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1 Reducing the Short-Circuit Current of MontazerQaem Bus Using a Proposed H∞ Controller for the Corresponding Generator 1852 Abstract—In Iran power network especially in Tehran Regional Electric Company like other power systems, Short-circuit current increases by extension of the electrical power system because of rising demand of electrical power. This fault current magnitude is more than the circuit breaker interrupting ratings especially in MontazerQaem power plant. Fault currents have a great influence on power system. For reducing these risks, some expensive or complicated solutions are proposed based on increasing the impedance of power network like FCLs or series reactors or split bus. The approach of this paper is controlling the sources of the faults. It proposes a new solution for reduction of the fault current by a controller. The controller is designed by H∞ mixed-sensitivity minimization method to control the fault current through controlling the field current of the generator. This method is simulated on a generator unit which its exciter system is considered for modeling and control design. The results show that this economical solution is efficient enough. Index Terms—Short circuit current, Power system faults, Field current, H∞ method. NOMENCLATURE vdp, vqp SG terminal voltages in dq frame. idp, iqp SG stator currents in dq frame. vf , if voltage and current of the main field winding. Ld, Lq SG direct and transverse stator inductances. LD, LQ SG direct and transverse dampers inductances. Lf SG main field inductance. Msf SG mutual inductance between the direct stator winding and the main field one. MfD SG mutual inductance between the main field winding and the direct damper one. MsD,MsQ SG mutual inductance between the direct stator winding and the direct/transverse damper windings. Rs,Rf SG stator resistance and SG main field resistance. RD,RQ SG direct and transverse damper resistances. ωep SG electrical angular speed. vde, vqe Exciter machine (EM) armature voltages. ide, iqe EM armature currents. vexc, vexc Voltage and current of the EM main field winding. Lde, Lqe EM direct and transverse armature inductances. Le EM main field winding inductance. Mse EM mutual inductance between direct armature winding and main field one. Rse,Re EM armature resistance and main field resistance. ωee EM electrical angular speed. I. INTRODUCTION Fault currents have a great influence on power system planning and operation. Short-circuit current increases in the whole power system by permanent extension of the electrical power system and rising demand of electrical power. These currents can cause mechanical and thermal stresses and they may damage the equipment. Also at some points, the available short-circuit current may exceed the maximum short circuit ratings of the switchgear. Consequently, the reduction and control of short circuit currents is a must. One solution to reduce the risk of increasing short circuit levels in the power system is to upgrade the 2 protection equipment so that the estimated fault currents are kept within the equipment capacity. This usually involves complete rebuilding of the substation. Nevertheless, this solution does not represent a high cost ratio benefit. It is an expensive solution, especially if primary and secondary breakers with their associated equipment are numerous. In addition to the cost, upgrading of the existing substations can be a complicated process because of the number of equipment to be substituted, redesigned or tested [1]. Devices and techniques such as circuit breakers, fuses, air-core reactors, employing high-impedance transformers, bus-splitting (system reconfiguration) and fault current limiters (FCLs) have been used to limit the available short circuit currents, so that the underrated switchgear can be operated safely[2]. There are some components in power systems that cause the fault current. The four basic sources of short circuit current are: 1. Generators 2. Synchronous Motors 3. Induction Motors 4. Electric Utility Systems All these sources can feed the short-circuit current into a short circuit [3]. The approach of designing "fault current limiters" is based on limiting the current by increasing the impedance in the path of current from the sources to the fault location but the approach of this paper is reduction of fault current by controlling the sources. This approach can be applied on synchronous machines. The chosen method for designing the controller is H∞ and the simulations approve the efficiency of the controller whilst the cost of this method for reduction of fault current is very less. II. H∞ OUTPUT FEEDBACK CONTROLLER DESIGN