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Carlos Bordons 2017 1
Control of microgrids integrating renewable energy and hybrid storage
Carlos BordonsDpto. Ingeniería de Sistemas y Automática
Universidad de Sevilla, SpainWith the collaboration of Paulo Mendes, Luis Valverde,
Félix García-Torres and Pablo Velarde
Carlos Bordons 2017 2
Abstract
• Energy Management in microgrids with renewable sources (solar, wind) and hybrid storage (H2)
• Control issues in Model Predictive Control framework
• Control objectives: durability, economic profit, etc.• Consideration of Disturbances • Electric Vehicles • Interconnection of microgrids• Illustrated on a demonstration microgrid
Carlos Bordons 2017 3
Outline
1. Introduction
2. Energy Management in Microgrids
3. Extended control objectives
4. Disturbances Management
5. Integration of Electric Vehicles
6. Networks of Microgrids
7. Concluding remarks
Carlos Bordons 2017 4
Renewable Energy
Solar/Wind energygeneration:• Highly time-varying• Differs from the installed
Energy storage must become an integral element of the renewable adoption strategy
Storage allows a non-dispatchablegenerator (RES) to be dispatchable
Storage must be operated in an optimal way
Carlos Bordons 2017 5
Cover a range of time scales
Hybrid Energy Storage Systems
Need for hybridization:
Management
Different dynamics-Complementary
Carlos Bordons 2017 6
Hydrogen-based Energy Systems (HBES)
Also for FCHVs: Toyota Mirai
Distributed and mobile storage
Hydrogen can be an option: high energy density and high power density
02H20
H2 02
“The Green Hydrogen Cycle”
H2
Carlos Bordons 2017 7
Outline
1. Introduction
2. Energy Management in Microgrids
3. Extended control objectives
4. Disturbances Management
5. Integration of Electric Vehicles
6. Networks of Microgrids
7. Concluding remarks
Carlos Bordons 2017 8
Control objectives in microgrids (AC/DC)
• Supply and demand balancing• Power quality: avoid
variations as harmonic distortion or sudden events as interruptions or even voltage dips.
• In isolated mode: Voltage and frequency management
• Economic benefit
Adjust the manipulated units in the proper way (generators, storage and loads)
Main objective: supply the energy demanded by the loads using DGs and DS in an efficient and reliable way. Both in normal conditions and in contingency, independently of the main grid
F Katiraei, R Iravani, N Hatziargyriou, A Dimeas. Microgrids management. IEEE power and energymagazine 6 (3), 2008.
Bidram, A., Lewis, F. L., Davoudi, A. Distributed control systems for small-scale power networks. IEEE Control Systems Magazine 34 (6), 56–77. 2014.
Olivares et al. Trends in microgrid control. IEEE Transon Smart Grid 5 (4). 2014
Carlos Bordons 2017 9
Control Levels
Hierarchical control of droop-controlled ac and dc microgrids a general approach toward standardization. J. M. Guerrero, J. C. Vasquez, J. Matas, L. G. de Vicuña, and M. Castilla" IEEE Trans Ind. Electr. 58 (1), pp. 158-172, 2011.
Energy management
Power Quality
• Hysteresis (Ulleberg, 2003), (Ghosh,2003),(Ipsakis, 2008)
• GA(Dufo-López, 2007)• Fuzzy (Bilodeau, 2006), (Stewart, 2009)• MPC (Korpäs, 2007) (Del Real, 2007),
(Valverde, 2013), (De Angelis, 2013),(García, 2015)
• Droop Control (Vázquez 2009), (Vadak2011)
• H∞ (Zhong 2006)• MPC (Rodríguez 2007)
Carlos Bordons 2017 10
Model Predictive Control in microgrids
The use of MPC technique allows to maximize the economical benefit of the microgrid, minimizing the degradation causes of each storage system, fulfilling constraints (operational or imposed)
Optimization over a future receding horizon using a dynamic model
of the plant
Carlos Bordons 2017 11
Laboratory Microgrid
https://sites.google.com/site/laboratorioh2/
DC microgrid. Seville
Carlos Bordons 2017 12
EMS. Control Scheme
bat gen dem fc ez grid netP P P P P P P= − + − + +
Power in the battery bank:
Must be 0 to balance power
MPC States: Battery SOC
Metal Hydride Level
MPC:Constraints
Cost functionminimization
MPC outputs (MVs):FC PowerELZ PowerGrid Power
Disturbances
Carlos Bordons 2017 13
3 weighted objectives
Cost function
The behavior of the MPC is defined by the cost function (Objective)
The second group (β) is set to protect the equipment from intensive use (soft constraints)
The first group of weighting factors controls priority (based on costs)
The 𝛾𝛾 group penalizes the error in reference tracking in order to give flexibility to the plant operation
Different set of parameters for different objectives (or operating conditions: sunny, cloudy, etc.)
