Optimization in Energy and Power Management for. Renewable-Diesel Microgrids Using Dynamic. Programming Algorithm. Tu A. Nguyen and Mariesa L. Crow, ...
Proceedings of the 2012 IEEE International Conference on Cyber Technology in Automation, Control and Intelligent Systems May 27-31, 2012, Bangkok, Thailand
Optimization in Energy and Power Management for Renewable-Diesel Microgrids Using Dynamic Programming Algorithm Tu A. Nguyen and Mariesa L. Crow, IEEE Fellow Department of Electrical and Computer Engineering Missouri University of Science and Technology, Rolla, MO 65409, USA II. M ICROGRID SYSTEM DESCRIPTION
Abstract—This paper presents an optimization analysis for energy and power management in microgrids with renewable energy resources and diesel generators. Dynamic Programming (DP) algorithm and the simplex method have been used to minimize the total daily cost of the system and also maximize the total efficiency of the energy storage system during charge and discharge. The algorithm is validated on a hybrid system for military forward operating base camps that contain a PV array, wind generator, hydrogen-based fuel cell, batteries and diesel generators. Index Terms—microgrid, renewable energy, energy storage, power management, energy management, optimization, dynamic programming.
I. I NTRODUCTION Microgrids with integrated renewable resources and energy storage devices are emerging as a solution for reducing the dependency on conventional fossil fuel for power supply in military forward operating base (FOB) camps. These camps mainly using electric power from a local (and possibly unreliable) utility or from the camp’s diesel generators [1], [2]. For soldier safety and well-being, it is often desired to minimize the amount of diesel used during periods of unrest, thereby necessitating the efficient use of renewable resources and energy storage. The distributed microgrid systems designed for FOBs, are required to work continuously, efficiently and economically, dispatching the available resources to meet the power needs in daily normal operation while ensuring the constraints on energy reserve level and power limits of the system and for each component equipment are not violated. The constraints can be defined by the reserve requirement for emergency operation when diesel is not available; or by the lowest/highest state of charge (SOC) of the energy storage units to maximize cycle life. Considering these constraints, the optimal scheduling of resources cannot be determined separately in each time period, but must be optimized over the whole multi-cycle period. In this paper, a dynamic programming approach is proposed and implemented in MATLAB for minimizing the daily cost of the microgrid system and maximizing the efficiency of the energy storage devices to meet all constraints. The solution for the problem can be used to analyze the past data or to schedule the future operations of a given microgrid based on forecast data.
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Fig. 1.
Schematic diagram of a microgrid system for a FOB
Fig. 1 shows an example of a microgrid system for a FOB which had been proposed in a previous effort [2], [1]. The system’s components can be categorized in different groups based on their functionality: • • • • • •
Conventional generation: diesel generators Renewable generation: PV array, wind turbine Energy storage: electrolyzer/fuel cells, batteries Electrical distribution system: 48 VDC bus, 120/240 VAC bus Power conversion: MPPT controllers, charge controllers, DC/DC converters, Bi-directional inverter AC load: light tower, air conditioner
The microgrid is designed with two main buses including a 48 VDC bus and 120 (or 240) VAC connected through a bi-directional inverter. The renewable energy resources and energy storage units are connected to the DC side while the diesel generator and AC load are connected to AC side. Bidirectional flow between DC and AC side will allow power supply to the load from the DC side or to charge the storage units from the AC side when needed. The system can be connected to utility grid, coupled to other microgrids at the AC bus, or be scaled to increase the FOB’s capacity by adding multiple devices.
