Frequency Response Improvement in Microgrid Using Optimized VSG Control

Transcription

1 Frequency Response Improement in Microgrid Using Optimized SG Control B. Rathore, S. Chakrabarti, Senior Member, IEEE, S. Anand, Member, IEEE, Department of Electrical Engineering Indian Institute of Technology Kanpur, India. and Abstract In the recent years, the disadantages of the inerter based distributed energy resource, such as less inertia and lower aailable kinetic energy as compared to synchronous generator (SG), hae been addressed by researchers. As a result, the irtual synchronous generator (SG) or irtual synchronous machine (SM) is suggested in literature. SG controller allows the inerter to mimic the characteristic of the synchronous generator by emulating the swing equation of SG. In case of SG control, one can change the parameters of swing equation in real-time to improe the transient response of the system, which is not possible in an actual synchronous machine. Based on this concept, an optimized SG control is discussed in this paper, in which the inertia constant and damping factor are altered between two alues based on relatie irtual angular elocity and its rate of change. The optimized alues of irtual inertia constant and irtual damping factor are obtained, by formulating, aggregated fitness function of frequency deiation and oltage deiation. Particle Swarm Optimization (PSO) technique is used to imize the function. Lyapuno direct method is used for the transient stability analysis of the system Index Terms-- Distributed Energy Resource (DER), droop control, inertia, frequency stability, transient response, irtual Synchronous Generator (SG). I. INTRODUCTION A microgrid typically consists of distributed generators (DGs), energy storage units, and distributed loads that may operate in grid-connected mode or standalone mode []. Interconnection of arious types of DGs, such as photooltaic (P) panels, wind turbines, fuel cells, micro turbines, and energy storage to the network are done through power electronic conerters. Conentionally, power sharing among these conerters in a microgrid is realized by frequency-real power and oltage-reactie power droop controllers []. arious modifications to droop is suggested to oercome the problems in power sharing due to unequal line impedance between sources, different response time of inertial and noninertial sources, harmonic current sharing, and resistie line impedance [3] [8]. Due to less inertia or negligible kinetic energy of inerter based distributed energy resources (DERs), frequency regulation and system stability are main concerns for microgrid operation [7][8]. In grid-connected operation, the main grid doates the system dynamics due to high inertia compared to small DERs. In stand-alone mode, these DERs, and to some extent the network itself, goern the system dynamics. The synchronous generators help in reducing frequency deiation during transient condition at the expense of an increase in settling time of the oscillations because of their stored kinetic energy. The conerter-interfaced DERs may not be able to supply excess current during the fault, or and regulate the system frequency, in the case of large disturbances, because of their low inertia. In stand-alone mode, when inerter based sources paired with synchronous generator operate in oltage control mode, they proide poor transient load sharing. Inerter based sources respond more quickly and shares the majority of the load demand and the synchronous generators output power increases gradually. This poor load sharing with the limited size of the inerter based DERs affects the system frequency profile during a large load change. Researchers hae suggested the arious methods to improe the transient performance of microgrids. Modified droop control techniques [7]-[8], synchronerter [9], irtual synchronous generators (SGs) [0] or irtual synchronous machines (SMs) []-[8], and modified SG control [9] are used to enhance the system inertia irtually. A deriatie of the actie power in the frequency droop is suggested in [7], to aoid the confliction between the inertial and non-inertial sources to share the load demand. In [8], it is reported that instead of using an inertial source, irtually inertia is used by modifying the existing control strategy of inerters. The author suggested a modified droop characteristic as a function of the rate of change of frequency, a small alue of droop coefficient is adopted during transient condition to enhance system inertia irtually when the rate of change of frequency exceeds a threshold alue. This method improes the system transient stability and reduces unwanted outage of the source during a transient case. It also reduces the short-term storage requirement [8]. Other approaches to enhance system inertia irtually are reported in []-[8]. In these papers, the concept of irtual Synchronous Machine (SM) or irtual Synchronous Generator (SG) and synchronerter is presented. The main concept of SM or SG control is to mimic the steady-state as well as transient properties of a synchronous generator on an inerter /4/$ IEEE

