Gui-yan LI, Zhi-xiong LU

(1Office of Educational Administration, Nanjing Vocational Institute of Transport Technology, Nanjing 211188, China) (2College of Engineering,Nanjing Agricultural University, Nanjing 210031,China)

Abstract: Traditional control methods has low control precision, and it is easy to cause that the actual power of the switch exceeds the power provided by the engine to some extent, this paper proposed a new method of engine switch control based on power tracking constraint. The maximum power in the process of engine switch control was determined. In order to facilitate the analysis of the following engine switch control, the power expression of switch branch was introduced. The power tracing constraint of a branch was built when other branches were disconnected. The power tracking constraint was transformed into the form which was suitable for engine switch control. Under the condition of power tracing constraint, the roll-channel of engine was considered as a double integral link. The engine starting time and running time were adjusted so as to achieve the same effect as the switch torque, and the switch control was realized. The improvement process of switch control was given under the condition that the controlled quantity was less than the setting value. Experimental result shows that the proposed method has high precision and good convergence, which can meet the requirements of engine for the switch.

Key words: Power, Tracking constraint, Engine, Switch, Control

1 Introduction

At present, China’s industry has developed rapidly. As a key part of large machinery, engine is needed to be researched [1-2]. In order to improve the reliability, fault-tolerance and adaptability of engine, we need to research an effective method for engine switch control [3].

This paper proposes a new method of engine switch control based on power tracking constraint. The determination method of maximum power is given, and the power tracing constraint is introduced. Under this condition, the control of the engine switch is realized. Experimental result shows that the proposed method has high control accuracy and can effectively guarantee the performance of engine.

2 Analysis of power tracing constraint

2.1 Determination of maximum power

Firstly, this section determines the maximum power in the process of engine switch control.

If the branchklis disconnected in the engine switch line, and the voltage stability index of branchijis lower than given thresholdα, thenijbranch is the weak branch that does not meet the power constraint [4]. The formula that current branchijis in accordance with maximum powerSij-weakpermitted by power constraint is:

Sij-weakmax=ELSIij-weak×Sij-weak

(1)

Sij-weakmaxis used to describe the maximum power of branchijwhen branchklis disconnected;Sij-weakis used to describe the power of branchijobtained through load flow solution when branchklis disconnected; branchELSIij-weakis used to describe the voltage stability index of branchijwhen branchklis disconnected.

2.2 Condition of power tracking constraint

For ease of analyzing following switch control of engine, the power of branchijis described as:

Pij1=Pij0(e,f)+ΔPij(e,f)

(2)

Qij1=Qij0(e,f)+ΔQij(e,f)

(3)

(4)

(5)

(6)

Among them,bijandbklare used to describe the electrical susceptance of actual branch of branchijand disconnected branchkl;bi0is used to describe electrical susceptance to ground ofiside of node in branchij;bk0andbl0are used to describe the electrical susceptance to ground ofkside andlside of node in disconnected branchkl[8]; matrixS′ and matrixS″are inverse matrices of the coefficient matrixB′ andB″ in decoupled load flow.Pkl0(e,f) andQkl0(e,f) are used to describe the active power and reactive power transmitted from nodekto nodelby disconnected branchklbefore disconnecting;Plk0andQlk0are used to describe the active power and reactive power transmitted from nodelto nodekby disconnected branchklbefore disconnecting.

Through formula (1) and formula (4), we can set up the power tracing constraint of branchijwhen branchklis disconnected:

(7)

3 Engine switch control method

The previous section introduces the power tracing constraint, and we need to convert it into the form which is suitable for engine switch control [9,10]. Under the condition of power tracing constraint, the roll-channel of engine is considered as a double integral link.

Supposing that the roll angle is described byγkat this moment, and the speed of roll angle is described byωx,k. The control torqueux,kis obtained under power tracking constraints, and |ux,k|≤Mmax[11]. Among them,Mmaxis used to describe the torque which can be provided by engine. Thus, in the influence ofux,k, roll angle and angular speed at the next time can be described as followed:

(8)

(9)

Because the engine torque isMmax, in order to achieve control effect which is consistent with torqueux,k, we need to adjust the engine starting timet1and running timep[12], and the details are described in Fig.1.

Fig.1 Schematic diagram of switch control of engine

Fig.1 shows that a difference in the starting timet1of engine will have different effects on the angle at the next time [13]. However, the increment of angular velocity is unaffected byt1, and it only depends on the engine running timep. Therefore,t1andpcan be modified to achieve the control effect which is consistent withux,k[14]. Under the influence of engine torqueMmaxin Fig.1, the roll angle and the angular velocity at the next moment can be described in turn as follows:

(10)

(11)

According to:

(12)

We can get:

(13)

Because|ux,k|≤Mmax, according to the above formula, there is:

(14)

When |ux,k|≤Mmax, the control effect of the two is consistent. Therefore, the starting time and working time obtained by the engine according to formula (13) can achieve the control effect that is consistent with torqueux,k.

