Proceedings of 2014 International Conference on Modelling, Identification and Control, Melbourne, Australia, December 3-5, 2014
Orthogonal Relations Coupling Renewable Energy and Sustainable Plant Systems James N. Furze and Quanmin Zhu
specifically in terms of identification of driving dynamic variables within the adaptive neuro fuzzy inference systems (ANFIS) applied [4]. Individual locations (monitored at a lkm resolution) rich in plant characteristics display continual Gaussian process distribution function (Rastrigin's function), following the quantitative nature of natural character traits, seen both at the population and individual level. From the latter, we may recreate optimal conditions for each plant strategy type in closed sustainable growth environments. The distribution of the rudimentary elements of plant characteristics will show discrete expression patterns depending on the suitability of the growth environment; this is in part determined by the energy supply to the 'closed' plant environment. Renewable energy supply has also been shown to show discrete patterns of consistency in its supply across a global scale [5]. As with organic systems problems exist in the method and supply of renewable energy, splitting distribution networks effectivity differentially, attempts have been made to apply stochastic matrices to enable optimal efficiency and useage. In this paper the authors present a block design for closed sustainable agriculture systems and the same structure for renewable energy grid supply. The constitutive expression patterns of the plant species and renewable energy supply patterns have been determined by a generational algorithm fuzzy rule base system. Functional approaches are taken to estimate fitness functions in the genetic algorithm populations. Further we hope to show convergence between the blocks of sustainable agriculture and renewable supply using sliding mode, Lyapunov approaches to enable feed-forward predictability [6] in these uncertain systems. This paper is organised as follows: Section II presents the data used to form the ANFIS for plant and renewable system blocks. Sections III summarises resultant algorithms and details the TSK nodal structure for system blocks. Section IV gives the block design of each hybrid multi-objective genetic algorithm ( MOGA) applied and shows application of sliding mode fuzzy systems identifying convergence between the systems. Section V provides concluding remarks and further work.
Abstract-In order to distribute the rudiments of plant systems and renewable energy systems, a T-S-K fuzzy logic approach is taken in combination with multiple objective genetic algorithm approach. These approaches overcame non linearity in the water-energy dynamic and in the dynamic of easterly wind and shortwave solar flux present on a global scale. Hence system blocks for plant and renewable systems are presented. Increased rationality of the MOGA is shown with use of increased orders of differentiation. Consequently algorithms for plant systems and renewable systems presented orthogonal distribution
with
use
of
a
domain
flipping
function.
Furthermore, convergence between the two system blocks is identified with use of Lyapunov stability and sliding mode combinatorial technique effectively coupling the elements of each system block.
Index
Terms-plant
orthogonal
systems,
distribution,
renewable
domain
flipping,
energy, Lyapunov
stability.
I.
INTRODUCTION
lant systems productivity in sustainable agricultural systems and renewable energy grids are key areas for potential expansion in construction of planning support systems with global application. Growth in these two areas enables benefits in planning support given socio-economic pressures. Research in these areas holds the potential to redefine areas of high populations and their supply networks, which alleviates pressures on vulnerable natural systems in ecology whilst providing national organisational units with opportunities for stable human population and economic growth. In natural ecological systems plant life-history strategies, primary metabolic processes and life-forms are shown to be algorithmically distributed according to the discrete patterning of the water-energy dynamic (across 7 environments, where the first environment (E1) represents the conditions in which ruderal, C3 plants are found through to the seventh environment (E7 ) where stress tolerant CAM plants are found) [1], [2]. Poisson distribution (specifically Gumbel copula) may be used to show the distribution of plant characteristics following the water-energy dynamic [3]. Minimisation and increased efficiency of algorithmic statements of plant characteristics has been applied,
P
II. DATA USED TO CONSTRUCT ANFIS BLOCKS FOR PLANT AND RENEW ABLE ENERGY SYSTEMS Manuscript received 2014. J. N. Furze (corresponding author ) was with
A. Framework of plant environmental data for plant systems within a candidate CAM environment, E7.
the Faculty of Environment and Technology, University of the West of England,
Bristol,
UK
(Tel:
+44
(0 )
7526504881;
e-mail:
James.
[email protected]; james.n.
[email protected]). Q. Zhu is with the Faculty of Environment and Technology, University of
Climatic data of water (precipitation) and energy (temperature) is sourced from the Intergovernmental Panel on
the West of England, Frenchay Campus, Coldharbour Lane, Bristol, BSI6 IQY, UK (e-mail:
[email protected]).
