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Online management genetic algorithms of microgrid for residential application
Energy Conversion and Management 64 (2012) 562–568
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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Online management genetic algorithms of microgrid for residential application Faisal A. Mohamed ⇑, Heikki N. Koivo Department of Electrical Engineering, Omar Al-Mukhtar University, P.O. Box 919, El-Bieda, Libya Department of Automation and Systems Technology, Aalto University, P.O. Box 15500, 00076 Aalto, Finland
a r t i c l e
i n f o
Article history: Received 6 February 2012 Accepted 9 June 2012 Available online 25 August 2012 Keywords: Microgrid Genetic algorithms Optimization Online management Economic power dispatch
a b s t r a c t This paper proposes a generalized formulation to determine the optimal operating strategy and cost optimization scheme for a MicroGrid (MG) for residential application. Genetic Algorithm is applied to the environmental/economic problem of the MG. The proposed problem is formulated as a nonlinear constrained MO optimization problem. Prior to the optimization of the microgrid itself, models for the system components are determined using real data. The proposed cost function takes into consideration the costs of the emissions, NOx, SO2, and CO2, start up costs, as well as the operation and maintenance costs. The MG considered in this paper consists of a wind turbine, a microturbine, a diesel generator, a photovoltaic array, a fuel cell, and a battery storage. The optimization is aimed at minimizing the cost function of the system while constraining it to meet the costumer demand and safety of the system. We also add a daily income and outgo from sale or purchased power. The results demonstrate the efficiency of the proposed approach to satisfy the load and to reduce the cost and the emissions. The comparison with other techniques demonstrates the superiority of the proposed approach and confirms its potential to solve the problem. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction The need for more flexible electric systems, changing regulatory and economic scenarios, energy savings and environmental impact are providing impetus to the development of MicroGrids (MGs), which are predicted to play an increasing role in the electric power system of the near future [1]. One of the important applications of the MG units, is the utilization of small-modular residential or commercial units for onsite service. The MG units can be chosen so that they satisfy the customer load demand at minimum cost all the time. Ramanathan and Gupta [2] define the strategy of power management in power system as when the system can be interacting with its environment by servicing requests. and dictates when to shutdown after the requests from the environment ceases to arrive. The arrival of these requests is online and the problem of determining when the system should shut itself down is an online problem. The management of the MG units require an accurate economic model to describe the operating cost taking into account the output power produced. Such a model is discrete and nonlinear
⇑ Corresponding author at: Department of Electrical Engineering, Omar Al-Mukhtar University, P.O. Box 919, El-Bieda, Libya. E-mail addresses: [email protected] (F.A. Mohamed), heikki.koivo@hut.fi (H.N. Koivo). 0196-8904/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.enconman.2012.06.010
in nature, hence optimization tools are needed to reduce the operating costs to a minimum level. Significant research has been conducted in the areas of MGs, which may assume many different sizes and forms. Some model architectures have been proposed in the literature [3]. Communication infrastructure operating between the power sources to solve the optimization problem for the fuel consumption has been proposed in [1], a rational method of building MGs optimized for cost and subject to reliability constraints has been presented in [4]. In [5] the problem of management of MG is solved without considering the balancing with the uppergrid and without considering the thermal load. The emission dispatching option is an attractive alternative in which both cost and emission is to be minimized. In recent years, this option has received much attention since it requires only small modification of the basic economic dispatch to include emission [6]. The algorithm in [7] is modified in this paper, the modification is to optimizes the MG choices to minimize the total operating cost by adding the daily cost of purchased fuel for residential load if the produced thermal power in the MG is not enough to meet the thermal load demand. In this paper we investigate six different scenarios, while in [7] only four scenarios were investigated with only the electrical power were calculated. Here the thermal power is also included in the results. The algorithm consists of determining at each iteration the optimal use of the natural resources available, such as wind speed,
