Virtual Synchronous Generator Strategy for VSC-MTDC and the Probabilistic Small Signal Stability Analysis

Proceedings of the 20th World Congress Proceedings of the 20th World The International Federation of Congress Automatic Control Proceedings of the 20th World The International of Congress Automatic Control Available online at www.sciencedirect.com Toulouse, France,Federation July 9-14, 2017 The International Federation of Automatic Control Toulouse, France, July 9-14, 2017 Toulouse, France, July 9-14, 2017

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IFAC PapersOnLine 50-1 (2017) 5424–5429

Virtual Synchronous Generator Strategy for VSC-MTDC and the Probabilistic Virtual Synchronous Generator Strategy for VSC-MTDC and the Probabilistic Virtual Synchronous Generator Strategy for VSC-MTDC Small Signal Stability Analysis and the Probabilistic Small Signal Stability Analysis Small Signal Stability Analysis

Wang Weiyu*, Liu Fang**, Tan Yi*, Huang Jinhua***, Tang Shengwei***, Li Yong*, Cao Yijia* Wang Weiyu*, Liu Fang**, Tan Yi*, Huang Jinhua***, Tang Shengwei***, Li Yong*, Cao Yijia*  Wang Weiyu*, Liu Fang**, Tan Yi*, Huang Jinhua***, Tang Shengwei***, Li Yong*, Cao Yijia*  Hunan University, *College of Electrical and Information Engineering, Changsha, Hunan, China, 410082  Hunan University, Changsha, Hunan, China, 410082 *College of Electrical and Information Engineering, **School of Information Science and Engineering, Central South University, Changsha, Hunan, China, 410083 *College of Electrical Science and Information Engineering, Hunan University, Changsha, Hunan, China, 410082 **School of Information andofEngineering, Central South University, Changsha, Hunan, China, 410083 ***Electric Power Research Institute Guangdong Power Grid Co., Ltd, Guangzhou, Guangdong, China, 510080 **School of Information Science andofEngineering, CentralGrid South University, Changsha, Hunan, China, 410083 ***Electric Power Research Institute Guangdong Power Co., Ltd, Guangzhou, Guangdong, China, 510080 ***Electric Power Research Institute of Guangdong Power Grid Co., Ltd, Guangzhou, Guangdong, China, 510080

