2017 IEEE PES Innovative Smart Grid Technologies Conference - Latin America (ISGT Latin America). Quito, Ecuador Droop Control Based on Fuzzy Logic for Voltage and Frequency Regulation in Isolated Microgrids Gerônimo B. Alexandre João Batista M. dos Santos and Antonio M. N. Lima Coordination of Control and Industrial Processes Federal Institute of Pernambuco - IFPE Garanhuns, Pernambuco, Brazil. [email protected] Department of Electrical Engineering Federal University of Campina Grande - UFCG Campina Grande, Paraiba, Brazil. {joaobatista, amnlima}@dee.ufcg.edu.br Abstract— This paper proposes and validates a control strategy for simultaneous regulation of voltage and frequency in isolated microgrid. The proposed technique is based on the conventional Generalized Droop Control (GDC) structure, assisted by a fuzzy logic technique, which is used to determine the line parameters. An optimum tuning method is also proposed to adjust the controller gains which take into account the actual microgrid operating conditions and the legal prescriptions imposed for the voltage and frequency fluctuations of the power provided for the consumer. Simulation test results obtained for reference systems (IEEE 3 node and IEEE 14 node) show the correctness of the design method as well as the feasibility of the proposed droop controller. With the GDC based on fuzzy logic it was possible to track the dynamic profile of the load, stabilizing the voltage and frequency of the microgrid, at different loadswitching scenarios. Index Terms— GDC, Optimum Tuning, Fuzzy Logic, Stability and Operation of MG. A I. INTRODUCTION MICROGRID (MG) consists of a low-voltage network with multiple micro-generators and local loads installed. Some examples are islands, industries, or remote villages where the energy is obtained from renewable sources like photovoltaic systems which require some electronic converter for power processing. Under normal operating conditions, the MG is connected to the medium voltage grid. However, whenever a breakdown occurs, the MG starts to operate on the isolated operational mode which is inherently autonomous. In these cases the local loads must be fed only by the microgenerators installed in the MG, and thus the system operation will be based on a feedback control law which must be designed to meet the consumer demands. At the isolated operational mode, the dynamic switching of loads produces voltage and frequency fluctuations [2]-[5]. In the case of the traditional Electrical Power System (EPS), this problem is solved by controlling the excitation of the synchronous generator. In the case of decentralized EPS, since there is usually no synchronous generator installed in the MG, the problem must be solved by controlling individually each one of the micro-generators. This controller must regulate not only the voltage and frequency fluctuations, but also the power splitting between micro-generators [6]-[12]. This paper proposes a control strategy for regulating the voltage and frequency of a MG when the dynamic load switching takes place or when the connection to the medium voltage grid is lost. This control strategy uses the conventional GDC structure but eliminates the dependency of the line parameters by using fuzzy logic. The proposed technique also uses as reference the nominal values of the converter’s apparent power; the values of the charge’s apparent power; the estimated line parameters; the control set-points for voltage, frequency and active/reactive power; and the legal prescriptions imposed for the voltage and frequency fluctuations. Simulation test results obtained for reference systems are used to show the correctness of the design method as well as the feasibility of the proposed droop controller. One important feature of this controller is the fast accommodation of operational conditions on the occasion of an abrupt variation on the