DQ-axis Current-based Droop Controller

Transcription

1 DQ-axis Current-based Droop Controller Ibrahim Alsaleh and Lingling Fan 2 Abstract During an islanding operation of a microgrid comprised of multiple distributed generation (DG) units serving a load, DG units interfaced with voltage-sourced converters (VSC) are regarded as the only energy sources. Hence, DG units should be controlled to form the frequency and voltage, pick up the full load, and respond to any load changes. Conventional P f/q V droop controller enables a communication-less load sharing among DGs while maintaining close deviations of frequency and voltage. Utilizing the dq-frame power flow analysis, this paper presents an equivalent primary droop controller i d f/i q V based on the direct and quadrature components of the feeder currents, which are already existent in each voltage controller for disturbance rejection. More emphasis is placed on the phenomenon of inaccurate reactive power sharing caused by mismatched feeder impedances. Analysis is presented in terms of the droop equation, and compensation methods are examined with focus on computation and communication requirements, and PCC voltage profile. For validation of the controller s response, a testbed model exhibiting the dynamics of a two- DG microgrid is developed and simulated in Matlab/Simulink. I. INTRODUCTION The gradual reliance of renewable energy sources in power production has re-shaped the modern picture of the utility grid. The power generation is no longer exclusive to power plants, thanks to the distributed generation (DG) units which are integrated into the distribution network. In fact, the high penetration of DG units has led to dividing the grid into microgrids, constituting the futuristic smart grid [4]. The microgrid technology potentially facilitates controllablity over a number of paralleled DG units connected to a point of common coupling with the grid, and can operate autonomously realizing UPS features []. Load sharing can be achieved with or without communication. Schemes that employ communication require high-bandwidth communication channels, which reduce the reliablity and microgrid expandability as dispersed DG units would rely on one another. The P f/q V droop controller; on the other hand, achieves the desired communication-less operation, and has broadly been adopted [],[3]-[6]. The conventional droop controller counts on the notion that microgrids have high X /R ratios, while the feeder impedance in low-voltage distribution networks is typically resistive in practice. This inroduces coupling between the active and reactive powers. A few solutions have been proposed to dominate the inductive component using virtual impedance, and thereby avoiding any installations of I. Alsaleh is with the Dept. of Electrical Engineering, University of South Florida, Tampa FL 33620, USA; and the Dept. of Electrical Engineering, University of Hail, Hail, KSA ( ialsaleh@mail.usf.edu) 2 L. Fan is with the Faculty of Electrical Engineering, University of South Florida, Tampa FL 33620, USA ( linglingfan@usf.edu) Fig. : Microgrid structure. a phyical inductance. A thourough analysis of the virtual impedance concept is presented in [2]. In [3], a simple static virtual inductance based on the fundamental frequency is proposed for power decoupling. Another problem is encountered when feeders have mismatched impedances, provoking inaccurate reactive power sharing among DG units. This issue has been garnering a lot of attention, and numerous improvements on the conventional droop control have been developed to increase the adaptability of DG units to the feeder impedance. [4] proposed a strategy that injects a small active power disturbance in the system. Although results show accurate power sharing, processing the disturbance signal entails complex implementation, especially in a noisy environment [5]. In [3], the effect of approximated voltage drop across the feedr reactance, X/V ref, is estimated and incorporated into the droop coefficient. The estimation takes place during gridconnected operation. By using data exchanged via communication between DG local controllers, the strategy proposed in [5] tunes the adaptive virtual impedance without any estimation of the feeder impedances. When the d-axis terminal voltage is aligned with its space vector, P DG and Q DG are proportional to the dqaxis currents. In this paper, we explore a droop controller based on the dq-axis currents, and show that it can achieve accurate load sharing. Unlike the conventional droop, the droop coefficient in the modified droop is directly related to the feeder reactance, since currents multiplied by gains are deemed virtual voltage drops. Therefore, the adaptive virtual impedance is employed to correct the reactive power sharing. With knowledge of the PCC voltage phasor obtained by a single-direction communication signal from the central controller shown in Fig., the virtual impedance is realized.