Power balance with priorization
Keep storage levels (H2 and electricity) Protect equipment from intensive use
( ) ( )
2 2 2 21 ( ) 2 ( ) 3 ( ) 4 ( )
1
2 2 2 21 ( ) 2 ( ) 3 ( ) 4 ( )
2 2
1 ( ) 2 ( )1
Nu
fc t k ez t k grid t k net t kk
fc t k ez t k grid t k net t k
N
t k ref t k refk
J P P P P
P P P P
SOC SOC MHL MHL
α α α α
β β β β
γ γ
+ + + +=
+ + + +
+ +=
= + + + +
+ ∆ + ∆ + ∆ + ∆ +
+ − + −
∑
∑
Carlos Bordons 2017 14
Controller constraints and implementation
Constraints: power and powerrates limits. Storage limits
, ,100 900 ez min ez maxP W Pez W P= ≤ ≤ =
, ,max 100 900 fc min fcP W Pfc W P= ≤ ≤ =
, ,max 2500 6 grid min gridP kW Pgrid kW P= − ≤ ≤ =
net,min net,max P 2500 W Pnet 6 kW P= − ≤ ≤ =
fc,min fc,max P 20 W / s Pfc 20 W / s P ∆ = − ≤ ∆ ≤ = ∆
fc,min fc,max P 20 W / s Pfc 20 W / s P ∆ = − ≤ ∆ ≤ = ∆
grid,min grid,max P 1000 W / s Pgrid 1000 W / s P∆ = − ≤ ∆ ≤ = ∆net,min net,maxP 2500 W / s Pnet 6000 W / s P ∆ = − ≤ ∆ ≤ = ∆
min maxSOC 40 % SOC 75 % SOC = ≤ ≤ =
min maxMHL 10 % MHL 90 % MHL= ≤ ≤ =
Matlab/Simulink PLCReal-Time control
Quadratic cost function+ linear constraints: Quadratic Programming (QP)
Carlos Bordons 2017 15
Experimental validation
Sunny day
Carlos Bordons 2017 16
Improved performance over heuristic control (HB): Fewer start-up/shut downs, smooth power references to units. But
Issues not addressed:
Controller performance
• Durability of storage devices. Facilitated by constraints (smooth operation), but not imposed
• Different efficiencies for charge/discharge• Forecast of demand/generation (RES). Uncertainties• Different prices sale/purchase (quantify). Market
Carlos Bordons 2017 17
Outline
1. Introduction
2. Energy Management in Microgrids
3. Extended control objectives
4. Disturbances Management
5. Integration of Electric Vehicles
6. Networks of Microgrids
7. Concluding remarks
Carlos Bordons 2017 18
Include degradation in the cost function
• Durability is an important issue in ESS• Batteries: Manufacturers of batteries quantify the life of this ESS as a
function of the number of the charge and discharge cycles. Ultracapacitor: similar.
• Can be included in the cost function:
.
Metal hydride storage
Carlos Bordons 2017 19
Hydrogen
• Manufacturers of ELZ and FC give the life expression of this kind of systems as a function of the number of working hours. Start-up and shut-down cycles and fluctuating load conditions can affect seriously to these devices.
