter

The single-diode equivalent-circuit model of a PV cell is shown in Fig. 3, [18, 22, 23], which can be extended to establish the model of a PV farm by using the scheme presented in [18]. The schematic diagram of the DC/DC boost converter for connecting the output of the PV farm to the common DC link of rated 1200 V is shown in Fig. 4. The mathematical equations associated with the dynamic average-value model of the DC/DC boost converter shown in Fig. 4 can be referred to [18].

### 2.3 Models of the bidirectional DC/DC converter and the HESS

The equivalent circuit diagram of the bidirectional DC/DC converter for integrating the energy-storage unit into the common DC link of rated 1200 V is shown in Fig. 5. The two power semiconductor switches *S*_{1} and *S*_{2} of the bidirectional DC/DC converter are operated in a complementary manner [10, 18] and, thus, this converter can operate either as a buck converter (buck mode) or a boost converter (boost mode). The level of the power loss of the two power semiconductor switches *S*_{1} and *S*_{2} of the bidirectional DC/DC converter is around 500–600 W. It is assumed that the two power semiconductor switches *S*_{1} and *S*_{2} can properly neglect their power losses while the bidirectional DC/DC converter can be simulated by using its dynamic average-value model [18].

The equivalent circuit model of the employed VRFB-based ESS is shown in Fig. 6, where the resistance *R*_{fix} represents the parasitic loss, the resistances *R*_{rea} and *R*_{res} denote the internal losses, and *I*_{VRFB}, *I*_{sta}, and *I*_{pump} stand for the output current, the stack current, and the pump current, respectively. The equivalent-circuit model of the employed SC is shown in Fig. 7, where the capacitance *C*_{SC}, the parallel resistance *R*_{pSC}, and the series resistance *R*_{sSC} are used [10].

### 2.4 Controls of the DC/AC VSI

The control block diagram of the DC/AC VSI is shown in Fig. 8. The purpose of the DC/AC VSI is to keep the DC-link voltage *V*_{DC} at its reference value of *V*_{DC_ref} and control the reactive power to exchange with the AC system. To achieve the decoupled control between the active and reactive components, the *dq*-axis reference frame with the *d*-axis aligned with the voltage vector of Bus 15 shown in Fig. 1 is used. Thus, the *d*- and *q*-axis currents of the VSI (*i*_{dI} and *i*_{qI}) are employed to control the DC-link voltage and the reactive power that the VSI exchanges with the AC grid, respectively.

### 2.5 Controls of the HESS

The control block diagram of the proposed HESS is shown in Fig. 9. The main target of this control block is to smooth the output power of the HWPF. To take the average output active powers of the two farms and compare them with the actual current active powers, the total power reference of *P*_{Tot_ref} can be obtained by measuring the active powers of the WF and the PV farm fed into the common DC link. When the signal *P*_{Tot_ref} passes through the low-pass filter, the output power reference of the VRFB (*P*_{VRFB_ref}) can be obtained. By subtracting *P*_{Tot_ref} from *P*_{VRFB_ref}, the high-frequency power components (*P*_{Tran}) yield. When the output power error of the VRFB (*P*_{VRFB_err}) passes through the ratio of the two voltages and adds up *P*_{Tran}, the output power reference of the SC (*P*_{SC_ref}) can be determined.

## 3 Rated power design of the HESS

To determine the rated power of the HESS to smooth the total output power fluctuations of the HWPF, the employed dynamic output active powers of the WF and the PV farm are shown in Fig. 10a and b, respectively. Figure 11 shows the dynamic results of the total power reference (*P*_{Tot_ref}) required by the HESS. It can be discovered that the output active powers of the WF and the PV farm are fast changing while the actual wind power drops rapidly from 6 to 8 d. To effectively smooth power fluctuations, the HESS must output the required smoothing power *P*_{Tot_ref} when the system power demand suddenly rises. To directly observe the frequency of the peak occurrence of *P*_{Tot_ref}, the bar diagram shown in Fig. 12 is used to explain the dynamic response simulations of *P*_{Tot_ref} shown in Fig. 11. The horizontal coordinate in Fig. 12 represents all the total power smoothing reference absolute value |*P*_{Tot_ref}| that may occur while the vertical coordinate in Fig. 12 represents the numbers of occurrence of |*P*_{Tot_ref}| in all data. It can be observed from the results shown in Fig. 12 that the occurrence of the peak values of |*P*_{Tot_ref}| is very low when compared to the lower value of |*P*_{Tot_ref}*|*.