2 i q Im ω(t) DG, DG γ o 0 i d i V t V td Re, 0 Fig. 2: One-line diagram of a single-loaded DG unit. Space vectors and the dq components in the complex plane. II. STEADY STATE ANALYSIS A. i d f/i q V Droop Controller During islands, local controllers must be self-aware so that DG units pick up their share of the load with proportion to their capacities. The P f/q V droop controller is conventionally adopted, which is based on a predominant inductive behavior of the feeder achieved by physical or static virtual inductnace. Therefore, when (θ z 90 ) and a small phase angle, θ t, are considered, the power flow equations between the two buses in Fig. 2a are expressed as P DG V t X Q DG V t(v t ) X sin θ t θ t XP DG V t (V t ) XQ DG V t (a) (b) P DG and Q DG are proportional to the phase angle and voltage difference; respectively. The droop control should output the reference value for the terminal (capacitor) voltage phasor V t θ t. The formed phase angle, θ t, is used to transform the terminal voltages, filter currents and feeder currents to the dq frame, resulting in [V td 0] T, [i fd i fq ] T and [i d i q ] T, where quadrature currents are negative because their space vectors lag the voltage space vector. Fig. 2b illustrates the space vectors of the terminal voltage and feeder current, and their corresponding dq components in the complex plane. As a result, the dq-frame active and reactive powers derived from S 3 2 V td(i d ji q ) are P DG 3 2 V tdi d Q DG 3 2 V tdi q (2) i d and ( i q ) track the DG active and reactive powers; respectively. The conventional droop can therefore be replaced with current sharing i d f/i q V as follows ω ω mi d V td Vd ni q (3a) (3b) B. Power Sharing Analysis V t (t) First, the power flow in Fig. 2a at the sending and receiving ends, and across the feeder is expressed in the dq frame. After that, the power sharing in Fig. 3 will be examined with particular regard to feeder impedances, assuming X X δx and X 2 X. All phasors in Fig. 2a are transformed to the dq frame with respect to the terminal voltage phase angle, θ t. Thus the terminal voltage at the fundamental frequency is expressed as follows V td j0 (d jq ) (R k jx k )(i kd ji kq ) (4a) V td d R k i kd X k i kq (4b) To obtain the powers, (4b) is multiplied by the scaled conjugated feeder current 3 2 i kdq 3 2 (i kd ji kq ) ( 3 2 )V 3 tdi kd j ( 2 )V 3 tdi kq ( P DG k Q DG k 2 )di kd P L j ( 3 2 )di kq Q L ( 3 2 )i kd(r k i kd X k i kq ) P loss k j ( 3 2 )i kq(xi kq R k i kd ) Q loss k ) Without Droop: From (5), it is inferred that powers at the DG terminals are influenced by the feeder resistance and reactance. For a droopless power sharing of equally-rated DG units in Fig. 3, < and P DG <P DG2, which is dangerous as one unit could be forced to supply more than its capacity. In order to accurately share the load without droop controllers, and in proportion to DG units capacities, assuming their output voltage phasor V t θ t are exactly the same, the following constraints must be satisfied a) Even Sharing: When all DG units have the same capacities, resistances and reactances of both feeders must be unified. (5) R R 2 X X 2 (6) b) Uneven Sharing: When DG units have different capacities, resistances and reactances must be inversely proportional to i kd and i kq ; respectively. R i d R 2 i 2d X i q X 2 i 2q (7) Put simply, voltage drops across the feeders must be unified. 2) With Droop: Despite the impedance s influence on active powers, the i d f droop should promise accurate active power sharing because the frequency is a global quantity in the microgrid, hence (i d i d i 2d ). On the other hand, the i q V droop achieves accurate reactive power sharing if and only if feeders have matched voltage drops, satisfying (6)-(7). Otherwise, DG units will generate disparate reactive powers (i q i 2q ) as shown in Fig. 4a, and compensation is therefore required.

