power system stability control using voltage source ... · th 18 power systems computation...

18th Power Systems Computation Conference Wroclaw, Poland – August 18-22, 2014

Power System Stability Control using VoltageSource Converter Based HVDC in Power Systems

with a High Penetration of RenewablesMarkus Imhof, Goran Andersson

ETH Zurich,Switzerland

Email: {imhof, andersson}@eeh.ee.ethz.ch

Abstract—This paper demonstrates the stabilization of a largepower system with a high penetration of Renewable EnergySources, such as wind or photovoltaic, using Voltage SourceConverter based HVDC links. Due to the reduction of systeminertia, frequency oscillations are expected to increase unlessadditional control measures are added to the system. Based onglobal power system measurements, a Model Predictive Controlscheme, which modulates the power injections of the HVDC link,will enable the additional controllability to damp the poweroscillations and stabilize the system. Scenarios with differentpenetrations of renewables and disturbance cases are simulatedin the continental European power system. The simulationsillustrate the performance enhancement gained by the globalModel Predictive Control-based grid controller, compared toa local control scheme and HVDC links with constant powerinjections.

Index Terms—Converters, HVDC transmission, MPC, Powersystem dynamics, Power system modeling, Power oscillationdamping, Reactive power control, VSC-HVDC.

I. INTRODUCTION

In recent years, the role of Renewable Energy Sources(RES) have become much more prominent. In Germany theshare of RES, like wind and solar power, was 17 percentof the total energy production in the year of 2011 [1] andis predicted to grow up to 38 percent in the next ten years[2]. Other countries, such as Spain and Italy, made substantialinvestments into wind and solar power as well.

With the increasing share of RES, the classical structureof the transmission system, where large thermal power unitsinject power at the highest voltage level which is transmittedto the loads in the distribution system, changes to a moredistributed production of power [3]. The decommissioningof large thermal units, connected to the power system withsynchronous generators, reduces the amount of inertia of thesystem. Most RES are connected either through power con-verters, such as Photovoltaic (PV) or full converter wind tur-bines, which do not provide inertia, or through asynchronousgenerators, such as Doubly Fed Induction Generator (DFIG)wind turbines, which provide only a limited amount of inertia.It is expected that, with a lower system inertia, deviationfrom the nominal frequency will increase. This becomes ofincreasing concern with the liberalized market, when morepower is traded and the generators can change their set-pointsevery 15 minutes [1], [4].

Voltage Source Converter (VSC) based High Voltage DC(HVDC) links are a viable solution for grid expansion plan-ning. The power capacity has increased from 50 MW of thefirst commercial project in Gotland, Sweden in 1999 [5] toover 1000 MW for the Aachen Liege Electric Grid Overlay(ALEGrO) project which will be commissioned at the endof 2017 between Belgium and Germany [6]. One of themain advantages compared of Current Source Converter (CSC)based HVDC technology is that active and reactive powercan be controlled independently of each other. FurthermoreVSC-HVDC links can be connected to weak networks and thedirection of power can be reversed much faster, particularlyfor cable interconnections [7]. This puts the VSC-HVDCtechnology at an interesting point for use in power systemstability control. The HVDC links can not only be used forpower transmission, but also as power system stabilizers. Acontrol entity, such as the Transmission System Operator(TSO), is then able to control the set-points of the VSC-HVDClinks.

This paper shows how VSC-HVDC links are able to addcontrollability to a system with a high penetration of RES.With the modulation of active and reactive power of the VSC-HVDC links, using a global Model Predictive Control (MPC)controller, damping is added to the system.

This paper is structured as follows: Section II explainsthe challenges of introducing large shares of renewables tothe power system. Section III presents the global powermodulation controller of the VSC-HVDC links and Section IVexplains how the power system was modelled for this study.Section V shows how the global grid controller is able to helpstabilize the power system after a disturbance and Section VIconcludes the paper.