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temperature, and irradiation as they are the inputs to wind turbine, and photovoltaic cell, respectively. If the produced power from the wind turbine and the photovoltaic cell is less than the load demand then the algorithm goes to the next stage which is the use of the other alternative sources according to the load and the objective function of each one. This paper assumes the MG is seeking to minimize total operating costs. MicroGrids could operate independently of the uppergrid, but they are usually assumed to be connected, through power electronics, to the uppergrid. The MG in this paper is assumed to be interconnected to the uppergird, and can purchase some power from utility providers when the production of the MG is insufficient to meet the load demand. There is a daily income to the MG when the generated power exceeds the load demand. The second objective of this paper deals with solving an optimization problem using several scenarios to explore the benefits of having optimal management of the MG. The exploration is based on the minimization of running costs and is extended to cover a load demand scenario in the MG. It will be shown that by developing a good system model, we can use optimization to solve the cost optimization problem accurately and efficiently. 2. A illustrative microgrid model The MG study architecture is shown in Fig. 1. It consists of a group of radial feeders, which could be part of a distribution system. There is a single point of connection to the utility called point of common coupling (PCC). The feeders 1 and 2 have sensitive and normal loads which should be supplied during the events. The
feeders also have the microsources consisting of a photovoltaic cell (PV), a wind turbine (WT), a fuel cell (FC), a microturbine (MT), a diesel generator (DG), and a battery storage. The third feeder has only traditional loads. The static switch (SD) is used to island the feeders 1 and 2 from the utility when events happened. The fuel input is needed only for the DG, FC, and MT as the fuel for the WT and PV comes from nature. To serve the load demand and charge the battery, electrical power can be produced either directly by PV, WT, DG, MT, or FC. Each component of the MG system is modeled separately based on its characteristics and constraints. The battery storage is required to meet the load demand for a period of time. A charger controller is required to limit the depth of discharge of the battery, to limit the charging current supplied to the battery, and to prevent overcharging, while making use of the power from the other microsources when it is available. Each of the local generation unit has a local controller (LC). This is responsible for local control that corresponds to a conventional controller (ex. automatic voltage regulator (AVR) or Governor) having a network communication function to exchange information between other LCs and the upper central controller to achieve an advanced control. The central controller also plays an important role as a load dispatch control center in bulk power systems, which is in charge of distributed generator operations installed in MG [8]. 3. Optimization model The power optimization model is shown in Fig. 2 highlighting the following points. The output is the optimal configuration of a MG that takes into account technical performance of supply
MicroGrid Central Controller
PCC
SD
Feeder 3
Feeder 2
Feeder 1
Load
LC
LC LC
Load
Load
Wind Turbine
Load
Diesel Engine
Load
LC
LC Fuel Cell
Charger Controller LC
Load
Micro Turbine
Battery
Fig. 1. MicroGrid architecture.
Load
Heat load
Load
Load
PV array
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Fig. 2. Power optimization model structure.