Applying the Kernel smoothing density estimation (KSDE) [16] to the bar diagram shown in Fig. 12, the probability density function (PDF) results of |*P*_{Tot_ref}| can be obtained. The function is expressed below.

where |*P*_{Tot_ref}|_{i} represents the selected vector of 100 points equally spaced in the range of |*P*_{Tot_ref}| and *ϕ*_{HESS} represents the vector of KSDE corresponding to absolute values. This is theoretically optimal for estimating the density with a normal distribution.

Figure 13 shows the PDF results of |*P*_{Tot_ref}|, where the horizontal coordinate represents the power of |*P*_{Tot_ref}| while the vertical coordinate represents the probability density of the power in all data. It can be clearly observed the probability of occurrence of |*P*_{Tot_ref}| that most |*P*_{Tot_ref}| results almost distribute between 0 and 30 MW while the probability of occurrence of |*P*_{Tot_ref}| over 30 MW is very low. The following will use the cumulative density function (CDF) for the PDF results of |*P*_{Tot_ref}| obtained in Fig. 13.

According to Fig. 13 for the PDF of |*P*_{Tot_ref}| obtained, the CDF results of |*P*_{Tot_ref}| can be found below.

where *ϕ*_{HESS} is the function of variables and *F*(*x*) is integral of the function. The CDF results of |*P*_{Tot_ref}| shown in Fig. 14 are calculated by using Eq. (2), where the horizontal coordinate represents the occurrence of all data of |*P*_{Tot_ref}|, the vertical coordinate represents the probability density currently accumulated in all data, and the sum of the last accumulated probability must be equal to 1.

Figure 15 illustrates the characteristic curves of discharge efficiency versus output power of the VRFB-ESS when the values of the state of charge (*SOC*) of the VRFB-ESS are 20, 50, and 80%. It can be observed that the discharge efficiency of the VRFB-ESS remains at a higher position with higher *SOC* and higher output power. When the output power of the VRFB-ESS is less than 20% of its rated power, its discharge efficiency drops rapidly to be lower than 75%. Hence, the rated power of the SC-ESS will be selected to be 20% of the one of the VRFB-ESS. This configuration can enable SC-ESS to share the pressure of the VRFB-ESS and reduce the impacts of the VRFB-ESS subject to the variable output power of the HWPF. When the output power of the VRFB-ESS is lower than 20% of its rated power, the addition of the SC-ESS can keep the VRFB-ESS running at a higher efficiency. Therefore, the rated power of the VRFB-ESS is designed to be 25 MW and the rated power of the SC-ESS is selected to be 5 MW.

## 4 Small-signal stability analysis

### 4.1 System eigenvalues

In this paper, the wind speed of 11 m s^{−1} and the solar irradiance of 950 W m^{−2} are properly selected as the nominal operating conditions for the WF and the PV farm, respectively. The system eigenvalues of the studied system without ESS, with VRFB-ESS only, with SC-ESS only, and with the HESS under the selected nominal operating conditions are listed in Table 1. In Table 1, the eigenvalues Λ_{1}–Λ_{29}, Λ_{30}–Λ_{36}, Λ_{37}–Λ_{38}, Λ_{39}–Λ_{40}, Λ_{41}–Λ_{52} and Λ_{53}–Λ_{59} dominant the electromechanical modes of the synchronous generators of the MMPS, the modes of the PMSG-based WF with its AC/DC VSC, the modes of the PV farm with its DC/DC boost converter, the modes of the DC load with its DC/DC buck converter, the modes of the bidirectional DC/AC VSI with its common DC link, and the modes of the VRFB-ESS, the SC-ESS, and their bidirectional DC/DC converters, respectively.

