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![Page 1: Energy Cost Minimization for Small Building with Renewable Energy Sources Based on Prediction Control Viktor Ten, Zhandos Yessenbayev, Akmaral Shamshimova,](https://reader036.fdocuments.us/reader036/viewer/2022062805/5697c0151a28abf838ccd944/html5/thumbnails/1.jpg)
Energy Cost Minimization for Small Building with Renewable Energy Sources Based on Prediction Control
Viktor Ten, Zhandos Yessenbayev, Akmaral Shamshimova, Albina Khakimova
Nazarbayev University, NLA
Almaty, 2015
Посольство Республики Корея в КазахстанеКорейское научно-техническое общество «КАХАК»
Казахский национальный университет им. аль-Фараби
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Renewable Energy Test Site at Nazarbayev University, Astana, Kazakhstan
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Control Plant is a combination of two subsystems:
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Objectives and Implementation
Objective – simultaneously satisfied requirements: maintain the indoor temperature within a comfort zone; satisfy demand of electrical power from the electrical loads; minimize overall consumption of energy sourced by grid; minimize cost of consumed energy.
Implementation algorithm: obtain a control oriented state-space model which captures main thermal and
electric dynamics, activation of the pumps, heating coil and the connection to the grid system identification;
define operating constraints including logic constraints and limits on the system variables;
design an controller with preview capabilities on desired room temperature, electricity tariff, outside temperature and solar radiation: Model Predictive Control (MPC), Control based on Genetic Algorithm.
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Electrical subsystem
Load can be powered either directly by the grid (ugrid=1) or by the battery bank through an invertor (ugrid=0)
Current generated by PV is assumed to be linearly proportional to solar radiation(coefficient obtained by a linear regression):
0.1218pv ei E
Q = 800 AhSample at Ts = 10mins
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Grey-box model:
Discrete-time model structure:
11 12
21 22 23 24
32 33
42 43 44
( ) ( ) 0 0
( , ) 0 ( ) ( ) 00
c c
c rr r
a u a ua a a aA u u a u a u
a a a
2
0
00
bB
11 12
41 42
0 00 0
e e
D
e e
( 1) ( ), ( ) ( ) ( ) ( )th r c th res thx k A u k u k x k Bu k Ed k ( )
Model is nonlinear convert to a linear system with hybrid dynamics
4 possible combinations of 4 linear models combined into a switched linear system
The coefficients of matrices A, B and D were determined using a simple linear regression
( , ) {0,1} {0,1}c ru u
State vector: , ,[ ]th c out w r out roomx T T T T
Disturbance input vector: [ ]th amb ed T E
Thermal Subsystem
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Controller
PV
Battery pack
Thermal model
SoC
Troom
Resistor On/OffPumps On/OffGrid/Battery
βforecast
€
SystemTamb, Ee
Iload
ipv
Uload
Overall system
Discrete states: x(k) = temperatures, state of charge at time k Discrete output: y(k) = temperature tracking error at time k Discrete disturbances: d(k) = outside T, solar radiation, tariff at time k Binary inputs: u(k)= grid/battery switch, pumps on/off, resistor on/off at time k
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Optimal control problem: minimize the cost function – analogous to the overall electricity cost
1
, , ,
0
0
1
min ( )
( )
. . ( , , ) , 0,..., 1
, 1,...,
N
l k b e k grid ku
k
k k k k
i V q u
x x k
s t x f x u d k N
x k N
* * *0 1 1* { ... }Nu u u u
The input sequence for optimal behaviour
Stabilization problem: maintain all states of the system within the required ranges:
,
,
5 , 120 ,
3 , 80 ,
3 , 80 ,
20 , 23 ,
30%, 80% .
c out
w
r out
room
T C C
T C C
x T C C
T C C
S
Control Task
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Model Predictive Control (MPC)
Theory behind MPC
MPC is based on iterative, finite-horizon optimization of a plant model.
At time t the current plant state is sampled and a cost minimizing control strategy is computed (via a numerical minimization algorithm) for a relatively short time horizon in the future: [t,t+T].
Specifically, an online or on-the-fly calculation is used to explore state trajectories that emanate from the current state and find (via the solution of Euler–Lagrange equations) a cost-minimizing control strategy until time t+T.
