An Adaptive Sliding Mode Controller for Enhanced Q’-V Droop in a Microgrid Christopher N. Rowe1∗† , Terrence J. Summers2∗ , Robert E. Betz3∗ & Timothy G. Moore4† ∗ School of Electrical Engineering and Computer Science University of Newcastle, Australia, 2308 † CSIRO Energy Centre, Newcastle, Australia, 2304 email: 1
[email protected], 2
[email protected], 3
[email protected], 4
[email protected],
Abstract— The state of the art power balancing control utilized in microgrids is known as ‘Power Frequency Droop’. Contemporary power frequency droop schemes utilise Proportional Integral (PI) controllers for voltage magnitude control. The power quantity directly coupled to the voltage is Q’ (Q-dash power). Q’ is present in, and affects, the error signal of the PI voltage controller. The controller is acting on two input signals, voltage and Q’. To avoid control interactions, the filtering applied to Q’ must be significantly slower than the filtering applied to the voltage. Thus the need to avoid control interactions leads to decreased bandwidth of the power control loop. This paper introduces an adaptive sliding mode voltage controller that is able to increase the power control loop bandwidth. The effectiveness of the control scheme is proven by results presented from SABERr simulations and a dSPACEr hardware system consisting of two inverters. Index Terms— Distributed Generation, Microgrids, Power Electronics, Power Frequency Droop.
I. I NTRODUCTION The microgrid concept has been developed to address issues with power balancing in islanded power systems [1]. Interest is increasing in microgrids due to the demand to integrate renewable energy sources into an ever evolving power system. Microgrids offer a local solution to issues related to the distributed nature of renewable generation [2]. In many cases renewable generation cannot meet the security and reliability of supply requirements of the existing grid power system. However, characterising the microgrid as a small autonomous unit within a power system creates an environment where solutions can be developed on a microgrid level. Under this regime of operation the microgrid can mitigate the need for major augmentations to the distribution network. For example, a microgrid may have the capacity to isolate itself during transients or faults and reconnect when the power supply is stable. Furthermore, hierarchical control can be implemented to more clearly define the responsibilities of involved stakeholders, from distribution companies to microgrid operators [2].
Figure 1.
Hardware Configuration
Within a microgrid itself, the most widely accepted method to ensure that power sharing is maintained involves drooping the frequency of each DG unit to change the real power supplied. Similarly, the output voltage magnitude of each DG unit is changed to control the reactive power supplied. The remainder of this paper is organised as follows. The next section introduces power frequency droop and discusses the contemporary use of PI voltage controllers. Subsequently
Figure 2.
Proposed Control Scheme Implementing Adaptive Sliding Mode Controller
the Adaptive Sliding Mode Controller (A-SMC) is explained. In Section IV the experimental microgrid system is described. SABER simulations are developed of the the two inverter microgrid. Finally, results from the implementation of the new algorithm on this system are presented showing the controller’s improved performance over PI controllers. The paper is concluded with a summary of the contributions.
explanation of the basis of droop and the LRT can be found in [4]. The transform is provided in (3) and explained fully in [4].