II. INTEGRATION OF RENEWABLE ENERGY SOURCES

In the last 20 years the amount of energy produced by REShas increased tremendously. In Europe the production of REShas more than doubled from 2000 to 2010, and had an overallshare of 17.1% in 2010 [8]. It is expected that the share ofRES will rise in the next years to meet the European climategoals. This leads to the decommission of thermal power plantswhere synchronous generators are connected to the grid.


In a system consisting mostly of synchronous generators, thesystem frequency varies with the imbalance between energysupplied and the energy consumed. The principal frequencydynamics of the system can be described by the nonlineardifferential equation.

dΔω

dt=

ω20

2HSBω(Pm − Pe) , (1)

where ω is the frequency at the Center of Inertia (COI)

ω =

∑ngen

i=1 Hiωi∑ngen

i=1 Hi

, (2)

with ngen the number of synchronous generators connected tothe system and it holds as well

ω = ω0 +Δω . (3)

The total mechanical power is defined as Pm and the totalelectrical power as Pe. SB is the total rating of the system. His the total inertia constant and is defined as

H =

∑ngen

i=1 HiSBi

SB. (4)

Hi is the inertia constant and SBi the power rating of eachgenerator, ω0 is the nominal frequency [9].

In an event of a sudden loss of generation or a suddenconnection of a large load, the system frequency will start de-creasing as suggested by (1). The rate of change is determinedby the total inertia H of the system. If this inertia is reduced,for example due to the connection of generation without, oronly very small inertia, such as PV or wind, the system will beweakly damped and frequency oscillation will become moreprominent [10].

The frequency oscillations can be reduced by inertia mim-icking, either by the controller of the RES converters, as in[10] or [11], or by using other power system stabilizer likeVSC-HVDC. This paper will show that frequency oscillationscan be damped efficiently using already existing VSC-HVDClinks.

III. POWER SYSTEM CONTROLLER

The global grid controller will modulate the active andreactive power of all the VSC-HVDC terminals in the systemusing a MPC control scheme. A classical approach is thedesign of a controller using local measurements at the HVDCterminal [12], [13]. The optimal controller tuning dependsstrongly on the location of the VSC-HVDC link as well asthe grid topology and the oscillation modes of interest. On thecontrary, a MPC-based control scheme could react to changesto the system without additional tuning of the controller [14].The MPC based control scheme has been chosen because itdoes not has to be adapted to system changes, it is able topredict the future system behaviour according to the systemmodel and allows the VSC-HVDC link to react faster then aclassical control scheme. Another strengths is that constraintson inputs and outputs can be handled in a straightforwardmanner.

This MPC-based controller was first introduced in [15] andfurther developed in [16] for use in a large power system.The controller first obtains an estimate of the system model’sdynamic state. The future behavior of the system is predictedand the new VSC-HVDC set-points are determined by anoptimization on a time-discrete model of the system. Thecontroller operates with a fixed sampling rate.

A. Global MPC-based grid controller

The global MPC-based grid controller operates with asampling time of TMPC. At each sampling time tk the controllerobtains the system discrete state xk. This is determined by thelinearized and discretized system model

xk+1 = Axk + Buk + f0 , (5)

yk = Cxk + Duk . (6)

xk are the dynamic states and f0 the initial derivative term ofthe system at time tk. uk is the input vector and consists ofthe active and reactive power injection references

uk = [P1,ref,1, Q1,ref,1, Q2,ref,1, . . . ,

. . . , P1,ref,m, Q1,ref,m, Q2,ref,m]� (7)

for each terminal, where m denotes the number of HVDC linksin the system. yk is the system output vector used to formulatethe control objective. For this paper, the frequencies of the ngen

synchronous generators of the system were chosen:

yk = [ω1, . . . , ωgen]� (8)

The primary objective of the VSC-HVDC grid controllerduring transients is to damp power oscillations and giveadditional damping to the system. This means the frequencydeviations of the synchronous generators from the average sys-tem frequency (2) will be minimized. The objective functionJ is the weighted sum of the relative squared frequency errorsof each generator from the COI.

