IEE 2nd International Conference on Advances in Power System Control, Operation and Management, December 1993, Hong Kong

Integrated Optimal Control of Speed, Excitation and Load Sharing of Parallel Operating Diesel Generator Sets

Wenhua Liu, Renjie Ding,Zhonghong Wang Department of Electrical Engineering Tsinghua University, Beijing, 100084

P. R. China

ABSTRACT

This paper presents an integrated control strategy of speed, excitation and load sharing for parallel operating desel generator sets. The objective is to overcome the diffi- culties in the coordination of static performance and dy- namic performance and in the coordination of parallel op- eration stability and load sharing. On the basis of the multi-variable linear equivalent machine system model, the synthesis of the integrated optimal controller is achieved by minimizing a quadratic performance index. System behaviour under transient conditions is obtained from the digital simulation and field test. Results reveal that this in- tegrated control arrangement can provide satisfactory stat- ic and dynamic performance and load sharing performance. Kcy words: SCR oil drilling rig, Optimal control, Diesel generator set

1. Introduction

The work presented in this paper is a part of the re- search of SCR oil rig. In china, there are 1000 oil rigs or more, most of them are mechanically driven, only 20 or more imported ones are SCR oil rigs. SCR oil rig, which is driven by parallel operating diesel generator sets, SCR converters and DC motors, has 18-20% less energy comsumption than mechanically driven one, and has the advantage of better load characteristics, more convenient manipulation and maintenance and mare reliable. opera- tion. Thus SCR oil rigs are more and more widely used in the world.

The key technic in SCR oil rig is how to control the parallel operating generator sets to obtain satisfactory stat- ic and dynamic performance, and optimal load sharing among operating sets under the condition of a power sys- tem of limited capacity against heavy swinging loads. Usu- ally, the static voltage and frequency droop should be as small as possible in a power system. To achieve this, a strong propotional or integral control strategy should be employed in the excitation and speed controllers, but it will worsen the dynamic performance. Furthermore, the load should be allocated equally among parallel sets so as to use the capacity of each set fully, larger the static droop is , more equal the load sharing is. To meet all above demands, we use the integral control strategy plus the linear optimal control theory to design the controller. This approach has

achieved fairly good static and dynamic performance and optimal load sharing. In this paper, the mathematical mod- el of the system and the control law are illustrated first, then comparision of results of digital simulation and field test are made. The results revealed that both the thoeretical analysis and the implementation of the controller are cor- rect.

2. Mathematical modcl

Fig.1 shows the schematic diagram of the electrical system of SCR oil rig. It consists of N sychronous genera- tors, a SCR converter and a DC motor. The AC generators are N diesel generator sets of the same type. The objective of the load sharing control is to equally allocate loads among operating sets. So the parameters and operation points of N generators are equal, and the system shown in Fig.1 is equivalent to the system shown in Fig.2.

The power oscillation of N generator sets operating in parallel is a kind of electromechanical transient process, the oscillating frequency is from zero to several HZ. Thus we can use the load characteristics of SCR-DC motor drive system as its equivalent instead of considering its electromagnetic transient process. Under this condition, the system shown in Fig.1 can be reduced to the equivalent machine system shown in Fig.3.

In the electromechanical transient process , the electromagnetic transient equation of the stator and the ro- tor of a synchronous machine based on Park transforma- tion can be approximated into the practical substeady state mathematical model. So, we can establish the state equa- tion of the equivalent machine with the biasing method. The state equation of the equivalent system is shown in ( I ) , the block diagram is shown in Fig.4.

U1

Fig.1 The electrical system of SCR oil rig

" 1 Equ iva 1 en t machine@ P e + ~ Q , l ' L + J Q c + F M

Fig.2 The schematic diagram of the equivalent ma-

_ _

chine system

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Fig.3 The equivalent machine system

.-

Fig.4 The state equation of the equivalent machine system

i = A X + B u Y = C X

Where

Discussions about the state equation of the equivalent machine system:

(1) In the SCR-DC motor drive system , the SCR bridge can cause serious harmonic disturbance to the AC generator units. As the objective of the excitation control is to maitain the terminal voltage to the reference, we only consider the effect of the harmonic disturbance in the engi- neering design of the electrical system , not in the design of excitation control.

(2) In a system of N parallel machines, we can as- sume the equally shared electromagnetic power of each machine in the steady state is P,,, and Q,,, . To improve the stability of parallel operation and to allocate the load equally, the negative feedback control strategy of the load sharing error shuold be employed. Namely to employ the negative feedback of the error between dynamic active power P,, of each set and average active power allocated to each set into the speed control, to employ the negative feedback of the error between dynamic reactive power QCi of each set and average reactive power allocated to each set into the excitation control. In the state equation of the equivalent machine system, the output variable Y is the er- ror between the dynamic power PCi , QCi and steady state power P,, Q,. As

P, = P,,+P,,+.--+P,, Q e = Qei+QeZ+...+QcN Q,=NQeev the negative feedback control law of load sharing er-

ror of N parallel machine can be described by the negative feedback control law of the output variable Y in the state equation of equivalent machine system .