• Logical variables included: on/off states (δ), and transitions: startup and shutdown states (σ)
F. García-Torres and C. Bordons. Optimal Load Sharing for Hydrogen-based Microgrids with Hybrid Storage using Model Predictive Control. IEEE Transactions on Industrial Electronics 63 (8), 2016.
Mixed Integer Quadratic Program MIQP
Carlos Bordons 2017 20
Import/export
• To manage the purchase and sale of energy to the external network different prices for sale and purchase are used.
• Use different weights for the same variable (Pnetwork) depending on the situation.
• To make this possible a new variable is defined
• Cost function:Purchase
New variables
MIQP
Carlos Bordons 2017 21
Market and dispatchability
• Microgrid in the electricity market• The microgrid operator can act as a conventional power plant
(gas, coal, etc. ) and participate in the auction process• Optimal scheduling policy linked to the time-varying price of
energy. Microgrid´s non-dispatchable generation is converted into dispatchable using the ESS.
• Networks of microgrdis
Markets:• Day-ahead• Intraday• Regulation
services
Carlos Bordons 2017 22
Day-ahead market
• Daily market forecast• Daily market controller schedule• Purchase to the grid when price low.
Sell when price high• Constants setpoints to ELZ y FC to
minimize degradation• This will be recomputed.
(zoom)
Optimal economical schedule of hydrogen-based microgrids with hybrid storage using model predictive control. F Garcia-Torres, C Bordons. IEEE Transactions on Industrial Electronics 62 (8), 2015.
Carlos Bordons 2017 23
Outline
1. Introduction
2. Energy Management in Microgrids
3. Extended control objectives
4. Disturbances Management
5. Integration of Electric Vehicles
6. Networks of Microgrids
7. Concluding remarks
Carlos Bordons 2017 24
• MPC can be used to deal with the uncertainty in the energy demand and the renewable generation (disturbances)
• Approaches:– Robust MPC: min-max (computationally heavy)– Stochastic MPC:
• Multiple-scenario: single control sequence that takes into account different possible evolutions of the process disturbances and satisfies all their potential realizations with a certain probability
• Tree-based: One control sequence per scenario. Possible evolutions of the disturbances can be confined to a tree (reduce the possibilities)
• Chance constraints: uses an explicit probabilistic modeling of the system disturbances to calculate explicit bounds on the system constraint satisfaction.
Disturbances
G. Calafiore, M. Campi, The scenario approach to robust control design, IEEE Trans. Autom. Control 2006
Carlos Bordons 2017 25
Probabilistic/Chance constraints
• CC-MPC uses an explicit probabilistic modeling of the system disturbances to calculate explicit bounds on the system constraint satisfaction.
• Probabilistic constraints converted to deterministic• Advantage: the computational burden (on-line) is not
increased as in the scenario-based techniques.• Assumption: disturbances are Gaussian random variables,
which are modeled based on historical data, with a knowncumulative distribution function (CDF).
J. Grosso, P. Velarde, C. Ocampo-Martinez, J. Maestre, V. Puig, Stochastic model predictive
control approaches applied to drinking water networks. Optim. Control Appl Methods, 2016.
(state constraints)
Risk of constraint violation
Carlos Bordons 2017 26
Problem statement
Probabilistic constraints converted to deterministic
represents the cumulative distribution function of the random variable G D w(k). Built based on historical data. Drawback
Chance constraint converted to deterministic
Carlos Bordons 2017 27
Application to the microgrid
• The system is subject to uncertainties in the power generatedby the solar field, and the power demanded by the consumers
• Constraints on states and inputs• Linearized model
On the comparison of stochastic model predictive control strategies applied to a hydrogen-based microgridP. Velarde, L. Valverde, J.M. Maestre, C. Ocampo-Martinez, C. Bordons. Journal of Power Sources 2017.
Carlos Bordons 2017 28
Experimental results
Similar performance for the 3 methods
Deterministic MPC: 3.9 x 1013
Ts= 30 s. N=5.
