Chaos particle swarm optimization algorithm 181- 123docz.net

Chapter 7 Off-line parameter estimation of a single-phase induction machine

7.3 Off-line parameter estimation using particle swarm optimization algorithms 173

7.3.3 Chaos particle swarm optimization algorithm 181

The chaos PSO algorithm is another modification of the standard PSO algorithm [7.11]- [7.15] which was presented in detail in Chapter 3. This algorithm is also proposed for off-line parameter estimation of the SPIM.

In the chaos PSO algorithm, the velocity update equation of the particles is modified as follows:

(k ) wk i( )k crk( i( )k i( )k ) c rk ( ( )k i( )k )

i v pbest x gbest x

v +1 = + 1 1 − + 2 2 − , (7.46)

M i≤

≤

1 and 1≤k ≤n where

wk, rk1 and rk2 are chaotic maps.

In this application, the logistic map is chosen and utilised in the chaos PSO algorithm for off-line parameter estimation of the SPIM.

The logistic map is used in the parameter estimation application for initializing the positions, {X1mi, X1ai, R2fi, X2fi, R2bi, X2bi, RFefi, RFebi, Xmi, ai}, and velocities, {vX1mi,

X1ai

v ,

R2fi

v ,

X2fi

v ,

R2bi

v ,

X2bi

v ,

RFefi

v ,

RFebi

v ,

Xmi

v ,

v }, of the ith particle as follows:

( ) ( )( ) ( ( )( ) )

⎪⎪

⎪

⎩

⎪⎪

⎪

⎨

⎧

−

1 1

1 2 1

2 2

1 2 1

2 2

1 2 1

2 2

1 2 1

2 2

1 1 1

1 1

1 1 1

1 1

i i

i m i

m mi

i Feb i

Feb Febi

i Fef i

Fef Fefi

i b i

b bi

i b i

b bi

i f i

f fi

i f i

f fi

i a i

a ai

i m i

m mi

a a

b a

X X

b X

R R

b R

R R

b R

X X

b X

R R

b R

X X

b X

R R

b R

X X

b X

X X

b X

, 1≤i≤M (7.47)

where

( )1

X1m0 , X1a0( )1 , R2f0( )1 , X2f0( )1 , R2b0( )1 , X2b0( )1 , RFef0( )1 , RFeb0( )1 , Xm0( )1 and a0( )1 are initial values to produce the first particle positions at the first iteration. They are random numbers in the interval of (0, 1) and X1m0( )1 , X1a0( )1 , R2f0( )1 , X2f0( )1 , R2b0( )1 ,

( )1

X2b0 , RFef0( )1 , RFeb0( )1 , Xm0( )1 and a0( )1 ∉ {0.0, 0.25, 0.5, 0.75, 1.0}.

( ) ( )( ) ( ( )( ) )

⎪⎪

⎪

⎩

⎪⎪

⎪

⎨

⎧

−

1 1

1 2 1

2 2

1 2 1

2 2

1 2 1

2 2

1 2 1

2 2

1 1 1

1 1

1 1 1

1 1

i i

i m i

m mi

i Feb i

Feb Febi

i Fef i

Fef Fefi

i b i

b bi

i b i

b bi

i f i

f fi

i f i

f fi

i a i

a ai

i m i

m mi

a a

X X

R R

X X

R R

X X

R R

X X

v v

b v

v v

b v

v v

b v

v v

b v

v v

b v

v v

b v

v v

b v

v v

b v

v v

b v

v v

b v

, 1≤i≤M (7.48)

where

( )1

X1m

v , vX1a0( )1 , vR2f0( )1 , vX2f0( )1 , vR2b0( )1 , vX2b0( )1 , vRFef0( )1 , vRFeb0( )1 , vXm0( )1 and

( )1

v are initial values to produce the first particle velocities at the first iteration. They are random numbers in the interval of (0, 1) with vX1m0( )1 , vX1a0( )1 , vR2f0( )1 , vX2f0( )1 ,

( )1

R2b

v , ( )1

X2b

v , ( )1

RFef

v , ( )1

RFeb

v , ( )1

v and ( )1

v ∉ {0.0, 0.25, 0.5, 0.75, 1.0}.

Similarly, the ith particle positions and velocities are also limited as in (7.38) and (7.39).