When the VRFB-ESS, the SC-ESS, and the HESS are in service, respectively, it is seen from Table 1 that the real parts of the modes Λ_{41}–Λ_{52} move rightward toward the imaginary axis of the complex plane. Because both VRFB-ESS and SC-ESS are operated at “trickle charge” mode under steady-state conditions, they are equivalent to two electrical loads to absorb power from the common DC link. Therefore, the bidirectional DC/AC VSI with its common DC link has significant influences on the overall system stability to maintain stable operating conditions.

### 4.2 Root-loci analysis

When the wind speed of the WF increases from 4 to 12 m s^{−1} and the solar irradiance of the PV farm keeps at 950 W m^{−2}, the root-loci plots of some specified modes of the studied system are shown in Fig. 16. It can be discovered that the root-loci plots of the modes Λ_{45}–Λ_{46} for the common DC-link voltage move further away from the imaginary axis of the complex plane. When the wind speed of the WF exceeds the rated wind speed of 12 m s^{−1} of the wind turbine, the pitch angle control system of the wind turbine activates and the output active power of the WF keeps constant. Hence, when the wind speed increases from 13 to 15 m s^{−1}, the root loci of the modes Λ_{45}–Λ_{46} are identical. When the VRFB-ESS, the SC-ESS, and the HESS are in service, respectively, the root-loci plots of the modes Λ_{45}–Λ_{46} move toward the imaginary axis of the complex plane. This is because these ESSs are operated as electrical loads under steady-state conditions, and the studied system can still maintain stable operation.

When the solar irradiance of the PV farm increases from 10^{2} to 10^{3} W m^{−2} and the wind speed of the WF keeps at 11 m s^{−1}, the root-loci plots of the studied system are shown in Fig. 17. With the increase of solar irradiance, the output active power of the HWPF also increases and the root-loci plots of the modes Λ_{45}–Λ_{46} for the common DC-link voltage move further away from the imaginary axis of the complex plane. When the VRFB-ESS, the SC-ESS, and the HESS are in service, respectively, the root-loci plots of the modes Λ_{45}–Λ_{46} for the common DC-link voltage move closer to the imaginary axis of the complex plane to make the studied system stable operation.

Figure 16c and d show the root-loci plots of the modes Λ_{45–46} and Λ_{51–52} under different values of wind speed, respectively. It can be found in Fig. 16c and d that the modes Λ_{45–46} and Λ_{51–52} of the studied system without ESS have the largest root-loci variations on their real parts while the modes Λ_{45–46} and Λ_{51–52} of the studied system with different ESSs have smaller root-loci variations on their real parts. The differences between the root-loci variations on the real parts of the modes Λ_{45–46} and Λ_{51–52} of the studied system with different ESSs and without ESS are the quantitative indicators related to stability improvement of using the different ESSs.

Similar situations can also be observed in Fig. 17c and d. Figure 17c and d illustrate the root-loci plots of the modes Λ_{45–46} and Λ_{51–52} under different values of solar irradiance, respectively. It can be found in Fig. 17c and d that the modes Λ_{45–46} and Λ_{51–52} of the studied system without ESS have the largest root-loci variations on their real parts while the modes Λ_{45–46} and Λ_{51–52} of the studied system with different ESSs have smaller root-loci variations on their real parts. The differences between the root-loci variations on the real parts of the modes Λ_{45–46} and Λ_{51–52} of the studied system with different ESSs and without ESS are also the quantitative indicators related to stability improvement of using the different ESSs.

## 5 Time-domain simulations

### 5.1 Simulated variable wind speeds and simulated variable solar irradiances simultaneously applied to the HWPF

When the simulated variable wind speeds and the simulated variable solar irradiances are simultaneously applied to the HWPF, the dynamic time-domain simulations are shown in Fig. 18. When only the VRFB-ESS is in service, the total active power flowing into PCC (*P*_{Bus4}) has been smoothly improved. However, during the two-time intervals of *t* = 40–60 s and *t* = 85–90 s, the output active power of the VRFB-ESS reaches its rated power’s upper limit and, hence, the smoothing effect of the VRFB-ESS on the total active power input to PCC will be lost. When the HESS is in service, it can be observed that the total active power flowing into PCC can be effectively smoothed during the two-time intervals of* t* = 40–60 s and *t* = 85–90 s.

