Voltage Source Converter Modeling in DC Grid and Power System Studies: appropriateness and limitations

Transcription

1 UNIVERSITY OF STRATHCLYDE Voltage Source Converter Modeling in DC Grid and Power System Studies: appropriateness and limitations This work is part of twenties project-work package 5 and supported by European Union Under Seventh Framework Program (FP7) G.P. Adam, S.J. Finney and B.W. Williams 8/28/2012 This presentation tries to identify the attributes and limitations of the existing voltage source converter modeling approaches when used to analyzed hybrid power systems that contain ac and dc networks. The importance of such work is that it may assist power systems engineers to conduct their studies with appropriate converter models, knowing the scopes and limitations of each modeling approach. Therefore, brief discussions on converter modeling will be presented that include detail switch model, switching function approach, and time average mode; and limitation of each approach will be highlighted. This work will be substantiated by comparing the steady-state and transient responses of the four and six-terminals DC grids obtained from detail switch and average models. 1

2 V a0 ½Vdc -½Vdc Iabc Vabc1 0 t Under excitation Vgabc Vg Zero power factor line Over excitation Unity power factor line 1. Could reproduce transients associated with fundamental and harmonic voltages and currents, including interaction between ac and dc sides. 2. Its switches mimic conduction of physical IGBT; therefore, suitable for dc fault studies. 3. Suitable for wide range of studies where the detail converter behavior is of great importance. 4. Prohibitively slow for large power system simulation. 5. AC harmonic filters must be included. 6. Not applicable for small signal stability. Fig. 1: Detail switch model V a1 ½Vdc -½Vdc Iabc Vabc1 0 t Under excitation Vgabc Vg Zero power factor line Over excitation Unity power factor line 1. Its ideal switch representation does not permit reverse current flow into dc side of when converter dc link is suppressed; therefore, not suitable for dc fault studies of traditional converters. 2. Could reproduce transients associated with fundamental and harmonic voltages and currents. Could be used for dynamic interactions between ac and dc sides during ac network faults only. 3. AC harmonic filters must be included. 4. Prohibitively slow for large power system simulation. 5. Not applicable for small signal stability. Fig. 2: Ideal switch model (equivalent to switching function approach) 2

3 1. This approach ignores any harmonics while considers slow dynamics associated with power frequency components only. 2. Could be used to analyze dynamic interactions between ac and dc sides during ac network faults only. 3. Not suitable for fast transients, including dc network faults. 4. Relatively fast and suitable for transient stability studies of medium-scale power systems. 5. AC harmonic filters can be added to the model to represent their effect at power frequencies. 6. Not applicable for small signal stability. Fig. 3: Average model (controlled voltage source behind phase impedance) 3

4 Fig. 4: Differential equations approach DC side dynamics, including dc voltage controller: dv dt dξ dt dcj dc m 1 = Idcjk C j k = 1 = k V V * idc ( dcj dcj ) m * dcjj = pdc ( dcj dcj ) + ξdc dcjk k = 1, k j I k V V I (1) * 1 Vdcj Idcjj 2 2 Idj = Vq Iq R( Idj + Iqj ) Vdj Sbase V * qj Pj QjVdj Iqj = V + V 2 2 dj qj 1. This approach considers only power frequency dynamics. The converter model can be expressed in abc or d-q synchronous reference frame. However, modelling in d-q frame is preferred. 2. When all controllers are incorporated, it can be used to analyze transient and small signal stability of large power powers. Also it can be used to analyze dynamic interactions between converters controls in dc grid and synchronous machines in ac sides. 3. Small signal and transient analysis can be conducted without the need for conventional or sequential load flow, and manual linearization of power system equations. 4. The DC current at the converter node is set by the local dc voltage control loop and the current from the DC link which is a function of the local DC voltage and the voltages at all other DC nodes, in the steady state the local control will force the net current into the node to zero. AC side dyamics, including current controller: dψ dqj * = kii ( Idqj Idq ) dt V k I I i L I * cdqj = pi ( dqj dq ) + ω j dqj + ψ dqj didq ( Vcdqj Vdqj R j Idqj iω Lj Idq ) = dt L j (2) 4

5 1. Reproduces all the transients associated with power and harmonic frequencies and detail dynamic interactions between ac and dc sides. 2. Takes into account all the dynamics associated with capacitor voltage balancing, phase circulating and dc offset arm currents. 3. Its switches mimic operation of physical IGBTs, therefore suitable for detail studies. 4. Prohibitively slow, therefore this approach is not suitable for large dc grids. 5. Not applicable to small signal stability analysis. Fig. 5: Modular multilevel converter (M2C) detailed model 5

6 V dc V ce1 V ce2 m m abc1 abc1 i i abc2 abc2 V a1 ½V dc 0 wt -½V dc i abc1 I abc V gabc V abc0 i abc2 Fig. 6: Modular multilevel converter (M2C) detailed model 1. Capable of reproducing power frequency transients and ac/dc dynamic interactions initiated by disturbances in the ac side. 2. It is suitable for demonstration of M2C active and reactive power control, and voltage support capability. Therefore, it may be suitable for transient stability studies of relatively large ac/dc power systems. 3. This approach is unable to reproduce the transients when the M2C dc link is suppressed. Therefore. Not suitable for dc network fault studies. 4. Not applicable for small signal stability; however, it can be twig for small signal stability. 5. Dynamics of distributed M2C cell capacitors can be modelled by means of virtual single lumped capacitor and reflected current source. This models net energy transfer between the M2C cells and the AC and DC networks but neglects sharing effects. 6