In addition, the chaotic inertia weight is used in the chaos PSO algorithm and is given as follows:

( −1)(1− ( −1))

= k k

k bw w

w , 1≤k ≤n (7.49)

where

wk is the kth chaotic inertia weight, wk ∈ (0, 1) has the following initial conditions: w0 is a random number in the interval of (0, 1) and w0 ∉ {0.0, 0.25, 0.5, 0.75, 1.0}.

Moreover, the two independent chaotic random sequences in the chaos PSO algorithm are as follows:

( )( (1 1))

1 1

1 = k− 1− k−

k br r

r , 1≤k ≤n (7.50)

(2 )( (2 1))

2 = k− 1− k−

k br r

r , 1≤k≤n (7.51)

where

r1k and r2k are the two kth independent chaotic random sequences, r1k and r2k ∈ (0, 1) with the following initial conditions: r10 and r20: random numbers in the interval of (0, 1) and r10 and r20 ∉ {0.0, 0.25, 0.5, 0.75, 1.0}.

In this case, the acceleration coefficients, c1 and c2, are set to 2. The best position of the ith particle { ( )k

X1mi

pbest , ( )k

X1ai

pbest , ( )k

R2fi

pbest , ( )k

X2fi

pbest , ( )k

R2bi

pbest ,

( )k

X2bi

pbest , pbestRFefi( )k , pbestRFebi( )k , ( )k

Xmi

pbest , pbestai( )k } and the best position over the swarm {gbestX1m( )k , gbestX1a( )k , gbestR2f( )k , gbestX2f( )k , gbestR2b( )k ,

( )k

X2b

gbest , ( )k

RFef

gbest , ( )k

RFeb

gbest , ( )k

gbest , gbesta( )k } are obtained at each kth iteration using the fitness function (7.33). The evolution process of the chaos PSO algorithm is implemented according to the position and velocity update equations (7.35) and (7.46) respectively. Eventually, the chaos PSO algorithm stops at the nth maximum iteration number and the SPIM parameters are estimated as in (7.42). The flow chart of the chaos PSO algorithm in this parameter estimation application is described in Figure 7.5.

Figure 7.5 Flow chart of the chaos PSO algorithm for off-line parameter of the SPIM

7.4 Experimental results

The practical experiments are implemented with the capacitor-start SPIM. The stator resistances of the main and auxiliary windings are obtained using the DC test, R1m = 0.38165 p.u and R1a = 0.24783 p.u. The data acquisition process for the inputs of the estimator is based on four tests. The first two tests were made with a capacitor of 40 μF and voltages of 80 V and 100 V. The remaining two tests were made with a capacitor of 20 μF and voltages of 80 V and 100 V. The input values of the capacitors and voltages are the same for the real system and the estimated parameter model. Then, the outputs of the real system, including the currents and active powers of the main and auxiliary windings, are sampled and recorded. The measurement data processing and parameter estimation are performed in MATLAB.

Start

Initialize {X1m, …, a}, {vX1m, …, va} and the chaos PSO algorithm parameters using chaotic maps

Update the personal best (pbest) and global best (gbest) of {X1m,

…, a}

Update {X1m, …, a} and {vX1m,

…, va} using the position and velocity update equations of the chaos PSO algorithm, (7.35) and (7.46)

Stop Yes No

Compute the fitness value using the fitness function (7.33)

Termination criteria

Table 7.1 presents the set of parameters which are applied in the standard PSO, dynamic PSO and chaos PSO algorithms for parameter estimation. In all three algorithms, the particle number of a generation is 70 and the maximum iteration number is set to 300.

Each algorithm is run 50 times.

Figures 7.6-7.8 are the best fitness of the standard PSO, dynamic PSO and chaos PSO algorithms versus the iteration step number and show the convergence capability of each algorithm.

Figure 7.6 shows that the standard PSO algorithm became stuck in a local optimum in the search process and resulted in premature convergence. This is one of the main disadvantages of the standard PSO algorithm.

