混合交直流电力系统的非线性调制策略

第 22卷 第 7期 中 国 电 机 工 程 学 报 Vol.22 No.7 Jul.2002 2002年 7月 Proceedings of the CSEE © 2002 Chin. Soc. for Elec.Eng. 文章编号：0258-8013（2002）07-0001-06 混合交直流电力系统的非线性调制策略 杨卫东 1，徐 政 2，韩祯祥 2 （1. 国家电力公司电力自动化研究院，江苏 南京 210003；2. 浙江大学电机系，浙江 杭州 310027） A NONLINEAR MODULATION STRATEGY FOR HYBRID AC/DC POWER SYSTEMS YANG Wei-dong1, XU Zheng2, HAN Zhen-xiang2 (1. Nanjing Automation Research Institute，Nanjing 310027，China ；2.Department of Electrical Engineering Zhejiang University， Hangzhou 210003, China ) ABSTRACT: A nonlinear control strategy to improve tran-sient stability of a multi-machine AC power system with several DC links terminated in the presence of large disturbances is presented. The approach proposed in this paper is based on differential geometric theory, and the HVDC systems are taken as a variable admittance connected at the inverter or rectifier AC bus. After deriving the analytical description of the relationship between the variable admittance and active power flows of each generator, the traditional generator dynamic equations can thus be expressed with the variable admittance of HVDC systems as an additional state variable and changed to an affine form, which is suitable for global linearization method being used to determine its control variable. An important feature of the proposed method is that, the modulated DC power is an adaptive and non-linear function of AC system states, and it can be realized by local feedback and less transmitted data from, adjacent generators. The design procedure is tested on a dual-infeed hybrid AC/DC system. KEY WORDS: HVDC systems; multi-infeed; nonlinear modulation; variable admittance 摘要：针对大扰动情形, 文中提出了一种用于改善多机交直 流混合电力系统(有多条直流线路落点于其中)暂态稳定性的 非线性控制 方法 快递客服问题件处理详细方法山木方法pdf计算方法pdf华与华方法下载八字理论方法下载 。该方法基于微分几何理论，并将直流输电 系统等效为两个分别连接在整流侧和逆变侧的变导纳支路。 在推导出直流输电系统的等效变导纳与各发电机输出电磁 功率间的解析关系后，传统的发电机动态方程可被 表 关于同志近三年现实表现材料材料类招标技术评分表图表与交易pdf视力表打印pdf用图表说话 pdf 示成仿 射非线性的形式，因而可应用全局线性化方法来求得其控制 变量。本文方法的主要特点在于，所求得的调 基金项目：国家重点基础研究专项经费项目（G1998020312）； 国 家自然科学基金项目（59707005）。 Project Supported by National Key Basic Research Special Fund of China; Project Supported by National Natural Science Foundation of China（59707005）. 制功率是一个交流系统状态的自适应和非线性函数，它可通 过局部的反馈信号和少量来自其它发电机的信号来实现。文 中以一个双馈入直流输电系统为测试对象，给出了所提控制 器的 设计 领导形象设计圆作业设计ao工艺污水处理厂设计附属工程施工组织设计清扫机器人结构设计 过程和基于测试系统的仿真结果。 关键词：直流输电系统；多馈入；非线性调制；变导纳 中图分类号： TM732 文献标识码：A 1 INTRODUCTION In a hybrid AC/DC power system, emergency power request from the HVDC connection seems very important when a large disturbance occurs, because an appropriate fast change in dc power will reduce stress on the AC system and the magnitude of a transient swing. As a natural consequence of the growing use of HVDC technology, situations with two or more HVDC converters feeding into the same AC system have been arising. The emergence of multi-infeed HVDC system has brought new possibilities by using HVDC link to provide emergency power support[1], it also motivated extension of HVDC modulation control widely used in single-infeed HVDC system to such configurations. In this paper, we shall concentrate on transient stability enhancement of multi-machine power systems by means of fast nonlinear HVDC modulation control. The central procedure of this scheme is to bias the current reference quantity of the rectifier in order to rapidly increase or decrease the power through the DC system to prevent instability in ac system during a severe disturbance. With HVDC system being treated 2 中 国 电 机 工 程 学 报 第 22卷 as a variable admittance connected at the inverter or rectifier AC bus, the traditional generator dynamic equations can be expressed with a variable admittance of the HVDC system as an additional state. With some reasonable assumptions, the original state equations can be changed to an affine form, and the global linearization method can be used to determine the control variable, i.e., the modulated DC power. 