A Model Predictive Control Approach to Microgrid ... - ARSControl
Università del Sannio Department of Engineering The GRACE Group Benevento, Italy
A Model Predictive Control Approach to Microgrid Operation Optimization Luigi Glielmo, Alessandra Parisio* Università del Sannio * Currently at KTH, Stockholm
October 31st, 2012
Smart Power Grid Provide a sustainable way to meet the growing energy demand through • high penetra6on of renewable energy sources (RES) • storage u6liza6on • distributed local genera6on • energy efficiency New energy management systems are needed for op6mally • managing the distributed units • applying demand response policies • interac6ng with the u6lity grid (bidirec6onal power flow)
2
Opera6on Op6miza6on in Energy Systems
Goal: design an energy management system for distributed genera6on Approach: • Consider subsystems of the distribu6on grid • Build a model of the subsystem which is as simple as possible • Formulate a tractable opera6on op6miza6on problem • Cope with uncertainty Two promising paradigms for these energy subsystems: microgrids and energy hubs
3
Microgrid Opera6on Op6miza6on
1. MICROGRID CONCEPT AND OPERATION OPTIMIZATION 2. MODELING AND PROBLEM FORMULATION 3. MICROGRID CONTROL STRATEGY 4. MICROGRID EMISSION REDUCTION
Microgrid Concept The microgrid concept assumes a cluster of loads and distributed generators (DGs) opera6ng as a single controllable system that provides both electricity and heat to its local area. Microgrid components: • Distributed Generators (DGs) • Loads • Storage equipment (baWeries, capacitors, flywheels) • Microgrid Controller • Point of Common Coupling (PCC) to the u6lity grid 1
Microgrid Opera6on Op6miza6on Objec6ve: • Op6mize microgrid opera6ons over a planning horizon to fulfill a 6me-‐varying demand subject to opera6onal constraints while minimizing a cost func6on The Microgrid Opera6on Op6miza6on includes • Unit Commitment (UC) • Economic Dispatch (ED) • Op6mal scheduling of storage opera6ons • Demand side policies (curtailment op6ons) • When and how much energy should be purchased/sold from/to the u6lity grid
Main Contribu6ons Microgrid modeling needs both con6nuous and discrete decision variables resul6ng opera6on op6miza6on problem is very difficult to solve.
Contribu6ons Provide a microgrid model adop6ng a formalized modeling approach The problem is stated as a Mixed Integer Linear Problem
It can be solved efficiently (cplex solver)
Problem formula6on suitable for online control scheme (Model Predic6ve Control) • Parisio A. and Glielmo L., “Energy Efficient Microgrid Management using Model Predic6ve Control”, CDC 2011 • Parisio A. and Glielmo L., “A Mixed Integer Linear Formula6on for Microgrid Economic Scheduling”, SmartGridComm 2011 • Parisio A. and Glielmo L., ”A Model Predic6ve Control Approach to Microgrid Opera6on Op6miza6on”, submiWed to Control Systems Technology
Problem Formula6on It has to be pointed out that • voltage stability, power quality, and frequency are supposed to be controlled automa6cally at the lower control level
Minimize operaAng costs subject to:
• Storage dynamics (charging/discharging mode) • Power balance • Energy import/export from/to the uAlity grid • OperaAonal and capacity constraints
Opera6ng Costs T −1 N g
∑∑ ⎡⎣Ci k =0 i =1
where:
DG
Nc
g
( Pi (k )) + OM iδ i (k ) + SU i (k ) + SDi (k ) ⎤⎦ + C (k ) + ρρc ∑ β h (k ) Dhc (k ) h =1
Power genera6on costs
fuel consump6on costs for unit i at 6me k
curtailment penal6es at 6me k
Ci DG ( Pi (k )) = a + b ⋅ Pi (k ) + c ⋅ Pi 2 (k ) start up and shut down costs for unit i at 6me k
SU i (k ), SDi (k )
Nc
ρc ∑ βh (k ) Dhc (k ) h =1
maintenance costs for unit i at 6me k
OM iδ i (k ) energy purchase/sale at 6me k
C g (k )
Costs on power exchanged with storage are also included
Storage Dynamics (1/2) Discrete-‐6me model of a storage unit xb (k + 1) = xb (k ) + η Pb (k ) − x sb !# ! c , if P b ( k ) > 0 (charging mode) !=" d #$ 1/ ! , otherwise (discharging mode) with 0 < ! c ,! d < 1
Incorporate storage switching dynamics into the op6miza6on problem [1]:
1. Introduce a binary variable: Pb (k ) > 0 ⇔ δ b (k ) = 1 2. Introduce an auxiliary variable: z b (k ) = δ b (k ) ⋅ Pb (k ) [1] A. Bemporad and M. Morari, “Control of systems integra6ng logic, dynamics, and constraints,” Automa;ca, vol. 35, no. 3, 1999.
