A Control Scheme for Utilizing Energy Storage of the Modular Multilevel Converter for Power Oscillation Damping

Transcription

1 A Control Scheme for Utilizing Energy Storage of the Moular Multilevel Converter for Power Oscillation Damping Ael A. Taffese, Elisaetta Teeschi Dept. of Electric Power Engineering Norwegian University of Science an Technology Tronheim, Norway Erik e Jong Dept. of Electrical Engineering Technische Universiteit Einhoven Einhoven, The Netherlans e.c.w.e.jong@tue.nl Astract This paper presents a control scheme that utilizes energy storage of the Moular Multilevel Converter (MMC) for Power Oscillation Damping (POD) service. Such a service is use to enhance gri staility y proviing amping power in the electromechanical (0.22Hz) ynamics range. The scheme uses compensate moulation with average energy control. The aforementione service comes at the cost of aitional energy storage requirement for the MMC. A worst case estimate of this aitional capacity, together with potential options to otain it, is also aresse in this paper. The scheme is valiate y simulation stuies on a four terminal HVDC test gri. Inex Terms Power Oscillation Damping, HVDC, Energy Storage, MMC, Moulation, Arm Capacitor, POD average arm energy of the MMC using compensate moulation as propose in [5]. It requires an increase in the energy storage capacity such that the POD service can e provie without affecting normal operation. Sizing consierations for the of aitional storage are also aresse in this paper. The remainer of this paper is organize as follows. Section II eals with the moeling approach, followe y the control structure in Section IV. Then, the propose controller is escrie in Section V. The extra energy storage requirement is treate in Section VI. Simulation results are presente in Section VII. Finally, conclusion is presente in Section VIII. I. INTRODUCTION i c Power Oscillation Damping (POD) is one of the ancillary services that can e provie y a voltage source converter in a power system. It is a service that improves amping of electromechanical oscillations (typically Hz) in an ac gri y injecting a amping power. VSCHVDC converter can achieve POD y moulating either active or reactive powers [], [2]. It was foun in [2] that active power moulation gives more roust performance regaring ac voltage variations. However, a sie effect of using active power is that the oscillation is exporte to the c sie since active power is alance instantaneously. Ref. [3] aresse this issue y coorinating the POD service etween two terminals in such a way that their contriutions cancel on the c sie. A etter alternative solution is to prevent the oscillation from entering the c sie y using solutions that involve energy storage. The challenge with such solutions is that energy storage technology is relatively expensive an not wellevelope for HVDC applications. Fortunately, the Moular Multilevel Converter (MMC), which is the most wiely accepte VSC topology, has energy storage capaility istriute in its SuMoules (SM). This paper proposes a control scheme that will make energy storage of the MMC availale for POD. Existing work on POD using MMC[4] focuses on the esign of the POD controller an not on the utilization of MMC energy storage. The propose scheme is ase on a close loop control of the v c i u v c SM N v u = n uv cu v cu = v ci v ci SM i= (Upper arm voltage) v cn SM L arm i s C c i c v c SM L arm N v cl = v cj v cj SM j= v l = n l v cl (Lower arm voltage) v cn SM i l Fig.. Perphase circuit of the MMC. v g