The standard H∞ mixed sensitivity formulation for output disturbance rejection and control effort is shown in Figure 1, and its equivalent standard form for tracking is shown in Figure 2. In these figures, G(s) is the open loop system model; K(s) is the controller to be designed W1(s) and W2(s) are weighting functions for shaping characteristics of the open-loop plant. Normally, in the mixed sensitivity design, bounds (weights) are applied on S(s)/K(s)S(s). The sensitivity function S(s) denotes the transfer function from disturbance input d(s) to measured output y(s). K(s)S(s) is the transfer function from disturbance input d(s) to control input u(s). The complete details of the mixed sensitivity control design can be found in [4]. The design objective of control design is to minimize the sensitivity functions S(s) and K(s)S(s). Fig 1. H∞ Mixed Sensitivity in standard form (disturbance rejection). Fig 2. H∞ mixed-sensitivity minimization in standard form (tracking). For tracking, the partitioning of corresponding generalized plant P is such: u K (s )v z P11 P12 K ( I P22 K ) 1 P21 w (1) The state space description of the augmented plant P(s) is: 3 where x is the plant state vector, u represents the control input, w is a state vector of exogenous input which include disturbances d, measured noise n (not considered here), reference signals r, etc., y is the measured output, and z is a vector of output signals. The system is assumed to be stabilizable and detectable. This assumption ensures the existence of an internally stabilizing output feedback control law u = K(s) y. Without loss of generality, it is assumed that D11 =D22 = 0. This assumption makes the closed-loop state space matrices linear in the control matrices. In addition, the following assumptions are typically made in H∞ problems: (A1) (A;B2; C2) is stabilizable and detectable. (A2) D12 and D21 have full rank. (A3) has full column rank for allω. (A4) has full row rank for all ω. Let Twz(s) denotes the closed-loop transfer function from w to z for a dynamical output-feedback law u=K(s)y. The sensitivity function S(s) = [I+G(s)K(s)]-1 is that ensures disturbance attenuation and good tracking performance. K(s)S(s) = K(s)[I+G(s)K(s)]-1 handles the issues of robustness and constrains the effort of the controller. The goal of this work is to obtain a dynamical output-feedback controller law u = K(s)y, with the following state-space description where xk is state variable of the controller. The plant and controller K(s) are defined above. The constraint Twz (s ) can be interpreted as a disturbance rejection problem. This constraint is also useful to enforce robust stability [5]. III. THE PROBLEM DESCRIPTION Reducing the short circuit current of a power system is the main purpose of this paper; therefore, we try to define the problem to design a controller. A. Power System Short Circuit Safe and reliable application of over-current protective devices based on some requirements mandate that a short circuit study and a selective coordination study be conducted. These requirements include, among others: Interrupting Rating Component Protection Conductor Protection Equipment Grounding Conductor Protection Marked Short-Circuit Current Rating; Compliance with these code sections can best be accomplished by conducting a short circuit study as a start to the analysis. The protection for an electrical system should not only be safe under all service conditions but, to insure continuity of service, it should be selectively coordinated as well. A coordinated system is one where only the faulted circuit is isolated without disturbing any other part of the system. Once the short circuit levels are determined, the engineer can specify proper interrupting rating requirements, selectively coordinate the system and provide component protection. To determine the fault current at any point in the system, first draw a one-line diagram showing all of the sources of short-circuit current feeding into the fault, as well as the impedances of the circuit components. To begin the study, the system components, including those of the utility system, are represented as impedances in the diagram. It must be understood that short circuit calculations are performed without current-limiting devices in the system. Calculations are done as though these devices are replaced with copper bars, to determine the maximum “available” short-circuit current. This is necessary to project how the system and the current limiting devices will perform. Low voltage molded case circuit breakers also have their interrupting rating expressed in terms of RMS symmetrical amps at a specific power factor. However, it is necessary to determine a molded case circuit breaker’s interrupting capacity in order to safely apply it [6]. 