II. E XISTING C ONTROL
0
P Q0
"
=
Xln Zln Rln Zln
ln −R Zln
#
Xln Zln
P Q
(3)
ω − ω0 = −mp (P − P0 )
(1)
where Zln , Xln and Rln are the coupling (line) impedance, inductance and reactance respectively, shown in Fig. 1. The inverter number, 1 or 2 in this case, is denoted by the subscript n. The elements of real and reactive power directly related to frequency and voltage are P 0 and Q0 . The traditional droop equations are altered to consider the transform, with P and P0 becoming P 0 and P00 . Further Q and Q0 become Q0 and Q00 . As in
Vout − V0 = −mq (Q − Q0 )
(2)
ω − ω0 = −mp (P 0 − P00 )
(4)
Vout − V0 = −mq (Q0 − Q00 )
(5)
This paper is based on the implementation of the traditional power frequency droop method discussed in [2], [3] and [4]. The generally accepted form of the P-F and Q-V droop equations are
where ω is the system frequency, ω0 is the nominal frequency set point, mp is the real power droop coefficient, P is the inverter output power, P0 is the nominal power set point at ω0 , Vout is the inverter output voltage, V0 is the nominal voltage set point, mq is the reactive power droop coefficient, Q is the reactive power output and Q0 is the nominal reactive power set point at V0 . These equations are implemented in each of the DG units, with the system ω and V values slowly altered and the amount of real power P and reactive power Q delivered by each inverter being determined by the value of the coefficients mp and mq . The physical equations that govern the power flow across a single inductance change dependent on the inductance and resistance of the line (X/R ratio). To consider this phenomenon, De Brabandere [4] introduced a linear rotational transform (LRT). Considering the line’s X/R ratio; P 0 and Q0 are defined as the power components directly coupled to the inverter frequency and output voltage, respectively. A well written
In a two inverter microgrid with a known X/R ratio we can utilise this transform to create a P 0 entirely coupled to the frequency. The inclusion of the LRT is shown in Fig. 2. In modern droop systems, output voltage regulation is achieved by implementation of a Proportional Integral (PI) controller. The error signal takes into account both the system voltage and the Q’-V droop requirements of the control scheme as given by Verr = (V0 − mq (Q0 − Q00 )) − Vout
(6)
where Q00 is the set point for the Q0 power quantity and Verr is the voltage error input to the PI voltage controller. Remark 1. The voltage controller is affected by, and acts on, both the voltage set point (V0 ) and the offset added by droop control (m(Q0 − Q00 )).
Figure 3.
Sliding Manifold and Regions of Adaptive Sliding Mode Controller
The use of PI controllers in contemporary droop systems is widespread, PI is utilized to control the magnitude of the output voltage of the inverter in [5], [6] and [7]. In [8] cascaded control loops are employed, one PI controller on the outer voltage control loop and one on the inner current control loop. In [9] a Proportional Resonant (PR) controller with an added integral action is used. Vasquez notes in [9] that a Generalised Integrator (GI) is added to achieve zero steady state error. Thus both proportional and integral actions are also inherent in this system. III. S LIDING M ODE VOLTAGE C ONTROLLER The predominant use of PI controllers in droop leads to a decreased bandwidth of the outer power control loop. This is due to the need to design the outer reactive power loop slower than the inner voltage control loop to avoid control interactions and guarantee stability. Hardware results presented in [6] and [10] emphasise this phenomenon with slow responses to step changes in power demand. Sliding mode control has been utilised to improve the stability of microgrids [11] and in providing voltage support with doubly fed induction generators [12], however sliding mode control is yet to be implemented in microgrids utilising power frequency droop. The use of a sliding mode controller increases the control bandwidth whilst circumventing control loop interactions. The controller constantly converges to the sliding manifold [13]. The sliding mode control regions are defined in Fig. 3 and the augmented power frequency droop control scheme is shown in Fig. 2. Note that Arctan Power Frequency Droop is implemented in this control scheme [14].
The sliding manifold for the controller is the droop characteristic (V0 − mq (Q0 − Q0o )) − Vout = 0
(7)
Vout = V0 − mq (Q0 − Q0o )
(8)
or
If the Left Hand Side (LHS) of (7) is less than zero, Vout > V0 − mq (Q0 − Q0o ), the controller is in Region 1 (‘a’ or ‘b’). In Region 1 the control law implemented is out vk+1 = vkout − vstep x
(9)
out is the output voltage at the next control interval, where vk+1 vkout is the voltage output at the previous control interval, vstep x is the voltage step size of the sliding mode controller with subscript x denoting the regional step size ‘a’ or ‘b’. If the LHS of (7) is greater than zero, Vout < V0 −mq (Q0 − 0 Qo ), the controller is in Region 2 (‘a’ or ‘b’). In Region 2 the control law implemented is out vk+1 = vkout + vstep x
(10)
The adaptive nature of the control is determined by the selection of vstep x which varies in Sub-regions denoted ‘a’ or ‘b’. The ‘b’ Sub-regions begin at ±2.5 % of rated voltage, from the sliding manifold. Given a rated voltage of 169.7 Vpk , the ‘b’ Sub-regions begin at ±4.24 Vpk . These additional ‘b’ Sub-regions allow faster convergence for large voltage excursions. For all ‘a’ Sub-regions vstep x = vstep a
Figure 4.