2 II. MODELING This section presents a simplifie average moel of the MMC. The most important assumptions mae in the evelopment of the moel are: ) compensate moulation [5] is use, 2) average energies of upper an lower arms are alance, an 3) effect of ripples in the average energy can e neglecte. First, the concept of compensate moulation will e iscusse followe y the ynamic equations escriing the MMC. A. Compensate Moulation Moulation, in this context, refers to the way the insertion inexes, n u an n l, are calculate given the respective inserte voltage references v u an v l (). v u = 2 (v c v s 2v c ) v l = 2 (v c v s 2v c ) () where v c is the c link voltage reference, v s is the ac voltage reference, an v c is common moe voltage reference. Direct moulation is the simplest moulation techniques where it is assume that the arm voltage is ripplefree an equal to the c link. Thus, the reference voltages are ivie y v c as shown in (2). n u = v u v c an n l = v l v c (2) The corresponing inserte voltages are given y (3). v u = vu v cu an v l = v v cl l (3) v c v c where v cu an v cl are the upper an lower arm voltages, respectively. Since the arm voltages contain ominant first an secon harmonic ripples, the inserte voltages will also contain harmonic components resulting in circulating currents. In orer to avoi this, the references are ivie y the respective arm voltages which cancel out from the inserte voltage as shown in (4). This is the concept ehin compensate moulation [5]. The main implication is that the harmonic content in the inserte voltages comes only from the references. This means that unesire circulating current can e avoie without the nee for an aitional controller. n u = v u v cu = v u = vu v cu = vu (4) v cu The arm voltages are neee to implement compensate moulation. It was iscusse [6] that the use of measure arm voltages is not effective ecause of measurement istortion an the loss of open sloop staility of the arm voltage. The openloop approach, which uses estimate arm voltages, has een shown to have etter staility properties [7]. The work in this paper uses compensate moulation with an improve arm voltage estimation technique which inclues a close loop control of the average energy [8]. III. DYNAMIC EQUATIONS Before the ynamic equations can e presente, some asic efinitions will e given. All equations are in perunit with the ase values given in the Appenix. The upper an lower arm voltages are ecompose into common moe, v c, an ifferential components, v s, as shown in (5). v c = 2 (v u v l ) (5) v s = ( v u v l ) (6) The same ecomposition can e applie to the upper an lower arm currents resulting in i c an i s as given y (7). i c = 2 (i u i l ) (7) i s = 3 4 (i u i l ) (8) The ifferential components correspon to the ac sie quantities. After applying this ecomposition, the ifferential equation escriing a simplifie arm energy ynamics is given in Eq. (9). t w = 2 [ c p 2 v ci c ] 6 v sq i s (9) = [ v c ci c ( v p 3 s i s vsqi ) ] sq where w is the average arm energy, c p is the perunit arm equivalent capacitance, an i c is the circulating current. vsq an i sq are the ac voltage reference an the ac current in omain, respectively. Eq. (9) shows that there will e a change in energy only when there is imalance etween the ac an c sie powers. The circulating current, i c, plays a vital role in achieving power alance. Dynamics of i c is capture y Eq. (0). t i c = ( ) vc r c i c (0) l c where l c an r c are the arm inuctance an resistance in perunit to the c ase values. The c link voltage is governe y the ifferential equation given in Eq. (). t v c = ( ) i c 3i c () c c where i c is the c line current an c c is the equivalent c sie capacitance in perunit. Finally, the ac current ynamics is given y Eq. (2) where ω is the funamental frequency in ra/s an v gq is the gri voltage in q omain. l ac an r ac are equivalent ac sie inuctance an resistance in perunit. t i sq = ( ) vsq v gq r ac I i sq ωl ac J i sq (2) l ac I = [ 0 0 ] an J = [ ] 0 0 The sign conventions an aitional variale efinitions are shown in Fig. The next section iscusses the control structure use in this paper.