Abstract: In this paper, a new virtual synchronous generator (VSG) strategy based on the V22-P droop Abstract: In thisispaper, a new synchronous strategy based high on the V2-P droop control strategy proposed forvirtual the voltage source generator converter (VSG) based multi-terminal voltage direct Abstract: In thisispaper, a new virtual synchronous generator (VSG) strategy based high on the V -P droop control strategy proposed for the voltage source converter based multi-terminal voltage direct current strategy (VSC-MTDC) system. The VSG strategy enables the inverter stations tohigh damp the power control is proposed for the voltage source converter based multi-terminal voltage direct current (VSC-MTDC) The VSG for strategy enables inverter stations to damp the power oscillation and provide system. frequency support the AC system.the Virtual inertia coefficient is obtained to current (VSC-MTDC) system. The VSG for strategy enables theVirtual inverter stations to damp the power oscillation and provide frequency support the AC system. inertia coefficient is obtained to couple the DC voltage and the angular frequency. To provide the oscillation damping and frequency oscillation and provide frequency supportfrequency. for the AC Virtual inertia coefficient is obtained to couple voltagestations and thecould angular Tosystem. provideby thetheoscillation damping support,the theDC inverter adjust the output power adjustment of the and DC frequency reference couple the DC voltage and the angular frequency. To provide the oscillation damping and frequency support, could adjust power by thethere adjustment the DC reference -P droop method, is no of requirement for the voltage. the Dueinverter to the stations characteristic of thethe V22output support, the inverter stations could adjust theV output power by thethere adjustment of the DC reference -P droop method, is no requirement forsmall the voltage. Due to the characteristic of the 2 communication between inverter stations. The Monte Carlo method is used to test the probabilistic -P droop method,isthere is test no the requirement forsmall the voltage. Due tobetween the characteristic of the V communication inverter stations. The Monte Carlo method used to probabilistic signal stability of the VSG strategy. The The performance of the proposed controller is demonstrated by a communication between inverter stations. Monte Carlo method is used to test the probabilistic small signal stability of the VSG Theinperformance of the proposed controller is demonstrated by a hybrid AC/DC system whichstrategy. is modeled DIgSILENT/PowerFactory. signal stability of the VSG Theinperformance of the proposed controller is demonstrated by a hybrid AC/DC system whichstrategy. is modeled DIgSILENT/PowerFactory. hybrid AC/DC system which is modeled in DIgSILENT/PowerFactory. © 2017, IFAC (International Federation of Automatic Control) Hostingsmall by Elsevier Ltd. All rights reserved. Keywords: VSG, VSC-MTDC, Monte Carlo method, probabilistic signal stability. Keywords: VSG, VSC-MTDC, Monte Carlo method, probabilistic small signal stability. Keywords: VSG, VSC-MTDC, Monte Carlo method,  probabilistic small signal stability.  method and the burden of the power support is shared by all  1. INTRODUCTION method the burden of these the power support is shared alla inverter and stations. Among control strategies, thereby 1. INTRODUCTION alla method and the burden of these the power support is shared byis inverter stations. Among control strategies, there is 1. INTRODUCTION linearAmong relationship between the frequency Offshore wind farms (OWFs) develop rapidly in recent years. simplified inverter stations. these control strategies, there is a simplifiedandlinear between frequency Offshore wind source farms (OWFs) develop in recent years. the DCrelationship voltage variation, whichthe result in The voltage converter basedrapidly multi-terminal high deviation simplifiedandlinear relationship between themay frequency Offshore wind farms (OWFs) develop rapidly in recent years. deviation the DC voltage variation, which may result in The voltage source converter based multi-terminal inaccurate adjustment of variation, the power allocation ratio voltage direct current (VSC-MTDC) technology high is an deviation and the DC voltage which may result in The voltage source converter based multi-terminal high an inaccurate adjustment the power allocation ratio voltage direct current (VSC-MTDC) technology is between the inverter stations.of considered to be the most appropriate method to connect the an inaccurate adjustment of the power allocation ratio voltage direct current (VSC-MTDC) technology is between the inverter stations. considered be the most to connect the OWFs and to onshore powerappropriate grid. The method most critical control between the inverter stations. considered to be the most appropriate method to connect the A new technology called ‘virtual synchronous generator’ OWFs of andtheonshore power system grid. The most critical control object VSC-MTDC is to maintain stable DC A new technology called OWFs and onshore power grid. The most critical control (VSG) is proposed in recent‘virtual years. synchronous This method generator’ make the object of[1], the[2]. VSC-MTDC to maintain DC A new technology called ‘virtual synchronous generator’ voltage There are system several is mature control stable strategies (VSG) is proposed in recent years. This method make the object of the VSC-MTDC system is to maintain stable DC converters behave like a synchronous generator which could voltage [1], [2]. There are several mature control strategies is proposed in arecent years. This method make the for the VSC-MTDC system, such asmature voltagecontrol marginstrategies method, (VSG) converters behave like synchronous generator which could voltage [1], [2]. There are several contribute inertia for the power system. The grid frequency for the VSC-MTDC system, such as voltage margin method, converters behave like a synchronous generator which could voltage droop method and so on [3], [4]. Most of the contribute the power system. frequency for the VSC-MTDC system, such as voltage voltageinertia could for be coupled by using theThe VSGgrid strategy. The voltage droop method andonly so focus on [3], [4].margin Most method, of the and contribute inertia for the power system. The grid frequency traditional control strategies on the stability of the and voltage could be coupled by using the VSG strategy. voltage droop method and so on [3], [4]. Most of the power output of the inverterby stations is changing with The the traditional control strategies only focus on the stability of the and voltage could be coupled using the VSG strategy. DC grid, control while the state of AConsystem is ignored. powerofoutput the inverter stations changing with The the traditional strategies onlythe focus the stability of the state the ACof system [12] and [13]. is The VSG strategy is DC grid, while