active and reactive power. The contributions of this paper are: Fuzzy Generalized Droop controller design for simultaneous regulation of voltage and frequency; Methodology for tuning the fuzzy GDC controller, based on MG operating conditions; Use of the fuzzy logic method to estimate the MG line parameters; Mathematical formulation of the control region and operational stability of MG; Determination of minimum conditions for sample update rates for each microgrid component. This paper is organized as follows: First, we discuss the strategy control project in Section II. Then, in Section III, we present the test scenarios and the case studies that validated the Droop controller based on fuzzy logic. In this Section, we also present the results of the simulations and a discussion about the controller, focusing on the stability and in its physical implementation in hardware. Finally, in Section IV, we present the conclusions and the possible developments of this project in future works. II. THE ADAPTIVE GENERALIZED DROOP CONTROLER Fig. 1 shows the equivalent circuit for a micro generator connected at the common coupling point of the AC bus. The micro generator is connected to the load dynamic by the line impedance, . At point S the voltage supplied by DG is = ° and at point L the voltage delivered at dynamic load is ° = . Where, and are the voltage generated and the phase angle of the voltage generated 978-1-5386-3312-0/17/$31.00 ©2017 IEEE 2017 IEEE PES Innovative Smart Grid Technologies Conference - Latin America (ISGT Latin America). Quito, Ecuador respectively, is the voltage at the load and the line impedance, . Considering = ‖ ‖ is the angle of = + . In this scenario the individual Droop control − can be characterized by [3]: − The fundamental active and reactive powers injected to the grid by the DG (P and Q, respectively) can be expressed as follows [3] and [7]: = ( + sin + ( − + cos ) + − − s - Controlled AC voltage source Micro generator S (1) cos ) (2) Variable Load LINE + sin Measurements L O A D P and Q variant = − POWER CONTROL Fig. 1. Equivalent circuit of a DG unit connected to the common ac bus. The micro generator is a controlled power source for which one may dynamically adjust its amplitude (A) and frequency (f). sin In practical applications, decoupling approximation ( be considered [6], [7]: = Δ + ( − ) (6) In the (7) and (8) show that in MGs with inductive behavior, the active power must be controlled by the regulating and is controlled by . Thus, the fundamental active and reactive powers can be controlled by the phase angle and magnitude of the DG unit output voltage, respectively. These strategies are known in the literature as, respectively, − and − Droop control techniques. These approximations are valid for shorter transmission lines (up to 80 km long) represented by an RL circuit, typical of low voltage distribution systems, which are inserted micro grid. ) (8) Δ − + (9) Δ + (10) Δ and Δ = −1⁄ , = −1⁄ ; are, Where: respectively, the voltage and frequency deviations of the micro index helps us to identify the generator. In (9) and (10), the voltage and frequency simultaneous control. After some algebraic manipulations from (9) and (10) one may obtain Δ = = Δ + Σ 1 − 1 + − Δ − + (11) Δ − (12) + + - Σ + + Σ + - Σ (5) − Δ + is normally small; thus, a / ≈ 1 and ≈ ) can ≈ ≈ (4) (7) For the general case for and (i.e., no approximated relationship) the instantaneous active and reactive powers ( = and = , instantaneous measurements) are represented [3]: (3) cos − ≈ and where, and are the nominal values of the MG voltage and are the control set-points for active and frequency; and reactive power respectively; and are the droop controller coefficients for the GD active and reactive power. In the (1) and (2) display the dependence of the voltage and the angle of the inverter output power with the active and reactive