3 DG, DG, 0 n X 2 () n X In contrast, if the conventional droop were employed with the voltage drop effect approximated as 2(XQDGRPDG) 3V, the d ratio would be ω ω min P ω ω DER ω DER2 ω min ω P 2max Z o V inv DG 2, DG Z i V s 0 2 i 2 Z o Z 2 P, Q Fig. 3: Two t 2s DG units conected to a load with X >X 2.,2 V P inj P DER m P inj2 m 2 P DER2 i q n i 2q P n 2 i q,2 V P 2, Q 2 i q,2q V inv Fig. 4: i q V droop with uncompensated slopes compensated slopes with adaptive virtual reactance. C. Correction of Reactive Power Sharing For simplification, even sharing case is considered with two equally-rated DG units using the i d f/i q V droop controller, where an accurate reactive power sharing is equivalent to having matched i q and i 2q. With effective terminal voltage regulation, (V td Vd ni q ) is substituted into (4), yielding Vd ni q d R i d X i q Vd ni 2q d R 2 i 2d X 2 i 2q The quadrature-current error is i q i 2q X 2i 2q X i q (R R 2 )i d n n n 2 i q (8a) (8b) Assuming inductive feeder impedance, and (R R 2 0), the following ratio is obtained i q n X 2 n X i 2q n X n X δx (9) (0) Therefore, for accurate reactive power sharing, the ratio should be constrained to unity. (0) can also be expressed in terms of reactive powers, with the approximation Q DG 3 2 i qvd Z i approximately P, Q Pbe 2, Q 2 unity. 2X 2 3V d n n 2X 3V d (2) The compensation methods based on the constraint in (0) are as follows Z o2 ) Large V s 0 Droop i 2 Coefficient: Z 2 Z o2 By enlarging n in (0), the feeder reactances will be outweighed, and the ratio will n X i q n X i 2q n X δx (3) However, n is bounded by the voltage deviation. With the voltage deviation being fixed at 5%, it can be concluded that n depends primarily on the reactive power rating. Therefore, for small reactive power ratings, i q is small and n can be set large to limit the error. Although difficult to achieve accuracy, n partially compensates for the mismatched impedance. 2) Adaptive Mismatch Virtual Reactance: The adaptive virtual reactance, δx v, is calculated (X X 2 δx v ), and incorporated into n. This suggests that different droop coefficients should be assigned to result in a unity ratio as i q i 2q n 2 X n X δx n X (n δx v ) X δx (4) However, the method requires communication between DG local controllers to exchange feeder reactances and calculate the mismatch. 3) Adaptive Feeder Virtual Impedance: It is based on compensating for the entire feeder impedance. With knowledge of the PCC voltage as shown in Fig., the virtual impedance is realized utilizing separate real and imaginary equations in (4a) as follows. R vk R k V d d i kq i kd q i kd i2 kq i kd X vk X k q R k i kq i kd By incorporating the virtual voltage drops, (8) becomes V d (n i d R v X v) i q d R i d X i q i q n (5) (6a) Vd (n i 2d R v2 X v2) i 2q d R 2i 2d X 2i 2q (6b) i 2q n 2 This method does not require further communication. After realizing the virtual impedance, the signal carrying the PCC voltage phasor can be disrupted. Moreover, increasing the terminal voltage by the amount of the voltage drop improves the PCC voltage. The 5% voltage deviation will be allocated for the PCC voltage rather than the terminal voltage.