Storage Dynamics (2/2) 3. Express the ‘if . . . then’ condi6ons as mixed integer linear inequali6es
⎧⎪P b > m(1 − δ b ) P > 0 ⇔ δ = 1 is true if and only if ⎨ ⎪⎩P b ≤ Mδ b ⎧ z b ≥ mδ b ⎪ b b b b z = δ ⋅ P is equivalent to ⎪ z ≤ Mδ b ⎨ b b b ⎪ z ≤ P − m(1 − δ ) ⎪ z b ≥ P b − M (1 − δ b ) ⎩ b
b
4. Collect the inequali6es and rewrite the storage dynamics and the corresponding constraints in the following compact form:
(
)
x b ( k +1) = x b ( k ) + ! c !1/ ! d z b ( k ) + (1/ ! d ) P b ( k ) ! x sb b bb b b b ⋅ P ( k ) + E subject to E1bδ⋅ δb (b k(k) )++EEb2b2z⋅b z(kb ()k≤) ≤EE P ( k ) + E 3 3 4 4
Power Balance Balance between power genera6on and demand Ng
Nt
Nc
i =1
j =1
h =1
P b (k ) = ∑ Pi (k ) + P res (k ) + P g (k ) −∑ D j (k ) − ∑ [1 − β h (k )]Dhc (k ) Define: δ ( k ) : binary variables storing the on/off state for the DG units at 6me k
(k )) = [P ' (k ) δ' (k ) P g (k ) β' (k )] ' uu(k (k) = [P res (k ) D' (k ) Dc' (k )] ' ww(k
Decision variables Disturbances
Pb (k ) = F ' (k ) ⋅ u(k ) + f '⋅w(k )
Energy Import/Export from/to the U6lity Grid How to model the possibility to purchase/sell energy from/to the u6lity grid? 1. Introduce a binary variable:
P g (k ) > 0 ⇔ δ g (k ) = 1 g
2. Introduce an auxiliary variable: C (k ) P g g ⎧ c ( k ) P ( k ), if δ (k ) = 1 g C (k ) = ⎨ S g c ( k ) P (k ), otherwise ⎩
3. Express the ‘if . . . then’ condi6ons as mixed integer linear inequali6es [1] 4. Collect the inequali6es and rewrite constraints in the following compact form: g g gg g g g g g E11g δ⋅ δ (g k(k) )++EE2 2C ⋅ C(k ()k≤) E ≤ 3E(3kg )⋅ P g (k ) + E 4g4
Opera6onal Constraints For each DG unit i at 6me k , the following constraints must be sa6sfied Opera6onal constraints (minimum up/down 6mes) down δ i (k − 1) − δ i (k ) ≤ 1 − δ i (τ ), τ = k + 1,…, min(k + Ti − 1, k + T − 1) δ i (k ) − δ i (k − 1) ≤ δ i (τ ), τ = k + 1,…, min(k + Ti up − 1, k + T − 1)
Start up and shut down costs
SU i (k ) ≥ ciSU (k )[δ i (k ) − δ i (k − 1)], SDi (k ) ≥ ciSD (k )[δ i (k − 1) − δ i (k )], SU i (k ) ≥ 0, SDi (k ) ≥ 0.
