# PV-based virtual synchronous generator with variable inertia to enhance power system transient stability utilizing the energy storage system

- Ju Liu
^{1}Email author, - Dongjun Yang
^{1}, - Wei Yao
^{2}, - Rengcun Fang
^{1}, - Hongsheng Zhao
^{1}and - Bo Wang
^{1}

**2**:39

https://doi.org/10.1186/s41601-017-0070-0

© The Author(s) 2017

**Received: **20 June 2017

**Accepted: **13 October 2017

**Published: **22 November 2017

## Abstract

The Photovoltaic (PV) plants are significantly different from the conventional synchronous generators in terms of physical and electrical characteristics, as it connects to the power grid through the voltage-source converters. High penetration PV in power system will bring several critical challenges to the safe operation of power grid including transient stability. To address this problem, the paper proposes a control strategy to help the PVs work like a synchronous generator with variable inertia by energy storage system (ESS). First, the overall control strategy of the PV-based virtual synchronous generator (PV-VSG) is illustrated. Then the control strategies for the variable inertia of the PV-VSG are designed to attenuate the transient energy of the power system after the fault. Simulation results of a simple power system show that the PV-VSG could utilize the energy preserved in the ESS to balance the transient energy variation of power grid after fault and improve the transient stability of the power system.

## Keywords

## 1 Introduction

Photovoltaic (PV) power is one of the prominent renewable resources and likely to replace a significant proportion of fossil-fuels in the future. With the increasing penetration of PV power, power system operators will encounter severer challenges [1–3]. Unlike synchronous generators, PVs are connected to the power grid through the voltage-source converters (VSCs). Thus, the PVs are significantly different from the conventional synchronous generators in terms of physical and electrical characteristics. Thus the high penetration PVs will deteriorate the frequency stability of power system. For the protection of the PVs, the power system with high penetration PVs must own the capacity of low voltage and high voltage ride through. What is more, the transient stability of power system with high penetration PVs is also a problem should be followed.

Transient stability is the ability of the power system to maintain synchronism when subjected to a severe disturbance such as a fault on transmission facilities, loss of generation, or loss of a large load. In the case of disturbances, conventional synchronous generators (SGs) are able to utilize the kinetic energy preserved in their rotational inertia to balance the potential energy variation of the power grid. Therefore, the system tends to stabilize again after disturbances. However, the inverter-based photovoltaic (PV) power stations do not have rotating elements and usually operate under the maximum power point tracking (MPPT) control strategy, which means it could not provide adequate energy, neither kinetic energy nor potential energy, to stabilize the power grid. Consequently, a power system with high-penetration of PV is prone to lose stability once disturbed.

In recent years, as an important part of smart grid, energy storage system (ESS) has been widely applied in power system [4–6]. One of the applications is the virtual synchronous generator. The VSG control strategy of ESS has been introduced as a promising solution to improve the stability characteristic of power system with high penetration renewable power. The VSG systems addressed in [7–9] are designed to connect an energy storage unit to the main grid. Rather than the traditional phase locked loop (PLL), the VSGs utilize the swing equation to synchronize with the grid. The VSGs could provide better active and reactive power to the power grid to improve the stability of power grid [10, 11]. In [12–15], different virtual synchronous generator control strategies have been proposed to improve the frequency, voltage, transient stability and damping characteristic of power system with renewable power generators. In [16, 17], the control strategies are designed to control the PVs and wind power to emulate the behaviors of the synchronous generators with energy storage system.

VSGs could model the rotational inertia of a synchronous generator through coordinating the active power output of the PV power station and an energy storage system (ESS) [18]. Once disturbed, the electrical power stored in the ESS could be exploited to dissipate the unbalanced energy. Then the power system with high penetration PVs could recover to a stable state. Moreover, the virtual moment of inertia of the VSG is adjustable, which is more beneficial to the transient stability of the power system than the fixed moment of inertia of SGs. Hence, this paper explores the feasibility of improving the transient stability of power system by using PV-VSG control strategy with variable inertia.