J(t) =

∑ngen

i=1 Hi (ωi(t)− ω(t))2∑ngen

i=1 Hi

(9)

The parameter σ is introduced which is the standard deviationand expresses the average frequency deviation of the genera-tors from the COI. It is defined as

σ(t) =

√1

ngenJ(t) . (10)

The objective function (9) can be rewritten as a quadraticmatrix expression

Jk = J(tk) = z�k Qzk zk =[x�k u�

k 1]�

(11)

where

Q = Z�diag(h)Z , (12)

Z = [I − M] · [C,D, y] , (13)

M = [h,h, . . . ,h]� , (14)

h =[Hi, . . . , Hngen ]

�∑ngen

i=1 Hi

. (15)


The quadratic optimization problem for each sampling timestep k∗ is stated as follows:

minuk∗ ,...,uk∗+N

k∗+N∑k=k∗

Jk (16)

s.t. ∀k ∈ {k∗, k∗ + 1, . . . , k∗ +N}(5), (12). . . (15) ,

umin ≤ uk ≤ umax , (17)

dmin ≤ uk − uk−1 ≤ dmax . (18)

The future behavior of the system is considered over thehorizon of N time steps. The adjustment of the VSC-HVDCpower injections that best enhances the power system is thengiven by uk∗ , the first element of the resulting optimizationsequence. Inequality (17) makes sure that the power ratinglimits are not violated, and (18) states how large the referencechange compared with the last control action can be. The newreference values uk∗ are sent to all VSC-HVDC terminalswhich change to a new set-point for the active and reactivepower. The internal controller of the VSC-HVDC terminalsthen controls the powers and reassures that all values are keptwithin their limits. The reference is kept constant for the entiresampling interval TMPC until a new reference value is obtainedby the MPC grid controller.

B. Local Damping Controller

A local damping controller changes the power injectionsof the HVDC link based on measurements at the converterterminals and will be used for comparison to the HVDC linkoperated with the global MPC-based grid controller. In thisstudy, the controller of [13] is used, which chooses the HVDCsactive power adjustments ΔP with a PD-controller and a lowpass filter. The required measurement is the difference of thefrequencies (ω1, ω2) at the HVDCs two converter stations. Theresulting controller transfer function is

ΔP =

(KP +

sKD

1 + sTD

)· (ω1 − ω2) . (19)

The gains of the PD controller are tuning parameters andare selected as KP = 150 , KD = 20 and TD = 0.05 s. Thetuning was done by trial and error, the values of [13] yieldedthe best results.

IV. POWER SYSTEM MODEL

The power system model used for this study is a reduceddynamic model of the European Network of TransmissionSystem Operators for Electricity (ENTSO-E) continental Eu-ropean grid, shown in Fig. 1.

It consists of 74 busses connected by 131 AC lines witha nominal voltage of 380 kV. At each node, an aggregatedpower plant and load is connected. There are four differenttypes of generation technologies: thermal units, hydro storage,wind power plants and PV units as depicted in Fig. 1.

The thermal and hydro storage power plant models consistof an electrical and a mechanical part: The electrical model

Fig. 1. European dynamic test system. Black lines represent AC lines, andbold blue lines VSC-HVDC connections.

TABLE IPARAMETERS OF THE VSC-HVDC LINKS

Placement Name Length Rated Power DC Voltage

Italy to Greece HVDC1 316 km 1216 MW ±320 kV

France to Spain HVDC2 67 km 2432 MW ±320 kV

Belgium toHVDC3 94 km 1216 MW ±320 kV

Germany

North to SouthHVDC4 700 km 1216 MW ±320 kV

of Germany

comprises an automatic voltage regulator (AVR), a power sys-tem stabilizer (PSS) and the electrical part of the synchronousgenerator. The mechanical model includes the primary fre-quency control, the turbine model and the mechanical partof the synchronous machine. The synchronous generators aremodelled as a 6th order model according to [9]. The windturbines are assumed to be full converter units according to[17] and are modelled as controlled power source withoutinertia. The PV installations do not contribute any inertia andare modelled as controlled power sources without inertia.

