Multi-objective energy management methods for micro-grids
Systems and methods are disclosed for multi-objective energy management of micro-grids. A two-layer control method is used. In the first layer which is the advisory layer, a Model Predictive Control (MPC) method is used as a long term scheduler. The result of this layer will be used as optimality constraints in the second layer. In the second layer, a real-time controller guarantees a second-by-second balance between supply and demand subject to the constraints provided by the advisory layer.
1. A method to perform multi-objective energy management of micro-grids, comprising:
controlling a charge or discharge of a battery cell;
providing an advisory layer with a Model Predictive Control (MPC) as a long term scheduler, wherein the advisory layer determines an optimal set point or reference trajectory to reduce cost of energy;
determining battery off-peak charging level by the MPC;
providing a real-time layer coupled to the advisory layer with a real-time controller that guarantees a real-time second-by-second balance between supply and demand, subject to the optimal setpoint or trajectory generated by the advisory layer;
optimizing energy cost using forecasted renewable generation, load, time-of-use electricity price, battery depth of discharge, and battery power price;
maximizing battery lifetime and integrating with energy cost minimization, wherein the battery cell which has been operated for a certain period of time and experienced k discharge events, has an estimated lifetime, BL, as follows:
BL
=
L
R
D
R
C
R
∑
i
=
1
k
d
eff
(
i
)
τ
in which C R is rated amp-hour capacity at rated discharge current, D R is DoD for which rated cycle life was determined, L R is cycle life at rated DoD and rated discharge current, d eff (i) is the effective discharge (ampere-hours) for a particular discharge event i calculated as:
d
eff
(
i
)
=
(
DoD
(
i
)
D
R
)
x
1
ⅇ
x
2
(
DoD
(
i
)
D
R
-
1
)
C
R
C
A
d
act
(
i
)
where DoD(i), C A (i), and d act (i) are DoD, actual capacity of a battery, and measured discharge ampere-hours for the ith discharge event respectively, and coefficients X 1 and X 2 are calculated by applying a curve fitting procedure to cycle life versus DoD data;
transferring the battery's life time maximization into a power cost minimization problem such that energy cost and cost of battery usage is defined by:
J
:=
∑
t
=
0
T
C
G
(
t
)
P
G
(
t
)
+
C
B
(
P
B
(
t
)
,
DoD
(
t
)
)
P
B
(
t
)
in which T is optimization horizon, P G (t) is imported power from grid at time t, C G (t) is grid power price at time t that is extracted based on time-of-use grid electricity rates information, P B (t) is battery discharge power which is obtained from measured discharge ampere-hours at time t, and C B (P B (t), DoD(t) is the price of battery power that is a function of discharge power and its DoD at time t
that is subject to the following constraints including:
1) supply-demand balance defined by
P G D ( t )+ P B ( t )+ P renew D ( t )= D ( t )
where P G D (t) is the power generated by the grid and sent to a demand node at time t, P renew D (t) is the power from renewables at time t sent to the demand node, and D(t) is the demand at time t;
2) battery state of charge (SoC) difference defined by
soc ( t+ 1)= soc ( t )−α P B ( t )+α P G B ( t )+α P renew B ( t )
where soc(t) is battery SoC in ampere-hour (Ah) at time t, α is a coefficient which changes kW into Ah, P G B (t) is the power generated by the grid and stored in the battery at time t, and P renew B (t) is the power generated by renewables and stored in the battery at time t;
3) upper and lower bound for battery SoC which by considering the SoC difference is a dynamic inequality constraint defined by
soc min ≦soc ( t )≦ soc max
where soc min is a minimum state of charge for batteries and soc max is a maximum state of charge for batteries and soc(t) is state of charge at time t
4) all decision variables P G D (t),P G B (t),P renew D (t),P renew B (t),P B (t) are always greater than or equal to zero;
5) renewable inequality constraint which states that the summation of P renew D (t) and P renew B (t) is less than or equal to available renewable generation at each time (t) defined by
P renew D ( t )+ P renew B ( t )≦ P renew ( t )
in which P renew (t) is the available renewable power at time t and is obtained based on forecasted profile of renewable generations; and
6) peak shaving inequality constraint to guarantee that total extracted power from the grid at each time is less than a predetermined constant value P PSH defined by
P G D ( t )+ P G B ( t )≦ P PSH .