Capacity Constraints Physical bounds on the storage device b b b xmin ≤ x (k ) ≤ xmax b Pb (k ) ≤ Cmax Power flow limits of the DG units Pi ,minδ i ( k ) ≤ Pi ( k ) ≤ Pi ,maxδ i ( k ) Bounds on controllable loads curtailments β h ,min (k ) ≤ β h ( k ) ≤ β h ,max ( k ) Ramp up and ramp down rates
Pi (k + 1) − Pi (k ) ≤ Ri ,max
The Receding Horizon Approach
Microgrid Control Strategy Now, we incorporate feedback and predicAons into control acAon on the basis of opAmizaAon MODEL PREDICTIVE CONTROL
k th hour demand
k t h hour RES generaAon, price,
load and RES predicAons
Microgrid operation optimization problem Apply first control input
Measurements
Microgrid Decisions/ control actions
An Example The proposed scheduling strategy is inves6gated on an example of microgrid • with 4 DG units, 1 storage, 1 photovoltaic plant, cri6cal and controllable loads • with 1 hour sampling 6me, 24 hours planning horizon PV unit
DG unit 3
DG unit 4
Utility grid MV/LV Transformer DG unit 1 Storage unit
DG unit 2
Critical and controllable loads
A Heuris6c Algorithm for Microgrid Management • No prac6cal approaches to microgrid economic management have been proposed or adopted so as to have a prac6cal benchmark • Usually the main aim is balancing of supplied and demanded powers The proposed heurisAc algorithm is based on the following assumpAons: • no storage is available; • power surplus sold to the u6lity grid; • the power generated from the renewable energy sources is then always u6lized to sa6sfy the demand; • depending on the minimum cost among the DG unit genera6ng costs and the energy prices, the power deficit will be sa6sfied by either DG units or the u6lity grid; • the DG units are turned on from the cheapest to the most expensive one un6l the demand deficit is covered; • the DG units are run at their maximum power capacity.
Simula6on Results (1/3) InteracAon with the uAlity grid
MPC-‐MILP
HeurisAc algorithm
Simula6on Results (2/3) Unit commitment and dispatch
MPC-‐MILP
HeurisAc algorithm
Simula6on Results (3/3) We compare the following strategies: MPC-‐MILP: feedback control law MILP: open loop solution
Benchmark: the 24h horizon plan with no errors in forecasts
Computa6onal Burden Computa6onal 6mes needed for solving the MILPs as the predic6on horizon grows
The solu6on to the op6miza6on problem takes a much shorter 6me than the one hour sampling 6me.
Proposed scheduling strategy is suitable for online applica6ons
Experimental Results Experiments of 6 hours were run at Center for Renewable Energy Sources and Saving (CRES), Pikermi-‐Athens, Greece. • grid-‐connected microgrid 3-‐phase power line to the public grid • 15 minutes sampling 6me
Experiment 1: without high-‐level control; total cost of 27.43€ Experiment 2: MPC-‐MILP with 6-‐hours predic6on horizon;19.6 € (28.5% saving) Experiment 3: MPC-‐MILP with 18-‐hours predic6on horizon;17.9 € (34.7 % saving)
Microgrid Emission Reduc6on Goal: include emissions and solve a mul6-‐objec6ve op6miza6on problem Emission func6on for a DG unit: E ( P) = α + βP(k ) + γP 2 (k ) + ζeλP ( k ) Approach: • Approximate E(P) as a piecewise affine func6on the problem stays a MILP • Apply a weighted sum method:
ωJ r + (1 − ω )σJ e
total emissions
total running costs weight factor
1
Preliminary Results • Computa6onal 6mes: 3 s on average • 7.8% of increase in running costs if emission reduc6on is the most important objec6ve • Significant increase in emissions if running costs are the preferred objec6ve
Pareto curve
1
E-Gotham: A European Artemis Project
27
Thanks for your aWen6on!!