2 In [9]-[], the complete modelling of a DER unit as a synchronous generator (SG) is used, which increases the system algorithm complexity. In []-[5], only the parameters of swing equation are considered to calculate the irtual rotor angle frequency and hence the modelling is easy with simple calculations. The disadantage of a SG or SM technique with fix alue of inertia constant and damping factor is that it takes large time to settle down or to absorb the oscillation. To obtain faster and smoother operation, one can change the parameters of swing equation in real-time, which is not possible in an actual synchronous machine. This feature of SG control is used to introduce adaptie irtual inertia based SG control. An alternating moment of inertia scheme is suggested to improe the transient response during sudden load changes [9]. Based on the relatie irtual angular elocity and its rate of change, the alue of the irtual moment of inertia is altered between two alues [9]. The swing equation expresses that the alue of a damping factor also plays an important role together with inertia constant to improe the transient response. The alternating moment of inertia based SG control becomes more adantageous if the damping is added in the controller because it helps to absorb the oscillation. A SG controller, with alternating irtual damping factor and alternating irtual inertia constant is proposed in this paper. Maximum alues of inertia constant and damping factor are used during acceleration period to reduce acceleration time and imum alues are considered during deceleration period to boost the deceleration. It is obsered that in the case of SG control, during sudden load change, there is a drop in the teral oltage similar to SG due to the presence of irtual inertia. Inertia in SG and irtual inertia in SG do not allow them to supply the power to load during a sudden change. A large amount of current flows, resulting drop in teral oltage because of output impedance between the inerter and PCC teral. In this scheme, the optimal imum and imum alues of irtual inertia constant and irtual damping factor are obtained by using Particle Swarm Optimization (PSO) technique. The arrangement for basic SG control and droop control is gien in Section II. The concept of SG control haing imum and imum alues for both irtual inertia constant and irtual damping factor is gien in section III. Problem formulation and its solution using PSO is discussed in section I. In Section, the simulation results for a sample microgrid structure are compared for proposed control, droop control, and alternating inertia constant based SG using MATLAB/Simulink enironment. Finally, the conclusion is drawn in Section I. II. PRINCIPLE OF DROOP AND SG CONTROL In a microgrid, haing both an inerter and synchronous generator based distributed sources; the power-sharing is realized using either droop control [] or SG control []. In droop control, frequency and magnitude of the PCC oltage are regulated by adjusting real power, P and reactie power, Q of the inerter independently, according to the droop equations as gien below [4]. ( ω ) = k ( P P ) ω () ref g p ref ( ) = k ( Q Q ) ref q ref () where, ωref and ref are the rated frequency and rated oltage of the system, respectiely. Pref and Q ref are the set points for the real and reactie power of the inerter, respectiely. k = Δω, is the actie power droop coefficient and p P k = Δ, is the reactie power droop coefficient [4]. q Q P and Q are the rated actie and reactie power of the inerter, and Δ ω and Δ are the allowable ariation ranges in frequency and oltage magnitude, respectiely. As inerter based sources respond more quickly and share the majority of the load demands as compared to synchronous generators, when paired with SG in islanded mode. This poor load sharing with limited size of inerter based DER affects the system frequency profile during a large load change. As a result SG method is suggested to maintain the microgrid stability while increasing the integration of inerter based DERs. The block diagram of SG control is shown in Fig.. ere SG control block emulates the swing equation to increase the system inertia irtually. PWM scheme is used to generate the firing pulse for the DER unit and frequency detector is used to continuously track the frequency of PCC point. ωli ωc q q Fig.. SG control of inerter In the SG control, according to the swing equation of synchronous generator, irtual inertia is embedded into the control of inerter based DER to emulate the inertial nature of the synchronous generator. The actie power-frequency control of SG is expressed as [7],