powers. Assuming a mainly inductive electrical system ( ≈ and ≈ 90°), the fundamental active and reactive powers can be expressed as [3]: ≈ ) ( − =− = FUZZY GDC ( − =− − + + Σ + - Σ + - Fig. 2. Generalized Droop Control block diagram. From (11) it is possible to observe that the gain directly ponderation coefficients alters (has effects on) the Δ and on the second and third terms, respectively. Fig. 2 illustrates the block diagram of the Generalized Droop Controller, implemented by in (11) and (12). So the Controller has three gains, which must be tuned to adjust realtime fluctuations of voltage and frequency to legal conditions in response to the request for active and reactive power requested by the dynamic load. One important feature of this controller is the fast accommodation of operational conditions on the occasion of an abrupt variation on the active and 2017 IEEE PES Innovative Smart Grid Technologies Conference - Latin America (ISGT Latin America). Quito, Ecuador reactive power, setting the voltage and frequency fluctuations at the voltage source inverter (VSI) output. A. Description of the Control Strategy The Generalized Droop controller based on fuzzy logic proposed is illustrated by the block diagram of Fig. 3. It is worth mentioning that this control structure is installed at each microsource (DG) unit; if there are microsources present in the MG, there will be local controllers. Micro generator s + S LINE Variable Load L O A D Controller AC voltage source The controllers of each micro generators interact with each other and with the central control located in the operation center through a low band bidirectional communications channel. This interaction was implemented through a state machine, allowing the active power sharing among the several micro generators installed in the MG. MF degree Measurements Step (D): Usage of the Conventional GDC structure – with the optimal gains determined in Step (C), the proposed structure uses the droop strategy of control illustrated in Fig. 2, where the GDC receives the measured and , provides the amplitude and frequency for the generation of the sinusoidal signal, used as a modulating signal in the sinusoidal bipolar PWM (Pulse Width Modulation) strategy. Figure 2 Droop controller 1 L 0.8 0.6 M H MH 0.4 0.2 Sinusoidal signal 0 0 Calculates P& Q 2 4 6 8 10 12 14 16 18 20 Voltage of variation (V) Tunning of the controller 1 MF degree Fuzzy estimator ML − ) (13) = sin( − ) (14) where and are the active and reactive powers measured instantly, and are, respectively, the and are the angles of voltage and current modules, and the voltage and current phases. Step (B): Calculation of the line parameters – The fuzzy estimator receives as inputs: the active power error (∆ = − ), the reactive power error (∆ = − ) and the voltage and frequency deviations produced by the Conventional GDC, producing output to the line impedance seen from the inverter terminals (impedance of the Thévenin equivalent circuit). In addition to the estimated line impedance value, the parameter estimator provides the graph of the estimated current and the estimation error for the monitoring of the quality of the estimation by the microgrid operator. Step (C): Controller tuning - This block sets the optimal controller gains based on the operational conditions of the plant (isolated MG) according (19), (20) and (21). 