Hardware System Overview
and for all ‘b’ Sub-regions vstep x = vstep b The controller is implemented in discrete time with a discrete step size of TSM C = nTcontrol where n is an integer coefficient and Tcontrol is the period of the control interval. The selection of sub-regional step sizes and TSM C both influence steady state chatter and speed of convergence. This constitutes a simple yet effective sliding mode controller causes the system to converge to the sliding manifold. This implementation of the SMC is subject is chatter. Many methods exist to eliminate steady state chatter in SMC. In [11] a fuzzy logic controller is used to reduce chatter around the sliding manifold. It is also possible to define a small region around the sliding manifold utilising pure proportional control or removing the control action to eliminate steady state chatter. Remark 2. The definition of only two adaptive regions in this paper is somewhat arbitrary. The aim is to successfully demonstrate the adaptive nature of a control scheme utilising regional definitions. If implementing A-SMC in a commercial device the selection of regions will depend on system requirements in the country of installation. For example, allowable duration of voltage swells, sags etc. Conjecture 3. It is possible that a digital controller, such as A-SMC, could be utilised to perform intelligent protection operations. Phenomena such as voltage sags can be identified by defining additional regions in the controller and monitoring the duration of intermediate states. If the device operates outside the prescribed operational criteria the device can disconnect or change its operational mode.
Figure 5. Photograph of Microgrid Laboratory at the University of Newcastle, Australia
IV. E XPERIMENTAL S YSTEM The control scheme was implemented in a two-inverter microgrid. A hardware system was constructed and a simulation model of the hardware system developed. The nominal system parameters are given in Table I and the system configuration shown in Fig. 1. A. SABERr Simulation The simulation was performed in the SABERr simulation package. The new control algorithm was implemented in a dynamic link library written in the C language. In this way the control algorithm emulates a Digital Signal Processor (DSP) based system. The dynamic link library is executed once every 250 µs, emulating a DSP running with a main control loop speed of 4.0 kHz.
Table I S YSTEM PARAMETERS Voltage (V)
Value 4 kHz 700 VDC 120 Vrms 314 rad s−1 53 mH 470 nF 120 µH 0.74 0.0005 rad s−1 W −1 0.004 V var−1 2.5 Hz 2.5 Hz / 50 Hz
185.0
A−SMC Voltage − Inv 2
180.0
175.0
Voltage (V) :
Voltage (V)
175.0
Time (s)
Voltage − Inv 1
170.0 Voltage − Inv 2 165.0
160.0
Real / Reactive Power (W/var)
400.0 Real / Reactive Power (W/var)
Parameter fsw VDC bus V0 ω0 Lf 1 , Lf 2 Cf 1 , Cf 2 Ll1 , Ll2 ap ρ mq fc P’ LPF fc Q’ LPF
Time (s) A−SMC Voltage − Inv 1
Voltage (V) : 190.0
:
Time (s)
Real Power Output − Inv 1
Real Power Output − Inv 2
Reactive Power Output − Inv 1
200.0
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0.0
0.25
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0.45
0.5 0.55 Time (s)
0.6
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0.8
Figure 7. A-SMC with Q’ filter cutoff at 50 Hz; A-SMC Output Voltage, Inverter Output Voltage, Real and Reactive Power
V. R ESULTS Votlage (V) 175.0
:
Time (s)
A. SABERr Simulation
Voltage − Inv 1
Votlage (V)
172.5 Voltage − Inv 2
170.0
167.5
165.0
162.5
160.0
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Real / Reactive Power (W/var)
400.0
:
Time (s)
Real Power Output − Inv 1
Real Power Output − Inv 2
Reactive Power Output − Inv 1
200.0
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0.0
0.25
0.3
0.35
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0.45
0.5 0.55 Time (s)
0.6
0.65
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Figure 6. PI Controller with Q’ filter cutoff at 2.5 Hz; Inverter Output Voltage, Real and Reactive Power
B. dSPACEr Hardware System The hardware system consists of two inverters in parallel, connected to a passive resistive and inductive load. The two inverters are SEMITEACH three leg IGBT stacks from Semikron. Control of each stack is achieved via dSPACEr DS1103 controllers. Fig. 4 a schematic of the hardware feedback systems and Fig. 5 a photograph of the microgrid laboratory. The dSPACEr is also configured with a main control loop speed of 4.0 kHz. The control scheme originally designed in SABERr has been converted into a dSPACE / MATLABr Real Time Interface (RTI) model. Simulations are compiled down to ‘C’ code and run on the dSPACE DS1103 controllers. The majority of the control scheme is contained in ‘C’ Dynamic Link Libraries (DLL) for the SABER simulations, MEX DLLs in Simulinkr . Thus the control is almost identical across the two different software platforms. This made direct comparison of simulation and experimental results meaningful.