3 ( P P ) K ( ω ω ) dω = in ref (3) where, is the irtual inertia constant. P in, the irtual input power to the shaft, is the actie power supplied by the DER,ω is the irtual rotor angular frequency, is the irtual damping factor constant. When the inerter based DER paired with a synchronous generator, is operated in oltage control mode, it should be able to support the frequency of system for the stable operation of the microgrid. Therefore, droop characteristic is introduced into the actie power-frequency control block and gien by (). From () and (3), the irtual goernor model is obtained, and the irtual angular frequency of the output oltage in SG control can be obtained by taking integration of (4) [7]. k p dω ω ref g ref d, g = ( ω ) + ( P P ) K ( ω ω ) (4) TABLE I. MODES OF OPERATION Segment Δω Mode, > 0 > 0 Accelerating igh igh > 0 < 0 Decelerating Low Low < 0 < 0 Accelerating igh igh < 0 > 0 Decelerating Low Low dω Δω dω Case (i) > 0 and dω Case (ii) < 0 and Δ ω > 0 Δ ω < 0 dω Case (iii) > 0 and Δ ω < 0 dω Case (i) < 0 and Δ ω > 0 K d, K d, K d, K d, K III. SG CONROL WIT DYNAMIC INERTIA AND DAMPING COEFFICIENTS During a sudden change in load and faulty condition, there will be an oscillation in the output frequency and power of SG control, similar to a synchronous generator. The transient tolerance limit of an inerter-based DER is restricted due to its lower inertia and less kinetic energy as compared to SG. To obtain faster and smoother operation, the swing equation parameters of SG control can be changed in real time, which is not possible in a real synchronous machine. To introduce adaptie irtual inertia and alternating inertia based SG control is used [9]. An alternating inertia constant and alternating damping factor based SG is suggested in this paper. The alues of the irtual inertia constant and irtual damping factor are dynamically modified in this scheme by considering the sign of relatie irtual angular elocity and its rate of change. In Fig., when a sudden change in prime moer is introduced from P in to P in, the operating point oscillates from point a to c and then from c to a along the power cure. Four segments are considered in each cycle of the oscillation, and summarized in Table I. The proposed control technique is shown in Fig. 3, it is similar to SG method with additional control block. The acceleration or deceleration mode of operation in each segment is decided by the sign of the dω along with the sign of the Δω. P load P in P in 0 4 a 3 b c δ δ 0 δ δ 3 Fig.. Power-angle cure for a synchronous machine Π δ Fig. 3. Control logic The main function of the proposed controller is to damp out frequency oscillation quickly, by monitoring the acceleration or deceleration period, and proiding the alues of irtual inertia constant and damping factor. During any transient condition, the rotor angle deiation in the SG is restricted by its inertia constant. In a similar way, the frequency deiation or oltage angle deiation of the output oltage of DER unit is reduced by using irtual inertia concept. It can easily understand by the swing equation (3), according to that one can consider that the rate of change of irtual angular frequency is inersely proportional to the inertia constant in SG control. Based on this fact, a imum alue of is used during acceleration phases ( a to c and c to b ) to reduce the acceleration and a imum alue is considered in b to c and b to a segments to boost the deceleration. Oscillations in the SG can also reduce by introducing the damping; it also helps to reduce the settling time. Similar to alternating inertia concept, imum and imum alues of the damping factor are used during acceleration periods ( a to c and c to b ) and deceleration periods ( b to c and b to a ), respectiely. Due to the presence of inertia and damping in SG and irtual inertia and irtual damping in SG, they do not permit sudden injection of power to the load. A large amount of current flows, resulting in a drop in the teral oltage because of the output impedance between the inerter and PCC teral. Therefore, in this paper, the alues of irtual alternating inertia constant and irtual alternating damping factor are obtained by formulating imization problem of aggregated function of frequency deiation and oltage deiation using Particle Swarm Optimization (PSO)