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III. F ORMULATION OF THE OPTIMIZATION PROBLEM FOR MICROGRID POWER AND ENERGY AND POWER
min C1 =
MANAGEMENT
A. Optimization problem definition
=
m N 1 k=1 i=1 m N 1
⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨
k=1
In this project, the microgrid power and energy management is defined as the problem of finding an optimum loading pattern for each generation unit and a discharge/charge pattern for each storage unit in each time period of a day in order to meet a given load. The objectives of the optimization are:
max C2 =
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩
i=1 m 2 j=1
Fdgi (Pdgi,k ) Cdgi Hdgi (Pdgi,k )T Pesj,k
m 2
Pesj,k d j=1 ηesj (Pesj,k ) m 2 c Pesj,k ηesj (Pesj,k ) j=1 m 2 j=1
• •
C1: Minimize the total cost (or total fuel consumption) of any one day cycle C2: Maximize the total discharging/charging efficiency of energy storage in each time period of the day
•
• • • • • •
R1: The system should continuously meet the FOB’s load R2: There should always be sufficient reserve energy storage capacity to satisfy critical loads for a specified duration without additional diesel refueling R3: Each storage device should not be charged (or discharged) beyond the maximum (or minimum) SOC R4: The charge (or discharge) rate for each storage device should not exceed the maximum (or minimum) rates R5: One storage device cannot be discharged to charge another storage device R6: Each diesel generator should serve rated load when online R7: Once a generator is brought online, it should remain online for a minimum set time R8: When a generator is powered off, it should remain off a minimum time before it can be restarted
R1 : R2 :
• • • • • •
if discharging (3) if charging
Pesj,k
m1 i=1 m2
Pdgi,k +
m2
Pesj,k = Pload,k − PP V,k − PW T,k
j=1
SOCesj,k .M XCesj ≥ Eresv
j=1 min max R3 : SOCesj ≤ SOCesj,k ≤ SOCesj min,d max,d ≤ Pesj,k ≤ Pesj if esj is disharging Pesj R4 : min,c max,c Pesj ≤ Pesj,k ≤ Pesj if esj is charging
For simplicity, the following assumptions are made: •
(2)
where • N is the number of time periods in one day cycle; T is duration of each time period; • m1 and m2 are the number of diesel generators and the number of storage units respectively; • Fdgi , Hdgi and Cdgi are correspondingly the operating cost function, fuel consumption function, and fuel price for diesel generator i; • Pdgi,k and Pesj,k are the dispatched powers for diesel generator i and storage unit j in time period k; d c • ηesj and ηesj are respectively the discharging and charging efficiency of storage unit j. The above-mentioned constraints can be expressed as:
The following constraints are considered: •
(1)
R5 : ∀Pesj ≥ 0 or ∀Pesj ≤ 0
A1: Daily load, solar and wind profiles are known A2: Solar and wind energy are free and treated as negative loads A3: Energy storage units operate at no cost A4: Charging power for storage units is treated as negative generation A5: The Discharging/charging rate of energy storage units are controllable A6: The output power of the diesel generators are controllable A7: Distribution system losses are neglected
min max ≤ Pdgi,k ≤ Pdgi R6 : Pdgi up up,min ≥ Tdgi if dgi is up Tdgi,k R7 : dw,min dw Tdgi,k ≥ Tdgi if dgi is down
in which • Pload,k is the demand in period k; P P V,k and PW T,k are total power outputs of PV arrays and wind turbines in period k; • SOCesj,k , is the state of charge of storage unit j in period k; M XCesj is the maximum capacity of storage unit j; Eresv is the energy reserve requirement for storage; min max • SOCesj and SOCesj are respectively the highest and lowest state of charge recommended for storage unit j; min,d/c max,d/c • Pesj and Pesj are the discharging/charging limits of storage unit j; min min • Pdgi and Pdgi are power output limits of diesel generator i;
B. Optimization problem formulation With the above definitions and assumptions, the objective functions can be formulated [3], [4]:
12
up/dw
Tdgi,k is the up/down time of diesel generator i until up/dw,min is the minimum up/down time for period k; Tdgi diesel generator i.
3) Electrolyzer: Hydrogen mass flow of an electrolyzer can be found from input power:
C. Fuel consumption and efficiency of diesel generators and energy storage units
The efficiency ηez (in %) of the electrolyzer is calculated [6]:
•
Qez =
ηf c =
As seen in (1), (2) and (3), fuel consumption and efficiency of diesel generators and energy storage units are needed as inputs to set up the objective functions for the optimization problem. In this paper, fuel consumption and efficiency of diesel generators, hydrogen-based fuel cells, electrolyzer and batteries are characterized. 1) Diesel generators: Fuel consumption of a diesel generator can be modeled as a linear function of output power [5]: rated Hdg (Pdg ) = Bdg Pdg + Adg Pdg
ηdg
(4)
Hf c (Pf c ) =
Bf c Pfrated ⎪ c ⎪ ⎪ ⎩
+Af c Pf c (1 + Kf c if Pf c ≤
ef Pmax
Crated
(10)
(11) (12)
and pc =
ln(T2 ) − ln(T1 ) ln(I1 ) − ln(I2 )
(13)
where I1 and I2 are discharge currents corresponding to discharge time T 1 and T2 , which are provided from manufacturer’s data.