### 5.2 Actual wind-speed variations and actual solar irradiance variations simultaneously applied to the HWPF

When the actual wind speeds and the actual solar irradiances are simultaneously applied to the HWPF, the dynamic time-domain simulations are shown in Fig. 19. When only the VRFB-ESS is in service, the total active power flowing into PCC has been obviously smoothed. However, the active-power fluctuations of the HWPF are too large during the time interval from 6 to 8 d since the active-power output of the VRFB-ESS reaches its rated power’s upper limit and, hence, the obvious fluctuations of the total active power flowing into PCC can be seen. When the proposed HESS is in service, the total active power flowing into PCC can be effectively smoothed during the time interval from 6 to 8 d.

### 5.3 PV farm suddenly tripped

When the PV farm is suddenly tripped at *t* = 10 s, the transient time-domain simulations without ESS, with only VRFB-ESS, and with the HESS under the nominal operating condition are shown in Fig. 20. It can be observed from Fig. 20c that when no ESS is in service, the active power flowing into PCC drops to as low as about 0.45 per unit (p.u.) at *t* = 10 s and then reach a new operating point after the trip of the PV farm. When only the VRFB-ESS is in service, the active power flowing into PCC drops as low as about 0.59 p.u. at *t* = 10 s and then slowly returns to the original operating point after 0.025 s due to the active-power compensation of the VRFB-ESS. When the HESS is in service, the same active-power compensation effect can be obtained from the HESS and the active power flowing into PCC drops as low as about 0.62 p.u. at *t* = 10 s and then quickly returns to the original operating point after 0.025 s.

### 5.4 WF suddenly tripped

When the WF is suddenly tripped at *t* = 10 s, the transient time-domain simulations without ESS, with the VRFB-ESS only, and with the HESS under the nominal operating condition are plotted in Fig. 21. It can be found from Fig. 21c that when no ESS is in service, the active power flowing into PCC drops to as low as about 0.09 p.u. and then reach a new operating point after the trip of the WF. When only the VRFB-ESS is in service, the active power flowing into PCC drops to as low as about 0.19 p.u. at *t* = 10 s and then slowly returns back to the original operating point after 0.025 s. When the proposed HESS is in service, the active power flowing into PCC drops to as low as about 0.3 p.u. at *t* = 10 s and then slow recoveries back to the original operating point after 0.025 s.

## 6 Conclusions

This paper has proposed a HESS consisting of an SC and a VRFB, which has been used to stabilize the generated power from an HWPF with a WF and a PV farm fed to an MMPS. This paper has compared system-eigenvalue results for the studied system without ESS, with the VRFB-ESS, with the HESS, and has plotted the root-loci plots of the system under variable values of wind speed of the WF and the solar irradiance of the PV farm. Both dynamic and transient time-domain simulations subject to different disturbance conditions have also been performed. It can be concluded from the simulation results that the power smoothing characteristics of the studied system can be effectively improved by using the proposed HESS connected to the common DC link of the HWPF of the studied system.

## Availability of data and materials

Not applicable.

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## Funding

This research was supported in part by Higher Education Sprout Project, Ministry of Education to the Headquarters of University Advancement at National Cheng Kung University (NCKU).

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## Appendix

### Appendix

The employed parameters of the studied system are listed in Table 2.

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Wang, L., Ke, W.JY., Wu, RX. *et al.* Stability evaluation of a grid-tied hybrid wind/PV farm joined with a hybrid energy-storage system.
*Sustain Environ Res* **33**, 21 (2023). https://doi.org/10.1186/s42834-023-00181-y

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DOI: https://doi.org/10.1186/s42834-023-00181-y