4 technique. After offline PSO analysis, the obtained imum optimal alues of are chosen as d, respectiely to reduce acceleration and imum alues are used to boost deceleration. I. OPTIMIZATION PROBLEM FORMULATION AND PSO ALGORITM As discussed in preious section, the inclusion of irtual inertia and irtual damping factor in SG control results in improement of the frequency response at the cost of decrement in the teral oltage during sudden load switching. Therefore, it is necessary to find out the optimal alues of irtual inertia and irtual damping factor to get a compromised solution for frequency and oltage improement. This is achieed by imizing the aggregated weighted function of, square of frequency deiation and square of oltage deiation. ere, the imization problem is multi-objectie non-conex type, therefore eolutionary optimization techniques should be used. Compared to the other eolutionary optimization strategies the attributes of the PSO is simpler to implement with fewer parameters to tune up in finding a number of high quality solution [0]. PSO is more efficient in maintaining the diersity of the swarm, since each particle uses the information related to the most effectie particle in order to improe them. Using PSO, the obtained optimal alues are considered as high alues for damping factor and inertia constant. There are two objectie functions, which helps to define main objectie function are gien by, f (, K d, ) = Δω and f (,K ) = Δ (5) As these two problems conerge for two different alues of, and do not proide a common solution for the suggested control, aggregated weighted function of these two functions is considered as main function, ( ) w f (, K ) w f ( K ) J = +, (6) subject to: < < 0 and < K < Both weight factors w and w are decided on the basis of the indiidual impacts and importance of the particular index on the frequency deiation. The main aim is to imise the oerall function. So the f gets the highest weight of 0.85 and f gets lowest weight of 0.5. Optimal alues of the irtual inertia constant and irtual damping factor, found after execution of PSO algorithm, considered as constants alues for SG control. For alternating irtual inertia constant and irtual damping factors the optimal alues of are considered as and K d,, respectiely. And the obsered smallest alues of after offline PSO analysis are considered as, respectiely.. TRANSIENT STABILITY ASSESMENT BY ENERGY FUNCTION ANALYSIS The main concern of transient stability is to maintain the rotor angle of SG under synchronism (and reduce the angle and frequency deiation of teral oltage of inerter in case of SG), when a large disturbance is introduced, such as sudden large load change, fault, islanding, etc. Lyapuno direct method may use for the transient stability analysis of the system []. In Lyapuno method, a system can be considered a set of nonlinear differential equation, and expressed as; ( y) ẏ = f (7) where, y is a state ariable ector and f (y) is system function. The equilibrium point of such system is obtained as; ( y ) = 0 f (8) here, y is the equilibrium point. From initial point to equilibrium point the solutions of the system forms a trajectory. According to Lyapuno stability theorem, a system is asymptotically stable if; ) The trajectory reaches at the equilibrium point of the system as time, t. ) A continuous differentiable function E(y) should exist, 3) ( y) 0 Ė. For the transient stability analysis of a synchronous generator, an energy function is calculated at the first equilibrium point b of the power-angle cure as shown in Fig., by integration of a function, obtained by multiplying the swing equation with ω (remoing damping factor). The energy function is gien by [9], E = Ek + Ep = ω0δω (9) P δ δ + B cosδ cosδ [ ( ) ( )] in where, E is the transient energy function of the system after a change in input shaft power at point b shown in the powerangle cure. E k, is the kinetic energy and irtual kinetic energy in SG and SG, respectiely. E P, is the potential energy stored in the system. In [0], it is shown that E satisfies the Lyapuno function criteria. In proposed method an assumption is made; > 0 d, > 0. At point b all the transient energy is in the form of kinetic energy as ω increases and (δ δ ) decreases with large alues of d,. At this point, the alues of are switched to imum alues. Therefore, after point b the transient in the form of kinetic energy decreases to small alue with the same but with. The total transient energy is transformed in the form of potential energy at point c, adopt their large alues. oweer, the total transient energy of the system is in the form of potential energy at point c as = 0, and δ δ has its imum alue. Therefore, the imum alues of do not increase energy leel