Carlos Bordons 2017 29
Outline
1. Introduction
2. Energy Management in Microgrids
3. Extended control objectives
4. Disturbances Management
5. Integration of Electric Vehicles
6. Networks of Microgrids
7. Concluding remarks
Carlos Bordons 2017 30
Electric Vehicles Charge
• Microgrid management includingEVs charge
• Vehicle to Grid (V2G): use EVsbattery as storage while parking
• Selection of charge mode:– Slow: battery charged during parking
time– Fast: charged in the final 30 minutes.
Used as a buffer the rest of the time
• Selection of pickup time• Optimization: constrained MPC
(QP)
Energy management of an experimental microgrid coupled to a V2G system. PRC Mendes, LV Isorna, C Bordons, JE Normey-Rico. Journal of Power Sources 327, 702-713.
Carlos Bordons 2017 31
Objective function:Minimize cost of energy purchased from the grid
Logical (binary) variables: Different price buy/sell, EZ/FC interlocking, minimumtimes for switch on/off
MPC formulation
MIQPZ=1 buy
Guarantee that the vehicles’ batteries will be fully charged at the end of the charging time
Carlos Bordons 2017 32
Simulations
Simulations with 4 EVs, 24 h– Use all the available RES (and sell to the
grid)– Fulfill demand (loads and EVs)
Carlos Bordons 2017 33
Outline
1. Introduction
2. Energy Management in Microgrids
3. Extended control objectives
4. Disturbances Management
5. Integration of Electric Vehicles
6. Networks of Microgrids
7. Concluding remarks
Carlos Bordons 2017 34
R&D Roadmap in microgrids
Source: US DOE
Carlos Bordons 2017 35
Future power grids
• Power flow no longer static and flowing one way from the substation transformers to the end users, but instead is dynamic and flowing two ways.
• Network of microgrids
Carlos Bordons 2017 36
Centralized vs. Distributed
• Centralized control has important limitations when considering very large and complex systems.
– Prohibitive computational burden of a very large network, – Sharing of subnetwork models required. It is usually impossible – Number of generation and customer units involved exponentially increases the
computational demand.• Efficient centralized heuristic optimization algorithms to solve EED
problems: Fuzzy, Neural Networks, simulated annealing, genetic algorithm, particle swarm optimization etc. [1][2][3] or centralized MPC [4]
• A distributed formulation can be adopted – to solve simpler optimization problems– taking advantages of the smart grid communications– Distributed scheme provides better scalability
[1] Chen PH, Chang HC. Large-scale economic dispatch by genetic algorithm. 1995[2] Rajan CCA. A solution to the economic dispatch using EP based SA algorithm on large scale power system, 2010[3] Chaturvedi KT, Pandit M, Srivastava L. Modified neo-fuzzy neuron-based approach for economic and environmental optimal power dispatch., 2008[4] Arnold M, Andersson G. Investigating renewable infeed in residential areas applying model predictive control, 2010
divide et impera
Carlos Bordons 2017 37
Distribution of the control effort
Notice that, in the case of a network of microgrids, a centralized solution may not exist: different owners.
• Distributed Control: control responsibility shared by several agents, each one solving the control problem of its subnetwork
• A distributed formulation is adopted to solve simpler optimization problems intercommunicated each other in parallel computation stations.
• Overall network control problem is the aggregation of all local control problems:
Subject to local dynamics, interconnecting constraints and operational constraints
Carlos Bordons 2017 38
Lagrange-Based MPC• Each control agent incorporates terms related to the interconnecting
constraints
• Distributed objective function
• The aggregation of the local solutions obtained through an iterative process at each sampling time k is equivalent to the optimal solution calculated in a centralized way [1] (convexity of the cost function and affinity of the model)
• Proof of convergence [2]
[1] R. Negenborn, B. D. Schutter, and H. Hellendoorn, “Multi–agent model predictive control of transportation networks,” in Proc. of IEEE ICNSC 2006,
2] D. P. Bertsekas, Constrained Optimization and Lagrange Multiplier Methods, 1996.
Carlos Bordons 2017 39
Lagrange-based DMPC
.