0 2 4 6 8 10 12 14 16 Reactive Power of variation (Var) MF degree (a) 1 M L 0.5 H 0 0 MF degree cos( 0 5 10 15 20 25 30 Active Power of Variation (W) 35 40 1 M L H 0.5 0 0 0.2 0.4 0.6 0.8 1 1.2 Frequency of variation (Hz) 1.4 1.6 1.8 2 (b) 1 MF degree = H MH 0.4 0.2 L M ML 0.5 H MH 0 0 1 MF degree Step (A) Calculation of the active and reactive power from the measured data (voltage and current at the output of the LCL filter), being given as, M ML 0.6 Fig. 3. Block diagram for the proposed fuzzy GDC Controller. The fuzzy logic calculates the line parameters (R and X) from the voltage (∆ = ±20 ) and frequency (∆ = ±2 ) deviations established by law and the active (∆ ) and reactive power error (∆ ). The control structure of the GDC based on fuzzy logic operates in four ordered steps: L 0.8 1 2 -4 x 10 R (Ohms) L M ML H MH 0.5 0 0 0.2 0.4 0.6 0.8 1 X (Ohms) 1.2 1.4 1.6 1.8 2 -3 x 10 (c) Fig. 4. Membership functions (MF) for the inputs, (a) Voltage deviation and reactive power; (b) frequency and active power deviation; (c) for the R and X outputs. L=Low; ML = Medium Low; M = Medium; MH = Medium High; A = High. 2017 IEEE PES Innovative Smart Grid Technologies Conference - Latin America (ISGT Latin America). Quito, Ecuador B. Calculation of Line Paramenters Using Fuzzy Logic The operating conditions determine the operational regions (2D regions) of the and distributed generation, as shown in Fig. 6. The Fuzzy system implemented to map the input data (∆ , ∆ , ∆ and ∆ ) in the line parameters (R and X), is a system with four inputs, two output, 40 rules, Mandani method and method Of the centroid for Defuzzyfication. The ∆ and ∆ inputs each with five membership functions, the ∆ and ∆ inputs each with three membership functions and the outputs (R and X) with five membership functions respectively (See Fig. 4). In the design of the Fuzzy GDC controller were used the functions of triangular and trapezoidal membership because they are the most popular for the Mandani method. The the logic used in the rule base follows the reasoning, The gains of the controller are defined for the minimum and maximum conditions of the operation, which define a region of control in the shape of a parallelepiped, for this case, with vertices at points. =( ; ; ), = ( ; ; ), =( ; ; ), = ; ; ), =( ; ; ), = ( ( ; ; ), =( ; ; ) and = ; ; ). The gains , and that define ( this region of control are set by in (19), (20) and (21). IF ∆ = AND ∆ THEN = E = From the individual droop control droop’s definition, = AND ∆ = AND ∆ = Where: , = 1, 2,3 and , = 1, 2, . . . 5. ∆ , ∆ , ∆ and ∆ are the antecedents; R and X are consequent. =− C. The Tuning of the Fuzzy GDC Controller =− The adjustment of the gains of the Fuzzy GDC controller is motivated by the micro generator operating conditions and the MG restrictions for the voltage and frequency levels imposed by the legislation ([1]: ∆ = 2 e ∆ = 20 ). The block of the Fig. 5 was designed to determine the optimal gains of the Droop Control structure of the Fig. 2. 1 ∴ =− ∴ =− and 1 − (15) 1 (16) Substituting (21) and (22) into (6) and (7), ∆ =− ( − ∆ ( − =− Isolating Equation (19) Equation (20) Equation (21a or 21b) and )→∆ = )→∆ 1 ( 1 = ) − ( (17) ) − (18) , it follows as, = = Fig. 5. Generalized Droop Control tuning block diagram. The block in Fig. 5 receives as input: the reactive and active powers measured in the electrical network (instantaneous voltage and frequency measured at the inverter output); the tolerable minimum and maximum values for the operational voltage and frequency; the control set-points – where is the active power reference, is the reference of the reactive power, is the reference of the electric frequency ( = = 60 ), and = = 220 is the reference of the electrical voltage; and the estimated line parameters. As to the output, the block provides the , controller gains. and 1 − ( − ∆ ) ( − ∆ ) (19) (20) According to the concept of generalized droop, the gain is a variable influenced by the line parameters, especially by the dissipative effect of the line (Joule effect). Applying (19) and (20) in (11); (19) and (20) in (12), it follows as, = =− Δ ( ∆ − ( (1 − ) )Δ ( − ) + , = ‖ ‖ )−( − ∆ ( (21 ) − − ) ) (21 ) gain can be adjusted by Equation (21) shows that the the active power, as well as by the reactive power, or that it can be calculated as an arithmetic mean of the two values, that is = . To set the 3D control region for the , and gains, it is necessary to evaluate the extremes of the operational region (See Fig. 6), setting the minimum and maximum values. Evaluating minimum and maximum Fig. 6. and operational regions. values, 2017 IEEE PES Innovative Smart Grid Technologies Conference - Latin America (ISGT Latin America). Quito, Ecuador = → (22 ) ∆ − = =0 → = = → values, (23 ) ∆ − = (23 ) ∆ values from the =0 , Evaluating minimum and maximum active and reactive power, when = 0 =− (1 − ) Δ (24 ) ∆ When the active and reactive powers assume the nominal is: values, the gain = Δ ( − ( − ∆ )Δ ( − ) + )−( ∆ ( ) − ) − Fig. 7. Micro grid with three micro generators and two banks of loads. (24 ) The quality of the controller tuning described in this Section will be robust whenever the estimation of the line and gains parameters is robust. This is the case because are influenced, respectively, by the active – see in (19) – and reactive power – see in (20). While the gain is dependent on the active power and on the reactive power – see in (21), it is also influenced by the line parameters. III. TEST SCENARIOS AND CASE STUDIES A. 3-Bus Test MG In order to test and evaluate the effectiveness of the Generalized Droop control based on Fuzzy Logic, it was initially evaluated in the 3-bus MG shown in Fig. 7 [3] (IEEE standard) with loads with a purely inductive behavior considering: 0.6 kVar initially for load 1, located in bus 1 and 0.2 kVar initially for load 2, located in bus 3. It should be noted that the nominal apparent power at the inverter output (control references) of each micro generator considered was of the S=3+j0.85 kVA, because during load-bank switching, consumer demand S=1+j0.8 kVA. 315 310 GD1 GD2 GD3 305 300 0.0 0.2 0.4 Time instant (s) . . . . . − − − − − . . . . . + ) [kVA] 2+ 2− 2+ 2+ 2+ 1 1 1 1 1 1 1.2 1.4 1.6 60 59.9 0.0 0.2 0.4 0.6 0.8 Time (s) Fig. 8. 3-Bus Voltage and frequency profiles. Impedance (Ω) 0.1 + 1 0.1 − 1 0.1 + 0.5 0.1 + 1 0.1 + 1 Observing Fig. 8, the MG operates within the prescribed values for voltage and frequency fluctuations, operating 0.8 GD1 GD2 GD3 LOAD MAPPING IN R AND X VALUES. ( = 0.6 60.1 Table I maps the active and reactive power profile representing the local variable load into resistance and reactance values (inductive or capacitive). TABLE I. and ∆ = ±5 60.15 , ∆ = (22 ) ∆ Evaluating minimum and maximum between ∆ = ±10 , ∆ = ±6 for tensions and between 59.85 ±0.3 for frequency deviations. Voltage (Vrms) = → Frequency (Hz) =0 Fig. 9. 14-bus microgrid [3]. 1 1.2 1.4 1.6 2017 IEEE PES Innovative Smart Grid Technologies Conference - Latin America (ISGT Latin America). Quito, Ecuador B. 14-Bus Test MG In order to test and evaluate the effectiveness of the GDC based on Fuzzy logic, it was initially evaluated in the 14-bus MG shown in Fig. 9 [3] (IEEE standard / CIGRE). The dynamic loads are connected to buses 7, 8 and 9 and their respective switching times are shown in Table III. The fixed load values connected to these buses are shown in Table II. The voltage and frequency profiles for this scenario are illustrated in Fig. 10. The microgrid operates within the operational range prescribed by law, showing fluctuations of ±10 V for voltage and ±0.02 Hz for frequency. TABLE II. FIXED LOADS CONNECTED IN THE 14-BUS MG. Bus 2+ 1 2.5 + 0.5 5 + 2.5 TABLE III. 5 + 2.5 This research was funded by CNPq and CAPES, Brazil. VARIABLE LOADS CONNECTED IN THE 14-BUS MG. REFERENCES Load 2 in bus 9 [kVA] Load 3 in bus 7 [kVA] − − − − − − 3 5+ 2 8+ 3 6 4 + 2.5 2+ 2 2 4+ 2 6 2 5 4+ 2 3 3 + 1.5 2.5 1.5 4 5+ 3 . . . . . . GD3 GD4 GD5 GD6 GD7 GD8 GD GD10 GD11 GD12 GD13 GD14 Upper Limit 320 Voltage (Vpp) ACKNOWLEDGEMENTS Load 1 in bus 8 [kVA] GD2 The proposed solution proved to be efficient when evaluated not only on several MG’s topologies, but also in multiple test scenarios of dynamic switching of loads that operate in closed loop: The Adaptive GDC was able to preserve both the stability of the MG operation, the synchronization between micro generators installed in MG and the generation-consumption balance, while met the legal prescriptions to voltage and frequency fluctuations. 