2 THE SYSTEM STUDIED For the testing of the proposed method, a simplified double converter multi-infeed HVDC system model as shown in Fig.1 is used in this paper. It is a simplified model, the two HVDC subsystems have the same parameters as that given in reference [2], except that inverter side AC system is replaced by the simplified AC system as shown in Fig.1, the parameters of the inverter side AC system are given in reference [3]. To simplify the comparison, the conventional control used in this paper is as follows, i.e. the rectifier has a constant current control, and the inverter is subjected to constant extinction angle control as usual, and both of them are PI controllers. Pd1 Pd2 DC1 DC2 Yr1 Ðqr1 Yr2 Ðqr2 E r2 Ðjr2 Er1 Ðjr1 Qcr1 Qcr2 U2 Ðd2 U1 Ðd1 Qci2 Qci1 PL5, QL5 PL4, QL4 PL1, QL1 PL2, QL2 PL3, QL3 G1 512MVA G3 G2 700MVA 700MVA ~ ~ ~ ~ ~ 1 2 3 4 5 Y12 Ðq12 图1 两路 HVDC馈电系统简化模型 Fig. 1 Simplified double-infeed HVDC systems model 3 ANALYTICAL RELATIONSHIP BET-WEEN THE GENERATOR OUTPUT PO-WER AND THE EQUIVALENT ADMI-TTANCE OF A HVDC NODE For a hybrid AC/DC system as illustrated in Fig. 1, its inverter side AC system can be expressed as a general network that includes n generator nodes, m HVDC nodes, p load nodes and some physical nodes. For theoretical purposes, generators are modeled by constant voltage electromotive forces (emfs) behind transient reactance, and static load model is employed in this paper. Only the generator internal nodes and HVDC nodes are retained and all other nodes are eliminated through network reduction [4]. For simplicity, we first suppose only one HVDC node (connected at node p) is included in the hybrid AC/DC system in the following derivation. For the reduced network (see more detail in [5] ), we have ú û ù ê ë é ú û ù ê ë é =ú û ù ê ë é p G pppG GpGG p G U E YY YY I I (1) The electrical power of the ith generator ( ni ,,2,1 L= ) with the effect of HVDC node p taken into account, is given in [5] as follows: å å ¹ ¹ + + + - + + += n ji ijpppjip n ji ijpppjipijji ppipiiiei B g g B g BEE B g g GEP dbb dbb b cos 1 sin) 1 1 ( 1 2 2 2 2 2 DC DC DC DC DC （2） Where, ijB ， ipB ， pjB ， ppB are elements of the admittance matrix in equation（1）, and pp ipi ip B BE =b , ppB G g DC DC = (3) DCG is the equivalent admittance of HVDC system at node p and can be expressed as 2DCDC / pUPG = (4) DCP is the injected active power by the HVDC system; pU is the AC voltage at the HVDC converter bus; Usually， 3.0DC £g ，utilizing the Taylor series， equation（2）can be simplified to å å ¹ ¹ - +++= n ji ijpppjipijji n ji ijpppjipppipiiiei BBEE BBgGEP dbb dbbb sin)( )cos( 22 DC (5) 4 ASSUMPTIONS In this paper, we only consider the case, when the DC system can function smoothly, in spite of the AC 第 7期 杨卫东等： 混合交直流电力系统的非线性调制策略 3 voltage fluctuations that might exist during the fault period. In order to implement the control strategy proposed in this paper, we assume a constant AC voltage control strategy is implemented at the inverter side to maintain the AC voltage constant during a contingency. With the dynamic processes of a DC link neglected, a DC system can be treated as an one order inertial element, and the state equation of DC power can be written as follows: )( 1 DCDCrefDCDC u ppt 关于艾滋病ppt课件精益管理ppt下载地图下载ppt可编辑假如ppt教学课件下载triz基础知识ppt P d ++-=& (6) where, DCrefP is the given value of the DC power, dT is the equivalent time constant of DC system, DCu is the control variable of the DC system. From (3) and (4), we have 2 DCDC DC ppppp UB P B G g == , if assume pU is constant, then we get DC2DCrefDCDC 1 )( 1 u BUT gg T g pppdd ++-=& (7) where pppBU P g 2 DCref DCref = . 