4 Improvement of engine switch control

From the analysis of formula (13), we can see that with the gradual decrease ofux,k, the running time of engine becomes fewer and fewer. Because the engine is constrained by power tracking, under the condition that the control quantityux,kis lower than the setting value, the switch can not reach the control effect that is suppressed by itself. Therefore, the switch control result in formula (13) shall be adjusted. It is assumed that the minimum running time of engine is described byΔ×Ts, and the process of rise and fall of engine torque is ignored. It is regarded as ideal switching quantity [15]. The torque corresponding to the minimum running timeΔ×Tsof engine can be obtained by the second formulas in formula (13):

ux,k=Δ×Mmax

(15)

Then, the actual switching control formula can be described as:

(16)

The above analysis shows that the lower the minimum running time of engine, the more consistent the control effect of the switch quantity and the limited quantity of control. If the engine can be started at will, formula (16) is equivalent to formula (13), which means that both of them can achieve the same control effect.

5 Analysis of experimental results

5.1 Analysis of control result in proposed method

Through the method of switch control of engine based on power tracking constraint proposed in this paper, experiments are carried out on the principle prototype.

Fig.2 shows the measured waveform of starting state of switch after controlling the engine switch through the proposed method.

Fig.3 shows the variation of the voltage waveform in case of load mutation.

Fig.2 Measured waveform of starting state of switch under control of proposed method

From the analysis of Fig.2 and Fig.3, the starting state of engine switch is controlled by this method, and the current and voltage waveform changes are stable. In the case of load mutation, the switching voltage has changed to a certain extent, but the change is not evident.

Fig.3 Variation of voltage waveform under condition of load mutation

5.2 Power analysis

The power consumption of engine is described in Fig.4 without considering the power tracking constraint.Fig.4 shows that in the absence of power tracking constraints, the actual power consumption of engine switch exceeds the power provided by engine for the switch, and it can not guarantee the stable operation of engine.

In the case of considering power tracking constraints, the power consumption of engine is described in Fig.5.

Fig.4 Power consumption of engine without considering power tracking constraint

Fig.5 Power consumption of engine under power tracing constraint

Fig.5 shows that the actual power consumption of engine switch has been lower than the power that the engine can supply to the switch, and the power consumption is low, which can ensure the safe and stable operation of engine.

5.3 Contrast test of different control methods

In order to verify the effectiveness of engine switching control method based on power tracking constraint proposed in this paper, this section tests SPC method and EPC method as a contrast. For 100 samples of engine switch, sample switches are controlled by the proposed method, SPC method and EPC method. The control results of three methods are described in Table 1.

From the analysis of Table 1, we can see that controlling the engine switch sample, the current error and the voltage error through the proposed method, the starting time error and the minimum running time error are lower than that of SPC method and EPC method, which proves that this method has high control accuracy and verifies the reliability of the proposed method.

5.4 Convergence test

The convergence of the proposed method, the SPC method and the EPC method are verified by the Newton iteration method, and results are described in Fig.6～8 respectively.

Analysis of Fig.6～8 shows that when the operation is repeated 5 or 6 times, the control results of proposed method tend to be the same. However control results of SPC method after computing about eight times tend to be the same. The control results of EPC method after computing about 11 times tend to be the same, which shows that the proposed method has the best convergence performance.

Fig.6 Analysis of convergence in proposed method

Fig.7 Analysis of convergence in SPC method

Fig.8 Analysis of convergence in EPC method

Table 1 Comparison of control results between three methods

Method SampleCurrent control error/AVoltage control error/Acontrol error of start-up time/msControl error of mini-mum runtime/msProposed methodSample 10.190.351.193.58Sample 20.250.412.354.22Sample 30.370.521.683.97Sample 40.260.441.225.11Sample 50.230.611.754.93……………Sample 990.180.272.262.68Sample 1000.290.392.375.11SPCSample 10.390.832.724.97Sample 20.510.671.936.11Sample 30.620.742.116.29Sample 40.940.762.353.65Sample 50.880.792.767.11……………Sample 990.861.052.817.36Sample 1000.921.923.054.68EPCSample 10.691.133.225.67Sample 21.131.622.954.66Sample 31.021.372.865.29Sample 41.291.113.116.38Sample 50.871.063.597.26……………Sample 990.951.243.664.13Sample 1001.331.683.276.68

6 Conclusion

This paper proposed a new method of engine switch control based on power tracking constraint. The maximum power in the process of engine switch control was determined, and the power tracing constraint condition was introduced. On this basis, the starting time and running time of engine were adjusted to achieve the same effect as the switch torque, so as to realize the switch control. The improvement process of switch control was introduced. Experimental results show that the proposed method has high precision and good convergence, which can satisfy requirements of engine to the switch.

Acknowledgements

Supported by Jiangsu University Blue Project (No.201608120).