Four bipolar VSC-HVDC links, dynamically modeled ac-cording to [18] with a DC voltage of ±320 kV, are placedin the European system, shown as bold blue lines in Fig.1. The placement of these links was done (a) accordingto already existing CSC-HVDC corridors, such as the DCconnection between Italy and Greece (HVDC1) [19], (b) VSC-HVDC links which are under construction as the France-SpainElectrical Interconnection (inelfe) between France and Spain(HVDC2) which will be commissioned 2014 [20], or theALEGrO Project between Belgium and Germany (HVDC3)[6], or (c) distant projects, such as the Germany north-southinterconnection (HVDC4). The length, power and voltageratings are presented in Table I.


TABLE IISIMULATION SCENARIOS

Scenario Installed Ca- Share Tot. System Controlpacity of RES of RES Inertia H Type

1. no RES – – 6.29 1/s no

2a. RES72.66 GW 21% 4.96 1/s no

normal

2b. RES72.66 GW 21% 4.96 1/s local

normal

2c. RES72.66 GW 21% 4.96 1/s MPC

normal

3a. RES116.85 GW 32% 4.20 1/s no

high

3b. RES116.85 GW 32% 4.20 1/s local

high

3c. RES116.85 GW 32% 4.20 1/s MPC

high

V. SIMULATION RESULTS

This paper investigates two disturbance cases on threedifferent RES generation scenarios. In each scenario the totalinstalled capacity of the system is 352 GW and the total load is256 GW. The initial operating point of the simulated scenariosis derived from measurements in the ENTSO-E grid. The threescenarios differ by the amount of RES installed in the systemand thus by the total system inertia H . The first scenario is thereference scenario without any RES installed in the system. Inthe second scenario the amount of RES is increased to 21% ofthe total load of the system. The initial production technologyis changed to RES as seen in Fig. 1 depicted with black windturbines. It is mainly produced in the north at the coasts ofGermany, Belgium, the Netherlands and France and in thesouth at the coast of Spain. In scenario 3 the production fromRES is further increased to 32% of the total energy production.The production in the south of Germany is changed to PV,depicted by PV panels in Fig. 1. In Austria, Portugal and inthe south of Italy it is changed to wind production, depictedby white wind turbines in Fig. 1. These two scenarios aresimulated with the global grid controller, with a local dampingcontroller and without controlling the setpoints of the HVDClinks. Table II shows an overview of the installed capacity,the share of the total energy production of RES and the totalsystem inertia for each scenario.

The system is simulated using MATLAB. The initial set-points of the VSC-HVDC terminals and the initial conditionsfor the system are determined via an AC power-flow solution.The VSC-HVDC loadings are quite low, this is due, that thesystem has not been optimized for a high HVDC utility ratherthen that the inter-area oscillations represent the phenomena ofthe European system. The system dynamics are then simulatedusing a dynamic simulator for MATLAB developed in [21]and the optimization for the MPC-based gird controller is

solved using the gurobi optimization toolbox for MATLAB[22]. In both simulation cases the global MPC-based gridcontroller operates with a sampling time TMPC = 500 msand has a prediction horizon N = 10 time steps, i.e. 5 s.The change of active and reactive power are constraint bythe power rating constraint (17) to Pmax,min = ±0.9p.u.and Qmax,min = 0.5p.u. and by the rate constrained (18) todmax,min = ±0.2p.u. of the rated power of the HVDC link.

A. Loss of Load in Spain

This simulation case considers the sudden loss of a1000 MW load in the middle of Spain. It is about 15% ofthe total load in that node. The simulation results are shownin Fig. 2. Fig. 2a) plots the mean frequencies for the differentscenarios according to Table II. The solid red curve showsthe frequency for scenario 1 in which no RES are installed.The solid blue and the solid green curve show the results forscenarios 2a and 3a, respectively, where the HVDC set-pointskept constant. It can be observed that as more renewables areintegrated, i.e. the inertia is reduced, the frequency deviationincreases. The dotted blue and dotted green curve show theresults for scenarios 2b and 3b, where the active power ismodulated with the local damping controller. It can be seenthat the mean frequency is slightly better than without anycontrol. On the other hand, the blue dashed and the dashedgreen curve show the frequency for scenarios 2c and 3c,where the active and reactive power of the HVDC links aremodulated, respectively. It is seen that the global MPC-basedgrid controller effectively damp the system oscillation.