4 Droop Controller DG dq abc () () Limiter 0 () Voltage/Current Controllers () 2 Limiter RLC Plant dq abc 2 2 Feeder-Load Equations 2 2 DG2 Fig. 5: Block diagram of a two-dg microgrid with linear loads. III. SIMULATION: TWO-DG MICROGRID A mathematical model is built in Matlab/Simulink to depict the dynamics of a microgrid with two DG units connected to a load through mismatched feeders. A. Testbed Modeling ) RLC Plant and Averaged VSC Models: As shown in Fig. 5, each DG-unit block consists of an averaged VSC and RLC plant models. For their simple tracking requiremnts, the PI controllers are used to regulate the inductor current and capacitor (terminal) voltage at prespecified operating points in the dq frame. The RLC plant is also expressed in the dq frame, and Laplace transformed to obtain a consolidated MIMO framework. The PI parameter tuning is wellestablished in [6]-[7], and presented as follows a) Inner Current Controller: The proportional and integral gains of K i (s) are tuned to cancel the low-frequency RL pole and set the current transfer function bandwidth, ω B. k pi L f ω B k ii R f ω B l i (s) k pis k ii s(l f s R f ) (7) G i i fd i d l i(s) l i (s) ω B s ω B (8) b) Outer Voltage Controller: The parameters of K v (s) are tuned to design a stable open-loop gain, K v (s)g i (s)(c f s), which has double integrators. A designated stable phase margin, typically selected within the limit (45 θ pm 60 ), can be fulfilled by adopting the Symmetrical Optimum method [7]. α sin θ pm sin θ pm k vp C f αωb k vi αω B k vp (9) G v (s) V td V d αω 2 B (s αω B ) s 3 ω B s 2 αω 2 B s α 3 ω 3 B (20) Therefore, upon choosing ω B and θ pm, parameters of both K i (s) and K v (s) can be designed. Moreover, u dq and i dq are modified with feedforward loops to reject the disturbance of the capacitor voltage and feeder current, and to decouple the dq current and voltage loops as shown in Fig. 5.

5 Frequency (Hz) Voltage Magnitude (V) Active Power (W) Active Power (W) c) Droop Controller: The i d f/i q V controller is added as the outmost loop to provide the operating point V d, and improved by the adaptive feeder virtual impedance. 2) Feeder-load Network Model: Assuming linear loads contribute larger than non-linear loads, harmonic powers are omitted, and a parallel resistive-inductive load is adopted. With i kabc and i Labc identified as the feeder and load state variables and V tkabc as inputs, the network s dynamic model is expressed as a state space matrix d dt i abc i 2abc i Labc R T R L L L R L R T 2 L 2 L 2 R L R L L L L L L 0 0 L R L L R L L 2 R L L L [ ] Vtabc abc i abc i 2abc i Labc where R T k R k R L, k,2. The matrix is computed using Matlab embedded function, where first-order derivatives are integrated and injected as inputs with the DG terminal voltages. The load and feeder mismatch inductance are injected using step functions to emulate load change and reactive power inaccuracy. TABLE I: Simulation Parameters Quantity DG terminal voltage Nominal frequency RLC filter Feeder parameters Controller parameters B. Operation Scenario Value 0V (rms) 60Hz R f 0mΩ L f 0mH C f 20µF R,2 5mΩ L,2 5mH δl 2mH ω B 2000 rad/s θ pm 53 m 0.5 n 5 Considering the following scenario, the testbed model in Fig. 5 is validated with two DG units that should evenly share 540W and 270 VAR. The simulation parameters are listed in Table I. ) The microgrid is initially grid-tied, and the PCC voltage is provided. Each DG supplies W and VAR. 2) At t 3 s, the microgrid is islanded. Each DG unit should properly pick up its share of the full load, which is 270W and VAR. 3) At t 5 s, a mismatch inductance, δl, is instilled into F eeder. Conducted case studies and simulation analysis are presented as follows ) Without Droop: The microgrid is islanded without a droop controller. Fig. 6 shows an accurate power sharing with matched feeder impedances. However, when the mismatch reactance is introduced to F eeder at t 5s, inaccurate power sharing is triggered as analyzed from (5) P DG P DG2 Fig. 6: Load sharing without droop. 2) With i d f/i q V Droop: n and m are tuned such that f 0.05Hz, and V 5V. While an accurate active power sharing is ensured in Fig. 7a, the error between and in Fig. 7bis minimized because of the large n. Also, it is noted from Fig. 7c that the PCC voltage, VLd 2 q 2, is deteriorated due to the feeder voltage drops, which can adversely impact voltage-dependent loads P DG P DG (c) (d) Fig. 7: Load sharing with i d f/i q V droop. f f 2