3 IV. CONTROL STRUCTURE Fig. 2 epicts lock iagram of the controllers use in this paper. Only the control loops affecting active power are shown in the figure. Active power is controlle through the axis current, i s. Similarly, the average energy is controlle using the circulating current, i c. The two control loops are couple y the ac power. All the controllers in Fig. 2 are tune using moulus an symmetric optimum techniques [9]. From Fig. 2, it can e oserve that a change in ac power causes the energy to eviate. This triggers the energy controller to respon y ajusting i c which in turn affects the c power, P c. Therefore, eviations in ac power will eventually appear in the c power. If the converter is proviing POD, it has to inject oscillating power into the ac gri when the oscillation moe is excite. This oscillation will e exporte to the c sie ecause of the action of the energy controller. Since the MMC is equippe with energy storage, it can provie the oscillating power from the capacitors keeping the c sie ieally unaffecte. This is achieve y employing the auxiliary energy controller presente in the next section. V. PROPOSED AUXILIARY ENERGY CONTROLLER The main function of the auxiliary controller is to inform the energy controller (C w in Fig. 2) not to alance the oscillating part of the ac power ( P ac ) with the c power. This is achieve y removing the contriution of P ac from the energy feeack signal (W m ). In such a way, C w oes not see the oscillation an hence will not export it to the c sie. Fig. 2 shows a functional lock iagram of the auxiliary energy controller. The POD lock is responsile for calculating the oscillating power ( Pac ) injecte in to the ac gri when the electromechanical moe is excite. H an H 2 are the equivalent transfer functions from Pac to P ac an from P ac to W m, respectively. The term equivalent is use to inicate that these transfer functions represent the gain an phase responses of the complete transfer functions at the oscillation frequency in the form of gain an lealag locks. Such an implementation assumes that the system parameters are accurately known an there is only one moe of oscillation. These assumptions are mae to simplify the initial implementation. If the parameters are not accurately known, the gains an phase angles can e tune y performing tests efore the converter is commissione. The effect of parameter errors will e shown y simulation in Section VII. One important requirement for this control scheme to work is the availaility of excess store energy so that the POD oes not istur normal operation. This aspect will e iscusses in the next section. VI. ENERGY STORAGE REQUIREMENT Calculation of the extra energy storage require to implement the propose scheme will e presente in this section. First, erivation of the asic equations will e presente followe y potential options to otain the require aitional storage. Active power imalance, p, an energy eviation, w, are relate y (3). w = 2 c p p t (3) which is otaine y integrating (9). Fig. 3 shows how the power injecte y POD typically looks. The resulting energy eviation, as given y (3), is the area uner the curve. It is assume that the oscillation moe, on which the POD is applie, is stale. This implies that the area uner susequent halfcycles iminishes with time. Therefore, the worst case energy eviation is cause y the first swing which is inicate y the gray area in Fig. 3. The maximum energy eviation, w max, can e compute using (4). w max = 2 c p 2ˆp ω osc (4) where ˆp is peak value of the oscillation. Eq. (4) overestimates the eviation since it ignores the effect of amping. This is justifie ecause the amping is not constant an the intention is to consier the worst possile case which is when the amping is 0. The corresponing eviation in arm voltage, v max, can e compute, from the fact that w = v 2, using (5). w max = v max ( v max 2v) (5) where v is the nominal arm voltage. Having efine the maximum voltage eviation, the requirement for the extra energy storage can now e efine. The main constraint is that the arm voltages have to e more than the ac peak voltage (assuming sinusoial moulation) in orer to avoi overmoulation. v can e positive or negative epening on the sign of POD power injection. When v is negative, there is a risk of overmoulation. A positive v, on the other han, can result in overvoltage in the SMs. Therefore, the arm voltage shoul satisfy the constraint in (6). ˆv ac v max v V rate v max (6) where ˆv ac is the maximum ac peak voltage in pu an V rate is the sum of rate voltages of the SMs. From (6), it can e seen that the arm voltage has to e greater than.0 pu, since ˆv ac is typically close to.0 pu, in orer to provie the propose service. This can e achieve y increasing either the numer of SMs, N, or the SM voltage, V SM. The relation etween these quantities an the store energy, W in joules, is given in (7). W = C SM 2 N (N V SM) 2 (7) where C SM is the SuMoule capacitance. Increasing C SM is not consiere ecause it only helps in reucing v max ut not to increase v. The two options will e iscusse in the following sections.