This can be supported by observing the results of Fig. 2b)and 2c), where σ, the average frequency deviation of thegenerators from the COI, is shown. In scenarios 2a and 3a thestandard deviation grows, which means that the frequenciesof the generators diverge if the HVDC links keep their set-points constant. However, if the set-points are controlled, theyare able to reduce the standard deviation, as depicted in Fig.2c). The local damping controller is only able to decelerate thedivergence of the generators, since σ is still growing. However,the MPC based controller is able to stop the divergence of thegenerators.

The divergence of the generators can be seen in Fig. 2d)for scenario 2a. After about 20 s two groups of generatorsseparate. One group decelerates rapidly and starts to oscillatewith about 0.6 Hz, the other accelerate and starts to oscillatewith approximately the same frequency. The first group ofgenerators are the two generator equivalents of Greece, theother group of generators represents the Balkan region. If theeffect of protective devices were considered, the generatorsin Greece would be disconnected because of under-frequencyprotection. This would further weaken the system. Fig. 2e)shows the frequencies of all synchronous generators of sce-nario 2b. The local damping controller is able to damp thelocal inter-area oscillation between Greece and the Balkanregion. Furthermore an undamped east-west mode with afrequency of about 0.1 Hz can be detected. It also can beexamined in Fig. 2h), where all the bus voltages are depicted,


freq

uenc

y(H

z)

Scenario 2bScenario 2cScenario 3bScenario 3c

Scenario 1Scenario 2aScenario 3a

time (s)

49.98

50.00

50.02

50.04

50.06

50.08

50.10

0 5 10 15 20 25 30

(a) System frequency for all scenarios. Scenario 1:no RES and no control. Scenario 2a: RES withoutcontrol, scenario 2b: RES with local control, sce-nario 2c: RES with global MPC control. Scenario3a: High RES without control, scenario 3b: HighRES with local control, scenario 3c: High RESwith global MPC control.

freq

uenc

y(m

Hz)

time (s)

00

1

2

3

4

10 20 30

Scenario 1Scenario 2aScenario 3a

(b) Standard deviation σ, the average frequencydeviation of the generators from the COI forscenarios 1, 2a and 3a without control. It showsthat the frequencies deviation gets larger the moreRES is installed.

freq

uenc

y(µ

Hz)

time (s)

00

0.2

0.4

0.6

0.8

10 20 30

Scenario 2bScenario 2cScenario 3bScenario 3c

(c) Standard deviation σ, the average frequencydeviation of the generators from the COI for sce-narios 2b and 3b with local control and scenarios2c and 3c with global MPC control.

freq

uenc

y(H

z)

time (s)

49.0

49.2

49.4

49.6

49.8

50.0

50.2

50.4

0 5 10 15 20 25 30

(d) Frequencies of all synchronous generators forscenario 2a without control.

freq

uenc

y(H

z)

time (s)

49.96

49.98

50.00

50.02

50.04

50.06

50.08

50.10

0 5 10 15 20 25 30

(e) Frequencies of all synchronous generators forscenario 2b with local control.

freq

uenc

y(H

z)

time (s)

49.96

49.98

50.00

50.02

50.04

50.06

50.08

50.10

0 5 10 15 20 25 30

(f) Frequencies of all synchronous generators forscenario 2c with global MPC control.

time (s)time (s)

(MW

)(M

var)

InverterRectifier

HVDC1 loc. ControlHVDC2 loc. ControlHVDC3 loc. ControlHVDC4 loc. ControlHVDC1 glob. ControlHVDC2 glob. ControlHVDC3 glob. ControlHVDC4 glob. Controlsetpoints

10001000

1000

500

500

0

0

0

0

0

0

0

0-500

-500

-1000-1000

-1000

1010

1010

2020

2020

3030

3030

(g) Power injections of all HVDC links for scenario 2b with local control and 2c with globalMPC control.

volta

ge(p

.u.)

volta

ge(p

.u.)

time (s)

1.15

1.15

1.10

1.10

1.05

1.05

1.00

1.00

0.95

0.95

0

0

5

5

10

10

15

15

20

20

25

25

30

30

(h) Bus voltages, upper plot for scenario 2b withlocal control and lower plot for scenario 2c withglobal MPC control.