5 of the system according to (9). This process continues in eery half-cycle of oscillation untilω reaches a desired alue. To analyze the positie effect of the alternating inertia constant and alternating damping factor scheme on frequency oscillation, Lyapuno s third criteria is considered. According to it, the first deriatie of energy function should be negatie, which shows reduction in energy function during time until its state ariables are conerged at the equilibrium point of the system. For alternating and alternating K based SG, the deriatie of E is expressed as, de ω d dk 0 (0) = Δω + Δω As the alues of ary discretely, the alues of d and dk d, are gien by their aerage alue at the points, at which are altered dynamically. At points a and c, K change their alues from and to to K d,, respectiely. But these changes do not affect the system transient energy function as Δ ω is zero at these points. Whereas, at point b, aried from to d, to K respectiely. At b, Δ ω has its imum alue and the change in inertia constant and damping factor are negatie. Therefore, the terms d and dk d, are effectie and make the system transient energy function negatie, and satisfy Lyapuno third criterion. I. RESULTS AND DISCUSSION The microgrid, haing inerter based DER and synchronous generator, is simulated using MATLAB/ Simulink software to compare the operation of proposed controller with droop control, and alternating inertia constant based SG control. The microgrid structure used is shown in Fig. 4. Where, DER and SG operate in parallel to share the actie and reactie power of the load and maintain the oltage and frequency within the allowable range at PCC. ere both R-L load and Induction motor load are considered to analyze the controller s performance under load disturbances. ka with 0.9 lagging power factor is considered. An induction motor load with 5% loading is switched at t=.5 sec. TABLE II PARAMETERS USED FOR DIFFERENT CONTROL TECNIQUES PARAMETERS Droop Alternating based Proposed SG (z/kw).5e-5.5e-5.5e-5 (olt/kar) 5e-4 5e-4 5e-4 DER (ka) SG (ka) DC (olt) IM Load (kw) R-L Load (ka) LL (rms) (sec) ,, - 9.e5 9.e5 (Nm/(rad/s)), - - 3e5 Fig. 5, shows the frequency response of the system for droop control, alternating based SG control, and for proposed control. It is obsered that the frequency deiation just after the t=.5 sec is more in alternating based SG control as compared to proposed SG control and lesser than droop control. The proposed control has large settling time as compared to droop control because of irtual inertia and irtual damping factor, which makes its response slow. The droop control has large peak oershoot in frequency during switching of IM due to its fast action to supply the load demand. IM with 5 % loading is switched to see the transient performance of the controllers. As the total actie power change is less, there is no significant change in steady state frequency. Fig. 5. Frequency response for different control schemes under disturbances. Fig. 4. Microgrid Structure. In suggested control, at the initial stage of operation, the optimal alues of irtual inertia time constant and irtual damping factor of a single unit of 85 ka are calculated using PSO. The parameters used for the operation is gien in Table II. In the operation of microgrid, an initial R-L load of Fig. 6 shows the power injected by the DER unit for different control schemes. In all the schemes, at t =.5 sec the power injected by DER unit is ery high because IM requires a large amount of current during starting (approximately 5 to 7 times of full load current). It is obsered that in alternating irtual inertia based SG and proposed control schemes, the injected powers take the larger time to reach the steady-state leel as compared to droop control. After few seconds, it is obsered that peak oershoot in the power is the largest in alternating inertia based SG control. It also takes the large settling as compared to droop

6 control and proposed control. From the result, one can conclude that proposed control has less frequency deiation with reasonable settling time. Table III summarizes the simulation results. Fig. 6. Injected actie power by the DER for different control schemes TABLE III SIMULATION RESULTS FOR DIFFERENT CONTROL PARAMETERS Max. freq. deiation (z) Settling Time (sec) Droop Alternating based SG Control Proposed Control II. CONCLUSION A microgrid consisting of a SC based DER unit with SG is considered and is simulated in MATLAB/Simulink enironment. The results show that by emulating swing equation in controller to enhance system inertia, the DER unit allows it to share the large amount of load, with reduced frequency deiation at the cost of large settling time. 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