the state of the AC system is ignored. power output of the inverter stations is changing with the However, VSC-stations have no inherent inertia. An state of the AC system [12] and [13]. The VSG strategy is DC grid, while the state of the AC system is ignored. mostly used in the distributed generators (DGs), such as However, VSC-stations have noenergy inherent inertia. An state of the AC system [12] and [13]. The VSG strategy is increasing amount of renewable and VSC-MTDC mostly used in the distributed generators (DGs), such as However, VSC-stations have noenergy inherent inertia. An photovoltaic, wind turbine and energy storage [14]. The increasing renewable andstability VSC-MTDC used in the turbine distributed generators (DGs),[14]. suchThe as system mayamount lead to of a negative result that the of the mostly photovoltaic, wind andsource energyconverter storage increasing amount of renewable energy andstability VSC-MTDC capacity of grid-side voltage (GSVSC) system may lead to a negative result that the of the photovoltaic, wind turbine and energy storage [14]. The hybrid system will be reduced [5]. the stability of the capacity of grid-side voltage source converter (GSVSC) system AC/DC may lead to a negative result that station large enoughvoltage to have noticeable effect(GSVSC) on the hybrid AC/DC system will be reduced [5]. capacityis grid-side source converter isofoflarge enoughThe to VSG have noticeable effect onto the hybrid AC/DC system will be reduced [5]. control strategies station stability the system. technique is suitable be To overcome the defects of the traditional station isof large enoughThe to VSG have technique noticeableis effect onto the stability the system. suitable be To overcome the defects of the traditional control strategies applied on the VSC-MTDC system. of the VSC-MTDC system, many researchers have made stabilityon of the theVSC-MTDC system. The system. VSG technique is suitable to be To overcome the defects of the traditional controlhave strategies applied of the VSC-MTDC system, many researchers made great efforts to system, develop many innovative methodss. A applied on the VSC-MTDC system. of the VSC-MTDC researchers have made great efforts to control develop innovative methodss. A Because of the fluctuation of wind speed, the power output of communication-free strategy has been proposed in [6] of the fluctuation of wind power output of great efforts to control develop innovative methodss.in [6] A Because wind turbines is inconstant. Thespeed, loadthe demand and the communication-free strategy has been proposed Because of the fluctuation of wind speed, the power output of and [7], which could enable the inverter stations to adjust the wind turbines is inconstant. The load demand and the communication-free control strategy has stations been proposed in the [6] operation state of transmission tie-lines are also stochastic. and [7], which could enable the inverter to adjust wind turbines is inconstant. The load demand and the output to thethestate of thestations AC system. What’s operation state of transmission tie-lines are(PSSSA) also stochastic. and [7],power whichaccording could enable inverter to adjust the Probabilistic small signal stability analysis is often output power according to the state of the AC system. What’s operation state of transmission tie-lines are(PSSSA) also stochastic. more, wind turbines store a large quantity of kinetic energy Probabilistic small signal stability analysis ispower often output powerturbines according to the statequantity of the AC system. What’s performed to evaluate the stability of the hybrid more, wind store a large of kinetic energy Probabilistic small signalthe stability analysis (PSSSA) ispower often which could turbines be used to provide frequency support. However, performed to evaluate stability of the hybrid more, wind store a large quantity of kinetic energy system. Theto most accurate method ofis the the hybrid Monte power Carlo which could be used to provide frequency support. However, performed evaluate the stability drawing too much kinetic energy from the rotor may lead to system. The accurate method is the Monte Carlo which could be used to provide frequency However, [15].most drawing too much kinetic thesupport. rotor to simulation system. The turbines stalling. Power energy marginfrom method of may the lead wind simulation [15].most accurate method is the Monte Carlo drawing too much kinetic energy from the rotor may lead to turbines stalling. Power to margin of the wind simulation [15]. 2 generators are also utilized providemethod the primary frequency turbines stalling. Power to margin method of the wind In this paper, a novel VSG strategy based on the V2-P control generators are also utilized provide the primary frequency -P provide control In this paper, a novel VSG strategy based on the V regulation [8] and [9], which could not make full use of wind is proposed. controller enablesbased the GSVSCs generators are and also[9], utilized tocould provide the primary frequency -P provide control In this paper, The a novel VSG strategy on the V2to regulation [8] which not make full use of wind is proposed. The controller enables the GSVSCs to energy. In[8] [10] and [11], a could frequency droop controller is frequency support and oscillation damping. The DC reference regulation and [9], which not make full use of wind is proposed. The controller enables the GSVSCs to provide energy. In [10] a frequency droop controller is frequency support and oscillation damping. The DC reference investigated. The and AC [11], grid frequency is used as the feedback is changed autonomously in a narrow range to mimic energy. In [10] and [11], a frequency droop controller is voltage frequency support and oscillation damping. The DC reference investigated. The AC grid frequency is used as the feedback voltage is changed autonomously inmover. a narrow range to mimic signal to change the power output instructions of inverter the action of the valve of prime Thus, the output investigated. The AC grid frequency is used as theoffeedback voltage is changed autonomously inmover. a narrow rangethe to mimic signal to change the power output instructions inverter the action of the valve of prime Thus, output stations. The frequency deviation could be minimized by this power will be redistributed among the GSVSCs according to signal to change the power output instructions of inverter the action the valve of among prime the mover. Thus,according the output stations. The frequency deviation could be minimized by this power will of be redistributed GSVSCs to stations. The frequency deviation could be minimized by this power will be redistributed among the GSVSCs according to Copyright © 2017, 2017 IFAC 5604Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Copyright 2017 responsibility IFAC 5604Control. Peer review©under of International Federation of Automatic Copyright © 2017 IFAC 5604 10.1016/j.ifacol.2017.08.1077