It can be observed that there is a basic difference between the standard PSO and dynamic PSO algorithms from Table 7.1. The cognitive and social parameters are time- varying variables in the velocity update equation of the dynamic PSO algorithm. This results in a significant improvement for the convergence value as well as the solution quality of the parameter estimation problem. The convergence value of the standard PSO algorithm is 0.011402 whereas the convergence value of the dynamic PSO algorithm is 0.0060475 in Table 7.2. The standard PSO and dynamic PSO algorithms are converged by the 39th and 86th iteration steps in Table 7.2 respectively. The standard PSO algorithm converges to the best fitness value faster than the dynamic PSO algorithm since the standard PSO algorithm became stuck in a local optimum in the search process and resulted in premature convergence. These are shown in Figures 7.6 and 7.7.

Similarly, several differences also exist between the standard PSO and chaos PSO algorithms in Table 7.1 such as the initialization of the particles’ positions and velocities, the chaotic inertia weight and the two chaotic independent random sequences in the velocity update equation of the chaos PSO algorithm using the chaotic map.

These enhance both the convergence speed and value of the chaos PSO algorithm. The convergence value of the standard PSO algorithm is 0.011402 whereas the convergence value of the chaos PSO algorithm is 0.0061486 in Table 7.2. The standard PSO and chaos PSO algorithms are converged by the 39th and 24th iteration steps in Table 7.2 respectively. This means that both the convergence speed and value of the chaos PSO algorithm are better than those of the standard PSO algorithm as shown in Figures 7.6 and 7.8.

All of the modifications in both the dynamic PSO and chaos PSO algorithms have improved the performance of the standard PSO algorithm as illustrated in Figures 7.7 and 7.8. These figures also show that the dynamic PSO and chaos PSO algorithms have overcome the premature convergence disadvantage of the standard PSO algorithm and are therefore better than the standard PSO algorithm.

Table 7.3 shows the experimental results of the estimated parameters when using the standard PSO, dynamic PSO and chaos PSO algorithms whereas Table 7.4 shows the error percentages of the estimated parameters using the three algorithms.

Figures 7.9 (parameter values) and 7.10 (percentage errors) show a comparison between the SPIM parameters obtained using the load tests and estimated parameters using the standard PSO, dynamic PSO and chaos PSO algorithms. The errors produced by the two new algorithms, the dynamic PSO and chaos PSO algorithms are always less than 5%

and less than the errors achieved when using the standard PSO algorithm. This shows that both the dynamic PSO and chaos PSO algorithms are better than the standard PSO algorithm for parameter estimation of the SPIM.

Table 7.1 Parameters in the standard PSO, dynamic PSO and chaos PSO algorithms for off-line parameter estimation of the SPIM

Parameter Standard PSO Dynamic PSO Chaos PSO

Initial particles’

positions

Random

numbers ∈ (0, 1)

Random numbers

∈ (0, 1)

Chaotic maps, using (7.47)

Initial particles’

velocities

Random

numbers ∈ (0, 1)

Random numbers

∈ (0, 1)

Chaotic maps, using (7.48)

Inertia weight, w w = constant = 0.9

w = constant = 0.9 A chaotic map, using (7.49)

Acceleration coefficients, c1

and c2

c1 = c2 = constant = 2

Time-varying

variables, using (7.44) and (7.45)

c1 = c2 = constant = 2

Independent random

sequences, r1 and r2

Random

numbers ∈ (0, 1)

Random numbers

∈ (0, 1)

Chaotic maps, using (7.50) and (7.51)

Table 7.2 Convergence value and converged iteration step number of the standard PSO, dynamic PSO and chaos PSO algorithms for off-line parameter

estimation of the SPIM

Index Standard PSO Dynamic PSO Chaos PSO

Convergence value 0.011402 0.0060475 0.0061486

Iteration step number 39 86 24

Table 7.3 Estimated parameter values for off-line parameter estimation of the SPIM

Parameter (p.u)

Load tests

Standard PSO

Dynamic PSO

Chaos PSO

X1m 0.439 0.425 0.437 0.432

X1a 0.230 0.223 0.228 0.232

R2f 0.075 0.090 0.077 0.076

X2f 0.300 0.288 0.289 0.285

R2b 0.272 0.324 0.276 0.285

X2b 0.300 0.288 0.289 0.285

Rfef 263.937 210.386 252.694 258.033

Rfeb 263.937 210.386 252.694 258.033

Xm 1.848 1.855 1.856 1.876

a 0.409 0.399 0.410 0.403

Table 7.4 Percentage errors of the estimated parameters for off-line parameter estimation of the SPIM