5 CONSIDERATION FOR MULTI-INFEED HVDC SYSTEMS Only one HVDC node was considered in section 3. When there are m HVDC nodes existing in the inverter side AC system, the dimension of the admittance matrix in (1) will reach m+n, and the analytical expression for the output power eiP of generator i will be very complicated. However, it does exist and can be derived, and will have a form as follows: ),...,,,...,( DCDC11 mniei ggKP dd= (8) where, ),...,,,...,( DCDC11 mni ggK dd is the function of id （ ni ,,1 L= ）and ),...,1(DC mjg j = . Substituting equation (8) into the conventional dynamical model of the ith machine with steam valving control, and with the state equation for the dc links’ equivalent admittance being considered, the dynamical model of the ith machine can be rewritten as followings i si mi si mi si mi uT P T P T P 111 0 ++-=& (9) k ppkpkdk k dk k u BUT gg T g DC2DCrefDCDC 1 )( 1 ++-=& (10) mk ,,1 L= )),...,,,...,(,...,( 22 DC1DC1 0 mnimi i i i i i ggKPHH D ddwww -+-=& (11) ii wd =& (12) Where iu is the valve opening in p.u.; Ti is the time constant of the turbine with typical numerical value of 0.2 to 2.0 sec.; Pmi0 is the initial operating value of the mechanical power of generator i; Di is the damping coefficient. 6 SYSTEM MODEL For the sake of convenience and simplicity, the test system as shown in Fig.1 will be considered in this paper. We also assume generator 1 and 2 has a constant output power, and will have a HVDC link modulation control instead of the steam valving control, the other generators will have their conventional steam valving control. With all the above assumptions, equation (9) to (12) will be changed to the form as nnC uxuxuxuxx )()()()()( 332D21DC1 ggggfx +++++= L& (13) where T 13 2 1 1 0,...,0, 1 )( ÷ ÷ ø ö ç ç è æ = - 321 nPppd UBT xg , T 23 2 2 2 0,...,0, 1 ,0)( ÷ ÷ ø ö ç ç è æ = - 321 nPppd UBT xg T 1 0,...,0|0,...,0|0,...,0, 1 ,0,...,0)( ÷ ÷ ø ö ç ç è æ = -- 321321321321 nninsii i T xg , (14) ] ... )),...,,,...,(( 2 ))...,...,,,...,(( 2 )),...,,,...,(( 2 )),...,,,...,(( 2 )...( 1 ... )( 1 )( 1 )( 1 [)( T 1 DCDC11 0 0 DCDC1133 0 3 3 3 0 DCDC1122 0 2 2 2 0 DCDC1111 0 1 1 1 0 DC4ref4DC 4 DC3ref3DC 3 DC2ref2DC 2 DC1ref1DC 1 n mnnn n mn n mnm mnm mnm dd dd ggK D P H ggK D P H ggK D P H ggK D P H gg T gg T gg T gg T x ww ddw w w ddw w w ddw w w ddw w w -- -- -- -- +-+- +-+-=f (15) 4 中 国 电 机 工 程 学 报 第 22卷 [ ]T113DC2DC1 ,,,,,,,,, nnmnm PPgg ddww LLL=x (16) T3DC2DC1 ),,,,( nuuuu L=U (17) where n=3, m=2 in this case, and the suffix p and q in the above expressions corresponds to the node 4 and 5 in Fig.1 respectively. The expressions for ),...,,,...,( DC1DC1i mn ggK dd ( 1,2,3i = ) can be found in reference[6]. 7 DIFFERENTIAL GEOMETRIC APP- ROACH According to [7], for an affine form nonlinear system as shown in (13), the necessary and sufficient condition for global linearization, can be easily satisfied using the method shown in [7,8] and prosecuting the global linearization in the light of the constructive proof of Theorem 1 in [7], we can finally obtain a mapping UM ®:f , defined as :f iiin iin ii z z z ww w d && D== D= D= + + 2 ni ,,2,1 L= （18） which can transform the original system (13) to a globally linearized system as following: BvAzz +=& iin inin ini vz zz zz = = = + ++ + 2 2 & & & Uz Î (19) It has the Brunovsky