4 P ac v v Dc roop PI i s PI v s l s r ac ac i s v g P ac POD P ac H Ts a K T s Auxiliary Energy Controller P ac H 2 Ts c K2 T s P acm Ts p limit w max Ts i P v i v i v i ac g s s s sq sq Ignoring arm an transformer losses W W PI i c PI v c l s r c c i c 3v c W cs P c P ac 3 p C w W m Ts w Ts i Active Power Fig. 3. Active power oscillation. Fig. 2. Auxiliary controller lock iagram. Time Parameter TABLE I HVDC CONVERTER PARAMETERS[0] Value Base apparent power, S 900 MV A Base c voltage, V c 640 kv Frequency, ω 2π50 ra/s Arm capacitance, C arm = C SM /N 29 µf Arm inuctance, L arm 84 mh Arm resistance, R arm Ω Transformer reactance, X t 7.7 Ω Transformer resistance, R t.77 Ω A. Increasing the Numer of SuMoules The effect of introucing aitional SMs will e investigate y replacing N y ( α) N in (7). Where α is a numer etween 0 an. The aitional energy ue to α, W α, is given y (8). W α = αw (8) where W is the nominal energy calculate using (7). The maximum availale POD power can e calculate y comining (8) with (4) as shown in (9). ˆP max = 2 W max ω osc α 6 [MW ] (9) where W max = W w max is the maximum energy eviation in joules. The factor 6 is inclue ecause the ac power oscillation is assume to e share equally y the 6 arms. ˆPmax is calculate for cominations of ω osc an α using the parameters in Tale I. The result is shown in Fig. 4. It can e seen that the maximum availale POD power is very limite at low frequencies. The amount of extra storage gaine is linearly proportional to α. This option can e more attractive ecause there will usually e some extra moules ae for reunancy. These moules can e utilize for the POD service. B. Increasing the Rate Voltage of SuMoules In this section an increase in SM voltage from V SM to ( β)v SM is consiere. Where β is a numer etween 0 an. By following a similar approach to the previous section, the maximum POD power can e calculate as shown in (20). A plot of ˆP max for ifferent values of β is epicte in Fig. 5. ˆP max = 2 W max ω osc (β 2 2β ) 6 [MW ] (20) It can e oserve that more POD power can e otaine y increasing β compare to α. However, this option will likely e more expensive since it requires upgrae of all SMs. The optimal solution, which is a comination of the two options, is a result of an optimization prolem which is eyon the scope of this paper. A value of β = 0.5 which is equivalent to α = 0.32 is assume for simulation in the next section. It shoul e note that the maximum POD power iscusse

5 Maximum POD Active Power [MW] α = 5% α = 0% α = 5% α = 20% Oscillation Frequency [Hz] Fig. 4. Maximum POD power as a function of oscillation frequency for ifferent values of α. Maximum POD Active Power [MW] β = 5% β = 0% β = 5% β = 20% Oscillation Frequency [Hz] Fig. 5. Maximum POD power as a function of oscillation frequency for ifferent values of β. in this section is the maximum that can e provie without isturing the c sie. The converter can still provie more POD power at the cost c sie oscillation. In such cases, output of the Auxiliary controller shoul e limite to w max efine in this section. Two options for limiting the output will e compare y simulation in the next section. VII. SIMULATION RESULTS Simulation results showing effectiveness of the propose auxiliary controller are presente in this section. The simulation moel is ase on the four terminal test gri propose in [0], (Fig. 6). The moel is implemente in SIMULINK with the parameters shown in Tale I. Effect of the POD lock is emulate y injecting oscillating power of magnitue 0.06 pu an amping of ζ 5% at t = 7 sec in to that ac gri connecte to Converter 3, (Fig. 6). Each terminal is roop controlle with a voltage roop of 5%. The cales are moele Case No. Case Case 2 Case 3 Case 4 Case 5 Case 6 Fig. 6. Test gri use for simulation [0] Description TABLE II SIMULATION TEST CASES Base case: No POD action POD action without Aux. Controller POD action Aux. Controller POD with ifferent frequencies: Hz, 2 Hz, an 5 Hz. Effect of output limiter Effect of parameter inaccuracies using the frequency epenent moel propose in []. All converters are MMCs which are moele using average arm capacitor ynamics [2]. Six test cases escrie in Tale II will e use to test the propose scheme. The results are isplaye in Figs. 7 to 3. From the ase case (Fig. 7), it can e seen that the system exhiits a stale operation uner normal conitions. All the reference signals are ratelimite y using