Only the first step of the control strategy is implemented, then the plant state is sampled again and the calculations are repeated starting from the new current state, yielding a new control and new predicted state path. The prediction horizon keeps being shifted forward and for this reason MPC is also called receding horizon control.
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Model Predictive Control (MPC)
Principles of MPC:
Model Predictive Control (MPC) is a multivariable control algorithm that uses:•an internal dynamic model of the process•a history of past control moves and•an optimization cost function J over the receding prediction horizon, to calculate the optimum control moves.An example of a non-linear cost function for optimization is given by:
without violating constraints (low/high limits)
With:xi = i-th controlled variable (e.g. measured temperature),ri = i-th reference variable (e.g. required temperature),ui = i-th manipulated variable (e.g. control valve),wxi
= weighting coefficient reflecting the relative importance of xi,
wui = weighting coefficient penalizing relative big changes in ui, etc.
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Genetic Algorithm (GA)
GA – a heuristic evolutionary optimization algorithm 1) Representation:
2) Population initialization:
3) Crossover:
4) Mutation:
5) Selection:- parents selection- best individuals selection
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Genetic Algorithm (GA)
Selection
Crossover
Mutation
Renew population
Start
Initial population
Fitness evaluation
Stop?
Final population
Finish
Yes
No
Notes: 1) Population generation must
respect the constraints 2) Elitism might be used in
population generation
General procedure of GA
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Genetic Algorithm (GA)
GA specifications in MATLAB
Parameter Value
Representation Binary vector u(k) = [ugrid(k), ures(k), uc(k), ur(k)] stacked together for each time k, T = 2880
Fitness function Energy cost as described above
Constraints Non-linear constraints described as above
Initialization Uniformly
Selection function Stochastic uniform (walk through random intervals)
Crossover function Scattered algorithm (mask random binary vector)
Mutation function Gaussian distribution (add a random number with mean 0)
Generation size 500 chromosomes
Elite count 2
Termination criteria Stall generation (=20) + Function tolerance (=1010)
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MPC Simulation resultsController: Ts=30 mins, Prediction: 8 hours; N=16; Simulation: 5 days; Ts=10 mins Economy: ~ 3 EUR (European Tariffs)
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GA Apply Simulation ResultsController: Ts=30 mins, Prediction: 8 hours; N=16; Simulation: 5 days; Ts=10 mins Economy: ~3 Euro
0 20 40 60 80 100 12019
20
21
22
23
24
time (h)
Room temperature [C]
TRoom
0 20 40 60 80 100 120
0
50
100
time (h)
Other temperatures [C]
Tcout
TroutTwater
Tamb
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0 20 40 60 80 100 1200
200
400
time(h)
Solar irradiance [W/m2] and energy price qe [euro cents]
0 20 40 60 80 100 1205
10
15
0 20 40 60 80 100 120-0.5
0
0.5
1
1.5
time(h)
Grid/Battery switch, Ugrid
0 20 40 60 80 100 12054
54.5
55
55.5
56
time(h)
State of charge [%]
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0 20 40 60 80 100 120-0.5
0
0.5
1
1.5
time(h)
Collector pump on/off, Uc
0 20 40 60 80 100 120-0.5
0
0.5
1
1.5
time(h)
Radiator pump on/off, Ur
0 20 40 60 80 100 120-0.5
0
0.5
1
1.5
time(h)
Heating coil on/off, Ures
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Thank you for attention!
Acknowledgements
Organizers of the seminar and ‘Kahak’ staff:
Пак Иван Тимофеевич, проф., почетный президент НТО «Кахак»,Мун Григорий Алексеевич, проф., президент НТО «Кахак»,Ю Валентина Константиновна, проф., вице-президент НТО «Кахак»,Югай Ольга, зам. отв. секретаря журнала «Известия НТО Кахак», и др.
Research Team and Administration of NLA at NU:
Prof. Alex Tikhonov – Director for Center for Energy Research,Dr. Zhandos Yessenbayev – Senior Researcher,Akmaral Shamshimova – Junior Researcher,Albina Khakimova – Junior Researcher,Dana Sharipova – Research Assistant,Aliya Kusatayeva – Junior Researcher, and others.