options, locally available energy resources, demand characteristics, and system reliability. To use the model, the following have to be defined: The power demand by the load. Locally available energy information: This includes solar irradiation data (W/m2), temperature (°C), wind speed (m/s), as well as cost of fuels ($/l) for the DG and natural gas price for supplying the FC and MT ($/kW h). Daily purchased and sold power tariffs in ($/kW h). Start-up costs in ($/h). Technical and economic performance of supply options: These characteristics include, for example, rated power for PV, power curve for WT, fuel consumption characteristics DG and FC. Operating and maintenance costs and the total emission: Operating and maintenance costs must be given ($/h) for DG, FC, and MT. Emission level must be given in kg/h for DG, FC, and MT. 4. Proposed objective function The major concern in the design of an electrical system that utilizes MG sources is the accurate selection of output power that economically satisfy the load demand, while taken into account the environmental externality costs by minimizing the emissions of oxides of nitrogen (NOx), sulfur oxides (SO2), and carbon oxides (CO2). The objective function is developed according to the above mentioned assumptions to minimize the operating cost of the MG in the following form[9]: N X CFðPÞ ¼ ðC i F i ðPi Þ þ OMðPi Þ þ STC i þ DCPEi þ DCPGi IPSEi
of emission type k, EFik the emission factor of generating unit i and emission type k, N the number of generating units i, M the Emission types (NOx or CO2 or SO2), DCPEi the daily cost of purchased electricity if the load demand exceeds the generated power in $/h, DCPGi the daily cost of purchased gas for residential application if the produced thermal power in the MG is not enough to meet the thermal load demand in $/h, IPSEi is the daily income for sold electricity if the output generated power exceeds the load demand in $/ h. The solution of the optimization procedure produces the optimal decision variables:
fPi ¼ PFC i ; Pj ¼ P MT j ; Pk ¼ P DGk : j ¼ N þ 1; . . . ; N2 ;
þ
ak ðEF ij P i Þ
T off ;i STC i ¼ ri þ di 1 exp
si
i¼1 k¼1
where Ci is the fuel costs of generating unit i, Fi(Pi) the fuel consumption rate of generator unit i, OMi(Pi) the operation and maintenance cost of generating unit i, Pi the decision variables, representing the power output from generating unit i, P the decision variable vector, STCi the start-up cost in $/h, ak the externality costs
ð2Þ
ri is the hot start-up cost, di the cold start-up cost, si the unit cooling time constant and Toff,i is the time a unit has been off. The operating and maintenance costs OM are assumed to be proportional with the produced energy, where the proportionally constant is K OMi for unit i. OM ¼
ð1Þ
k ¼ N2 þ 1; . . . ; Ng:
where P FC i is the output power of fuel cell i [kW],i = 1, . . . , N1, PMT j the output power of microturbine j [kW],j = N + 1, . . . , N2, P DGk is the Output power of diesel generator k [kW], k = N2 + 1, . . . , N. The generator start up cost depends on the time the unit has been off prior to the start up. The start up cost for unit i in any given time interval can be represented by an exponential cost curve:
i¼1 N X M X
i ¼ 1; . . . ; N 1 ;
N X K OMi P i
ð3Þ
i¼1
The values of K OMi for different generation units are as follows [10]: where
K OM ðDEÞ ¼ 0:01258 $=kW h K OM ðFCÞ ¼ 0:00419 $=kW h K OM ðMTÞ ¼ 0:00587 $=kW h:
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ð4Þ
IPSE ¼ C s maxðP i PL ; 0Þ
where Cp and Cs are the tariffs of the purchased and sold power respectively in ($/kW h), and PL is the load demand. The thermal output power depends on the electrical power, and can be described by a nonlinear equation [11]. The daily cost of the purchased fuel for residential applications when the produced thermal power is not enough to meet the thermal load demand is given by:
DCPG ¼ cF maxðLth Pi ; 0Þ
ð6Þ
i¼1
where PL is the total power demanded in kW, PPV the output power of the photovoltaic cell in kW, PWT the output power of the wind turbine in kW, Pbatt the output power of the battery storage kW. Generation capacity constraints: For stable operation, real power output of each generator Pi is restricted by lower and upper limits as follows:
i ¼ 1; . . . ; N
ð7Þ P max i
where is the minimum operating power of unit i, is the maximum operating power of unit i. Each generating unit has a minimum up/ down time limit (MUT/MDT) time limits. Once the generating unit is switched on, it has to operate continuously for a certain minimum time before it is switched off again. On the other hand, a certain stop time has to be terminated before starting the unit. The violation of such constraints can cause shortness in the life time of the unit. These constraints are formulated as continuous run/stop time constraint as follows [9]:
ð8Þ
on Time t 1 T off t1;i =T t1;i denotes unit i off/on time, while ut1,i denotes the unit off/on [0, 1] status. The number of starts and stops (estart–stop) should not exceed a certain number (Nmax).