first orer low pass filters. The ifference etween the ac an c powers in Fig. 7 is ecause of losses in the converter. With the emulate POD power injecte from converter 3 (Fig. 8), the c voltages exhiit oscillations as shown in Fig. 9a. When the auxiliary controller is enale, the POD power is iverte into the arm capacitors instea of the c sie as is evient from Fig. 8. Doing so, the controller can effectively remove the oscillation from the c sie, (Fig. 9). Because of the power taken from the capacitors, the average store energy exhiits oscillatory response, (Fig. 0a). This confirms that the oscillation is supplie from the arm capacitors instea of the c sie. The worst case eviation in energy is compute using (4) to e 0.25 while the value rea from Fig. 0a is 0.5. The ifference is ecause the effect of amping which was neglecte in (4). Fig. 0 shows impact of the POD action on the store energy of converter 2 where it is clearly visile that the converter oes not see the oscillation when the propose controller is active. In orer to investigate the correlation etween energy eviation an oscillation frequency, POD at ifferent frequencies was also simulate. Fig. a shows store energy of the POD terminal with the auxiliary controller enale. It can e clearly seen that the eviation grows with ecrease in frequency. This is inline with the iscussion in Section VI an (4). The corresponing power injections are epicte in Fig. where it can e

6 c voltages in (p.u) ac an c powers in (p.u) Converter Converter 2 Converter 3 Converter c power ac power 0.4 () c voltages in (p.u) c voltages in (p.u) Converter Converter 2 Converter 3 Converter 4 Converter Converter 2 Converter 3 Converter () Fig. 7. Base case (Case ) system performance: c voltages an () ac an c powers of converter Fig. 9. c voltages with POD: Case 2 without Aux control an () Case 3 with Aux control ac an c powers in (p.u) ac an c powers in (p.u) c power ac power c power ac power 0.4 () Arm energy in (p.u) Arm energy in (p.u) without Aux Control with Aux Control without Aux Control with Aux Control.30 () Fig. 8. ac an c powers of converter with POD: Case 2 without Aux control an () Case 3 with Aux control Fig. 0. Arm energies with (Case 2) an without (Case 3) Aux control: Converter 3 an () Converter 2

7 Arm energy in (p.u) ac power in (p.u) ω osc = 2π 2 ω osc = 2π ω osc = 2π () ω osc = 2π 2 ω osc = 2π ω osc = 2π 5 Fig.. Results at ifferent oscillation frequencies with Aux control: Arm voltages an () ac power at converter 3. Arm energy in (p.u) c voltages in (p.u) Phase Accurate 20 Phase Error.00 () Phase Accurate 20 Phase Error Fig. 3. Effect of phase angle error (Case 4, ω osc = 2π ): Arm voltages an () c voltages. Arm energy in (p.u) c voltages in (p.u) Normal Operation Simple Limiter Gain Reuction 0.99 () Normal Operation Simple Limiter Gain Reuction Fig. 2. Effect of output limiter on the Aux. controller (Case 4 ω osc = 2π ): Arm voltages an () c voltages seen that the magnitues are the same in all the cases. The auxiliary controller lock output is limite to ±0.32 pu which is equivalent to ±0.5 pu limit on the arm voltage. They are chosen to keep the arm energy aove.0 pu in all cases. Fig. 2 shows how the system respons when the energy eviation is larger than the limits. It can e seen that the simple limiter (which is a simple clamping limiter) is ale to keep the energy eviation within the specifie limits. However, the c voltage (Fig. 2) exhiits a larger magnitue istortion uring the perio when the output is limite. The secon option to limit the output is to reuce gain of the auxiliary controller which in effect reuces the amount of power iverte into the capacitors. This results in a smoother limit ut at the cost of more oscillation in the c voltage, (Fig. 2). Comining the two approaches, ynamic ajustment of the gain with simple limiter on the output can give etter results. Finally, the effect of parameter inaccuracies is stuie. Parameter errors result in either gain or phase error in the oscillation. Effect of phase angle error is epicte in Fig. 3. The effect of gain error is similar to the gain reuction case in Fig. 2. The main consequence is that some of the oscillating power is taken from the c sie resulting in c voltage oscillation, Fig. 3. This implies that scheme can work well even with significant parameters errors. Further improvement can e gaine y tuning the parameters from test results.