12
Proceedings of 2014 International Conference on Modelling, Identification and Control, Melbourne, Australia, December 3-5, 2014 Climate Change (IPCC), [7]. Data is processed with Matlab (Version R2010a ©) in order to construct the images below. o a Q) rt.l
-g�
}"iiii"iilijiiiM�
�r-- ���--��--���� .� � 18 0 o E oo 180 o VV
�� If)
r---�==---=----'"
r-o
a
Latitude
-7 5
-60
-45
-30 -15 Celsius
0
15
30
-10
45
Fig.
Fig. 1. Sudan quarterly temperature 1961-90 mean at 10 minute
3.
Quarterly global surface eastward wind
Fig. 3 is a representation of projected global surface eastward wind. The data are quantified in each quarter according to Table I.
Fig. 1 is quarterly mean temperature in the Sudan, 18.5km resolution. The data are quantified in each quarter according to the framework given [8]. Temperature is designated AI.
� V)
� V)
r-
r-
0
0
0
0
C/J
C/J
V) r-
V) r-
0
0
1800E
1800W
� V) 0
0
0
C/J
C/J
V) r-
0
100 150 200 250 300 350 400 450 Kg m' 2
V) r-
0
1800W
Fig. 2. Sudan quarterly precipitation 1961-90 mean at 10 minute (IS.Skm) resolution.
0°
1800E 1800W Latitude 240 W m,2
0
Fig. 2 is quarterly precipitation in the Sudan, 18.5km resolution. The data are quantified in each quarter, designated A2 and split into 5 quintiles.
0°
r-
0
Latitude
1800W
� V)
r-
50
climatology,
2011-2030 mean.
(IS.Skm) resolution
o
10
o ms-1
420
Fig. 4. Quarterly global shortwave flux climatology, 2011-2030 mean.
Fig. 4 is a representation of projected global shortwave flux. The data are quantified in each quarter according to Table I.
B.
Framework of climatic data used in implementation of wind and solar renewable energy.
III. ALGORITHMS FOR SYSTEM BLOCKING AND TSK NODAL STRUCTURE
A.
Climatic data of easterly wind and solar flux is sourced from the IPCC [9]. Data is processed with Matlab (Version R2010a©).
Quantification of renewable energy algorithm block
Table I gives quintile partitions for Figs. 3 and 4. Fig. 3 data is designated A3, Fig. 4 data is designated A4.
13
Proceedings of 2014 International Conference on Modelling, Identification and Control, Melbourne, Australia, December 3-5, 2014 to a type-2 fuzzy system [12] within the block constructed for FE(REN).
TABLE I GrDBAL WIND'SOlAR!lDNGITUDlNAL QUANTIFICATION
I Not'n
Eastward Shortwave E9 Lon(0 ) Wind (ms·l) Flux (W m)2
Low Low-Med
0-20/1 20-4012
-12.5 to-7.5 -7.5 to-2.5
88 to176
-80 to-48 -48 to-16
Med Med-High High
40-60/3 60-80/4 80-100/5
-2.5 to2.5 2.5 to7.5 7.5 to 12.5
176 to264 264 to 352 352 to440
-16 to16 16 to48 48 to80
Lingexp
Ling exp
% Quant
=
linguistic expression, Quant
% percentage, m S·l =
=
quantiiication, Not'n
metres per second, W m2
® Earth, Lon Longitude, 0 =
=
o to88
=
=
=
=
Layer Input
1
Layer 2 Input .MF
Layer 3 Rules
Layer4 Output .MF
Layer 5 Output
notation,
Watts per metre squared,
degrees
Plant systems of E7, being the optimal environment for stress tolerant, crassulacean acid metabolism (CAM) species are summarized within the following TSK algorithm:
If 0.2SA 1(4) --< A1(5)0.7SA 1(5) /\ 0.5A2(1) --< A2(3) 0.2SA2(1) (1) Then B(265611400) E7(CAM)
0.2SA2(1) --< A2(2)
=
Where the linguistic connector 'If is given in the inferential statement. The consequential statement (B ) number used is the same as the total number of renewable installments (wind, solar) proposed [lO]. (1) Represents the first block expanded using MOGA in Section IV. E.