2. The method of claim 1 , comprising time-triggering the operation of the MPC.
3. The method of claim 1 , comprising event-triggering the operation of the MPC.
4. The method of claim 1 , wherein the advisory layer receives feedback from the real-time layer in a closed loop.
5. The method of claim 1 , wherein the real-time controller applies a battery ampere-hour cost model.
6. The method of claim 1 comprising sending optimal commands for the micro-grid to the real-time layer.
7. A method for multi-objective management of a storage device, comprising:
generating a battery power cost model;
generating an energy cost model;
controlling a charge or discharge of the battery storage device;
dispatching energy sources from a micro-grid to minimize a marginal cost of operation and maximize a storage unit lifetime over a time horizon;
utilizing a peak-shaving inequality constraint such that the total extracted power from the grid at each time is less than a predetermined constant value;
optimizing energy cost using forecasted renewable generation, load, time-of-use electricity price, battery depth of discharge, and battery power price;
maximizing battery lifetime and integrating with energy cost minimization, wherein a battery cell which has been operated for a certain period of time and experienced k discharge events, has an estimated lifetime, BL, as follows:
BL
=
L
R
D
R
C
R
∑
i
=
1
k
d
eff
(
i
)
τ
in which C R is rated amp-hour capacity at rated discharge current, D R is DoD for which rated cycle life was determined, L R is cycle life at rated DoD and rated discharge current, d eff (i) is the effective discharge (ampere-hours) for a particular discharge event i calculated as:
d
eff
(
i
)
=
(
DoD
(
i
)
D
R
)
x
1
ⅇ
x
2
(
DoD
(
i
)
D
R
-
1
)
C
R
C
A
d
act
(
i
)
where DoD(i), C A (i), and dact(i) are DoD, actual capacity of a battery, and measured discharge ampere-hours for the ith discharge event respectively, and coefficients X 1 and X 2 are calculated by applying a curve fitting procedure to cycle life versus DoD data and
transferring the battery's life time maximization into a power cost minimization problem such that energy cost and and cost of battery usage is defined by:
J
:=
∑
t
=
0
T
C
G
(
t
)
P
G
(
t
)
+
C
B
(
P
B
(
t
)
,
DoD
(
t
)
)
P
B
(
t
)
in which T is optimization horizon, P G (t) is imported power from grid at time t, C G (t) is grid power price at time t that is extracted based on time-of-use grid electricity rates information, P B (t) is battery discharge power which is obtained from measured discharge ampere-hours at time t, and C B (P B (t), DoD(t) is the price of battery power that is a function of discharge power and its DoD at time t
that is subject to the following constraints including:
1) supply-demand balance defined by
P G D ( t )+ P B ( t )+ P renew D ( t )= D ( t )
where P G D (t) is the power generated by the grid and sent to a demand node at time t, P renew D (t) is the power from renewables at time t sent to the demand node, and D(t) is the demand at time t;
2) battery state of charge (SoC) difference defined by
soc ( t+ 1)= soc ( t )−α P B ( t )+α P G B ( t )+α P renew B ( t )
where soc(t) is battery SoC in ampere-hour (Ah) at time t, and a is a coefficient which changes kW into Ah, P G B (t) is the power generated by the grid and stored in the battery at time t, and P renew B (t) is the power generated by renewables and stored in the battery at time t;
3) upper and lower bound for battery SoC which by considering the SoC difference is a dynamic inequality constraint defined by
soc min ≦soc ( t )≦ soc max
where soc min is a minimum state of charge for batteries and soc max is a maximum state of charge for batteries and soc(t) is state of charge at time t
4) all decision variables P G D (t),P G B (t),P renew D (t),P renew B (t),P B (t) are always greater than or equal to zero;
5) renewable inequality constraint which states that the summation of P renew D (t) and P renew B (t) is less than or equal to available renewable generation at each time (t) defined by
P renew D ( t )+ P renew B ( t )≦ P renew ( t )
in which P renew (t) is the available renewable power at time t and is obtained based on forecasted profile of renewable generations; and
6) peak shaving inequality constraint to guarantee that total extracted power from the grid at each time is less than a predetermined constant value P PSH defined by
P G D ( t )+ P G B ( t )≦ P PSH
8. The method of claim 7 , comprising performing peak shaving wherein an inequality constraint is added to restrict a total power extracted from the grid for both load supplying and battery charging at each time instance.
9. The method of claim 7 , comprising charging the battery at a constant level by considering an equality constraint in an optimization problem which lets a charging power to be either a constant level or zero.