8 VIII. CONCLUSION This paper proposes a control scheme to minimize the impact of POD action on the c sie of an MMC converter station. This is achieve y iverting the oscillating component of the ac power into the arm capacitors. Simulation results show that the scheme is promising. The enefits come at the cost of increase energy storage requirement. The extra energy storage requirement an potential options to achieve this have een iscusse in this paper. Increasing the numer of moules or the rate voltage of each moule can e use to get the extra storage. A comination of the two shoul e use to get optimal solution. It was foun that the amount of require storage increases at low frequencies. In cases when enough storage is not availale, partial cancellation of the oscillation can e one with the help of output limiters. Output limits play a vital role in the performance of the scheme. Simple limiter an gain reuction were evaluate. Dynamic gain ajustment can give etter results. The scheme can also e extene to support multiple oscillation frequencies. APPENDIX The ase values use for perunit calculations are epicte in (2). I ac L ac = 2S 3V ac = Z ac Z ac = V ac I ac C ac = Z ac V c = 2V ac I c L c = S V c = Z c W = Cc REFERENCES ( ) V c 2 2 Z c = V c I c C c = Z c (2) [] L. Harnefors, N. Johansson, L. Zhang, an B. Berggren, Interarea oscillation amping using activepower moulation of multiterminal [8] A. A. Taffese, E. Teeschi, an E. e Jong, Arm Voltage Estimation Metho for Compensate Moulation of Moular Multilevel Converters, in 2th IEEE PES PowerTech Conference, Manchester, UK, Jun HVDC transmissions, IEEE Trans. Power Syst., vol. 29, no. 5, pp , 204. [2] L. Zeni, R. Eriksson, S. Goumalatsos, M. Altin, P. Sørensen, A. Hansen, P. Kjær, an B. Hesselæk, Power Oscillation Damping From VSC HVDC Connecte Offshore Win Power Plants, IEEE Trans. Power Deliv., vol. 3, no. 2, pp , Apr [3] M. Nreko, A. van er Meer, M. Giescu, B. Rawn, an M. van er Meijen, Damping Power System Oscillations y VSCBase HVDC Networks: A North Sea Gri Case Stuy, in Proc. WIW 203: 2th Int. Workshop LargeScale Integration of Win Power Into Power Systems as Well as on Transmission Networks for Offshore Win Power Plants, 203. [4] N. T. Trinh, I. Erlich, an S. P. Teeuwsen, Methos for utilization of MMCVSC HVDC for power oscillation amping, in 204 IEEE PES General Meeting Conference Exposition, Jul. 204, pp. 5. [5] G. Bergna Diaz, J. A. Suul, an S. D Arco, Smallsignal statespace moeling of moular multilevel converters for system staility analysis, in Energy Conversion Congress an Exposition (ECCE), 205 IEEE. IEEE, 205, pp [6] L. Ängquist, A. Haier, H. P. Nee, an H. Jiang, Openloop approach to control a Moular Multilevel Frequency Converter, in Proc. 20 4th European Conf. Power Electronics an Applications (EPE 20), Aug. 20, pp. 0. [7] A. Antonopoulos, L. Ängquist, L. Harnefors, K. Ilves, an H. P. Nee, Gloal Asymptotic Staility of Moular Multilevel Converters, IEEE Trans. In. Electron., vol. 6, no. 2, pp , Fe [9] J. W. Umlan an M. Safiuin, Magnitue an symmetric optimum criterion for the esign of linear control systems: What is it an how oes it compare with the others? IEEE Trans. In. Appl., vol. 26, no. 3, pp , May 990. [0] W. Leterme, N. Ahme, J. Beerten, L. Angquist, D. V. Hertem, an S. Norrga, A new HVDC gri test system for HVDC gri ynamics an protection stuies in EMTtype software, in th IET International Conference on AC an DC Power Transmission, Fe. 205, pp. 7. [] J. Beerten, S. D Arco, an J. A. Suul, Frequencyepenent cale moelling for smallsignal staility analysis of VSCHVDC systems, Transm. Distri. IET Gener., vol. 0, no. 6, pp , 206. [2] L. Harnefors, A. Antonopoulos, S. Norrga, L. Angquist, an H. P. Nee, Dynamic Analysis of Moular Multilevel Converters, IEEE Trans. In. Electron., vol. 60, no. 7, pp , Jul. 203.