A Model Predictive Control Approach to Microgrid Operation Optimization Luigi Glielmo, Alessandra Parisio* Università del Sannio * Currently at KTH, Stockholm
October 31st, 2012
Smart Power Grid Provide a sustainable way to meet the growing energy demand through • high penetra6on of renewable energy sources (RES) • storage u6liza6on • distributed local genera6on • energy efficiency New energy management systems are needed for op6mally • managing the distributed units • applying demand response policies • interac6ng with the u6lity grid (bidirec6onal power flow)
2
Opera6on Op6miza6on in Energy Systems
Goal: design an energy management system for distributed genera6on Approach: • Consider subsystems of the distribu6on grid • Build a model of the subsystem which is as simple as possible • Formulate a tractable opera6on op6miza6on problem • Cope with uncertainty Two promising paradigms for these energy subsystems: microgrids and energy hubs
3
Microgrid Opera6on Op6miza6on
1. MICROGRID CONCEPT AND OPERATION OPTIMIZATION 2. MODELING AND PROBLEM FORMULATION 3. MICROGRID CONTROL STRATEGY 4. MICROGRID EMISSION REDUCTION
Microgrid Concept The microgrid concept assumes a cluster of loads and distributed generators (DGs) opera6ng as a single controllable system that provides both electricity and heat to its local area. Microgrid components: • Distributed Generators (DGs) • Loads • Storage equipment (baWeries, capacitors, flywheels) • Microgrid Controller • Point of Common Coupling (PCC) to the u6lity grid 1
Microgrid Opera6on Op6miza6on Objec6ve: • Op6mize microgrid opera6ons over a planning horizon to fulfill a 6me-‐varying demand subject to opera6onal constraints while minimizing a cost func6on The Microgrid Opera6on Op6miza6on includes • Unit Commitment (UC) • Economic Dispatch (ED) • Op6mal scheduling of storage opera6ons • Demand side policies (curtailment op6ons) • When and how much energy should be purchased/sold from/to the u6lity grid
Main Contribu6ons Microgrid modeling needs both con6nuous and discrete decision variables resul6ng opera6on op6miza6on problem is very difficult to solve.
Contribu6ons Provide a microgrid model adop6ng a formalized modeling approach The problem is stated as a Mixed Integer Linear Problem
It can be solved efficiently (cplex solver)
Problem formula6on suitable for online control scheme (Model Predic6ve Control) • Parisio A. and Glielmo L., “Energy Efficient Microgrid Management using Model Predic6ve Control”, CDC 2011 • Parisio A. and Glielmo L., “A Mixed Integer Linear Formula6on for Microgrid Economic Scheduling”, SmartGridComm 2011 • Parisio A. and Glielmo L., ”A Model Predic6ve Control Approach to Microgrid Opera6on Op6miza6on”, submiWed to Control Systems Technology
Problem Formula6on It has to be pointed out that • voltage stability, power quality, and frequency are supposed to be controlled automa6cally at the lower control level
Minimize operaAng costs subject to:
• Storage dynamics (charging/discharging mode) • Power balance • Energy import/export from/to the uAlity grid • OperaAonal and capacity constraints
Opera6ng Costs T −1 N g
∑∑ ⎡⎣Ci k =0 i =1
where:
DG
Nc
g
( Pi (k )) + OM iδ i (k ) + SU i (k ) + SDi (k ) ⎤⎦ + C (k ) + ρρc ∑ β h (k ) Dhc (k ) h =1
Power genera6on costs
fuel consump6on costs for unit i at 6me k
curtailment penal6es at 6me k
Ci DG ( Pi (k )) = a + b ⋅ Pi (k ) + c ⋅ Pi 2 (k ) start up and shut down costs for unit i at 6me k
SU i (k ), SDi (k )
Nc
ρc ∑ βh (k ) Dhc (k ) h =1
maintenance costs for unit i at 6me k
OM iδ i (k ) energy purchase/sale at 6me k
C g (k )
Costs on power exchanged with storage are also included
Storage Dynamics (1/2) Discrete-‐6me model of a storage unit xb (k + 1) = xb (k ) + η Pb (k ) − x sb !# ! c , if P b ( k ) > 0 (charging mode) !=" d #$ 1/ ! , otherwise (discharging mode) with 0 < ! c ,! d < 1
Incorporate storage switching dynamics into the op6miza6on problem [1]:
1. Introduce a binary variable: Pb (k ) > 0 ⇔ δ b (k ) = 1 2. Introduce an auxiliary variable: z b (k ) = δ b (k ) ⋅ Pb (k ) [1] A. Bemporad and M. Morari, “Control of systems integra6ng logic, dynamics, and constraints,” Automa;ca, vol. 35, no. 3, 1999.
