Tsinghua Science and Technology Tsinghua University, China ISSN: 1007-0212 Vol. 6, Num. 5, 2001, pp. 484-487

Tsinghua Science and Technology, December 2001, 6(5), pp. 484-487

Decoupling of Double Extraction Turbo-Unit by Nonlinear  Multivariable Inverse System Method

LI Haorong  , LI Liqin  , LI Donghai  ,  SONG Zhaoxing  , WANG Wei

Department of Thermal Engineering, Tsinghua University, Beijing 100084, China

Received: 2000-06-15, revised: 2001-05-17

Code Number: ts01101

Abstract:

A  multivariable inverse nonlinear control scheme is developed to decouple the strongly nonlinear double extraction steam turbo-unit, improving the transient stability of the power and heating system. Computer simulation tests show that not only does the control scheme achieve satisfactory decoupling of the high and low pressure turbines and the electric power, remarkably improving the transient stability, but also the design is very intuitive and concise

Key  words: inverse system; nonlinear control; decoupling; double extraction

Introduction

Combined heat and power generation units are frequently used in power systems with digital electro-hydraulic control systems rather than machine-hydraulic control systems. The control systems need improved ability to adjust the electrical frequency and the load adaptability, including electrical and thermal ability to maintain the stability of the power and heat supply systems through improved decoupled control of the steam pressure and the electrical power. The  linearity control approaches often fail to perform well, especially for large disturbances, although they can improve stability for small disturbances. Consequently, nonlinear control theory is being rapidly developed. For example, Lu and Sun have investigated steam-valve nonlinear control using nonlinear differential geometry control[1]. However, nonlinear differential geometry control is based on too many complex and abstract mathematical theories which are not understood by most control engineers or professors, so it is not easily accepted by engineers. A more intuitive nonlinear multivariable inverse system approach was proposed by Li and Feng[2], which only involves linear algebra and dispenses with complex mathematical theory, so it is easily understood by most control engineers. Moreover, unlike the nonlinear differential geometry control approach which is based on a complex mathematical model, this approach is not confined to a given nonlinear mathematical model but can use various nonlinear models including lumped parameter form, distributed parameter form, continuous form, and discrete form. In addition, the control result was shown to be equal to other nonlinear feedback linearity approaches[3,4]. This paper presents a novel nonlinear non-interacting control scheme using the multivariable inverse system approach.

1 Mathematical Model of Double Extraction Turbogenerator Unit Steam-Valve Opening

Assume that the double extraction turbo-unit has an excellent excitation controller, therefore, the transient potential E^'_qof the q-axis is stable during the whole transient process.

Then, the mathematical model for the double extraction turbo-unit is[1,5] :

In this state equation, T_p1 and T_p2  are the time constants for the high and low pressure extraction steam turbines; T_c1 , T_c2, and T_c3 are the actuator time constants of the three steam-valves; a, b, and g are the power coefficients; u₁ , u₂, and u₃ are the electrical control signals directing the high, medium and low pressure steam valves; m1, m₂, and m₃ are the openings of high, medium and low pressure steam valves; l₁ , l₂ , l₃ are the disturbances; c is the low and medium pressure cylinder steam flow rate; e is the medium and high pressure cylinder steam flow rate; p₁ and p₂ are the high and low  extraction steam pressures; d is the operating angle of the turbogenerator rotor; w is the electrical frequency; H is the rotational inertia; D is the damping coefficient; E^'_q is the transient potential of the q-axis; x^'_d is the transient reactance of the d-axis; x_q is the  transient reactance of the q-axis; x_T is the short circuit reactance; x_L is the line reactance; x^'_dS = x^'_d + x_T+ x_L and x_qS =x_q + x_T+ x_L are the total transient reactance of the d-axis and the q-axis; V_s is the infinite-bus voltage; P_m0 and w_o are the initial values of the total mechanical power and electrical frequency.

2  Nonlinear Steam-Valve Opening Controller Design Using the Multivariable Inverse System Approach

2.1  Design of an a (S)-order integral inverse system and its pseudo-linear system

From  Eq.(1) , the following prototype S is a three-input three-output system.

According to the nonlinear multivariable inverse system approach:

2.2  Target response design of the pseudo-linear system and control system design

For the pseudo-linear system ,the follo_{wing simple three-order transfer function matrix should be chosen as the target response form because the response does not have stability errors and the transient control can be optimized by adjusting the three parameters a, wn}, and x:

The transfer function matrix is first written as a set of differential equations which can be rearranged to give ÿ₁, ÿ₂, ÿ₃.

In the Eq.(3), j is the output, r_i (i=1,2,3) is the set input, and y₁ , y₂, y₃ , are the feedback signals from the prototype S.

The target system S_r is put in front of the pseudo-linear system _a in series to construct the complete control system _aS_r. The block diagram of its control system is shown as Fig. 1.

3  Simulation Tests

The parameters for a typical double extraction turbo-unit are[5,6] shown in Table 1.

Figure 2 shows that p₁ and p₂ remain stable whend is increased by +20%, which suggests that the control scheme has achieved complete decoupling. Figures 3 and 4 show that d fluctuates little (less than 0.2%) and the system will quickly become stable when p₁ or p₂ has a step change.

4  Conclusions

The nonlinear multivariable inverse model for decoupled control of a double extraction steam turbo-unit is intuitive and concise. The control response is very satisfactory, with good decoupled control between d and p₁ and p₂ , thus improving transient stability.

References

1. Lu Qiang, Sun Yuanzhuang. Nonlinear Control of Power System. Beijing: Science Press,  1993. (in Chinese)
2. Li Chunwen, Feng Yuankun. Inverse Method of Multivariable Nonlinear Control. Beijing: Tsinghua University Press,  1995. (in Chinese)
3. Li Donghai, Miao Jianming. Inverse theory of power system nonlinear control. Application of Electronic Technique, 1995, 21(11): 23 - 25. (in Chinese)
4. Li Donghai, Jiang Xuezhi, Li Liqin,et al. Inverse system method applied to the derivation of power system nonlinear control laws. J North China Institute of Elect, 1997, 24(4): 65-70. (in Chinese)
5. Zhong Qixin, Zhang Jiachen, Yuan Qichang. Regulation of Steam Turbine. Wuhan: Huazhong University of Science and Technology Press, 1983. (in Chinese)
6. Wang Ben, Mao Zongyuan.Turbogenerator's variable structure governor control. Automation of Electric Power System, 1999, 23(4): 25-31. (in Chinese)

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