estart—stop 6 Nmax
Emission factors for FC (lb/MW h)
Emission factors for MT (lb/MW h)
NOx SO2 CO2
4.2 0.99 0.014
21.8 0.454 1.432
0.03 0.006 1.078
0.44 0.008 1.596
MICROTURBINE
0.06 0.04 0.02
0
5
10
15
20
15
20
15
20
FUEL CELL
0.2 0.1 0
0
5
10 DIESEL GENERATOR
6 4 2
0
5
10
Iteration
N X Pi PL þ ðPPV þ PWT þ Pbatt Þ ¼ 0
T on t1;i MUT i ðut1;i ut;i Þ P 0 T off t1;i MDT i ðut1;i ut;i Þ P 0
Emission factors for DE (lb/MW h)
Cost [$/h]
Power balance constraints: To meet the active power balance, an equality constraint is imposed
P min i
Externality costs ($/lb)
ð5Þ
4.1. Objective constraints
Pmin 6 Pi 6 Pmax ; i i
Emission type
Cost [$/h]
DCPE ¼ C p maxðPL Pi ; 0Þ
Table 1 Externality costs and emission factors for NOx, SO2, and CO2.
Cost [$/h]
As shown in Fig. 1, the main utility balances the difference between the load demand and the generated output power from microsources. Therefore there is a cost to be paid for the purchased power whenever the generated power is insufficient to cover the load demand. On the other hand, there is income because of sold power when the power generated is higher than the load demand but the price of the sold power is lower than the purchased power tariff. It is possible that there will be no sold power at all. Therefore, to model the purchased and sold power, two different conditions are considered. The following equations define these conditions [11]:
ð9Þ
Externality costs and emission factors of the DG, FC, and MT used in this paper are stated in [12], and summarized in Table 1. In order to explore the minimum costs of the DG, FC, and MT, we used the well known golden search technique which is an elegant and robust method of locating a minimum for all the three cost functions individually as shown in Fig. 3.
Fig. 3. Minimization of the MT, FC, and DG costs.
5. Implementation of the algorithm When designing MGs, several goals could be set, including reduction in emissions and generation cost. To achieve this, it is important to highlight all factors influencing the main goal.The key characteristics of the implemented strategy is summarized in the following items: Power output of a WT is calculated according to the relation between the wind speed and the output power. Power output of a PV is calculated according to the effect of the temperature and the solar radiation that are different from the standard test condition. There will be income whenever the power from the wind and PV are greater than the load. Since the WT and PV deliver free cost power (in terms of running as well the emission free), the output power is treated as a negative load, so the load which is the difference between the actual and microsource output can be determined if the output from the PV and WT is smaller than the load demand. The power from the battery is needed whenever the PV and the WT are insufficient to serve the load, meanwhile the charge and discharge of the battery are monitored. Calculate the net load. Choose serving the load by other sources (FC or MT or DG) according to the objective functions. If the output power is not sufficient then purchase power from the main gird, and if the output power is more than the load demand, sell the exceed power to the main grid 6. Genetic algorithms Genetic algorithms are probabilistic search algorithm. They combine solution evaluation with randomized, structured exchanges of information between solutions to obtain optimal solution.
7. Results and discussion The optimization model described in the previous section is applied to a load demand at different electricity and fuel prices. The available power from the PV and the wind generators were used first. The inputs to the wind turbine model and the model of the photovoltaic were measured data. The load demand is served with the battery storage and at the same time the SOC is monitored and in the end of the simulation the battery should be charged. From the results obtained we can see that the battery capacity was not large enough to supply the load for the period of time. The charged values of the battery power are added to the power demand. Then the algorithm calculates the needed power to charge the battery and serve the load. To evaluate the effect of varying the tariffs on the optimal settings, some comparisons are given in Figs. 4 and 5 for load curve. One tariff is changed each time, while the other is held constant. Fig. 4 shows the effect of varying the sold tariff US $ 0.0/kW h in first case and 0.1/kW h in second case, while purchased tariff is kept constant at $ 0.16/kW h. Varying varying the purchased tariff is illustrated in Fig. 5, where US $ 0.12/kW h in first case and 0.18/kW h in second case, while sold tariff is kept constant at $ 0.04/kW h.