Different to the PV-VSG for frequency stability improvement, the main purpose of our research is to improve the transient stability of the power system. Thus the control strategy of the virtual inertia of the PV-VSG is also different from that of the PV-VSG for frequency stability improvement. In our paper, the PV-VSG control strategy is adopted to improve the transient stability of the power system. In order to achieve this goal, the virtual inertia of the PV-VSG should change according to the change of the transient energy of the power system. Hence, the main innovation and contribution of this paper is that a variable inertia control strategy of the PV -ESS is purposed according to the change of the transient energy of the power system, which is different from the PV-VSG for frequency stability improvement.

The rest of the paper is organized as follows. The overall PV-VSG control strategy is described in section 2. Section 3 proposes the inertia control strategy for transient stability improvement of power system with PV-VSG. A case study is undertaken on power system to verify the effectiveness of the proposed strategy in section 4. Discussion and Conclusions are drawn in section 5 and 6 respectively.

## 2 PV-VSG control strategies

VSC based converters have no inertia and the frequency of them is controlled just to follow grid frequency. Thus power systems will become unstable with high penetration PVs. Since synchronous generators have good capacity to regulate the frequency of power system, the concept that converters are controlled to express as a synchronous generator has been proposed which is called VSG. In this paper, we propose the PV-VSG control strategy to control the power output of the VSC based PVs and the ESS. The overall control strategy of the PV-VSG will be introduced in the follows.

### 2.1 Overall control scheme

*V*

_{grid}and the current

*I*

_{grid}at the PCC bus to calculate the power output

*P*

_{ out }of the PV-VSG and the rotation speed

*ω*

_{grid}of the power grid. Then the PV-VSG controller gives out the rotation speed deviation

*Δω*

_{VSG}of the PV-VSG and the ESS controller calculate the reference power output of the ESS. The detail control strategy of the controllers will be given out in the fellows.

### 2.2 Block diagram of VSG control strategy

*P*

_{ in },

*P*

_{ out },

*J*

_{vsg},

*ω*

_{ vsg }and

*D*are the input power (the same as the prime mechanical power of the SG), the output power, the virtual moment of inertia, the virtual angular velocity, and the virtual damping factor of the VSG, respectively.

*ω*

_{ grid }is the grid frequency,

*P*

_{ pv }and

*P*

_{ ess }is the power output of the PVs and the ESS. The input power

*P*

_{ in }of the VSG controller is the total power injected to the power grid by the PVs and the ESS.

### 2.3 Block diagram of ESS control strategy

*K*

_{ ess },

*T*

_{ ess },

*P*

_{ ess }and

*P*

_{max}are the gain, time constant, active power output and maximum power output of the ESS, respectively. If

*P*

_{ bess }is positive, the ESS releases energy to the power grid, otherwise, it absorbs energy from the power grid.

Since the stability controller is the main contribution of this paper, the next section will show the main idea of the stability controller.

## 3 Methods

The main purpose of the stability controller is to give out a variable inertia of the PV-VSG, thus the transient energy of the power system will attenuate and the power grid with PVs will recover to a stable state after the disturbance. This section will analyze the transient energy of the power system after the fault and obtains the relation between the virtual inertia of the VSG and the transient energy. According to the above relation, the virtual inertia control strategy of the PV-VSG is designed to make the transient energy decay to zero after disturbance.

### 3.1 Transient energy function (TEF)

*δ*

_{ AB }and

*ω*

_{ AB }denote the difference in power angles and angular speed between the center of inertia (COI) of areas A and B, respectively.

*P*

_{ A0}and

*P*

_{ B0}are the intimal differences between the total power generation and consumption in the two areas.

*P*

_{ A }and

*P*

_{ B }are the transmission power as shown in Fig. 4.

*J*

_{ A }and

*J*

_{ B }denote the moment of inertia of the two areas.

In (3), the first and second terms are the transient kinetic energy (TKE) and the transient potential energy (TPE), respectively. When a fault occurs, the power system will oscillate correspondingly. The transient KE and transient PE will transform mutually, however, their sum, the total OTEF will remain constant for a zero-damped oscillation. Hence the TEF descent method can be proposed to design an inertia controller to dissipate the unbalanced energy and suppress the power oscillation. Thus the power system recoveries to a stable state after fault quickly.