TSK algorithmic detail of system blocks for renewable energy
Efficient, TSK algorithms are given here representing the projected conditions (Figs. 3 and 4); the data results from stochastic weather generators developed by the IPCC and are consistent with projective models, GATOR-GCMOM [11].
Logical Operator
,
And
If EBLon(1) E A 3(l) --< A3(4) /\ A4(3) --< A4(s) /\ EBLon(2) E A 3(2) --< A3(4) /\ A4(3) --< A4(S) /\ EBLon(3) EBLon(4) EBLon(s)
E A 3(1) --< A3(4) E E
/\
A 4(2) --< A4(4)
/\
/\ A3(1) --< A3(s) /\ A4(1) --< ThenB(26S611400) A (l) A 3(s) /\ 4 A 3(1)
Fig. 5. Simplified ANFTS model structure for structuring of Global Future
--< A4(3)
=
Solar and Wind Energy installations.
(2 )
(2) Expands into 34 rules in Fig. 5. The use of discrete-time slices provides logical reasoning for application of Lyapunov principles / sliding systems [13], [14] shown in Section IV.
FE(REN)
Algorithms are written by following Table I and expanded into the rule-base used to construct the nodal engine of Fig. 5 across an annual period.
C.
Equation (2) represents the conditional statement for wind and solar renewable systems implementation (Future Renewable Energy (FE(REN») across January 2011-2030, given as an examples of the rule base which is expanded in Fig. 5, the full nodal structure represents all four sets of data for the renewable energy system block across an annual period. The ANFIS nodal diagram of Fig. 5 represents Y4 of the 2011-2030 mean period for the variables, as such it is akin
Ef f iciency ofTSK algorithms for conditions suited to renewable energy implementation
3-D Efficiency of the TSK algorithm is seen in Fig. 6. The distribution of driving dynamic variables shows a Gaussian Process / continual functional spread when considered in all longitudinal bands (2).
14
Proceedings of 2014 International Conference on Modelling, Identification and Control, Melbourne, Australia, December 3-5, 2014 resource supply, psip
Fig. 6. 3-D surface plot of TSK algorithm efficiency for January
Discrete/stochastic relations are seen when considering each longitudinal band considered within the algorithm, consistent with patterns observed in climatology [15], the latter point enables stochastic approaches to be taken, which are developed in the following section, with use of hybrid MOGA technique.
IV. MOGA DISPERSAL OF PLANT SYSTEM AND RENEWAB LE ENERGY SYSTEM BLOCKS A. Characteristics of renewable energy systems for dispersal. MOGA programmed dispersal of the attributes of CAM species present in E7 were distributed across the combined objective plane to give a Pareto distribution [16]. Table II lists the main elements of renewable (solar, wind) systems [17] with objective quantification of the variables. In Table II: hot height of turbine, nog number of gears, lotb length of turbine blades, notb number of turbine blades, ge generator efficiency, ce capacitor efficiency, be battery efficiency, tc transmission cost, aolr area of land required, dtie disturbance to indigenous ecology, irfi infrastructure resistance for integration, irnrlba industry material requirement limited by availability, Iwhfs link with hydrogen fuel storage, ld local demand, noogssp number of off grid small scale producers, lwhs link with heating system, Iwhfc link with hydrocarbon fuel conversion, hsdp hybrid system development potential, cors consistency of =
=
=
=
=
=
=
=
=
=
The characters shown in Table II display a Pareto distribution when distributed over the combined objective Z plane. The distribution is orthogonal to that of the plant systems block, as shown in Fig. 7 (combined objectives 1 and 2 are water and energy) for plant systems) and Fig. 8 (combined objectives 3 and 4 are wind and solar) for renewable energy systems).
=
=
=
=
=
=
=
policy structure in place.