(3) The state equation of the equivalent machine sys- tem is very suitable for the design of controller. The control result of N parallel machines with the control law designed on the basis of the equation can be verified with digital simulation.

P, = NP,,,

3. Thc intcgratcd optimal control law

In this section , we will propose the integrated optimal control strategy of speed, voltage and load sharing of par- allel operating diesel generator sets on the basis of the state equation of the equivalent machine system.

To maitain the frequency and terminal voltage of the equivalent machine system shown in Fig.4, the propotional feedback control strategy should be employed in the speed and excitation control. To achieve the automatic load shar- ing control, the negative feedback of load sharing error should be employed in the speed and excitation control. T o obtain a steady-state load sharing error of high perform- ance index, the negative feedback of the load sharing error should be integral negative feedback. We can call the sys- tem with above two control strategies the basic closed-loop system, and assume that the gains of the propotional feedback of speed and excitation control are K,,,, and K,,,, , the gains of the integral feedback of active and reactive power sharing error are K,,, and KciQ Then the basic control law of the equivalent machines can be expressed as follows:

In matrix form is:

1 S

U = K,,X + - K,,, Y

where

K P O =

K , P Q =

The bl

(4)

["x' Kf lQ 1 ck diagram o f the basic closed-loop system is

shown in fig.5. In the basic closed-loop system, the propotional negative feedback control of speed and excitation will cause the contradiction between the static and the dynamic performance. When a higher static per- formance index is demanded, we should increase the gain of the propotional feedback, but a larger propotional feedback gain would reduce the stability margin and wors- en the dynamic performance. Furthermore, when the inte- gral negative feedback of the load sharing error is em- ployed, the stability margin and the dynamic performance will be further worsened. So the control result o f the basic closed-loop system is not satisfactofy and some new feedback control strategies should be employed.

Fig. 5 Block diagram of the basic closed-loop system

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C A KI 4 1 Fig. 6 Block diagram of the optimal control of the

basic closed-loop system

Fig. 7 Bloack diagram of the integrated optimal con- trol

To the new control variable u l in Fig.5, U and u0 can be expressed as follows:

U = u o + K,,X

U ,=u ,+K, , ,Y

The basic closed-loop system can be expressed as the state equation below:

x , = A , X I + B , u , (7)

where

A + BKpo

To improve the performance index of the equivalent machine system, we must design the optimal control strate- gy of the basic closed-loop system. We assume that the quadratic performance index of the basic closed-loop sys- tem is:

In the equation (8), Q 1 is a non-negative symmetrical matrix, RI is positive matrix. According to the optimal control theory under the quadratic performance index of the linear system we know that if the basic closed-loop sys- tem is completely controllable, the optimal control law of the basic closed-loop system is:

11' = - R - l 1 BTPIXI (9)

The matrix PI in equation (9) is the only positive symmetrical solution of the Matrix Riccati Equation (IO).

P , A , + A T P , - P , B , R ; I B ~ P , + Q , = O From equation (9) we have:

(IO)

where

K , = - R ; ' P , ,

K , = - R , - ' P , ,

The optimal control thoery of the basic closed-loop system is shown in Fig.6. This control law can be trans- formed into the PI feedback control , in which the state va- riables are the feedback variables.

From (1) :

B U = X - A X

B'BU = B ~ X - B ~ A X

then

If B is fully ranked, we have

Substituting u l into equation (6), we have

U = K , X + B , u , + K,,, Y ( 1 5 )

Substituting ( 5 ) and (14) into (15), we have:

U = K , , X + ( K , - K , K I , ) X + K 2 u + K I P Q Y

= K ~ X + K , X + K , , , Y (16) where

K , = K,, + K , ( B ' B ) - ' B ~

K , = K , - K , K , - K ~ ( B ~ B ) - ' B ~ A

With the integral of both sides of equation (16), we have

Eqution (17) reveals that the optimal control law of the equivalent machine system is the integration of the PI feedback of state variables and the integral feedback of output variables, the block diagram is shown in Fig.7. We call this control strategy the integrated optimal control strategy of speed, excitation and load sharing of parallel operating diesel generator sets.