10. The method of claim 7 , comprising determining a first objective function J 1 as a grid power cost over an optimization window as:
J
1
:=
∑
t
=
0
T
C
G
(
t
)
P
G
(
t
)
11. The method of claim 7 , comprising determining a second objective function J 2 as a grid power cost over an optimization window as:
J
2
:=
∑
t
=
0
T
C
B
(
P
B
(
t
)
,
DoD
(
t
)
)
P
B
(
t
)
12. A multi-objective energy management system, comprising:
a processor coupled to a micro-grid;
computer code for utilizing a peak-shaving inequality constraint such that the total extracted power from the grid at each time is less than a predetermined constant value;
computer code for optimizing energy cost using forecasted renewable generation, load, time-of-use electricity price, battery depth of discharge, and battery power price;
computer code for controlling a charge or discharge of a battery cell
computer code for maximizing battery lifetime and integrating with energy cost minimization, wherein the battery cell which has been operated for a certain period of time and experienced k discharge events, has an estimated lifetime, BL, as follows:
BL
=
L
R
D
R
C
R
∑
i
=
1
k
d
eff
(
i
)
τ
in which C R is rated amp-hour capacity at rated discharge current, D R is DoD for which rated cycle life was determined, L R is cycle life at rated DoD and rated discharge current, d eff (i) is the effective discharge (ampere-hours) for a particular discharge event i calculated as:
d
eff
(
i
)
=
(
DoD
(
i
)
D
R
)
x
1
ⅇ
x
2
(
DoD
(
i
)
D
R
-
1
)
C
R
C
A
d
act
(
i
)
where DoD(i), C A (i), and dact(i) are DoD, actual capacity of a battery, and measured discharge ampere-hours for the ith discharge event respectively, and coefficients X 1 and X 2 are calculated by applying a curve fitting procedure to cycle life versus DoD data;
a long term scheduler in an advisory layer with a Model Predictive Control (MPC); and
a real-time controller that guarantees a second-by-second balance between supply and demand, subject to one or more optimality constraints provided by the advisory layer; wherein
the battery's life time maximization is transferred into a power cost minimization problem such that energy cost and cost of battery usage is defined by:
J
:=
∑
t
=
0
T
C
G
(
t
)
P
G
(
t
)
+
C
B
(
P
B
(
t
)
,
DoD
(
t
)
)
P
B
(
t
)
in which T is optimization horizon, P G (t) is imported power from grid at time t, C G (t) is grid power price at time t that is extracted based on time-of-use grid electricity rates information, P B (t) is battery discharge power which is obtained from measured discharge ampere-hours at time t, and C B (P B (t), DoD(t)) is the price of battery power that is a function of discharge power and its DoD at time t
that is subject to the following constraints including:
1) supply-demand balance defined by
P G D ( t )+ P B ( t )+ P renew D ( t )= D ( t )
where P G D (t) is the power generated by the grid and sent to a demand node at time t, P renew D (t) is the power from renewables at time t sent to the demand node, and D(t) is the demand at time t;
2) battery state of charge (SoC) difference defined by
soc ( t+ 1)= soc ( t )−α P B ( t )+α P G B ( t )+α P renew B ( t )
where soc(t) is battery SoC in ampere-hour (Ah) at time t, and a is a coefficient which changes kW into Ah, P G B (t) is the power generated by the grid and stored in the battery at time t, and P renew B (t) is the power generated by renewables and stored in the battery at time t;
3) upper and lower bound for battery SoC which by considering the SoC difference is a dynamic inequality constraint defined by
soc min ≦soc ( t )≦ soc max
where soc min is a minimum state of charge for batteries and soc max is a maximum state of charge for batteries and soc(t) is state of charge at time t
4) all decision variables P G D (t),P G B (t),P renew D (t),P renew B (t),P B (t) are always greater than or equal to zero;
5) renewable inequality constraint which states that the summation of P renew D (t) and P renew B (t) is less than or equal to available renewable generation at each time (t) defined by
P renew D ( t )+ P renew B ( t )≦ P renew ( t )
in which P renew (t) is the available renewable power at time t and is obtained based on forecasted profile of renewable generations; and
6) peak shaving inequality constraint to guarantee that total extracted power from the grid at each time is less than a predetermined constant value P PSH defined by
P G D ( t )+ P G B ( t )≦ P PSH
13. An energy storage system with multi-objective management, comprising:
an energy storage system;
a computer to control the charging of the energy storage system, the computer executing:
computer code for generating a battery power cost model and an energy cost model;
computer code for controlling a charge or discharge of the battery storage device;