Proceedings of the 20th IFAC World Congress Toulouse, France, July 9-14, 2017 Wang Weiyu et al. / IFAC PapersOnLine 50-1 (2017) 5424–5429

the state of the AC system. The Monte Carlo simulation is utilized to test the performance of the VSG strategy. The test system is modelled in DIgSILENT. The rest of the papers are organized as followings: Part 2 presents the new VSG strategy based on the V2-P droop method. Part 3 introduces the implication of the Monte Carlo method on the PSSSA. Part 4 shows the performance of the VSG strategy and the result of PSSSA. 2. SYNCHRONVERTER CONTROL STRATEGY

5425

C V dc d V dc S vsc

dt

 Pr e c *  Pin v *

(2)

where the Svsc is the rated power capability of VSC-station; Prec represents the rectifier power input to VSC-MTDC system; Pinv is the GSVSC power output to AC grid; C represents the capacitance of DC capacitors; Vdc is DC voltage of MTDC system. According to equation (2), the V2-P control method can be derived as 2

 P  K droop  V dc

The power balance in the GSVSC is similar to synchronous generator, which can be explained by Fig. 1. Prime mover

Ek

Pm

where Kdroop is the droop coefficient; ΔV dc is the DC voltage deviation and the ΔP is the additional power signal for GSVSC. The Kdroop determines the power allocation ratio of the VSC-MTDC system. However, Kdroop will keep constant in a relatively short period until the transmission system operator (TSO) change it. Thus, traditional V2-P control method is unable to provide oscillation damping or fast frequency support.

grid

SM

Pe

Prec

Pinv PCap

+ MTDC network

Vdc

Equation (3) indicates that GSVSC will get more power by the adjustment of the DC reference voltage. With this characteristic, the DC reference voltage would change with the frequency deviation in order to provide frequency support, which is just like the adjustment of prime mover’s valve. Based on equation (1) and (2), the relationship between the DC voltage and angular frequency can be derived as

GSVSC grid

Fig. 1 The comparison of GSVSC and synchronous generator

2H

The imbalance power of AC grid will lead to frequency deviation, which could be explained by swing equation. 2H

d* dt

 Pm *  Pe *  D (  *   0 * )