7 vx0 ( t ) π 2π ωt v a 0( t ) π 2π ωt 1. Models transient associated with power and harmonic frequencies, dynamic interactions between ac and dc sides that could be initiated in ac or dc sides. Also it models cell capacitor dynamics accurately, including dc fault reverse blocking capability. 2. Suitable for detail studies; however, it is prohibitively slow. Therefore, it is not suitable for large power systems. v x0 v a0 vhb ( t ) π 2π ω t Fig. 7: Hybrid cascaded multilevel converter detail model 7

8 V dc V c V a1 V g 1. Assumes ideal series active power filter that is capable of attenuating all the harmonics from the twolevel output voltage. 2. Suitable for ac side fault studies of medium-scale dc grids, and other applications that involve manipulation of active and reactive power exchange with ac networks. 3. Relatively fast, therefore could be used to model number of HVDC links embedded in relatively large power systems. V a1 ½V d c 0 -½V dc Fig. 8: Hybrid cascaded multilevel converter average model 8

9 Simulations illustrate appropriateness and limitation of two-level converter models a) Active and reactive power at B 1 and B 2 b) Active and reactive power at B 3 and B 4 9

10 Fig. 8: Waveforms illustrate responses of the detailed and average models of the two-level converter based dc grid to solid pole-to-pole dc fault at D5, with 200ms fault duration a) Active and reactive power at B 3 and B 4 b) Active and reactive power at B 3 and B 4 10

11 Converter 3 dc link current Converter 3 dc link voltage Voltage magnitude at B3 Fig. 9: Waveforms illustrate steady-state and responses of the detailed and averaged models of the two-level converter to three-phase fault at G3 11

12 Model validation of differential equations approach P 1 P 4 750MVA 400kV/300kV B 1 Z t1=0.005+j0.2 I 1 VSC 1 I dc1 R c1 I 14 P 14 R c4 I dc4 VSC 4 750MVA 400kV/300kV Z t4=0.005+j0.2 B 4 I 4 I c1 I c4 V1 V c1 V dc1 V dc4 V c4 V 4 B 2 I 2 P 2 750MVA 400kV/300kV Z t2=0.005+j0.2 VSC 2 P 12 P 45 I 12 I 45 I dc2 R c2 I 25 R c5 I dc5 I c2 I c5 P25 VSC 5 P 5 750MVA 400kV/300kV Z t5=0.005+j0.2 B 5 I 5 V 2 V c2 V dc2 V dc5 V c5 V 5 P 3 P 6 VSC 3 VSC 750MVA 6 750MVA 400kV/300kV I 23 I kV/300kV B 3 Z t3=0.005+j0.2 Z t6=0.005+j0.2 B 6 I 3 P23 I dc3 I36 P 56 I dc6 I 6 V 3 V c3 R c3 I c3 V dc6 P 36 V dc6 I c6 R c6 V c6 V 6 (a) Six-terminal DC Grid illustrative model (b) Active power VSC 1, VSC 2 and VSC 3 inject into DC grid (c) Active power dc voltage regulator (VSC 4, VSC 5 and VSC 6) inject in to AC grids 4,5 and 6 12

13 (d) Voltage magnitude at the dc nodes (V dc1, V dc2, V dc3, V dc4, V dc5 and V dc6) (e) Power flow in the DC lines (P 14, P 25 and P 36) (f) Power flow in the DC lines (P 12, P 23, P 45 and P 56) Fig. 9: Key results illustrate validation of the presented DC grid mathematical model against detailed model that represents each converter station by its three-phase switch model (do lines represent detail model) 13

14 Table II: Eigenvalues demonstrate the stability of the DC grid in Fig, 1 under assumed operating condition modes eigenvalues Damping time (s) Damping ratio λ 1, ±j λ 3, ±j λ 5, ±j λ 7,8,9, λ λ 12, λ 14,15,16,17,18, ±j λ 20,21,22,23,24, ±j λ 26,27, λ 29,33, λ 30,31, λ 34,35, λ 36,37, Sample results illustrate response of M2C detail and average models to ac network faults Active and reactive power converter exchanges with ac network Current waveforms converter injects into ac network 14

15 Phase voltage at converter terminal relative to supply mid-point Voltages across the M2C cell capacitors Sample waveforms illustrate M2C detail and average models responses during ac faults Conclusions There is no single voltage source converter model that could be used in all power system studies. Model selection must be based on the scale and type of studies need to be conducted, taking into account the model limitations. Detailed converter models could be used in conjunction with simplified converter models where is appropriate to represent part of the network needs to be investigated in detail. Average voltage source converter model seems to be appropriate for power systems studies of relatively large hybrid ac/dc power systems, where the focus on the dynamics due to ac network disturbances. Differential equations approach appears to be suitable and efficient for transient and small signal stability studies of very large power systems. However, this has to be confirmed. The efficiency of this approach in very large power system could be further improved using more advanced routines from IMSL and NAG libraries. 15