• Augmented cost function
• The optimal solution is found when the Lagrange multipliers do not change with respect to the last iteration
Lagrange multipliers
Carlos Bordons 2017 40
Case study: aggregation of microgrids
• Microgrids with EV charging stations• Each microgrid is composed by renewable energy sources and a V2G system to
charge 10 EVs• Maximize the energy exchange among microgrids to reduce the amount of energy
purchased from the DNO.
Carlos Bordons 2017 41
Problem complexity
• Microgrid has 12 binary variables related to the physical dynamics:– 1 for energy sell/purchase to DNO– 1 to battery bank– 10 related to electric vehicles
• Prediction horizon of Np= 6• Total number of binary variables is 72. • This way each microgrid has 272
72possible instances to the local controller:
configurations for the binary variables in the global optimization problem.
CPLEX or suboptimal solutionsA practical approach for hybrid distributed MPC. Paulo R.C. Mendes, Jose M. Maestre, Carlos Bordons, Julio E. Normey-Rico. Journal of Process Control, 2017.
Carlos Bordons 2017 42
Simulation Results
Jul/2016
Energy management in each uG
Storage (SOC)
Carlos Bordons 2017 43
These exchanges reduce the energy purchased from the grid
Energy exchange among microgrids
Interconnection variables
Carlos Bordons 2017 44
Outline
1. Introduction
2. Energy Management in Microgrids
3. Extended control objectives
4. Disturbances Management
5. Integration of Electric Vehicles
6. Networks of Microgrids
7. Concluding remarks
Carlos Bordons 2017 45
• MPC: good candidate for microgrid control with hybrid storage (H2)
• Outstanding features in smooth operation, lower cost, higher lifetime
• Changes in cost function, tuning parameters and logical constraints can help fulfil different objectives
• Non-dispatchable RES can be converted into dispatchableusing the ESS and advanced control. Optimal economic schedule can be achieved (market)
• Stochastic disturbances can be included• Centralized/Distributed approaches• V2G included in microgrid management
Concluding remarks
Carlos Bordons 2017 46
Open lines for research
• Dispatchable microgrids in the pool market• Contribution of (up-to-now) non-dispatchable RES to frequency
regulation (virtual inertia)• Reconfiguration. Failures / Plug & Play• Coupling/stability issues• Networks of microgrids (SoS). Coalitional control (game theory)• Microgrids for EVs: Distributed storage (electricity and H2). V2G.
New business models• Combination of several types of energy: electricity, gas, ethanol,
H2, heat, etc.
Carlos Bordons 2017 47
Control of microgrids integrating renewable energy and hybrid storage
Carlos BordonsDpto. Ingeniería de Sistemas y Automática
Universidad de Sevilla, SpainWith the collaboration of Paulo Mendes, Luis Valverde,
Félix García-Torres and Pablo Velarde
Carlos Bordons 2017 48
Extra slides
Carlos Bordons 2017 49
Coalitional Games in networks of microgrids
• Analyze how coalitions form and evolve in physically coupled SoS.
• Development of methods for determining coalition structures which best fulfill system-wide objectives.
• Design information-aware coalition mechanisms.• Development of efficient computational tools for analysis and
engineering of coalition formation and behavior in SoS.
Coalition: clusters of control agents where communication is essential to ensure the cooperation
Carlos Bordons 2017 50
In coalitional control, the agents merge into coalitions that evolve dynamically with time
Coalitional control
Cooperative Game Theory Tools in Coalitional Control Networks. Ph. D thesis US, Francisco Muros, septiembre 2017.
Carlos Bordons 2017 51
Adapt to changing situations
Coalitional control
Carlos Bordons 2017 52
CNH2 (Puertollano)
Grid Emulator30, 45, 90 kVA
Solar Pannels10, 30, 60
kWp
Electrolyzer1, 5, 56 kW
Fuel Cell1, 5, 30 kW
BatteriesAGM: 3.9 kWhLi: 38.8 kWh
Ultracapacitors
714 Wh
Programmable Loads45 kW
Wind Turbine Emulator
30,90 kVA
Opal-RT
OP5600 OP4500 OP4500 OP4500 OP4500 OP4500 OP4500
LabVIEW
Ethernet/Modbus TCP-IP
Tomlab -CPLEX
30 kW90 kW
30 kW 30 kW 30 kW 30 kW 30 kW 30 kW
Carlos Bordons 2017 53
Annual Total Microgrid Market Capacity and Implementation Revenue by Region,World Markets: 2015-2024.