ef Pf c −Pmax ) Pfrated c
IV. DYNAMIC PROGRAMMING ALGORITHM FOR FOB MICROGRIDS
A. Forward dynamic programming algorithm Dynamic programming (DP) is the method to determine the best set of decisions to identify the optimal route to the destination by breaking it down to a sequence of steps over time; at each step the DP finds the set of possible optimum sequences (routes) based on the possible optimum subsequences in the previous steps and finally find the optimum sequence at the last step. The main advantage of DP is it reduces the dimension of the problem by its ability to maintain the solution’s feasibility. For this reason, DP is used in this research to solve the optimization problem for microgrid where energy management and power balance can be considered simultaneously. A DP algorithm can be set up to run backward from the final to the initial stage or to run forward from the initial to the last stage as shown in Fig. 2. In the case of a microgrid, the forward DP is more suitable for several reasons [9]:
The efficiency ηf c (in %) of fuel cells is specifed as [6]: 100Pf c Hf c LHVH2
Cp
Cp = I pc T = constant pc
Crated = Trated Trated
(6)
ηf c =
(9)
where I is discharge current (in A); C rated is the rated capacity (in Ahr) given by the manufacturers at a certain discharge time Trated (in hr); pc is Peukert’s coefficient; Cp is Peukert’s capacity. In (10), Cp and pc are specified by Peukert’s law [8]:
(5)
+Af c Pf c ef if Pf c ≤ Pmax
100Qez HHVH2 Pez
ηbat = 100I (1−pc)
where LHVgas is the lower heating value of the fuel (in kW h/gal), which for diesel is LHVdg = 43.75kW h/gal. 2) Fuel cells: Hydrogen consumption of fuel cells is characterized [6]: ⎧ Bf c Pfrated ⎪ c ⎪ ⎪ ⎨
(8)
are respectively mass flow and rated where Qez and Qrated ez mass flow (in kg/h); Pez is the electrical input power (in kW ); Aez and Bez are the cofficients of consumption curve (in kW h/kg); HHVH2 = 39.4kW h/kg is the higher heating value of hydrogen. 4) Batteries: For this work, the charging and discharging efficiency (in %) of a battery are assumed equal and can be estimated [7]:
rated in which Hdg is the fuel consumption (in [gal/hr]); P dg and Pdg are respectively rated power and output power of the diesel generator (in kW ); A dg and Bdg are the cofficients of consumption curve (in gal/kW h) and can be determined experimentally. The efficiency ηdg (in %) of the diesel generator is calculated based on fuel consumption function [6]:
100Pdg = Hdg LHVgas
Pez − Bez Qrated ez Aez
(7)
with LHVH2 = 33.3kW h/kg. and In (6), Hf c is hydrogen consumption (in kg/hr); P frated c Pf c are respectively rated power and output power of the fuel cells (in kW ); Af c and Bf c are the cofficients of consumption curve (in kg/kW h) which are given by manufacturers or ef determined experimentally; P max is the output power at which the fuel cells operate at highest efficiency and K f c is the factor representing the high hydrogen consumption due to high ef output power above P max .
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Fig. 2.
Path search in forward DP algorithm
The initial stage is provided or easily specified. The schedule for each unit’s operation can be calculated at each stage. • The computations can go forward in time as far as required. The algorithm to compute the minimum cost to state I i in stage K is [9]: • •
C(K, Ii ) = min[F (K, Ii ) + S(K − 1, Lj → K, Ii ) {L}
+ C(K − 1, Lj )]
(14) Fig. 3.