Thermal power (kW)
15 10 5 0
0
5
10
15
20
10
15
20
15 10 5 0
0
5
Time [h] ____ load demand
....... 0.0$/kWh
−−o−−o 0.1$/kWh
Fig. 4. Effect of sold power tariffs on the MG optimal operation.
Thermal power (kW) Electrical power (kW)
Genetic algorithms are considered to be robust methods because no restrictions on the solution space are made during the process. The power of this algorithm comes from its ability to exploit historical information structures from previous solution guesses in an attempt to increase performance of future solution structures. GAS evaluate encodings of the original parameters instead of the actual parameters. The parameter set is reduced to a series of representative symbols from an arbitrary yet effective alphabet and solutions are evaluated based on certain symbol structures. GAS maintain a population of solution structures throughout the process, therefore they are not limited by the selection of initial single point solution guesses. In this way the entire solution space may be considered and multiple solutions detected. GAS incorporate probabilistic transition rules rather than simple deterministic rules. The programmer only has to define the objective function and the encoding technique. The GA is implemented in this paper to define the optimal settings by minimizing the cost function (1) subjected to the given constraints (6)–(9), were Population Size = 20 Crossover Fraction = 0.8 Generations = 100. The operation cost model of the MG is discrete and comprises many constraints. In case of tightly constrained problems, the infeasible solutions are known to cover the search space at the initial generations. Complete avoidance of infeasible solutions in this case leads to a high possibility of missing the area of global minimum. Also, moving the infeasible individuals to the nearest feasible area would be too complex and an extremely timeconsuming process. Therefore, a penalty function approach is applied to convert the constrained problem to an unconstrained one by augmenting additional cost terms with the main cost function. The additional terms assign nonlinear costs for solutions that do not satisfy constraints depending on their location relative to the feasibility boundary. The adequate choice of the penalty functions and their parameters is an essential factor in the evolution process. A higher additional cost value has to be assigned to any infeasible solution to ensure the rejection of all individuals that violate the constraints. Exponential penalty factors are used for ramp rate violation, while quadratic ones are applied when violating either minimum up/down time limits or maximum number of daily start–stop times constraints. This choice of penalty functions is found to achieve fast rejection of the infeasible members.
Electrical power (kW)
F.A. Mohamed, H.N. Koivo / Energy Conversion and Management 64 (2012) 562–568
15 10 5 0
0
5
10
15
20
0
5
10
15
20
15 10 5 0
Time [h] ___ load demand ......... 0.12 $/kWh
..o...o 0.18$/kWh
Fig. 5. Effect of purchased power tariffs on the MG optimal operation.
Thermal power (kW) Electrical power (kW)
566
15 10 5 0
0
5
10
15
20
0
5
10
15
20
15 10 5 0
Time [h] ___ Load demand ...... 0.02$/kWh −o−o−o 0.05 $/kWh Fig. 6. Effect of fuel tariffs for thermal residential applications on the MG optimal operation.
Fig. 6 illustrate the effect of the fuel tariff for thermal residential applications on the MG optimal operation, with two cases applied US $ 0.025/kW h in first case and 0.05/kW h in second case.
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F.A. Mohamed, H.N. Koivo / Energy Conversion and Management 64 (2012) 562–568 Table 2 Total optimal generation and total cost of the MG.
Case Case Case Case Case Case
1 2 3 4 5 6
PE (kW/day)
PT (kW/Day)
Cp ($/kW h)
Cs ($/kW h)
CF ($/kW h)
Th. Opt. Gen (kW/D)
El-Opt. Gen (kW/D)
329.9725 329.9725 329.9725 329.9725 329.9725 329.9725
508.9320 508.9320 508.9320 508.9320 508.9320 508.9320
0.16 0.16 0.12 0.18 0.16 0.16
0.0 0.1 0.04 0.04 0.04 0.04
0.05 0.05 0.05 0.05 0.02 0.05
536.9814 572.0691 574.300 568.3191 568.700 571.0927
364.1601 359.1087 360.0957 366.1765 368.4700 359.0400
Table 3 Cost savings and average difference with respect to optimal case.