canonical form and it is a pure linear state equation, the behavior of the original nonlinear system is just equivalent to a linear one as (19) after linearization, one can use linear control theory, such as LQ optimal methods to design a feedback law iniiniiii zkzkzkv ++ ---= 2 * 3 * 2 * 1 * ni ,,2,1 L= (20) to give the desired stability and performance properties. where jik , 3,2,1=j ni ,,2,1 L= are the feedback gain coefficients, which are obtained by solving the algebraic Riccati equation corresponding to system (19). The control law for system (13) can be finally achieved as × ¶ ¶-= 1DC 1 1 0 11D 2 [ g K H Cu C w ] 2 )( 2 )( *11 1 0 2 2DC 1 1 0 1 vPH xf g K H xf e +-¶ ¶ - & ww (21) ] 2 )( 2 )( 2 [ * 22 2 0 2 2DC 2 2 0 1 1DC 2 2 0 22D vP H xf g K H xf g K H Cu e C +- ¶ ¶ - × ¶ ¶-= &ww w (22) ] 2 )( 2 )( 2 )( 2 [ * 33 3 0 3 3 0 2 2DC 3 3 0 1 1DC 3 3 0 33 vP H xf H xf g K H xf g K H Cu e +-- × ¶ ¶ -× ¶ ¶ -= &ww ww (23) where ),,,...,( 2 2DC1DC1 2DC 2 0 2 11 1 ggG g K UBTH C n pppd ddw ¶ ¶ -= ， ),,,...,( 2 2DC1DC1 1DC 1 0 2 22 2 ggG g K UBTH C n qqqd ddw ¶ ¶ -= ， 3 3 3 0 2 sH TC w = ，and expressions for f1(x), f2(x), f3(x), can be found in (15). 8 IMPLEMENTATION OF THE CONT- ROLLER It should be noted that, to construct feedback control law as shown in (21) and (22), the power angle )( ijj Îd should be available. Usually, the power angle jd is difficult to measure, thus a jd detector as been shown in [9] has been used in this paper, i.e. introduce jj wd = &) into the feedback control law，and let jd ) has an initial value of 0jd , where jd ) is the evaluated value of jd , and 0jd is the pre-fault steady-state operating point value of the generator j, which is a known variable. Before )(1 tudc and )(2 tudc are exerted to HVDC subsystem 1 and 2, they should pass through a limiter at first as shown in Fig. 2 in order that the overload capacity of HVDC converters is not exceeded. The present DC power transfer capacity and some other aspects (such as the temperature of valve cooling media) have to be considered to determine the maximum permitted DC power modulation. 9 SYSTEM PARAMETERS AND SIMULA- TION RESULTS In this section, the system model as shown in Fig. 1 is used for the testing of the proposed control 第 7期 杨卫东等： 混合交直流电力系统的非线性调制策略 5 channel Control center channel Allowable overload Current control unit Information of generator i K1k K2k s Ik max Ik min Vdk Irefk Udck(t) wj(jÎi) Up or Uq (Pmi,Pei,wi) ak max ak min ak Idk qv S S S + + + _+ + Udck(t) ¸ 图2 HVDC系统 k（k=1,2）的非线性调制控制结构 Fig.2 Nonlinear modulation control structure for HVDC systems k (k=1,2) strategy. The generator parameters and its excitation and governor parameters can be found in [10]. The simulation is conducted on the test system under the following two conditions: Case I: A step increase of the load at bus 1 by 200 MW and 100 Mvar, for a time duration of 2s, is introduced. Case II: A temporary three-phase fault occurs at Bus 3, the fault is cleared after five cycles and the transmission line remains in service. Only the following two cases are recorded for each of the above two disturbances. (1) The two DC links are operated with only constant current and constant extinction control, all the generators use conventional governors without fast valving control; (2) All the conditions are same as in (1), except that the two dc links are operated with the proposed nonlinear modulation control strategy. Fig.3 shows the system response following a step increase of the load at bus 1 by 200 MW and 100 Mvar, only the frequency deviation, power angle of generator 1 and 2 are demonstrated. It is seen from