(3) 2

The mismatch between Pm and Pe which is caused by the change of load demand or the disturbance on the prime mover will change the rotor speed. The kinetic energy stored in the rotor could compensate partial of the imbalance power. With the deceleration (or acceleration) of the rotor speed, the governor of the generator will take a sequence of actions to adjust the position of valve of steam turbine. Thus the power output of prime mover will be adjusted until the system reaches a new equilibrium point. There is a similar feature for the GSVSC. The power injected by DC grid can be thought as the prime mover power and the power output of the GSVSC can be considered as the electromagnetic power. In consideration of the fluctuation of wind power, the DC voltage will change instantly as long as the GSVSC did not timely adjust its reference power. The energy stored in the DC capacitors will compensate partial of the imbalance power, which could be explain by the following equation



C V dc d V dc

dt

S vsc

(4)

dt

Integrating both sides of (4) yields the following equation:  V dc

(1)

where ‘*’ represents the per unit value; ω is the angular frequency and ω0 represent the rated angular frequency; Pm and Pe are the prime mover power and the electromagnetic power, respectively; H is the inertia constant; D represents the damping factor.

d* vsc

2



4H

vsc

S vsc



(5)

C

where Δω represents the deviation of angular frequency in AC grid; Hvsc represents the virtual inertia constant. The physical meaning of Hvsc is the time required for the capacitor to reach the rated voltage from zero. The value of Hvsc is determined by H



vsc

C V dcn

2

(6)

2 S vsc

where Vdcn represents the rated voltage of GSVSC. Considering that the regulation of the valve of steam turbine has a certain delay, the first order process should be taken into account.  V d c _ ref

2

1



 V dc

1  sT

2

(7)

where T is the time constant. The typical range of T is from 0.1s to 0.4s. Based on the above analysis, the virtual swing equation could be derived as 2H

2

d* vsc

dt

2

2

2

 Pr e f 0 *  K [V d c  (V d c _ r e f   V d c _ r e f )] 

(8)

Pin v *  D v s c (    0 )

where ΔV dc_ref is the correction of DC reference voltage, which can be obtained by equation (5) and (7).

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Equation (8) indicates that any imbalance power (whatever is in AC side or DC side), the GSVSC will adjust its DC reference voltage to compensate the mismatch power. Thus, the VSG strategy is able to damp oscillation and provide frequency support for the AC system. What’s more, there is no demand for the communication in the hybrid system. The control block diagram of VSG strategy is sketched in Fig 2. Prec

GSVSC

+ MTDC network

Pgrid

PCC

Vdc

P

PWM

Qref Pref Pref0

-

Q

- -

2

The Weak Law of Large numbers and the Central Limit Theorem are the foundations of the Monte Caro simulation. The random operation modes of the power system are independent of each other. According to the SSSA, the power system is instable when any one of the system eigenvalues’ real part σ is positive. The notation Ri is used to represent the stability of a random scenario of the power system

ω

dqcontroller

2sHvsc+Dvsc

K

Vdc_ref2

3.2 The process of PSSSA and the stability index

iq

id

θ

M

abc dq

(3) Random operation state of transmission tie-lines The operation state of transmission tie-lines are mutualindependent. A transmission line will be cut off according to the uniform distribution between [0, L] (L represents the total number of transmission lines) in each random scenario.

Grid

iabc

-

where Pm0 and Pm represent the mean and random load value respectively; r1 and r2 are the random number generated by the uniform distribution.

Equation (7)

Equation (5)

ΔVdc Δω

Vdc

V 2-P Droop controller

-

ω0

Fig. 2 The control block diagram of VSG strategy 3. PSSSA FOR the VSC-MTDC SYSTEM

Set the total sample number N i=1 Generate random wind speed, random load and random fault on transmission lines

3.1 Distribution of random variables (1) Random wind speed Two-parameter Weibull distribution is used to describe the random wind speed: v

v k 1  ( ) ( ) e c c c

Power flow calculation

Small signal stability analysis i=i+1

k

(9)

where v is the wind speed; c represents the scale parameter, which reflects the mean wind speed; k represent the shape parameter, which reflects the characteristic of the distribution of wind speed. In this paper, c=11m/s, k=2.06. The random wind speed can be obtained by v   c k ln ( rw  1)

Calculate the Punstable by (13) Satisfying the convergence condition? yes

(10)

(2) Random load demand The load demand generally meets the normal distribution, which can be obtained by the Box-Muller method.  2 lo g r1  c o s 2  r2 )

no

yes

where rw is a random number which generated by the uniform distribution.