Fig. 2. Loss of a large load in Spain, comparing the different RES scenarios.

that the voltages slightly oscillate with the same frequency.Fig. 2f) shows the frequencies of all synchronous generatorsof scenario 2c. The global MPC-based controller is able tocontrol the HVDC links in a manner so that after about10 s almost all oscillations in the system are damped andall generators are in a stable operating condition. The MPCcontroller performs significantly better than the local controlscheme. This is due to the facts that the MPC controller isable to predict the future behavior of the system and is able to

perform larger and faster control actions, compared to the localcontroller. Another reason is the coordinated control of all theVSC-HVDC links. The MPC controller is able to calculateoptimal set-points for all the four VSC-HVDC links in oneoptimization and thus finds a better solution for the systemthan the local control scheme which independently controlseach link.

Fig. 2g) shows the reaction of the VSC-HVDC terminals onthe set-point changes for the active power on the rectifier side


and the reactive power on both terminals. For the MPC basedcontrol scheme, it can be seen that both the active and reac-tive power are utilized. HVDC2, France-Spain, and HVDC3,Belgium-Germany, contribute the most to the stability of thesystem. It is an interesting fact that these two HVDC links arecurrently built and are able to contribute to the system stabilityin the near future.

HVDC1 does not have to change its set-point too muchfrom the initial power flow to damp the oscillations of theGreek generators. This is the case because these generatorsare weakly connected with one AC-line to the Balkan areaand the HVDC link to Italy. The total power of these twogenerators, with 1600 MW, is quite small compared to thetransfer capacity of HVDC1 of 1260 MW.

B. Variation of Wind Energy

The second simulation case considers a steady increaseof wind production in the north of Germany, Denmark, theNetherlands and Belgium. The increase of the power injected

pow

er(M

W)

time (s)

00

200

400

600

800

1000

1200

1400

10 20 30

Fig. 3. Increase of power injected from renewable energy sources in the northof Germany, Denmark, the Netherlands and Belgium.

is depicted in Fig. 3 with Fig. 4 showing the results of thesimulation.

Fig. 4b) shows the mean frequencies of all simulatedscenarios. The solid blue and solid green curves show the meanfrequency for scenarios 2a and 3a, the dotted blue and dottedgreen curves for scenarios 2b and 3b and the dashed blue anddashed green curves for scenarios 2c and 3c respectively. Itcan be observed, that if the VSC-HVDC links are controlledby the global power modulation controller, they are able toreduce the rise in frequency. The local damping controller,scenarios 2b and 3b, has only very little effect on the dampingof the system. The advantage of a lower frequency rise is thatless primary frequency control of the generators has to beactivated. If another disturbance occurs the primary frequencycontrol has more possibilities to react, thus the system is morerobust.

This also can be seen in Fig. 4a) where the frequencyresponse of every synchronous generator for scenarios 2a, 2band 2c are depicted. It can be observed that scenarios 2a and 2b

do not differ very much and the generators have a small inter-area oscillation mode, of about 0.1 Hz, between the westernand the eastern part of the system. The installed HVDC linksare able to dampen this inter-area mode with the global powermodulation controller. The standard deviation σ, the averagefrequency deviation of the generators from the COI is depictedin Fig. 4c).

Fig. 4d) shows the active and reactive power injected forall VSC-HVDC terminals for scenarios 2b and 2c. It can beobserved for scenario 2b that HVDC4, the north-south linein Germany, and HVDC3, Belgium to Germany, are utilizedthe most. HVDC4 ramps up the active power to transport theexcess power to the south to relieve the northern part network.

The upper plot of Fig. 4e) shows the voltages of all bussesfor scenario 2b and the lower plot for scenario 2c.