[1] https://www.navigantresearch.com/research/market-data-microgrids
Microgrid market
Carlos Bordons 2017 54
Binary variables
Energy flow exchanged with the network (part of the first term of the objective function):
New variables
Different price for sale/purchase: new binary variable
Purchase
Carlos Bordons 2017 55
Summary
• Overview of the challenges related to the control of renewable energy microgrids.
• Optimal management of the microgrid (islanded/connected):– Dispatch– Integration into the market
• Experimental and simulation examples. Hybrid storage including hydrogen
Carlos Bordons 2017 56
• Voltage and current regulation in the DGs, tracking references with adequate damping.
• Frequency and voltage regulation in the grid (isolated/grid connected).• Power balance, with adaptation to changes in generation and load.• Demand Side Management (DSM) mechanisms that allow load shedding.• Bumpless switch between operating modes.• Economical dispatch, sharing loads among the DGs and DS, minimizing
operational costs while keeping reliability.• Power flow management with main grid or other microgrids.
Bidram, A., Lewis, F. L., Davoudi, A. Distributed control systems for small-scale power networks. IEEE Control Systems Magazine 34 (6), 56–77. 2014.Olivares, D. E., Mehrizi-Sani, A., Etemadi, A. H., Canizares, C. A., Iravani, R., Kazerani, M., Hajimiragha, A. H., Gomis-Bellmunt, O., Saeedifard, A., Palma-Behnke, R., Jimenez-Estevez, G. A., Hatziargyriou, N. D. Trends in microgridcontrol. IEEE Trans on Smart Grid 5 (4). 2014
Control functions
Carlos Bordons 2017 5757/25Interconnection of Microgrids Using Distributed Model Predictive Control
Mixed Logic Dynamic Formulation
𝑥𝑥 𝑡𝑡𝑘𝑘+1 = 𝐴𝐴𝑥𝑥 𝑡𝑡𝑘𝑘 + 𝐵𝐵1𝑢𝑢 𝑡𝑡𝑘𝑘 + 𝐵𝐵2𝛿𝛿 𝑡𝑡𝑘𝑘 + 𝐵𝐵3𝑧𝑧 𝑡𝑡𝑘𝑘𝑦𝑦 𝑡𝑡𝑘𝑘 = 𝐶𝐶𝑥𝑥 𝑡𝑡𝑘𝑘 + 𝐷𝐷1𝑢𝑢 𝑡𝑡𝑘𝑘 + 𝐷𝐷2𝛿𝛿 𝑡𝑡𝑘𝑘 + 𝐷𝐷3𝑧𝑧 𝑡𝑡𝑘𝑘𝐸𝐸2𝛿𝛿 𝑡𝑡𝑘𝑘 + 𝐸𝐸3𝑧𝑧 𝑡𝑡𝑘𝑘 ≤ 𝐸𝐸1𝑥𝑥 𝑡𝑡𝑘𝑘 +𝐸𝐸4𝑥𝑥 𝑡𝑡𝑘𝑘 +𝐸𝐸5
Source: A. Bemporad and M. Morari, “Control of systems integrating logic, dynamics, and constraints.” Automatica, 35(3), 407-427, 1999.