A SABERr simulation was configured as described in Section IV-A. The simulation was first utilised to show the response to a step change in real and reactive power. Subsequently control interactions were simulated by perturbing the Q0 set point. 1) Step Response: Fig. 6 shows the traditional PI controller response to a step change in real and reactive power. In this experiment the Q’ Low Pass Filter (LPF) cut off frequency was 2.5 Hz. In [15] it was noted that power filters are designed with a cut off frequency of 2-10 Hz to maintain system stability and guarantee control loop frequency separation. Fig. 7 shows the A-SMC under an identical step change in real power. The implemented Q’ LPF cut off frequency was 50 Hz, the A-SMC was configured such that n = 60, vstep a = 0.8 V and vstep b = 4.0 V. The steady state error in the A-SMC was dependent on the chatter present, thus it was equal before and after the power transient. 2) Control Interactions: The control interactions were evaluated by perturbing the reactive power set point (Q00 ), of inverter one, for 0.1 seconds to observe physical interaction and the response of the controller. The perturbation of the Q00 set point is shown in the upper plot of Fig. 8. The aim perturbing the Q00 set point was to explore the later proposition. Proposition 4. If there is insufficient decoupling between V and Q0 quantities, in (6), control interactions may lead to a drift or transient error in the integral sum of the PI controller. During transient excursions in power and voltage, if sign{4V } = 6 sign{4(mq (Q0 −Qo ))} the two terms cancel and the PI controller does not observe the correct voltage error. A-SMC avoids this problem as during transients it has a fixed speed of convergence based on regional control laws. Fig. 8 and 9 show the PI controllers implementing Q’ LPF cut off frequencies are 2.5 Hz and 50 Hz respectively. In both
0.0
−100.0
Real Power (W) :
Time (s)
Real Power Output − Inv 2
252.0 251.0
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75.0
:
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65.0
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30.95
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30.9 30.85
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251.0
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254.0
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Time (s)
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150.0
−100.0
0.7
Figure 11. Control loop interactions in PI controller with Q’ LPF fc = 2.5 Hz, Integral and Proportional Errors
Reactive Power (var)
0.7
Figure 8. Control loop interactions in PI controller with Q’ LPF fc = 2.5 Hz, active and reactive power sharing
Reactive Power (var)
Numeric
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:
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Numeric : Time (s) PI Controller, Intergral Sum Term − Inv 2
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1.0 1.1 Time (s)
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Figure 9. Control loop interactions in PI controller with Q’ LPF fc = 50 Hz, active and reactive power sharing
Figure 12. Control loop interactions in PI controller with Q’ LPF fc = 50 Hz, Integral and proportional errors
figures the power sharing is degraded by the perturbation. The convergence of the reactive power after the removal of the perturbation is slow. This is due to the fact that the control action causing convergence is the reactive power control loop, where mq is deliberately designed with a weak control action to maintain voltage bounding and stability. The real power convergence is caused by mp in the P 0 − f droop control. Fig. 11 and 12 provide a deeper understanding of the cause of this phenomenon. The voltage error and integral sum of the PI controllers are shown, for different cut off frequencies.