### 3.2 TEF descent method

Phase I is the backward acceleration phase. In this phase, the difference of the angular speed*ω*
_{
AB
} between the two areas is less than zero and the differential rate of *ω*
_{
AB
} is also less than zero. As a result, *ω*
_{
AB
} will decrease from zero to a minimum value *ω*
_{
ABmin} and *δ*
_{
AB
} will also decrease. The transmission power of the tie line will decrease to the minimum value, and the power change of the transmission power Δ*P*
_{
A
} will increase from zero to the maximum value as shown in Fig. 5 during the time from *t*
_{
a
} to *t*
_{
b
}.

Phase II is the backward deceleration phase. As shown in Fig. 5 during the time from *t*
_{
b
} to *t*
_{
c
}, *dω*
_{
AB
}/*dt* > 0 and *ω*
_{
AB
}will increase from the minimum value to zero. The difference of the angular speed satisfies *ω*
_{
ABmin} < *ω*
_{
AB
} < 0.

Phase III is the forward acceleration phase. During the time from *t*
_{
b
} to *t*
_{
c
}, the differential rate of *ω*
_{
AB
} keeps larger than zero. Thus the difference of the angular speed *ω*
_{
AB
} between the two areas will across zero to be positive and will reach the maximum value. That means 0 < *ω*
_{
AB
} < *ω*
_{
ABmax} and *dω*
_{
AB
}/*dt* > 0.

Phase IV is the forward deceleration phase. In this phase, during the time *t* ∈ [*t*
_{
d
}, *t*
_{
e
}] as shown in Fig. 5, 0 < *ω*
_{
AB
} < *ω*
_{
ABmax} and *dω*
_{
AB
}/*dt* < 0.

*t*

_{ e }could be calculated from the TPE at the time

*t*

_{ a }by the following equation.

*t*

_{ a }and

*t*

_{ e }will equal to each other. That meansOPE(

*t*

_{ e }) = OPE(

*t*

_{ a }), and we could obtain:

*P*

_{ B0}+

*P*

_{ B })

*dδ*

_{ AB }> 0, let \( \frac{1}{J_B^{\prime }}=\frac{1}{J_B}+\frac{1}{\Delta J} \); in phases III and IV, (

*P*

_{ B0}+

*P*

_{ B })

*dδ*

_{ AB }< 0, let \( \frac{1}{J_B^{\prime }}=\frac{1}{J_B}-\frac{1}{\Delta J} \). Then the OPE at the time

*t*

_{ e }becomes:

Since during the time from *t*
_{
a
}to *t*
_{
c
}, *dδ*
_{
AB
} < 0 and *P*
_{
B0} + *P*
_{
B
} < 0, the first term in (8) is larger than zero. The second term in (8) is also larger than zero because *dδ*
_{
AB
} and *P*
_{
B0} + *P*
_{
B
} are both larger than zero during the time from *t*
_{
c
} to *t*
_{
e
}. Thus with the control strategy proposed above, ΔTPE will be a positive value. The total TEF will descend continuously in every oscillation cycle and hence the unbalanced energy will be efficiently dissipated and the power swing will be effectively suppressed. The transient stability of the power system with high penetration PVs could be enhanced.

### 3.3 Stability controller for the VSG

*ω*

_{ AB }between the two areas is large than zero, increasing the virtual inertia of the PV-VSG is beneficial for the stable of the power system. When

*ω*

_{ AB }< 0, decreasing the virtual inertia of the PV-VSG could improve the stability of the power system. According to this rule, a bang-bang control strategy of VSG’s moment of inertia is proposed. The control strategy is illustrated in Fig. 6.

*J*

_{ vsg }is the variable moment of inertia of the PV-VSG. It is consisted by the variable part Δ

*J*and constant part

*J*

_{con}. Δ

*J*is a positive value,

*ε*is a small value chosen to eliminate measurement errors. Since in phase I and II, the difference of the angular speed

*ω*

_{ AB }is large than zero, the inertia of the VSG will be increased by Δ

*J*. The inertia of the VSG will be decreased by Δ

*J*when

*ω*

_{ AB }< 0. By applying this control strategy, the transient energy of the PV power system will attenuate quickly after the disturbance. Thus the transient stability of the PV power system will be enhanced.

## 4 Results

### 4.1 Description of the test system

*S*

_{ B }= 100MW,

*V*

_{ B }=

*V*

_{ N },

*f*

_{ B }= 50Hz.