4. Digital simulation

After we have obtained the integrated optimal control law, we carried out the digital simulation of the control sys- tem. Fig.8 shows the electrical system model used for digital simulation. The simulation program is the dynamic simulation program (DR) for parallel operating diesel gen- erator sets. The parameters used in the digital simulation is the practical parameters of 8V190 diesel generator sets. The

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parameters are as follows: rated operation points: V,= 1.0, P,=0.8, Q,=0.6 parameters of diesel generator sets: X, = 2.97,

X', = 0.176, T,, = 0.756, T,= 0.1, T, = 3.0

Fig.8 The electrical system model

The results are shown in Fig.9, Fig.10, Fig. 1 I . U d P U )

1.000 t QL

Fig. I 1 Dynamic process of load sharing

Fig.9 Dynamic response to 100% step load imposi- tion

Ut(p U )

1.eoo 1. I R"n , t(S) ___c

,000 L O O 0 7.000 3 . 0 0 0

(b) Fig.10 Dynamic response to 100% load rejection

a. Single machine against 100% step load imposition. The results are shown in Fig.9. In Fig.9(a), the maximum voltge drop is less than 15%, response time is less than 1. 5 seconds. In Fig.9(b), the maximum freguency drop is less than 5%, response time is less than 2 seconds.

b. Sigle machine against 100% load rejection. The re- sults are shown in Fig.10. In Fig.lO(a), the maximum volt- age rise is less than 15%, response time is less than 1 . 5 sec- onds. In Fig.lO(b), the maximum frequency rise is less than 5%, response time is less than 2 seconds.

c. The automatic load sharing process between two machines. The results are shown In Fig.11. Fig.ll(a) shows the dynamic process of the active power sharing process.Fig.1 I(b) shows the dynamic process of the reactive power sharing process. We can see that the dynam- ic process is fast and stable, the response time is less than 3 seconds, the steady-state load sharing error is less than 2%.

System behaviour under transient process shown in Fig.9, Fig.10 Fig.] 1 reveals that:

a. Under the extreme operation condition, the con- trol result of the integrated optimal control law designed on the basis of the linearized mathematic model of the equivalent machine system is satisfactory.

b. The electrical performances can meet with the de- sired values.

c. The dynamic processes is less than 3 seconds. This result is very important to the oil rig. I t reveals that the voltage and frequecy can be maintained normal as long as the interval of the 100% load variation is less than 3 sec- onds.

d. The integrated optimal control can meet with both the static and the dynamic performance index and can coordinate the parallel operation stability and the load sharing.

5. Field tcst

The field test of the integrated optimal controller of parallel operating diesel generator sets was carried out in

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Shichuan province from Sept. I989 to dec. 1989. The diesel generator sets were three 8V190 diesel gernerator sets, rat- ed parameters are:SOHZ, 400V, 370KVA, coscp =0.8, 1000rpm. The actuator of the diesel is Heinsman E6 actuator. The excitation system of the generator is the brushless T H Y RIPART-excitation. The rated parameters of D. C. windings of exciter are IOOV, 6A. The type of the SCR driven D C motor is ZQDR-410 and rated parameters of ZQDR-410 are 4IOKW, 550V, 800A and 640rpm.

Results of the field test are shown in Fig.12 and Fig. 13.

Fig. 12 (a) shows the dynamic response of terminal voltage to step load imposition(75KW asynchronous mo- tor).

Fig. 12 (b) shows the dynamic response of speed to step load imposition(75KW asynchronous motor).

Fig. 13 (a) shows the dynamic response of active pow- er sharing to the parallelling of' two generator sets.

Fig. 13 (b) shows the dynamic response of reactive power sharing to the parallelling of two generator sets.

Field results show that system behaviour under transi- ent conditions is satisfactory and that the implementation of the controller is correct.

(1)) Fig. 12 Dynamic response to load imppsition

Fig. 13 Dynamic pfocess ofload sharing

6. Conclirsion

Integrated optimal control strategy of speed, voltage and load sharing of parallel operating diesel generator sets is designed on the basis of the multi-variable linear optimal control theory. System behaviour under transient conditions obtained from digital simulations and field tests is satisfactory. I t shows that both the theoretical analysis and the implementation of the controller are correct and that this control strategy can overcome the difficulties in coordination of the static performance and the dynamic performance and in the coordination of the parallel opera- tion stability and load sharing.

7. Rcfcrcnccs

Calvin D . Neithamer and Gary K. Langsing, "New Trends in Electric Drilling Systems", Dril- ling-DCW, July 1979.

General Electric Company, u-drill-TM 3000 RIG DRIVE SYSTEM, Instruction Book, 1984.

Ross Hill Controls Corporation, oilfield SCR DRIVE SYSTEM, Technical Manual, April 1978. Y. N. YU, K . Vongsuriya and L. N . Wedman,

"Application of' an Optimal Control Theory to a Power System", IEEE Trans-PAS, Jan. 1970.

Lu Qiang, Wang Zhong-hong, and Han Ying-duo, "Optimal Control for Transimission System", Science Publishing House, Beijing, 1982

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