Both controllers exhibit integral windup of the integral sum term, of inverter one, during the perturbation. The results therefore show that perturbations in reactive power can cause integral windup in the PI controller. This integral windup causes a problem when combined with the physical properties of the system. Normally integral windup in PI controllers causes overshoot and oscillations that eventually decay. However in a two inverter microgrid, one inverter may simultaneously act at a higher voltage than, and supply reactive power to, the other inverter. This leads to a
Time (s)
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Figure 10. Control loop interactions in sliding mode controller with Q’ LPF fc = 50 Hz, active and reactive power sharing
0.6
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1.0
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1.2
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Figure 13. Control loop interactions in sliding mode controller with Q’ LPF fc = 50 Hz, A-SMC Voltage
scenario where an intermediate steady state can be reached. The identical PI controllers of inverter one and two observe no voltage error but exhibit reactive power imbalance, due to differing integral sum terms. Without sufficient decoupling of the V and Q0 quantities this leads to a steady state imbalance in reactive power output. Remark 5. It is hypothesised that this physical phenomenon is unobservable to the PI controller described in (6), given sign{4V } 6= sign{4(mq (Q0 − Qo ))}. This remains the subject of future research. The A-SMC was configured with the parameters noted above. The A-SMC is affected by the perturbation of the Q0 quantity as shown in Fig. 10, the power quantities diverge under the perturbation. However after the removal of the perturbation the A-SMC converges to the sliding manifold in 0.6 seconds regaining balanced power sharing. Fig. 13 shows the A-SMC voltages during the perturbation. Further, the adaptive nature of the SMC it is able to cause rapid convergence to the sliding manifold under large excursions while circumventing the control interaction issues. Conjecture 6. Another option to correct integral windup, in this test, is to slowly ramp up the perturbation. The secondary control loop in droop [2] effectively creates a slow ramping of reactive power perturbations and should gain superior performance to the traditional scheme yet the time frame for correction is longer if relying entirely on the secondary loop for imbalance correction. B. dSPACEr Hardware The hardware system described in Section IV-B was used to verify the operation of the A-SMC algorithm. Results presented were logged with two individual dSPACEr DS1103 controllers and collated in MATLAB. Control interactions are yet to be explored in the hardware system. The adaptive modes of operation are evident in Fig. 14, the controller is oscillating between Regions 1a and 2a before t = 8 s. At this time a step change in real power is applied. The controller is forced into Region 2b and quickly corrects the voltage (with zero overshoot). Inverter one and two controllers act equivalently in the transient due to the limited discrete states of the A-SMC. A zoom of the transient is provided in Fig. 15. At t = 12 s and t = 15 s, two step increases in reactive power were applied. After this the additional loads are sequentially removed. In Fig. 14, voltage control is fast and power sharing is balanced. Further, it is evident in Fig. 15 that the transient response of the A-SMC is excellent. These experimental results confirm the correct operation of the algorithm.