To verify the effectiveness of the proposed control strategy of VSG’s moment of inertia, the following three typical control strategies are chosen to be studied.

MPPT: No VSG control strategy is applied, and the PV is operated under the MPPT mode.

Variable inertia: PV-BESS combined system operates under the modified VSG control strategy, the virtual moment of inertia is controlled by the bang-bang control strategy.

Constant inertia: PV-BESS combined system operates under the traditional VSG control strategy, the virtual moment of inertia is fixed. It is chosen as the average value of the inertia under the bang-bang control strategy.

### 4.2 The PVs under strong light

*ω*

_{ AB }> 0, namely the SG’s angular speed is faster than the VSG’s virtual angular speed, the virtual inertia of the PV-VSG

*J*

_{ vsg }turns to the maximum values and it equals to 35 pu. When the SG’s angular speed is lower than the PV-VSG’s virtual angular speed, namely

*ω*

_{ AB }< 0, the virtual inertia of the PV-VSG turns to a small value

*J*

_{ vsg }= 5 pu. Otherwise, if the angular speed difference between the SG and the PV-VSG satisfies the following relation |

*ω*

_{ AB }| < 0.001pu, the virtual inertia of the PV-VSG

*J*

_{ vsg }= 20pu. Under the constant inertia control strategy, the virtual inertia of the PV-VSG is fixed. It equals to the average value under the variable inertia case

*J*

_{ vsg }= 20pu.

### 4.3 The PVs under weak light

When the PV-VSG control strategy with constant inertia is utilized, the oscillation of the PV power system will slowly decay after the fault. The PV power system will recover to a stable state after more than ten oscillation cycles. The PV power system will be able to keep stable under the same fault. It indicates that the PV-VSG control strategy could improve the stability of the PV power system.

If the PV-VSG control strategy with variable inertia proposed in this paper is adopted, the ESS wills response to the disturbance after the fault. The virtual inertia of the PV-VSG is shown in Fig. 14. When the angular speed difference between the SG and the PV-VSG is larger than zero, the virtual inertia of the PV-VSG increases to 35 pu. Compared with that of the constant inertia case, the power output of the ESS will decrease. Then less unbalance transient energy will be injected into the PV power system. When the angular speed difference between the SG and the PV-VSG is less than zero, the inertia of the PV-VSG decreases to 5 pu. Then the power output of the ESS will be increased to suppress the unbalance transient energy. Under such a control strategy, the transient energy of the PV power system will decay quickly. The PV power system will recover to the stable state fast after the fault. The PV-VSG control strategy with variable inertia could further improve the stability of the PV power system.

## 5 Discussion

The PV-VSG control could help the PV power system keep stable after the fault. Especially, the variable inertia control strategy based on transient energy could help the PV power system suppress the transient energy. Thus the oscillation after the fault will decay quickly, which is beneficial for the PV power system to keep stable.

## 6 Conclusions

The VSG control strategy has been introduced to improve the power output characteristic of the renewable energy. Considering the adjustability of VSG’s virtual moment of inertia, we proposed a bang-bang control strategy for the VSG’s virtual inertia based on the TEF decay method. When the PV-VSG is on the receiving side, and the difference of the angular speed between the sending side and receiving side is positive, the inertia of the PV-VSG is set to a larger value, otherwise, it is set to a smaller value. Under this control strategy, the TEF of the power system after disturbance will decay quickly, and the transient stability of the power system with high penetration PVs will be improved.

## Declarations

### Authors’ contributions

Dr. LJ proposes the control strategy of the virtual synchronous generators (VSG); Dr. YDJ and Dr. YW offer the ideal of alternating inertia of VSG; Dr. ZHS, Dr. FRC and Dr. WB help to collect the data for simulation and achieve the simulation in MATLAB. All authors read and approved the final manuscript.

### Competing interests

The authors declare that they have no competing interests.