Case A Case B Case C SQP GA
Average cost
Average difference with respect to the optimal case
Cost $/Day
Cost $/Day
Cost%
23,400 2760 633 2630 2610
20,790 150 1977 20 00.0000
796.5500% 5.7500% 75.7500% 0.7700% 00.0000
Table 2 summarizes the six cases applied. In the first two cases the changes in the sold tariffs, when the purchase and fuel tariffs are kept constant. It is noticeable from the table and the figure with the 0.1$/kW h tariff that the optimal setting is generate the required electrical power in the MG itself and sale the extra power to the main grid. In the third and fourth cases we change the purchase tariffs and keep the two other tariffs constants, finally in the tow last cases the fuel tariffs were changed, in all cases there is a power sold back to the main grid. From the results we can see there is a reduction in the total cost per day comparing to the results obtained in [7]. To investigate the effective of the optimal setting we applied in the reduction of the total daily operating cost. The results of optimization process is applied to the MG, are compared with three convectional settings. The first case is to operate the MG units always as their rated power. The second and third cases are to follow up the electrical or thermal load demands respectively. Table 3 presents a direct comparison of the outcomes achieved by the different cases. The results obtained using our proposed technique to minimize the total cost are compared with the different strategies of settings. The result obtained for Case A shows how uneconomical it is to let the generators work at their rated power for the whole day. In the second case, the cost is reduced somewhat, but still high. In Case C, the cost decreased compared to Case B and the optimal choice is to purchase more power from the main grid. For achieving the completeness and checking the effectiveness of the proposed cost function and proposed solution, the problem is solved with Sequential Quadratic Programming (SQP), With the proposed GA method, the total operating cost is 2610 $/day. It can be noticed that the GA is more capable of handling the optimization problem of the MG when the problem becomes more complex. Furthermore, the proposed technique produces better results in reducing the operating cost compared with SQP. The proposed approach is general in that multiple fuels, multiple pollutants and a highly nonlinear cost function can be dealt with. The effectiveness of the approach has been demonstrated throughout different scenarios. The total electrical output power from the three microsources together for GA is similar in the three last cases. However, the contributions from individual units vary depending on the load,
the operating tariffs and the operating cost of each one. In some cases, one or two units are not used. In other cases, one or two units are used only for short periods, particularly at peak-load time. Switching on one or two units increases the total operating cost as a result of the start-up costs. In addition, the utilization of the three units in parallel results in operating the units at lower efficiencies compared to a single unit since they generate a higher percentage of power based on their ratings. The result from GA reflects the high accuracy of finding the minimum and ensures the high capability of the GA to extract the features of the optimal performance. The GA outputs show good performance to meet the load demand, which demonstrates the capability of the GA and the effectiveness of the presented approach. It is expected that including more constraints, such as the starting costs leads to a significant increase in the operating cost. 8. Conclusion This paper has presented the GA approach to solve the problem of electric power dispatch optimization of MG. A model to determine the optimum operation of a MG with respect to load demand and environmental requirement is constructed and presented. The optimization problem includes a variety of energy sources that are likely to be found in a MG: a fuel cell, a diesel engines, a microturbine, PV arrays, and wind generators. Constraint functions added to the optimization problem to reflect some of the additional consideration are often found in a small-scale generation system. From the results obtained, it is clear that from the optimal power curves for the MG that the optimization works in good manner and assigns optimal power to the generators after taking into account the cost function for each of them. These results reflect the success of the GA to capture the optimal behavior of the MG with high accuracy even with new six different cases. The responses are effected by several variables including weather conditions, emissions operation and maintenance costs and, of course, the actual power demand. References [1] Hernandez-Aramburo CA, Green TC, Mugniot N. Fuel consumption minimization of a microgrid. IEEE Trans Ind Appl 2005;41(3):673–81. [2] Ramanathan D, Gupta R. System level online power management algorithms. In: Proc design, automation, test Eur; March 2000. p. 606–11. [3] Lasseter R. MicroGrids. IEEE power engineering society winter meeting, New York, NY; 2002. p. 305–8. [4] Patra Shashi B, Mitra Joydeep, Ranade Satish J. Microgrid architecture: a reliability constraind approach. IPower engineering society general meeting. IEEE,12-16, vol. 3; June 2005. p. 2372–7. [5] wMohamed F, Koivo H. System modelling and online optimal management of MicroGrid with battery storage. In: 6th International conference on renewable energies and power quality (ICREPQ’07), Sevilla, Spain, 26–28 March; 2007. [6] Basu M. Dynamic economic emission dispatch using nondominated sorting genetic algorithm-II. SIAM Electr Power Energy Syst 2008;30(2):140–9. [7] Mohamed Faisal A, Koivo Heikki. Solving economic power dispatch problem of microgrid using genetic algorithms for residential application. In: Proceedings of the international renewable energy congress – IREC 2011, Hammamet, Tunisia: CMERP; 2011. p. 102–7.