computer code for integrating an energy cost minimization and battery life maximization objective functions for optimizing a Model Predictive Control (MPC);
computer code for dispatching energy sources from a micro-grid to minimize a marginal cost of operation and maximize the storage unit lifetime;
computer code for utilizing a peak-shaving inequality constraint such that the total extracted power from the grid at each time is less than a predetermined constant value;
computer code for optimizing energy cost using forecasted renewable generation, load, time-of-use electricity price, battery depth of discharge, and battery power price; and
computer code for maximizing battery lifetime and integrating with energy cost minimization, wherein a battery cell which has been operated for a certain period of time and experienced k discharge events, has an estimated lifetime, BL, as follows:
BL
=
L
R
D
R
C
R
∑
i
=
1
k
d
eff
(
i
)
τ
in which C R is rated amp-hour capacity at rated discharge current, D R is DoD for which rated cycle life was determined, L R is cycle life at rated DoD and rated discharge current, d eff (i) is the effective discharge (ampere-hours) for a particular discharge event i calculated as:
d
eff
(
i
)
=
(
DoD
(
i
)
D
R
)
x
1
ⅇ
x
2
(
DoD
(
i
)
D
R
-
1
)
C
R
C
A
d
act
(
i
)
where DoD(i), C A (i), and dact(i) are DoD, actual capacity of a battery, and measured discharge ampere-hours for the ith discharge event respectively, and coefficients X 1 and X 2 are calculated by applying a curve fitting procedure to cycle life versus DoD data; and
computer code that transfers the battery's life time maximization into a power cost minimization problem such that energy cost and and cost of battery usage is defined by:
J
:=
∑
t
=
0
T
C
G
(
t
)
P
G
(
t
)
+
C
B
(
P
B
(
t
)
,
DoD
(
t
)
)
P
B
(
t
)
in which T is optimization horizon, P G (t) is imported power from grid at time t, C G (t) is grid power price at time t that is extracted based on time-of-use grid electricity rates information, P B (t) is battery discharge power which is obtained from measured discharge ampere-hours at time t, and C B (P B (t), DoD(t)) is the price of battery power that is a function of discharge power and its DoD at time t
that is subject to the following constraints including:
1) supply-demand balance defined by
P G D ( t )+ P B ( t )+ P renew D ( t )= D ( t )
where P G D (t) is the power generated by the grid and sent to a demand node at time t, P renew D (t) is the power from renewables at time t sent to the demand node, and D(t) is the demand at time t;
2) battery state of charge (SoC) difference defined by
soc ( t+ 1)= soc ( t )−α P B ( t )+α P G B ( t )+α P renew B ( t )
where soc(t) is battery SoC in ampere-hour (Ah) at time t, and a is a coefficient which changes kW into Ah, P G B (t) is the power generated by the grid and stored in the battery at time t, and P renew B (t) is the power generated by renewables and stored in the battery at time t;
3) upper and lower bound for battery SoC which by considering the SoC difference is a dynamic inequality constraint defined by
soc min ≦soc ( t )≦ soc max
where soc min is a minimum state of charge for batteries and soc max is a maximum state of charge for batteries and soc(t) is state of charge at time t
4) all decision variables P G D (t),P G B (t),P renew D (t),P renew B (t),P B (t) are always greater than or equal to zero;
5) renewable inequality constraint which states that the summation of P renew D (t) and P renew B (t) is less than or equal to available renewable generation at each time (t) defined by
P renew D ( t )+ P renew B ( t )≦ P renew ( t )
in which P renew (t) is the available renewable power at time t and is obtained based on forecasted profile of renewable generations; and
6) peak shaving inequality constraint to guarantee that total extracted power from the grid at each time is less than a predetermined constant value P PSH defined by
P G D ( t )+ P G B ( t )≦ P PSH
14. The system of claim 13 , comprising computer code for performing peak shaving wherein an inequality constraint is added to restrict a total power extracted from the grid for both load supplying and battery charging at each time instance.
15. The system of claim 13 , comprising computer code for charging the battery at a constant level by considering an equality constraint in an optimization problem which lets a charging power to be either a constant level or zero.
16. The system of claim 13 , comprising computer code for determining a first objective function Ji as a grid power cost over an optimization window as:
J
1
:=
∑
t
=
0
T
C
G
(
t
)
P
G
(
t
)
.
17. The method of claim 13 , comprising computer code for determining a second objective function J 2 as a grid power cost over an optimization window as:
J
2
:=
∑
t
=
0
T
C
B
(
P
B
(
t
)
,
DoD
(
t
)
)
P
B
(
t
)