Fig.3, the oscillation of above variables after the occurring of such a disturbance is more serious when the two DC links are operated with only constant current and constant extinction control. The system frequency is decelerated substantially because it is controlled only by the generator’s control system, which is comparatively slow to the fast DC control, which in this case, does not contribute to the balance of power. With the proposed nonlinear modulation HVDC systems with constant current and constant extinction angle control HVDC systems with proposed nonlinear modulation control 1 0 -1 D f/Hz d1/(°) 40 0 -40 d2/(°) 40 0 -40 0.0 1.0 2.0 3.0 4.0 5.0 t/s 图3 母线1负荷跃增 200MW和 100MW的系统响应 Fig.3 System responses with load step increase of 200 MW and 100 Mvar at bus 1 0.0 1.0 2.0 3.0 4.0 t/s Df/Hz 0 -1 1 0.0 3.0 -3.0 I/kA 0 -90 d /(°) V/p.u. -1.5 0.0 0 -90 0 -90 d /(°) d /(°) HVDC systems with constant current and constant extinction angle control HVDC systems with proposed nonlinear modulation control 图4 母线3三相故障瞬时故障系统响应 Fig. 4 System responses with a temporary three-phase fault at bus 3 control strategy adopted, the oscillations in the system variables are minimized to a greater extent. DC power transfer has increased to compensate the power mismatch in ac system, and the total modulated DC power is about 200 MW that is equal to load increase. It can be found in Fig.4 that, with constant current and constant extinction control adopted only, there are five successive commutation failures occurred at the HVDC subsystem 1 after a temporary three-phase fault occurred at Bus 3. It is due to the strong electrical connection between the AC bus 4 and bus 5 and the simultaneous power increase of the 2 HVDC subsystems, which has led to a rapid and high 6 中 国 电 机 工 程 学 报 第 22卷 requirement for reactive power, that in turn caused a depressed AC bus voltage and successive commutation failures. Fig.4 clearly shows that, with the proposed nonlinear modulation strategy implemented, both DC and ac variables has calmed down quickly, a 'softer' transient interaction has been resulted and just two more commutation failures occurred after the AC fault removal. 10 CONCLUSION In this paper, a non-linear modulation control strategy using differential geometric theory has been proposed to improve the performance of AC/DC system during a large disturbance. The quantities of the modulated DC power is basically a nonlinear and adaptive function of system states, and can be realized without increasing the burden of data transferring around the system so much. Simulation results show that the proposed control scheme can greatly enhance transient stability of the studied system when a large disturbance occurred. REFERENCES [1] Szechtman M, Pilotto L A S, Ping W W, et al. The behavior of several HVDC links terminating in the same load area [C]. CIGRE Paper 14-201, Paris, 1992. [2] Szechtman M, Wess T, Thio C V, et al. First benchmark model for HVDC control studies [J]. Electra, 1991, 135： 54-67. [3] Yang W D,Xu Z,Han Z X Transient stability enhancement of AC power system by nonlinear modulation control of multi- infeed HADC systems[C].Proceedings of the International Conference on Power Systems(ICPS 2001),September 12-16,2001,Wuhan,China： 345-350 [4] Pai M A Computer techniques in power system analysis [M]. NewDelhi : Tata McGraw-Hill Publishing Company Limited , 1979. [5] Hammons T J, Yeo R L, Gwee C L, Kacejko P A. Enhancement of power system transient response by control of HVDC converter power [J]. Electric Machines and Power Systems, 2000, 28(5) ： 219-241. [6] Yang W D,XU Z,Han Z X