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[8] Zoka Y, Sasaki H, Yorino N, Kawahara K, Liu CC. An interaction problem of distributed generators installed in a MicroGrid. In: Proceedings of IEEE on electric utility deregulation, restructuring and power technologies conference, Hong Kong, vol. 1; April 2004. p. 795–9. [9] Mohamed Faisal A, Koivo Heikki. System modelling and online optimal management of microgrid using mesh adaptive direct search. Int J Electr Power Energy Syst 2010;32(5):398–407.
[10] Hggmark S, Neimane V, Axelsson U, Holmberg P, Karlsson G. Kauhaniemi K et al. Aspects of different distributed generation technologies CODGUNet WP 3. Vattenfall Utveckling Ab 2003-03-14; 2003. [11] Azmy AM, Erlich I. Online optimal management of PEM fuel cells using neural networks. IEEE Trans Power Deliv 2005;29(2):1051–8. [12] The Regulatory Assistance ProjectEmission rates for new DG technologies; May 2001..
Contents lists available at SciVerse ScienceDirect
Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Online management genetic algorithms of microgrid for residential application Faisal A. Mohamed ⇑, Heikki N. Koivo Department of Electrical Engineering, Omar Al-Mukhtar University, P.O. Box 919, El-Bieda, Libya Department of Automation and Systems Technology, Aalto University, P.O. Box 15500, 00076 Aalto, Finland
a r t i c l e
i n f o
Article history: Received 6 February 2012 Accepted 9 June 2012 Available online 25 August 2012 Keywords: Microgrid Genetic algorithms Optimization Online management Economic power dispatch
a b s t r a c t This paper proposes a generalized formulation to determine the optimal operating strategy and cost optimization scheme for a MicroGrid (MG) for residential application. Genetic Algorithm is applied to the environmental/economic problem of the MG. The proposed problem is formulated as a nonlinear constrained MO optimization problem. Prior to the optimization of the microgrid itself, models for the system components are determined using real data. The proposed cost function takes into consideration the costs of the emissions, NOx, SO2, and CO2, start up costs, as well as the operation and maintenance costs. The MG considered in this paper consists of a wind turbine, a microturbine, a diesel generator, a photovoltaic array, a fuel cell, and a battery storage. The optimization is aimed at minimizing the cost function of the system while constraining it to meet the costumer demand and safety of the system. We also add a daily income and outgo from sale or purchased power. The results demonstrate the efficiency of the proposed approach to satisfy the load and to reduce the cost and the emissions. The comparison with other techniques demonstrates the superiority of the proposed approach and confirms its potential to solve the problem. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction The need for more flexible electric systems, changing regulatory and economic scenarios, energy savings and environmental impact are providing impetus to the development of MicroGrids (MGs), which are predicted to play an increasing role in the electric power system of the near future [1]. One of the important applications of the MG units, is the utilization of small-modular residential or commercial units for onsite service. The MG units can be chosen so that they satisfy the customer load demand at minimum cost all the time. Ramanathan and Gupta [2] define the strategy of power management in power system as when the system can be interacting with its environment by servicing requests. and dictates when to shutdown after the requests from the environment ceases to arrive. The arrival of these requests is online and the problem of determining when the system should shut itself down is an online problem. The management of the MG units require an accurate economic model to describe the operating cost taking into account the output power produced. Such a model is discrete and nonlinear
⇑ Corresponding author at: Department of Electrical Engineering, Omar Al-Mukhtar University, P.O. Box 919, El-Bieda, Libya. E-mail addresses: [email protected] (F.A. Mohamed), heikki.koivo@hut.fi (H.N. Koivo). 0196-8904/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.enconman.2012.06.010