2+ 1 Time instant (s) . . . . . IV. CONCLUSIONS Considering that the proposed control strategy does not depend on the topology of microgrid under study, this can be applied to any generic microgrid, since the tuning of controllers is made in accordance with the operating conditions of the MG. Load (kVA) 13 strategy is updated at a rate of the 10 seconds, the plant (MG) is updated at the rate of 10 seconds and the control strategy is updated at the rate of 10 seconds. [1] ABNT NBR 5410:2005, “Electrical installations of low voltage”, 2005. [2] H. Bevrani, M. Watanabe, and Y. Mitani, “Micro grid controls,” in Standard Handbook for Electrical Engineers, H. W. Beatty, Ed., 16 Edition New York: McGraw Hill, 2012, Section 16. [3] H. Bevrani and S. Shokoohi, “An intelligent droop control for simultaneous voltage and frequency regulation in islanded microgrids,” IEEE Transactions on Smart Grid. 2013; pp. 1505–13. [4] K. De Brabandere, B. Bolsens, J. Van den Keybus, A. Woyte, J. Driesen, and R. Belmans, “A voltage and frequency droop control method for parallel inverters,” IEEE Transactions on Power Electronics, vol. 22, pp. 1107–1115, 2007. [5] J. M. Guerrero, J. C. Vasquez, J. Matas,. G. de Vicuña and M. Castilla “Hierarchical control of droop-controlled AC and DC micro grids—A general approach toward standardization,” IEEE Transactions on Industrial Electronics, vol. 58, pp. 158–172, 2011. [6] J. M. Guerrero, J. Matas, L. G. Vicuña, M. Castilla, J. Miret, “Decentralized Control for Parallel Operation of Distributed Generation Inverters Using Resistive Output Impedance,” IEEE Transaction on Industrial Electronics, vol. 54, 2 (2007), pp. 994-1004. [7] H. Morteza, E. Mahmound & S. Reza, “Autonomous Control of Inverter-Interfaced Distributed Generation Units for Power Quality Enhancement in Islanded MicroGrids,” International Journal of Mechatronics, Electrical and Computer Technology, Vol. 4 (10), January, 2014, ISSN: 2305-0543. [8] J. A. P Lopes, C. L. Moreira and A. G. Madureira, “Defining control strategies for Micro Grids islanded operation,” IEEE Transactions on Power Systems, vol. 21, nº 2, pp. 916–924, May 2006. [9] Y. Mohamed and E. El-Saadany, “Adaptive decentralized droop controller to preserve power sharing stability of paralleled inverters in distributed generation micro grids,” IEEE Transactions Power Electronics, vol. 23, nº 6, pp. 2806–2816, Nov. 2008. 310 300 290 Lower Limit 280 0 0.2 GD2 GD3 0.4 GD4 GD5 0.6 GD6 0.8 GD7 GD8 1 GD9 GD10 1.2 GD11 1.4 GD12 GD13 GD14 Frequency (Hz) 60.2 60.1 60 59.9 59.8 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Time (s) Fig.10. 14-Bus Voltage and frequency profiles. The digital platform chosen to simulate the operation of an isolated MG was the Simulink Dynamics Systems of MathWorks MATLAB package, version 7.11 (R2014a) using variable integration step, ODE3-Bogacki-Shampine Solver integration method, duration of the 2 seconds. The Fuzzy estimator is updated at a rate of the 10 seconds, the PWM [10] N. Pogaku, M. Prodanovic and T. C. Green, “Modeling, analysis and testing of autonomous operation of an inverter-based micro grid,” IEEE Transactions on Power Electronics, vol. 22, pp. 613–625, 2007. [11] J. Vasquez, J. Guerrero, A. Luna, P. Rodriguez and R. Teodorescu, “Adaptive droop control applied to voltage-source inverters operating in grid-connected and islanded modes,” IEEE Transactions Industrial Electronics, vol. 56, nº 10, pp. 4088–4096, October 2009. [12] Q.-C. Zhong, “Robust droop controller for accurate proportional load sharing among inverters operated in parallel,” IEEE Transactions Industrial Electronics, vol. 60, nº 4, pp. 1281–1290, April, 2013.