Storage Dynamics (2/2) 3. Express the ‘if . . . then’ condi6ons as mixed integer linear inequali6es
⎧⎪P b > m(1 − δ b ) P > 0 ⇔ δ = 1 is true if and only if ⎨ ⎪⎩P b ≤ Mδ b ⎧ z b ≥ mδ b ⎪ b b b b z = δ ⋅ P is equivalent to ⎪ z ≤ Mδ b ⎨ b b b ⎪ z ≤ P − m(1 − δ ) ⎪ z b ≥ P b − M (1 − δ b ) ⎩ b
b
4. Collect the inequali6es and rewrite the storage dynamics and the corresponding constraints in the following compact form:
(
)
x b ( k +1) = x b ( k ) + ! c !1/ ! d z b ( k ) + (1/ ! d ) P b ( k ) ! x sb b bb b b b ⋅ P ( k ) + E subject to E1bδ⋅ δb (b k(k) )++EEb2b2z⋅b z(kb ()k≤) ≤EE P ( k ) + E 3 3 4 4
Power Balance Balance between power genera6on and demand Ng
Nt
Nc
i =1
j =1
h =1
P b (k ) = ∑ Pi (k ) + P res (k ) + P g (k ) −∑ D j (k ) − ∑ [1 − β h (k )]Dhc (k ) Define: δ ( k ) : binary variables storing the on/off state for the DG units at 6me k
(k )) = [P ' (k ) δ' (k ) P g (k ) β' (k )] ' uu(k (k) = [P res (k ) D' (k ) Dc' (k )] ' ww(k
Decision variables Disturbances
Pb (k ) = F ' (k ) ⋅ u(k ) + f '⋅w(k )
Energy Import/Export from/to the U6lity Grid How to model the possibility to purchase/sell energy from/to the u6lity grid? 1. Introduce a binary variable:
P g (k ) > 0 ⇔ δ g (k ) = 1 g
2. Introduce an auxiliary variable: C (k ) P g g ⎧ c ( k ) P ( k ), if δ (k ) = 1 g C (k ) = ⎨ S g c ( k ) P (k ), otherwise ⎩
3. Express the ‘if . . . then’ condi6ons as mixed integer linear inequali6es [1] 4. Collect the inequali6es and rewrite constraints in the following compact form: g g gg g g g g g E11g δ⋅ δ (g k(k) )++EE2 2C ⋅ C(k ()k≤) E ≤ 3E(3kg )⋅ P g (k ) + E 4g4
Opera6onal Constraints For each DG unit i at 6me k , the following constraints must be sa6sfied Opera6onal constraints (minimum up/down 6mes) down δ i (k − 1) − δ i (k ) ≤ 1 − δ i (τ ), τ = k + 1,…, min(k + Ti − 1, k + T − 1) δ i (k ) − δ i (k − 1) ≤ δ i (τ ), τ = k + 1,…, min(k + Ti up − 1, k + T − 1)
Start up and shut down costs
SU i (k ) ≥ ciSU (k )[δ i (k ) − δ i (k − 1)], SDi (k ) ≥ ciSD (k )[δ i (k − 1) − δ i (k )], SU i (k ) ≥ 0, SDi (k ) ≥ 0.