Error percentage (%) Standard PSO Dynamic PSO Chaos PSO

Error percentage of X1m (%) 3.16 0.42 1.67

Error percentage of X1a (%) 3.07 0.62 0.87

Error percentage of R2f (%) 19.57 3.59 1.01

Error percentage of X2f (%) 3.77 3.53 4.81

Error percentage of R2b (%) 19.18 1.60 4.98

Error percentage of X2b (%) 3.77 3.53 4.81

Error percentage of Rfef (%) 20.29 4.26 2.24

Error percentage of Rfeb (%) 20.29 4.26 2.24

Error percentage of Xm (%) 0.36 0.38 1.54

Error percentage of a (%) 2.28 0.19 1.25

1 50 100 150 200 250 300 0

0.01 0.02 0.03 0.04 0.05 0.06 0.07

0.08 Standard PSO

Iteration step number

Best fitness

Figure 7.6 Best fitness versus the iteration step number of the standard PSO algorithm for off-line parameter estimation of the SPIM

1 50 100 150 200 250 300

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Iteration step number

Best fitness

Dynamic PSO

Figure 7.7 Best fitness versus the iteration step number of the dynamic PSO algorithm for off-line parameter estimation of the SPIM

1 50 100 150 200 250 300 0

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Iteration step number

Best fitness

Chaos PSO

Figure 7.8 Best fitness versus the iteration step number of the chaos PSO algorithm for off-line parameter estimation of the SPIM

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

X1m X1a R2f X2f R2b X2b Xm a

Parameter values (pu)

Load tests Standard PSO Dynamic PSO Chaos PSO

a) Estimated parameter values, X1m, X1a, R2f, X2f, R2b, X2b, Xm and a

0 50 100 150 200 250 300

Rfef Rfeb

Parameter values (pu)

Load tests Standard PSO Dynamic PSO Chaos PSO

b) Estimated parameter values, Rfef and Rfeb

Figure 7.9 Comparison between the parameters obtained from the load tests and the estimated parameters using the standard PSO, dynamic PSO and chaos

PSO algorithms for off-line parameter estimation of the SPIM

0 5 10 15 20 25

X1m X1a R2f X2f R2b X2b Xm a Rfef Rfeb

Percentage errors

Standard PSO Dynamic PSO Chaos PSO

Figure 7.10 Percentage errors of the estimated parameters using the standard PSO, dynamic PSO and chaos PSO algorithms for off-line parameter estimation of

the SPIM 7.5 Conclusion

In this chapter, a new application of the dynamic PSO and chaos PSO algorithms has been proposed for off-line parameter estimation of the SPIM.

The experimental results of the estimated parameters obtained were compared with the SPIM parameters achieved using the load tests. Additionally, the results of the estimated

parameters using the standard PSO, dynamic PSO and chaos PSO algorithms were also compared. The results confirm the benefits of the latter two algorithms. The errors produced by the new algorithms are always less than 5% and less than the errors obtained when using the standard PSO algorithm for off-line parameter estimation of the SPIM.

7.6 References

[7.1] F. W. Suhr, “Towards an accurate evaluation of single-phase induction motor constants”, Transactions of the American Institute of Electrical Engineers on Power Apparatus and Systems, vol. 71, issue 1, pp. 221-227, January 1952.

[7.2] C. V. D. Merwe and F. S. V. D. Merwe, “A study of methods to measure the parameters of single-phase induction motors”, IEEE Transactions on Energy Conversion, vol. 10, issue 2, pp. 248-253, June 1995.

[7.3] O. Ojo, O. Omozusi, M. Omoigui and A. A. Jimoh, “Parameter estimation of single-phase induction machines”, 36th IEEE Industry Applications Conference, IAS 2001, USA, pp. 2280-2287, 30 September-4 October 2001.

[7.4] G. McPherson and R. D. Laramore, An introduction to electrical machines and transformers. John Wiley & Son, 1990.

[7.5] S. D. Umans, “Steady-state, lumped-parameter model for capacitor-run, single- phase induction motors”, IEEE Transaction on Industry Applications, vol. 32, issue 1, pp. 169-179, January/February 1996.