VI. C ONCLUSIONS & C ONTRIBUTIONS Contemporary power frequency droop control schemes utilise Proportional Integral (PI) controllers for control of the voltage magnitude. This paper contributes a novel Adaptive Sliding Mode Controller for use in Q’ - V droop systems. Results were presented from SABERr simulations and a dSPACEr hardware system consisting of two inverters. Results demonstrated control interactions present in PI controllers. The A-SMC controller was able to increase control bandwidth whilst circumventing PI controller integral windup. R EFERENCES [1] R. Lasseter and P. Paigi, “Microgrid: a conceptual solution,” in Power Electronics Specialists Conference, 2004. PESC 04. 2004 IEEE 35th Annual, vol. 6, 2004, pp. 4285 – 4290 Vol.6. [2] J. Guerrero, J. Vasquez, and R. Teodorescu, “Hierarchical control of droop-controlled dc and ac microgrids a general approach towards standardization,” in Industrial Electronics, 2009. IECON ’09. 35th Annual Conference of IEEE, 2009, pp. 4305 –4310. [3] M. Chandorkar, D. Divan, and R. Adapa, “Control of parallel connected inverters in standalone ac supply systems,” Industry Applications, IEEE Transactions on, vol. 29, no. 1, pp. 136 –143, 1993. [4] K. De Brabandere, B. Bolsens, J. Van den Keybus, A. Woyte, J. Driesen, R. Belmans, and K. Leuven, “A voltage and frequency droop control method for parallel inverters,” in Power Electronics Specialists Conference, 2004. PESC 04. 2004 IEEE 35th Annual, vol. 4, 2004, pp. 2501–2507 Vol.4. [5] X. Zhang, J. Liu, T. Liu, and L. Zhou, “A novel power distribution strategy for parallel inverters in islanded mode microgrid,” in Applied Power Electronics Conference and Exposition (APEC), 2010 TwentyFifth Annual IEEE, 2010, pp. 2116 –2120. [6] C.-T. Lee, C.-C. Chu, and P.-T. Cheng, “A new droop control method for the autonomous operation of distributed energy resource interface converters,” in Energy Conversion Congress and Exposition (ECCE), 2010 IEEE, 2010, pp. 702 –709. [7] G. Yajuan, W. Weiyang, G. Xiaoqiang, and G. Herong, “An improved droop controller for grid-connected voltage source inverter in microgrid,” in Proc. 2nd IEEE Int Power Electronics for Distributed Generation Systems (PEDG) Symp, 2010, pp. 823–828. [8] J. Kim, J. M. Guerrero, P. Rodriguez, R. Teodorescu, and K. Nam, “Mode adaptive droop control with virtual output impedances for an inverter-based flexible ac microgrid,” vol. 26, no. 3, pp. 689–701, 2011. [9] J. C. Vasquez, J. M. Guerrero, M. Savaghebi, and R. Teodorescu, “Modeling, analysis, and design of stationary reference frame droop controlled parallel three-phase voltage source inverters,” in Proc. IEEE 8th Int Power Electronics and ECCE Asia (ICPE & ECCE) Conf, 2011, pp. 272–279. [10] J. Vasquez, J. Guerrero, E. Gregorio, P. Rodriguez, R. Teodorescu, and F. Blaabjerg, “Adaptive droop control applied to distributed generation inverters connected to the grid,” Industrial Electronics, 2008. ISIE 2008. IEEE International Symposium on, pp. 2420–2425, 30 2008-July 2 2008. [11] M. H. Abdollahi and S. M. T. Bathaee, “Sliding mode controller for stability enhancement of microgrids,” in Proc. T&D Transmission and Distribution Conf. and Exposition IEEE/PES, 2008, pp. 1–6. [12] R. Aghatehrani and R. Kavasseri, “Sliding mode control approach for voltage regulation in microgrids with dfig based wind generations,” in Proc. IEEE Power and Energy Society General Meeting, 2011, pp. 1–8. [13] H. K. Khalil, Nonlinear Systems, 2nd ed. Prentice-Hall, Inc., 1996. [14] C. Rowe, T. J. Summers, R. E. Betz, and D. Cornforth, “Small signal stability analysis of arctan power frequency droop,” in Proc. 2011 Conf. Power Electronics and Drive Systems (PEDS 2011), 2011. [15] Y. Mohamed and E. El-Saadany, “Adaptive decentralized droop controller to preserve power sharing stability of paralleled inverters in distributed generation microgrids,” Power Electronics, IEEE Transactions on, vol. 23, no. 6, pp. 2806 –2816, 2008.
Figure 14.
DSPACEr hardware results, A-SMC Output Voltage, Inverter Output Voltage, Real and Reactive Power
Figure 15.
DSPACEr hardware results, Zoom on; Inverter Output Voltage and A-SMC Output Voltage