4 B. Modeling of a synchronous generator (SG) with Short Circuit Condition Models of complex interconnected network systems, such as an electric power grid, must capture both the natural response of its components to various disturbances, but also the effects of the interactions between individual components and/or aggregated groups of components. These interactions are often the result of distributed sensing, estimation, actuation, and decision making based on these internalized models of the environment[7]. The approach of this paper is using the voltage control to reduce the fault current then the controller synthesis takes into consideration a fixed impedance connected to the SG (see Fig. 3). This method is used in [8] for voltage control. Fig. 3. Modeling of the SG with Short Circuit Condition. (3) The system model given by (3) can be written as: During short circuit fault, the field current is changed with the field winding time constant, called the d-axis transient short circuit time constant[10]. A typical field current responses following a stator short-circuit is shown in Fig. 4 [11]. Therefore, field current as a state variable is useful to be observed for controller designing. The observation matrix is chosen as: c (2) Where idl and iql are the Park transformation of the currents in the three-phase inductance Ln. Rn and Ln can be chosen as the fault impedance or other equipments impedance. According to [9] we have these equations: f 0 0 0 0 0 1 0 0 Fig. 4. A typical field current response following a stator short-circuit This choice shows that the current of the main field winding is chosen as the output of the SG. Fig. 5 shows a representation of the global system. Bf1 is the first column of the matrix Bf. 5 Fig. 5. State space representation of SG. C. Approach to Solution The DC excitation (or field) current, required to produce the magnetic field inside the generator, is provided by the exciter. The excitation current, and consequently the generator’s terminal voltage is controlled by an automatic voltage regulator (AVR). According to the model and output observation, H∞ mixed-sensitivity minimization in standard form (tracking) is used to reduce the short circuit current. The field current as an output variable (feedback signal) is compared with its normal value and the error signal is used to control the plant (SM). A Simplified diagram of proposed control strategy is shown in Fig 6. In this approach, the control signal u is added to output of exciter vexc and the result is the voltage of the field winding Vf. estimated fault currents are kept within the equipment capacity. This resulted in complete rebuilding of the substation but this solution is expensive because the breakers with their associated equipment are numerous. In this paper, we try to reach the risk reduction through a very low cost solution i.e. designing a feedback controller for the power plant to reduce the short circuit current. B. Controller Design To design a controller for the generator, it is necessary to follow these stages: 1. Determining the input and output variables (in this paper input variable is the field voltage and the output variable is the field current). 2. Creating the state-space model of the system (according to physical equations that described before): it is a 12 state-system for the case of this paper. 3. Defining W1(s) and W2(s) as the weighting functions: for the case of this paper we choose: 150 (s+1)2 1100 W2 (4) (s+2)2 4. Calculating and obtaining the controller K(s): Using H∞ mixed-sensitivity minimization in standard form (tracking) for the case of this paper, results in a state-space model of a SISO controller with 1 outputs, 1 inputs, and 12 states. The resulted constraint for the total system is Twz (s ) 23.18 5. Reducing the order of the controller: The reduced order controller can be achieved by an approximation method [14] and the 4-order controller K(s) can be given by: W1 Fig.6. Simplified diagram of proposed control strategy. IV. MONTAZERQAEM POWER PLANT STUDY A. Case Representation MontazerQaem power plant is in Tehran Regional Electric Company and its fault current magnitude is more than its circuit breaker ratings [12]. The corresponding data is obtained from Iran Grid Management Company (IGMC) [13]. The rated parameters of the steam generator are 14.4kV, 176MVA, 50Hz. The excitation system is also considered in the modeling and calculations. Engineering Studies on the problem resulted in some solutions but because of operation limits especially reliability issues; these solutions could not be used. Therefore the selected solution is upgrading the protection equipment so that the K r (s ) 1.92 s4 + 1.02 105s3 +2.17 106s2 + 1.3 107s +3.74 106 s4 +1336s3 + 1.1 106s2 -3.52 105s+2.76 107 (5) Bode magnitude diagram of full order and reduced order controller is shown in Fig. 7. it is clear that the reduced order controller can be used for simulation. 