Forward DP algorithm flow chart
where {L} is the set of feasible states in stage K −1; C(K, I i ) is the least cost to arrive at state (K, Ii ); F (K, Ii ) is the operating cost for state (K, I i ) and S(K − 1, Lj → K, Ii ) is the transition cost from state (K − 1, L j ) to state (K, Ii ). One challenge in this case is the large amount of state combination that need investigation. For an N -unit system, there are 2N −1 combinations at each period and for M periods the total number of combinations is (2 N − 1)M . However, not all of the states are valid due to the constraints in the system. By applying (14) at each period, only the optimum routes which lead to the valid states are considered. In this paper, the full enumeration forward DP algorithm (Fig. 3) is applied [9]. B. Implementation of DP in MATLAB The implementation of the forward DP has been performed in MATLAB as shown in Fig. 4. The main modules of the program are described: 1) Determine valid states: In each period, constraints R2, R3, R5 and R7 are used to find the feasible units (including diesel generators and storage discharge and charge units) which can be ON in that period. A valid state is a combination of feasible units which satisfy the following condition: P min ≤ Pload,k − PP V,k − PW T,k ≤ P max (15)
Fig. 4.
Matlab program flow chart
is used to solve for the optimum dispatch for each diesel unit and the total dispatched load for all storage. The second dispatch problem is set up to find the optimal discharging/charging pattern for each storage unit. It uses objective function C2, constraints R4 and a new constraint of total load for storage found in the first problem. The problem is solved by the priority list method. 3) Find lowest-cost subroutes: The lowest-cost subroutes are found by (14). In this paper, the transition costs between states are assumed to be zero.
2) Determine economic dispatch and cost: For each valid state identified, an economic dispatch is performed. The first dispatch problem is set up using objective function C1 (for one period) and constraints R1, R2 and R6. The simplex method
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4) Update SOC for storage units: SOC of storage unit esj in period k is updated as follows: ⎧ ⎨ SOCesj,k−1 − d Pesj,k T if discharging ηesj MXCesj c SOCesj,k = Pesj,k ηesj T ⎩ SOCesj,k−1 − if charging MXCesj
7
5
Power (kW)
(16) C. Results
4
3
The data of the microgrid system in section II are given in Table I to Table V including all coefficients, physical limits and initial conditions which are needed to specify the objective functions C1 and C2 and constraints from R1 to R7. The 24hour PV, wind power and load profile are given in Fig. 5 and Fig. 6. The results for the optimization problem are shown in Fig. 7 and Fig. 8.
2
1
0
TABLE I D IESEL GENERATOR DATA DG #
1
max Pdg kW 8
Initial state hr 2
up,min Tdg hr 1
dw,min Tdg hr 1
F uel cost $ 4
Hydrogen tank Batteries
F uel cells Batteries
min,d Pes kW 0.1 0.01
Initial SOC % 60 50
max,d Pes kW 1.2 5
12
Time of day (hr)
16
20
24
Output power of PV array and wind turbine
6
min SOCes % 30 50
4
2
0
TABLE III E NERGY STORAGE DISCHARGE DATA ES unit
8
Pload Pload−Ppv−Pwt
8
Power (kW)
M ax capacity kW h 24 12.4
4
10
TABLE II E NERGY STORAGE DATA ES unit
0
Fig. 5.
min Pdg kW 0.1
1 DG #
Ppv Pwt Ppv+Pwt
6
−2
−4
P riority
0
4
8
2nd 1st
12
Time of day (hr)
Fig. 6.
16
20
24
Load profile
TABLE IV E NERGY STORAGE CHARGE DATA
Electrolyzer Batteries
min,d Pes kW −2 −5
max,d Pes kW −1 −0.01
P riority 2nd 1st
Power (kW)
ES unit
Power (kW)
Power (kW)
Power (kW)
From the solution, the daily period can be analyzed in three main periods: • Period 1 is from 12 am to 7 am when output power from the renewable resources are lower than the load. The batteries cannot discharge any further during this period since the SOC is at the minimum limit. The fuel cells stops discharging at 1 am to maintain the capacity of the storage above the required reserve level. Therefore, the diesel generator is turned ON to balance the system. • Period 2 is from 7 am to 3 pm when the renewable resource capability is higher than the load. From 7 am to 10 am the excess power is mainly used to charge the batteries due to its higher priority in charging. From 10 am, the electrolyzer is charged at its maximum rate.
8 6 4 2 0
Pdg
0 2
15
8
12
16
20
24 Pfc−ez
−2 0 4
4
8
12
16
20
24 Pbat
2 0 −2 0 1
4
8
12
16
20
24 Mismatch
0.5 0 0
Fig. 7.