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

## Authors’ Affiliations

## References

- Kundur, P. (1993).
*Power System Stability and Control*. New York: McGraw-Hill.Google Scholar - Fang, D. Z., Xiaodong, Y., Wennan, S., & Wang, H. F. (2003). Oscillation transient energy function applied to the design of a TCSC fuzzy logic damping controller to suppress power system interarea mode oscillations.
*IEE Generation Transm Distrib, 150*(2), 233–238.View ArticleGoogle Scholar - Alipoor, J., Miura, Y., & Ise, T. (2015). Power system stabilization using virtual synchronous generator with variable moment of inertia.
*IEEE J Emerg Sel Topic Power Electron, 3*(2), 451–458.View ArticleGoogle Scholar - Khayyer, P., & Özgüner, U. (2014). Decentralized control of large-scale storage based renewable energy systems.
*IEEE Trans Smart Grid, 5*(3), 1300–1307.View ArticleGoogle Scholar - Sui, X., Tang, Y., He, H., & Wen, J. (2014). Energy-storage-based low frequency oscillation damping control using particle swarm optimization and heuristic dynamic programming.
*IEEE Trans Power Syst, 29*(5), 2539–2548.View ArticleGoogle Scholar - Gong, Y., Jiang, Q., & Baldick, R. (2016). Ramp event forecast based wind power ramp control with energy storage system.
*IEEE Trans Power Syst, 31*(3), 1831–1844.View ArticleGoogle Scholar - van Wesenbeeck M. P. N., de Haan S. W. H., Varela P., K. Visscher. Grid tied converter with virtual kinetic storage. in Proc. IEEE Bucharest PowerTech, Bucharest; 2009, pp. 1–7.Google Scholar
- Torres M., Lopes L. A. C. Virtual synchronous generator control in autonomous wind-diesel power systems, in Proc. IEEE Elect. Power Energy Conf. (EPEC), Montreal; 2009, pp. 1–6.Google Scholar
- V. Karapanos, S. de Haan, and K. Zwetsloot, “Real time simulation of a power system with VSG hardware in the loop,” in Proc. 37th Annu. Conf. IEEE Ind. Electron. Soc. (IECON), Nov. 2011, pp. 3748–3754.Google Scholar
- Liu, J., Miura, Y. S., Bevrani, H., & Ise, T. Enhanced virtual synchronous generator control for parallel inverters in microgrids.
*IEEE Trans Smart Grid*. doi:10.1109/TSG.2016.2521405. - Li, C. Y., Xu, J. Z., & Zhao, C. Y. (2016). A coherency-based equivalence method for MMC inverters using virtual synchronous generator control.
*IEEE Trans Power Delivery, 31*(3), 1369–1378.View ArticleGoogle Scholar - Shintai, T., Miura, Y., & Ise, T. (2014). Oscillation damping of a distributed generator using a virtual synchronous generator.
*IEEE Trans Power Delivery, 29*(2), 668–676.View ArticleGoogle Scholar - Hirase, Y., Sugimoto, K., Sakimoto, K., & Ise, T. (2016). Analysis of resonance in microgrids and effects of system frequency stabilization using a virtual synchronous generator.
*IEEE J. Emerg Sel Top Power Electronic, 4*(4), 1287–1298.View ArticleGoogle Scholar - Zhao, H. L., Yang, Q., & Zeng, H. M. (2017). Multi-loop virtual synchronous generator control of inverter-based DGs under microgrid dynamics.
*IET Generation Transm Distrib, 11*(3), 795–803.View ArticleGoogle Scholar - Lu, L. Y., & Chu, C. C. (2015). Consensus-based secondary frequency and voltage droop control of virtual synchronous generators for isolated AC micro-grids.
*IEEE J Emerg Sel Top Circuits Syst, 5*(3), 443–455.View ArticleGoogle Scholar - Liu, J., Wen, J., Yao, W., & Long, Y. (2016). Solution to short-term frequency response of wind farms by using energy storage systems.
*IET Renewable Power Generation, 10*(5), 669–678.View ArticleGoogle Scholar - Ma, Y. W., Cao, W. C., Liu, Y., Wang, F., & Tolbert, L. M. Virtual synchronous generator control of full converter wind turbines with short term energy storage.
*IEEE Trans Ind Electron*. doi:10.1109/TIE.2017.2694347. - Ortega, and F. Milano. Generalized model of VSG-based energy storage systems for transient stability analysis.
*IEEE Trans Power System*. 2015. doi:10.1109/TPWRS.2015.2496217.