TABLE II RENEWAB LE SOLUTIONS AND QUANTIFICATION Grid Character / Wind Solar Chromosome (0, . . . ,5) (0, . . . ,5) (0, . . . ,5) height of turbine (0) (0) (1, . . . ,5) number of gears (0, . . . ,5) (0) (0) length of turbine (1, . . . ,5) (0) (0) blades number of turbine (1, . . . ,5) (0) (0) blades generator (1, . . . ,5) (1, . . . ,5) (1, . . . ,5) efficiency capacitor (1, . . . ,5) (1, . . . ,5) (1, . . . ,5) efficiency battery efficiency (0, . . . ,5) (0, . . . ,5) (0, . . . ,5) transmission cost (1, . . . ,5) (1, . . . ,5) (3, . . . ,5) of land (1, . . . ,5) area (0, . . . ,5) (1, . . . ,5) required disturbance to (3, . . . ,5) (3, . . . ,5) (1, . . . ,5) indigenous ecology infrastructure (0, . . . ,5) (0, . . . ,5) (0, . . . ,5) resistance for integration industry material (0, . . . ,3) (3, . . . ,5) (1, . . . ,5) requirement limited by availability link with (0, . . . 3) (0, . . . ,5) (0, . . . ,5) fuel hydrogen storage local demand (0, . . . ,5) (0, . . . ,5) (0, . . . ,5) number of off (0, . . . ,5) (0, . . . ,5) (0, . . . ,5) grid small scale producers link with heating (0, . . . ,5) (0, . . . ,5) (0, ... ,5) system link with (0, . . . 3) (0, . . . ,3) (0, . . . ,5) hydrocarbon fuel conversion system (1, . . . ,5) hybrid (0, . . . ,3) (1, . . . ,5) development potential of (1, . . . ,5) consistency (1, . . . ,5) (3, . . . ,5) resource supply policy structure in (0, . . . ,5) (0, . . . ,5) (0, . . . ,5) place
Easterly Wind, Shortwave flux 2011-30 mean.
=
=
=
15
Proceedings of 2014 International Conference on Modelling, Identification and Control, Melbourne, Australia, December 3-5, 2014
n
1.2
Fi �
1
.\
0.8
=
1,
... , n)
(7)
Quadratic --
0.6
.2: t)
(i
Mj Bji,
This results in a flipping of the domain as shown in Fig. 8.
Linear
Cubic ......
N
j=l
Pareto front data \. '\
L
.
:E 0
0.4 0.2
!
> ..0 u
0 I
-0.2 -9
-5 -4 Objective 1
-7
:E o
I
I
I
-3
-2
-1
0.6 0.4
I Pareto front data
-Linear
0
0.2
-- Quadratic
Fig. 7. MOGA Evolutionary Strength Pareto Front for Plant Systems of
-J'---'-I
In Fig. 7, linear utopia rule is given by: Z
8lx + 82 ± [;
=
Where
01
is -0.11,
02
-9
(3)
is -0.16 and error
&
is 0.58246.
IRl. 2
Z
8lx
=
+
02
is 0.014,
03
is 0.0078 and
Z
81x
=
Where
01
0.00045 and B.
3
+
82x
2
is -0.00034 &
83x + 84 ± [;
+ 02
is 0.0091,
03
is 0.0018,
04
is 0.0023036.
j=l
(i
=
1,
... , n)
I
-3
1
-2
1
----I--,
-1
0
is The MOGA Pareto dispersed blocks of plant and renewable energy systems converge at maximwn and minimum points shown in Fig. 7 and Fig. 8. At these points the systems may be said show Lyapunov stability as they have the following characteristic:
V E > 03a > OVy E X [d(x,y) Nd(rn(x),rn(y)) < E ]
n
Mj Bji,
-5 -4 Objective 3
C. instigating Lyapunov stability andJuzzy sliding mode to illustrate convergence between coupled system blocks.
Orthognality and domain flipping.
L
-6
(5)
IRl. 1.1Rl.2 and IRl. 3 represent the Pareto distribution shown in Fig. 7. As such each rule represents the generic framework of a Pareto distribution [18], given by:
Fi �
-7
is
&
Cubic utopia rule is given by: 1Rl.3
1
_'----'-_ -'------'-_.J..._ . --,:-_--,:-
In Fig. 8 objective 3 represents easterly wind and objective 4 represents shortwave flux as expressed in (2). The points of convergence between the two system blocks are reached at the start and end points of the MOGA evolutionary strength population (min x, max y; max x, min y) within the limits of IRl. \, IRl. z, IRl. 3, IRl. n, with exponentially decreasing error. The min and max of each objective plane represent the climatic data shown in Figs. 1-4.
(4 )
82x + 83 ± [;
Where 01 is 0.014, 0.033382.
-8
Fig. 8. Orthogonal distribution of Renewable Energy Systems.
Quadratic utopia rule is given by: 2
\\
·······Cubic
E7.
IRl.J
\