Pm  Pm 0 (1   % 

(12)

PSSSA start

The Monte Caro method can provide the most accurate evaluation of the system stability by a large number of random scenarios. Accumulation of the SSSA for all of the random scenarios constitutes the distribution of the dominant oscillation modes.

k

i  0

The random variable Ri meets the 0-1 distribution. When Ri equals to 1, it means that the power system is instable. Thus, the instability of the system can be measured by the expected value. A more detailed introduction of the application of the Monte Carlo method to power system can be found in [15].

VSG additional controller

f (v; c, k ) 

i  0

 1, Ri    0,

ω

i ≤ N? no end

Fig. 3 The procedure of PSSSA

(11) According to the Monte Caro simulation, a lot of results are obtained to evaluate the system stability. So long as the real 5606

Proceedings of the 20th IFAC World Congress Toulouse, France, July 9-14, 2017 Wang Weiyu et al. / IFAC PapersOnLine 50-1 (2017) 5424–5429

part of eigenvalue is positive, the power system is considered to be instable. The probability of instability can be defined as the following equation Pu n s ta b = R n =

R1 

 Rn

(13)

n

4. CASE STUDY

The change of D has a little impact on the eigenvalues, which means that D is not a critical parameter for system stability. To test the impact of different combinations of Hvsc and D on the damping oscillation, a three-phase fault at the bus 16 in 39-bus system has been set. After 4 cycles (0.08s), the fault is cleared. The power oscillation of the transmission line 1-2 is shown in Fig. 6.

A 5-terminal VSC-MTDC system which connects two OWFs and onshore power grids is used to test the probabilistic stability assessment (PSA) of the hybrid AC/DC system. Two of the GSVSCs are connected to the modified IEEE 39-bus system at bus 2 and bus 9, respectively. Another GSVSC connects an isolated grid which is modified by the WSCC 9bus system. Each OWF contains 60 DFIGs with a rated power of 4MW. The generator at bus 34 is out of service because of the integration of VSC-MTDC system. The topology of the system is shown in Fig. 4. The test system is developed in DIgSILENT/ PowerFactory. The parameters of DFIG and DC cable are obtained from the library of DIgSILENT/PowerFactory.

λ119

λ245

Offshore wind farm 1

GSVSC1

1

WFVSC1

5

Offshore wind farm 2

PCC1

6 9

13

7 8

PCC2

G G02

14

31

19 20

10 32 34 G G03

λ141

38 G G09 21

24 G

12 11

λ128

29

28 16

4 15

39

GSVSC2

26 27 17

18

3

G01 G

MTDC system

λ115

(a)

G08 25

λ132

λ134

IEEE 39-bus system G10 G 37 G 2 30

5427

33 G G G04 G05

36 23

22 35 G G07

WFVSC2 GSVSC3

41

40

42 G G11 44

43

45

Isolated grid

46 G G12

Fig. 4 The diagram of the test system (b) 4.1 The influence of the VSG parameters

Fig. 5 The root locus: (a) change Hvsc;(b) change D

The most significant parameters of the VSG strategy are Hvsc and D. The inertial time constant of synchronous generator is in a range of 2~10 s. However, one of the advantages of the VSG strategy is that the Hvsc can be changed by the requirement of the specific system. To investigate the influence of Hvsc and D on oscillation damping, the value of Hvsc is changed from 0 to 10s with a step of 0.1s and D is changed from 0 to 50 with a step of 1. The root locus of the hybrid system is shown in Fig. 5. With the increase of Hvsc, the damping ratio of some eigenvalues (e.g. λ126, λ115, λ132) increases, while some others decreases (e.g. λ141 λ119). Specifically, the traces of λ130, λ134, λ128 have a complicated movement. The damping ratio of λ134, λ128 increases at first and then decreases from the inflection point. λ130 have the opposite performance. Thus, it is important to find a reasonable Hvsc to enhance the stability of the hybrid AC/DC system. Fig. 6 The power oscillation under different parameters