VI. CONCLUSION

This paper presents and evaluates a global MPC-based gridcontroller which modulates the active and reactive power of theVSC-HVDC links in a system with a high penetration of RES.It is shown that with the reduction of the total system inertiathe frequency oscillation will be amplified. This can causethe power system to become instable, or lose generation unitsbecause of under- or over-frequency relays, without additionalcontrol. By modulating the power of the HVDC links, thepower oscillations can be reduced and the system stabilizedafter a large disturbance. Building HVDC purely for stabilitycontrol would be prohibitively expensive. However, once theyare installed in the system for the expanding transmission ca-pacity they could also be utilized for stability control, withoutaffecting their primary objective of power transmission, asshown in this paper. The additional costs for this are usuallyvery marginal. Especially the HVDC links between Franceand Spain and the line between Belgium and Germany provevery effective for the damping of frequency oscillations. Theselinks are currently under construction and should be utilized aspower system stabilizers. It was also shown that with only fourHVDC links with a total transmission capacity of 6300 MWor 2.5% of the total load, we were able to stabilize the systemeffectively for the studied contingencies.

ACKNOWLEDGMENT

We acknowledge the support of swisselectric research andABB for the project Power System Performance Enhancementby Use of Voltage Source Converter Based HVDC in theENTSO-E RG Continental Europe System.

REFERENCES

[1] T. Weissbach and E. Welfonder, “High frequency deviations within theeuropean power system origins and proposals for improvement,” VGBPowerTech, vol. 09, pp. 26–34, 2009.

[2] “Federal republic of germany - national renewable energy action planin accordance with directive 2009/28/ec on the promotion of the useof energy from renewable sources,” European Comission, Tech. Rep.,2009.

[3] REN21, “Renewables 2012 Global Status Report,” 2012. [Online].Available: www.ren21.net

[4] UCTE Ad-hoc Group, “Frequency quality investigation,” Final Report,2008.


freq

uenc

y(H

z)

time (s)

49.995

50.000

50.005

50.010

50.015

50.020

0 5 10 15 20 25 30

(a) Frequencies of all synchronous generators forscenario 2a, without control, scenario 2b withlocal control and scenario 2c with global MPCcontrol.

freq

uenc

y(H

z)

time (s)

50.000

50.005

50.010

50.015

50.020

50.025

0 5 10 15 20 25 30

(b) Mean system frequency for all scenarios. Sce-nario 2a: solid blue curve, scenario 2b: dotted bluecurve, scenario 2c: dashed blue curve, scenario 3a:solid green curve, scenario 3b: dotted green curve,scenario 3c: dashed green curve.

freq

uenc

y(m

Hz)

time (s)

00

5

10

10

15

20

20 30

(c) Standard deviation σ, the average frequencydeviation of the generators from the COI for allscenarios. Scenario 2a: solid blue curve, scenario2b: dotted blue curve, scenario 2c: dashed bluecurve, scenario 3a: solid green curve, scenario3b: dotted green curve, scenario 3c: dashed greencurve.

time (s)time (s)

(MW

)(M

var)

InverterRectifier

HVDC1 loc. ControlHVDC2 loc. ControlHVDC3 loc. ControlHVDC4 loc. ControlHVDC1 glob. ControlHVDC2 glob. ControlHVDC3 glob. ControlHVDC4 glob. Controlsetpoints

200

100

0

0

0

0

00

0

0

-100

-200-200

-200

-400-400

-600-600

1010

1010

2020

2020

3030

3030

(d) Power injections of all HVDC links for scenario 2b, with local control and 2c with globalMPC control.

volta

ge(p

.u.)

volta

ge(p

.u.)

time (s)

1.06

1.06

1.04

1.04

1.02

1.02

1.0

1.0

0.98

0.98

0

0

5

5

10

10

15

15

20

20

25

25

30

30

(e) Bus voltages, upper plot for scenario 2b, withlocal control and lower plot for scenario 2c, withglobal MPC control.

Fig. 4. Simulation results of an increased injection of wind power.

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