[7.6] A. B. Proco and A. Keyhani, “Induction motor parameter identification from operating data electric drive applications”, Proceedings of the 18th Digital Avionics Systems Conference, 1999, pp. 1-6, 24-29 October 1999.

[7.7] J. Kennedy and R. Eberhart, “Particle swarm optimization”, Proceedings of the IEEE International Conference on Neural Networks, Perth, Australia, pp.

1942-1948, 17 Nov-1 Dec 1995.

[7.8] F. V. D. Bergh, An analysis of particle swarm optimizers, Ph.D. dissertation, Dept. Comput. Sci., Pretoria Univ., Pretoria, South Africa, 2001.

[7.9] Y. Shi and R. Eberhart, “A modified particle swarm optimizer”, Proceedings of the 1998 IEEE International Conference on Evolutionary Computation, Anchorage, Alaska, USA, pp. 69-73, 4-9 May 1998.

[7.10] A. Ratnaweera, S. K. Halgamuge and H. C. Watson, “Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients”, IEEE Transactions on Evolutionary Computation, vol. 8, issue 3, pp. 240-255, June 2004.

[7.11] B. Alatas, E. Akin and A. B. Ozer, “Chaos embedded particle swarm optimization algorithms”, Journal on Chaos, Solitons & Fractals, vol. 40, issue 4, pp. 1715-1734, 30 May 2009.

[7.12] B. Liu, L. Wang, Y. H. Jin, F. Tang and D. X. Huang, “Improved particle swarm optimization combined with chaos”, Journal on Chaos, Solitons &

Fractals, vol. 25, issue 5, pp. 1261-1271, September 2005.

[7.13] H. J. Meng, P. Zheng, R. Y. Wu, X. J. Hao and Z. Xie, “A hybrid particle swarm algorithm with embedded chaotic search”, Proceedings of the 2004 IEEE Conference on Cybernetics and Intelligent Systems, Singapore, pp. 367- 371, 1-3 December 2004.

[7.14] Y. Feng, G. F. Teng, A. X. Wang and Y. M. Yao, “Chaotic inertia weight in particle swarm optimization”, Proceedings of the 2nd International Conference on Innovative Computing, Information and Control, ICICIC ’07, pp. 475-478, 5-7 September 2007.

[7.15] Y. Feng, Y. M. Yao and A. X. Wang, “Comparing with chaotic inertia weights in particle swarm optimization”, Proceedings of the 6th International Conference on Machine Learning and Cybernetics, Hong Kong, pp. 329-333, 19-22 August 2007.

CHAPTER 8

CONCLUSIONS AND AUTHOR’S CONTRIBUTION

8.1 General conclusions

In this thesis, off-line and on-line parameter estimation of an induction machine (IM) has been addressed.

Off-line parameter estimation approaches for a three-phase IM have been reviewed which include DC, no-load and locked-rotor tests, genetic algorithms (GA), particle swarm optimization (PSO) algorithms, a differential evolution (DE) algorithm, a dynamic encoding algorithm for searches (DEAS), a direct search (DS) algorithm and an ant colony optimization (ACO) algorithm. Amongst these approaches, the PSO algorithms have been emphasised due to their advantages. The PSO algorithm is simple as only a few parameters need to be adjusted. Its performance is high in terms of both the convergence value and speed. Modifications to the PSO algorithm have also been reviewed in this thesis such as PSO algorithms with a constriction factor and a time- varying inertia weight, a dynamic PSO algorithm and a chaos PSO algorithm. The dynamic PSO and chaos PSO algorithms are better than the others in terms of the convergence capability and search performance. A new application of these two algorithms has been proposed for off-line parameter estimation of the three-phase IM.

The experimental results showed that the percentage errors between the actual and estimated values produced by the dynamic PSO and chaos PSO algorithms are always less than 5% and less than the percentage errors obtained when using the GA and standard PSO algorithm for off-line parameter estimation of the three-phase IM.

Additionally, the dynamic PSO and chaos PSO algorithms have also been proposed for off-line parameter estimation of a single-phase induction machine (SPIM). The experimental results showed that the percentage errors between the actual and estimated values produced by the two new algorithms are always less than 5% and less than the percentage errors obtained when using the standard PSO algorithm.