4
0
4
8
12 Time of day (hr)
16
20
24
Power dispatch for diesel generator and storage units
TABLE V C OEFFICIENTS FOR CONSUMPTION AND EFFICIENCY CURVES Diesel generator Adg Bdg Af c gal/kW h gal/kW h kg/kW h 0.065 0.0215 0.05 Electrolyzer Aez Bez Qrated ez kW h/kg kW h/kg kg/h 50 30 0.0237
F uel cells Bf c Kf c kg/kW h − 0.004 1 Batteries Crated Trated Ah hr 258 24
SOC (%)
ef Pmax kW 0.24
VI. ACKNOWLEDGMENTS
pc − 1.1
The authors gratefully acknowledge the financial support of this project from the Leonard Wood Institute under subcontracts LWI-191-060 and LWI-400-041. R EFERENCES
Hydrogen tank
60 50
[1] X. Qiu, T. Nguyen, M. L. Crow, A. C. Elmore, and B. McMillin, “Computer models for microgrid applications,” in Proc. IEEE Power and Energy Society General Meeting, 2011, pp. 1–8. [2] T. A. Nguyen, X. Qiu, T. T. Gamage, M. L. Crow, B. M. McMillin, and A. C. Elmore, “Microgrid application with computer models and power management integrated using pscad/emtdc,” in Proc. North American Power Symp. (NAPS), 2011, pp. 1–7. [3] L. Xiaoping, D. Ming, H. Jianghong, H. Pingping, and P. Yali, “Dynamic economic dispatch for microgrids including battery energy storage,” in Proc. 2nd IEEE Int Power Electronics for Distributed Generation Systems (PEDG) Symp, 2010, pp. 914–917. [4] E. Alvarez, J. Gomez-Aleixandre, N. de Abajo, and A. Campos Lopez, “Algorithm for microgrid on-line central dispatch of electrical power and heat,” in Universities Power Engineering Conference (UPEC), 2009 Proceedings of the 44th International, sept. 2009, pp. 1 –5. [5] O. Skarstein and K. Ulhen, “Design considerations with respect to longterm diesel saving in wind/diesel plants,” Wind Engineering, vol. 13(2), pp. 72–87, 1989. [6] R. Dufo-Lopez and J. L. Bernal-Agustin, “Multi-objective design of pv-wind-diesel-hydrogen-battery systems,” Renewable Energy, vol. 33, no. 12, pp. 2559 – 2572, 2008. [7] “Battery Types and Battery Efficiency.” [Online]. Available: http://www.bdbatteries.com/peukert.php [8] D. Doerffel and S. A. Sharkh, “A critical review of using the peukert equation for determining the remaining capacity of lead-acid and lithiumion batteries,” Journal of Power Sources, vol. 155, no. 2, pp. 395 – 400, 2006. [9] B. F. W. Allen J. Wood, Power Generation, Operation, and Control. John Wiley & Sons INC., 1996, vol. 2nd.
40 30 20
0
4
8
12
16
20
100
SOC (%)
Future work in the area will include the generalization of assumptions upon which this study was performed, specifically that the insolation and wind speed profiles are known in advance.
24 Batteries
80 60 40 20
Capacity (kWh)
0 30
4
8
12
16
20
24
Total capacity
25 20 15 10
0
Fig. 8.
4
8
12 Time of day (hr)
16
20
24
SOC of storage units and total capacity
However, the mismatch during these hours, as seen in the fourth graph of Fig. 7, shows that some excess power from renewable is wasted. • Period 3 is from 3 pm to 12 am when the renewable resources are low again. During this period the energy storage can only discharge in the period from 3 pm to 4 pm since the reserve level is close to the lower limit. This analysis shows that some of the renewable energy is wasted during peak sun hours while the storage system can only discharge for a short period of time since the reserve required level is too high compared to total capacity of the energy storage. By adding more energy storage capacity or coupling the system to other microgrids, the problem can be solved. V. C ONCLUSIONS AND F UTURE W ORK In this paper, an optimization in energy and power management for FOB microgrids has been developed and solved using dynamic programming. The algorithm is implemented in MATLAB and used to investigate a proposed microgrid for FOB with PV array, wind generator, hydrogen-based fuel cell, batteries and diesel generator. The solution and analysis are given for an one-day period with varying load and renewable energy. The specified size of the energy storage units are too small to take full advantage of the renewable energy resources given the constraint that reserve capacity must be carried at all times. To better utilize the system, the reserve capacity constraint must either be relaxed or the size of the energy storage units must be increased.
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