Capacity Constraints Physical bounds on the storage device b b b xmin ≤ x (k ) ≤ xmax b Pb (k ) ≤ Cmax Power flow limits of the DG units Pi ,minδ i ( k ) ≤ Pi ( k ) ≤ Pi ,maxδ i ( k ) Bounds on controllable loads curtailments β h ,min (k ) ≤ β h ( k ) ≤ β h ,max ( k ) Ramp up and ramp down rates
Pi (k + 1) − Pi (k ) ≤ Ri ,max
The Receding Horizon Approach
Microgrid Control Strategy Now, we incorporate feedback and predicAons into control acAon on the basis of opAmizaAon MODEL PREDICTIVE CONTROL
k th hour demand
k t h hour RES generaAon, price,
load and RES predicAons
Microgrid operation optimization problem Apply first control input
Measurements
Microgrid Decisions/ control actions
An Example The proposed scheduling strategy is inves6gated on an example of microgrid • with 4 DG units, 1 storage, 1 photovoltaic plant, cri6cal and controllable loads • with 1 hour sampling 6me, 24 hours planning horizon PV unit
DG unit 3
DG unit 4
Utility grid MV/LV Transformer DG unit 1 Storage unit
DG unit 2
Critical and controllable loads
A Heuris6c Algorithm for Microgrid Management • No prac6cal approaches to microgrid economic management have been proposed or adopted so as to have a prac6cal benchmark • Usually the main aim is balancing of supplied and demanded powers The proposed heurisAc algorithm is based on the following assumpAons: • no storage is available; • power surplus sold to the u6lity grid; • the power generated from the renewable energy sources is then always u6lized to sa6sfy the demand; • depending on the minimum cost among the DG unit genera6ng costs and the energy prices, the power deficit will be sa6sfied by either DG units or the u6lity grid; • the DG units are turned on from the cheapest to the most expensive one un6l the demand deficit is covered; • the DG units are run at their maximum power capacity.
Simula6on Results (1/3) InteracAon with the uAlity grid
MPC-‐MILP
HeurisAc algorithm
Simula6on Results (2/3) Unit commitment and dispatch
MPC-‐MILP
HeurisAc algorithm
Simula6on Results (3/3) We compare the following strategies: MPC-‐MILP: feedback control law MILP: open loop solution
Benchmark: the 24h horizon plan with no errors in forecasts
Computa6onal Burden Computa6onal 6mes needed for solving the MILPs as the predic6on horizon grows
The solu6on to the op6miza6on problem takes a much shorter 6me than the one hour sampling 6me.
Proposed scheduling strategy is suitable for online applica6ons
Experimental Results Experiments of 6 hours were run at Center for Renewable Energy Sources and Saving (CRES), Pikermi-‐Athens, Greece. • grid-‐connected microgrid 3-‐phase power line to the public grid • 15 minutes sampling 6me
Experiment 1: without high-‐level control; total cost of 27.43€ Experiment 2: MPC-‐MILP with 6-‐hours predic6on horizon;19.6 € (28.5% saving) Experiment 3: MPC-‐MILP with 18-‐hours predic6on horizon;17.9 € (34.7 % saving)
Microgrid Emission Reduc6on Goal: include emissions and solve a mul6-‐objec6ve op6miza6on problem Emission func6on for a DG unit: E ( P) = α + βP(k ) + γP 2 (k ) + ζeλP ( k ) Approach: • Approximate E(P) as a piecewise affine func6on the problem stays a MILP • Apply a weighted sum method:
ωJ r + (1 − ω )σJ e
total emissions
total running costs weight factor
1
Preliminary Results • Computa6onal 6mes: 3 s on average • 7.8% of increase in running costs if emission reduc6on is the most important objec6ve • Significant increase in emissions if running costs are the preferred objec6ve
Pareto curve
1
E-Gotham: A European Artemis Project
27
Thanks for your aWen6on!!