On-line parameter estimation approaches for the three-phase IM have been reviewed which include a model reference adaptive system (MRAS), Kalman filters (KF),

recursive least-squares (RLS) algorithms and neural networks (NN). It is desirable to adapt to the IM parameter variations which are due to temperature variations, skin and saturation effects. The RLS algorithm with multiple time-varying forgetting factors has been proposed for on-line parameter estimation of the IM. Other RLS algorithm variants have also been reviewed and compared with the proposed algorithm. The simulation results showed that the percentage errors between the actual and estimated values are always less than 5% using the proposed RLS algorithm, especially for the case of time- varying IM parameters with different variation rates.

Energy efficient control of the three-phase IM has been reviewed and examined in this thesis as well. The model-based control and search control techniques are two basic approaches applied to this control problem which have used NNs, GAs, PSO algorithms, a fuzzy logic (FL) technique and a golden section technique. An energy efficient control strategy based on the IM loss model has been proposed using an optimal rotor flux reference. The derivative technique and the chaos PSO algorithm have been proposed to determine the optimal rotor flux reference. In addition, the IM parameter variations have been updated in the energy efficient control scheme using the RLS algorithm with multiple time-varying forgetting factors. The simulation results have showed the IM efficiency always remains optimal and has been significantly improved using the optimal rotor flux reference regardless of IM parameter variations, especially for light loads when compared with the IM efficiency for the case of using the rated rotor flux reference.

8.2 Author’s contribution

In chapter 4, a new application of the dynamic PSO and chaos PSO algorithms was proposed for off-line parameter estimation of the three-phase IM. The dynamic PSO algorithm is one of the PSO algorithm variants which modifies the cognitive and social parameters in the velocity update equation of the PSO algorithm as linear time-varying parameters. These parameters are varied during the evolution process of the PSO algorithm to improve the global search capability of particles in the early stage of the optimization process and to direct the global optimum at the end stage. The chaos PSO algorithm is another PSO algorithm modification which uses a logistic map as a tool for initializing random values of the estimated parameters, as well as the inertia weight in the velocity update equation of the PSO algorithm. This creates the best balance for the inertia weight during the evolution process of the PSO algorithm which results in the

best convergence capability and search performance. Additionally, the algorithm has also been improved with regards to the diversity in the solution space through two independent chaotic random sequences. A simple IM mathematical model has been presented for off-line parameter estimation. The dynamic PSO and chaos PSO algorithms use the measurements of the three-phase stator currents, voltages and the rotor speed of the IM as the inputs to the parameter estimator.

In chapter 5, a RLS algorithm with multiple time-varying forgetting factors was proposed for on-line parameter estimation of the three-phase IM. The regressive mathematical model of the IM was introduced which is simple and appropriate for on- line parameter estimation. The first and second derivatives of the stator voltages and currents are not required in the estimation model. Thus, the SVFs and polynominal interpolation techniques are not required for on-line parameter estimation of the IM.

This means that the computational burden is significantly reduced in this application.

The estimator inputs using the proposed RLS algorithms are easily measurable variables such as the stator voltages and currents, as well as the rotor speed of the IM. The proposed RLS algorithm is more effective than the other RLS algorithm modifications for the case of time-varying IM parameters with different variation rates. The new RLS algorithm variant allows the disadvantages of the existing RLS algorithms, such as covariance matrix vanishing, the covariance “wind-up” problem and the overshoot or undershoot problem to be overcome.

In chapter 6, a new energy efficient control strategy with an optimal rotor flux reference was proposed using the derivative technique and the chaos PSO algorithm. In addition, the RLS algorithm with multiple time-varying forgetting factors was used to update the IM parameter variations in the energy efficient controller. This energy efficient controller obtains a fast response time and is robust to parameter variations of the IM.

In chapter 7, a new application of the dynamic PSO and chaos PSO algorithms was proposed for off-line parameter estimation of the SPIM. The mathematical model of the SPIM off-line parameter estimator was introduced which is based on the currents and active powers of the main and auxiliary windings. Once again, the dynamic PSO and chaos PSO algorithms confirmed their effectiveness for off-line parameter estimation when the number of estimated SPIM parameters has been large (up to ten).

Chaos particle swarm optimization algorithm 181

Case 1 – Constant induction machine parameters 127