6 performance and it is less than the interrupting rating of the breakers. The short circuit current is about 25kA without control performance in the base case therefore the reduction of the fault current is 36% then it is desirable. 40 20 full order reduced order 10 40 0 35 -10 30 -20 -2 10 10 -1 10 0 1 10 10 Frequency (rad/s) 2 10 3 10 4 Fig. 7. The bode magnitude diagram of full and reduced order controller. C. Simulation Results To show the effects of the controller on the power plant performance in the fault condition, a 3-phase short circuit fault is studied on the terminal of the generator at t=50ms. Fig.8 shows the field current during the short circuit with and without control. The performance of the controller resulted in reduction of the field current. 12 with control without control Field Current(pu) 10 8 RMS Fault Current(kA) Magnitude (dB) 30 with control without control 25 20 15 10 5 0 0 50 100 150 200 Time(ms) 250 300 350 400 Fig. 9. The fault current with and without control. D. Economical Points It is important to know that the reduction of the fault current by an efficient controller has a very negligible cost in comparison with upgrading the equipments or other solutions which need new power element like FCLs. It can cancel or delay the huge investment for upgrading the substation interrupting rating. 6 V. CONCLUSION 4 2 0 0 50 100 150 200 250 300 350 400 Time(ms) Fig. 8. The field current with and without control. Fig.9 shows the R.M.S short-circuit current with and without control. The peak of the current is reduced by 8% and the breaking current is reduced from 30kA to 25kA at the t=150 ms i.e. after 5 cycles since fault occurring. According to engineering studies on transient stability of Iran power grid [15], the critical clearing time (CCT) of MontazerQaem power plant generators is more than 200 ms then the breaking action can be done safely at t=250 ms when the short circuit current is about 16kA with control There are some solutions based on increasing the impedance of power network for reducing the risks of high fault level of power systems. These solutions are not used in some power systems like substation of MontazerQaem power plant because of the constraints of operation or needing huge investment or complicated conditions. A new method for reduction of short circuit current based on controller design Using H∞ mixedsensitivity minimization is proposed in this paper. The control system uses the field current of the generator as a feedback signal and changes the exciter output to reduce the terminal voltage of the generator and consequently reduces the fault current. This method results in cancelling or delaying the extra investment on upgrading the interrupting rating of therefore substation equipments therefore it is very economical solution. 7 REFERENCES [1] Mahmoud Gilany, and Wael Al-HasawiT, " Reducing the Short Circuit Levels in Kuwait Transmission Network (A Case Study)", World Academy of Science, Engineering and Technology 53, 2009. [2] L. Ye, A. Campbell, "Behavior investigation of Superconducting Fault Current Limiters in Power Systems", IEEE Trans., Vol. 16, No. 2, June 2006 [3]General Electric Company, Application Information, "Short Circuit Current Calculations", 1989. [4] S. Skogested, L. Postlethwite. “Multivariable Feedback control and Design”, John Wiley and Sons 1996. [5]K. D. V. Narasimha Rao1,and Subrata Paul, "Design of Robust Power System Stabilizer using Mixed Sensitivity based H∞ Output-Feedback Control in LMI Framework", Chennai and Dr.MGR University Second International Conference on Sustainable Energy and Intelligent System (SEISCON 2011) , Tamil Nadu, India. July. 20-22, 2011. [6] Cooper Bussmann, "Short Circuit Current Calculations",2005, http://www.cooperindustries.com/content/dam/public/bussman n/Electrical/Resources/Solution%20Center/technical_library [7] Marija D. Ilic´, " From Hierarchical to Open Access Electric Power Systems ", Vol. 95,No. 5, May 2007 Proceedings of the IEEE [8] O. P. Malik and G. S. Hope, “An adaptive generator excitation controller based on linear optimal control,” IEEE Trans. Energy Convers., vol. 5, no. 4, pp. 673–678, Dec. 1990. 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[15] Power & Water University of Technology (PWUT), "Phase2 of Consulting, Extensive Study of Iranian HV Power System", Iran Grid Management Company (IGMC), Report number SER02-04, 2010-2012.