6 Voltage Magnitude (V) Voltage Magnitude (V) 3) Adaptive Mismatch Virtual Reactance: At t 7s, the mismatch virtual reactance, ωδl v, is incorporated into n as in (4). Consequently, the error between and is further minimized as shown in Fig. 8a. Therefore, by assigning different droop coefficients, the constraints of having unified voltage drops in (6) and a unity ratio in (4) are satisfied. However, acquisition of δl v can be cumbersome, especially with a large number of DG units connected to mismatched feeder impedances, and may require additional communication links. Furthermore, the PCC voltage is still deteriorated in Fig. 8b Fig. 8: i q V droop with mismatch virtual reactance. 4) Adaptive Feeder Virtual impedance: Fig. 9a shows an accurate reactive power accomplished alternatively by incorporating the entire feeder impedance into the i q V droop as in (6). With this method activated at t 7s, not only is a near zero error between and obtained, but the PCC voltage is also improved and kept at the designed voltage deviation. For this, more powers will be exerted. with and without the droop was analyzed and constraints on feeder impedance were addressed for accurate power sharing. Since the active power sharing is not a concern with the droop controller, compensation methods were examined to accomplish accurate reactive power sharing via modification on the i q V droop coefficient. A testbed model of a microgrid with two DG units was built in Matlab/Simulink, which could also be extended to include k-dg units. It was shown that a large coefficient could be assigned for the i q V droop minimizing the error between reactive powers to an acceptable extent and with a 5% voltage deviation. Two other compensation methods based on the adaptive virtual impedance are also shown in the simulation results which further minimized the error. Although both of which exhibit similar efficacy, the adoption of the adaptive feeder virtual impedance offers the advantages of less communication and computation requirements, and maintains the load voltage at the PCC bus within the designed voltage deviation. REFERENCES [] J. M. Guerrero, L. Hang and J. Uceda, Control of distributed uninterruptible power supply systems, IEEE Trans. Ind. Electron., vol. 55, no. 8, pp , Aug [2] X. Wang, Y. W. Li, F. Blaabjerg and P. C. Loh, Virtual-impedancebased control for voltage-source and current-source converters, IEEE Trans. on Power Electron., vol., no. 2, pp , Dec [3] Y. W. Li and C. N. Kao, An accurate power control strategy for power-electronics-interfaced distributed generation units operating in a low-voltage multibus microgrid, IEEE Trans. on Power Electron., vol. 24, no. 2, pp , Dec [4] J. He and Y. W. Li, An enhanced microgrid load demand sharing strategy, IEEE Trans. on Power Electron., vol. 27, no. 9, pp , Sept [5] H. Mahmood, D. Michaelson and J. Jiang, Accurate reactive power sharing in an islanded microgrid using adaptive virtual impedances, IEEE Trans. on Power Electron., vol., no. 3, pp , March 205. [6] L. Fan, Frequency and voltage control in a microgrid, in Control and Dynamics in Power Systems and Microgrids, CRC Press, 207. [7] A. Yazdani and R. Iravani, Controlled-frequency vsc system, in Voltage-Sourced Converters in Power Systems: Modeling, Control, and Applications, Hoboken, NJ: John Wiley & Sons, Inc., Fig. 9: i q V droop with feeder virtual impedance. IV. CONCLUSIONS This paper presents a modified droop controller based on the dq-axis feeder current sharing. The power sharing