Start up/Shut down States
Mixed Formulation
Working State
: Continuous and binary states: Input variables
: Logical variables
: MLD variables
𝑥𝑥 𝑡𝑡𝑘𝑘𝑢𝑢 𝑡𝑡𝑘𝑘
𝛿𝛿 𝑡𝑡𝑘𝑘
𝑧𝑧 𝑡𝑡𝑘𝑘
Power variation on Working State
Delays between states
Charging/Discharging States 𝑃𝑃𝑖𝑖 𝑡𝑡𝑘𝑘 ≤ 0 𝛿𝛿𝑖𝑖𝑑𝑑𝑖𝑖𝑑𝑑 𝑡𝑡𝑘𝑘 = 1,𝑃𝑃𝑖𝑖𝑑𝑑𝑖𝑖𝑑𝑑 𝑡𝑡𝑘𝑘 = 𝑃𝑃𝑖𝑖 𝑡𝑡𝑘𝑘 � 𝛿𝛿𝑖𝑖𝑑𝑑𝑖𝑖𝑑𝑑 𝑡𝑡𝑘𝑘
Carlos Bordons 2017 58
Multiple scenario
• Multiple-scenario MPC (MS-MPC) consists in calculating a single control sequence that takes into account different possible evolutions of the process disturbances.
• The control sequence calculated has a certain degree of robustness. Used for water systems and smart grids.
• It is required to know several scenarios with possible evolutions of the energy demand and generation. From historical data or random generation.
• Advantages:– it is possible to calculate bounds on the probability of constraint
violation as a function of the number of scenarios considered [*]– does not need a prior knowledge of the statistical properties that
characterize the uncertainty– Intuitive– Computation: deterministic convex optimization
[*]G. Calafiore, M. Campi, The scenario approach to robust control design, IEEE Trans. Autom. Control 2006
Carlos Bordons 2017 59
• K scenarios. Important tuning value• Upper limit of K to achieve a defined “risk acceptability level”
(compliance with the state constraints with a certain confidence degree) [*],
• The calculation of the controller will result in a unique robust control action that satisfies all the potential realizations of the disturbances with a certain probability.
w Disturbance forecast for scenario k
L. Giulioni, Stochastic Model Predictive Control with Application to DistributedControl Systems, 2015. Ph.D. thesis, Politecnico di Milano
Multiple scenario
Carlos Bordons 2017 60
Rooted trees. Tree-based MPC
• Uncertainty spreads with time: it is possible to predict more accurately both the energy demand and energy production by a renewable source in a short horizon than in a large one.
• Possible evolutions of the disturbances can be confined to a tree. In the tree, there is a bifurcation point whenever the disturbances branch into two possible trajectories.
Current disturbance
Carlos Bordons 2017 61
Tree-based MPC
• This technique consists of transforming the different possible evolutions of the disturbances into a rooted tree that, through its evolution, diverges and generates a reduced number of scenarios.
• Each scenario into the tree has its own control signal: moreoptimization variables are needed (computation)
• R < K. related to R-K (discarded scenarios)
Carlos Bordons 2017 62
Bifurcations
• The bifurcation points of the tree are checked: if they are equal, then the control actions are the same so that both the number of variables and the computational time can be reduced significantly.
• Constraint:
• This constraint can be used to reduce the number of optimization variables by removing the redundancy to lower the computational burden.
Carlos Bordons 2017 63
The weights can be changed to fulfill other objectives or change priorities
• SOC tracking• Setpoint at 40%• The power
developed by other unit changes accordingly
• Solved by a centralized QP
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 035
40
45
50
55
60
tiempo (horas)
Niv
el d
e ca
rga
(%)
NHMSOC
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
-1000
-500
0
500
1000
1500
tiempo (horas)
Pot
enci
as (W
)
FVDemandaEZFCBateríaRed
Weighting factors
Carlos Bordons 2017 64
Problem formulation
• Cost function
• Ts= 30 s. N=5.• Real solar and demand data (REE). One year
• Tree-based: R=250.Sunny and cloudy days
Carlos Bordons 2017 65
Distributed MPC: StructuresComplete review in (Negenborn, 2007). Apply the basic ideas of MPC but in a distributed form. There are several strategies:
Centralized MPC: A single agent controls everything (base case) Decentralized MPC: No interaction with neighbors Based on communication: Each agent takes into account the interactions with their neighbors in their dynamic model Based on cooperation. Each agent takes account of the interactions with their neighbors in the objective function, with access to the global cost function Based on Lagrange multipliers. Each agent has in mind Interactions with its neighbors in the objective function, through the use of Lagrange multipliers