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Fig. 6 verifies the result of root locus that Hvsc have a significant effect on oscillation damping. However, when Hvsc is greater than 1s, there is no more enhancements for the oscillation damping. According to Fig. 5 and Fig. 6, the Hvsc and D should be set to 1s and 10. 4.2 The frequency support by VSG strategy The ability to provide frequency support of VSG strategy can be verified by several cases. Considering the page limit, a GSVSC outage case is used to show the performance of the VSG strategy. GSVSC1 is out of service at t = 1s and the power output of GSVSC1 (236.41MW) is immediately redistributed to GSVSC2 and GSVSC3. Under the traditional droop strategy, the remaining GSVSCs have no ability to adjust output power. The generators 11 and 12 in the isolated grid decrease the generation power significantly and the rotor speeds increase rapidly. It can be observed from the dashed lines of Fig. 7(b) that the bulk power injection results in a large frequency deviation because of the small size of the isolated grid.

PSSSA was performed on a Samsung laptop with Intel (R) Core (TM) i7-5500U, 2.9 GHz processing speed, and 8 GB RAM. 20,000 trials are generated according to the combination of random wind speed, random load demand and random transmission tie-line fault. The eigenvalues of the dominant oscillation modes are shown in the Fig. 8. Fig. 8(b) indicates that more eigenvalues are located in the weak damping area (the red area) when the system adopted the traditional droop method. Fig. 8(a) shows that less eigenvalues located in the weak damping area. The VSG strategy is capable to increase the damping ratio of the poorly damped modes significantly and the instability probability of oscillation modes is eliminated.

With the VSG strategy, the power ratio between GSVSC2 and GSVSC3 is not fixed at 1:2. The power output of GSVSC is continually adjusted according to the frequency deviation of the adjacent AC system. Thus, much more power is allocated to GSVSC2 while GSVSC3 maintain nearly its initial output power (Fig. 7(a)). Fig. 7(b) shows the effectiveness of reduction of the frequency deviations in two onshore grids.

(a)

(b)

(a)

Fig. 8 The eigenvalues distribution on the s-plane: (a) VSG strategy; (b) traditional droop control method The comparison of the instable probabilities for the system with different control strategies is shown in Fig. 9.

(b)

Fig. 7 System responses in the case of the GSVSC outage: (a) power output of GSVSCs; (b) grid frequency 4.3 PSSSA for VSC-MTDC with VSG strategy

Fig. 9 The convergence of the different control method 5608

Proceedings of the 20th IFAC World Congress Toulouse, France, July 9-14, 2017 Wang Weiyu et al. / IFAC PapersOnLine 50-1 (2017) 5424–5429

Fig. 9 shows that the VSG strategy could enhance the stability of the hybrid AC/DC system. The instability probability of the system with traditional droop method is 3.16% while the VSG strategy is only 2.24%.

[14] T. Shintai, Y. Miura, and T. Ise, “Oscillation damping of a distributed generator using a virtual synchronous generator,” IEEE Trans. Power Del., vol. 29, no. 2, pp. 668–676, Apr. 2014. [15] Rueda J L, Colomé D G, Erlich I. Assessment and enhancement of small signal stability considering uncertainties[J]. IEEE Trans. Power Syst., 2009, 24(1): 198-207.

5. CONCLUSION This paper proposed a new virtual synchronous generator strategy for VSC-MTDC system. To minimize the frequency deviation, the DC grid could mimic the action of the prime mover’s valve to change the power injected into the GSVSC. Additional damping ability is obtained by the VSG strategy for the VSC-MTDC system to damp the power oscillation. The Monte Carlo method is used to test the stability of the hybrid AC/DC system. The results show that the probabilistic small stability of the hybrid AC/DC system which adopts VSG strategy is enhanced significantly. ACKNOWLEDGMNETS This work was supported by the project on "Advanced Application and Simulation System for Low Frequency Oscillation Analysis" under Grant GDDW2120160303AS00187. REFERENCES [1]

[2]

[3]

[4]

[5]

[6]

[7]

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