in nature, hence optimization tools are needed to reduce the operating costs to a minimum level. Significant research has been conducted in the areas of MGs, which may assume many different sizes and forms. Some model architectures have been proposed in the literature [3]. Communication infrastructure operating between the power sources to solve the optimization problem for the fuel consumption has been proposed in [1], a rational method of building MGs optimized for cost and subject to reliability constraints has been presented in [4]. In [5] the problem of management of MG is solved without considering the balancing with the uppergrid and without considering the thermal load. The emission dispatching option is an attractive alternative in which both cost and emission is to be minimized. In recent years, this option has received much attention since it requires only small modification of the basic economic dispatch to include emission [6]. The algorithm in [7] is modified in this paper, the modification is to optimizes the MG choices to minimize the total operating cost by adding the daily cost of purchased fuel for residential load if the produced thermal power in the MG is not enough to meet the thermal load demand. In this paper we investigate six different scenarios, while in [7] only four scenarios were investigated with only the electrical power were calculated. Here the thermal power is also included in the results. The algorithm consists of determining at each iteration the optimal use of the natural resources available, such as wind speed,
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temperature, and irradiation as they are the inputs to wind turbine, and photovoltaic cell, respectively. If the produced power from the wind turbine and the photovoltaic cell is less than the load demand then the algorithm goes to the next stage which is the use of the other alternative sources according to the load and the objective function of each one. This paper assumes the MG is seeking to minimize total operating costs. MicroGrids could operate independently of the uppergrid, but they are usually assumed to be connected, through power electronics, to the uppergrid. The MG in this paper is assumed to be interconnected to the uppergird, and can purchase some power from utility providers when the production of the MG is insufficient to meet the load demand. There is a daily income to the MG when the generated power exceeds the load demand. The second objective of this paper deals with solving an optimization problem using several scenarios to explore the benefits of having optimal management of the MG. The exploration is based on the minimization of running costs and is extended to cover a load demand scenario in the MG. It will be shown that by developing a good system model, we can use optimization to solve the cost optimization problem accurately and efficiently. 2. A illustrative microgrid model The MG study architecture is shown in Fig. 1. It consists of a group of radial feeders, which could be part of a distribution system. There is a single point of connection to the utility called point of common coupling (PCC). The feeders 1 and 2 have sensitive and normal loads which should be supplied during the events. The
feeders also have the microsources consisting of a photovoltaic cell (PV), a wind turbine (WT), a fuel cell (FC), a microturbine (MT), a diesel generator (DG), and a battery storage. The third feeder has only traditional loads. The static switch (SD) is used to island the feeders 1 and 2 from the utility when events happened. The fuel input is needed only for the DG, FC, and MT as the fuel for the WT and PV comes from nature. To serve the load demand and charge the battery, electrical power can be produced either directly by PV, WT, DG, MT, or FC. Each component of the MG system is modeled separately based on its characteristics and constraints. The battery storage is required to meet the load demand for a period of time. A charger controller is required to limit the depth of discharge of the battery, to limit the charging current supplied to the battery, and to prevent overcharging, while making use of the power from the other microsources when it is available. Each of the local generation unit has a local controller (LC). This is responsible for local control that corresponds to a conventional controller (ex. automatic voltage regulator (AVR) or Governor) having a network communication function to exchange information between other LCs and the upper central controller to achieve an advanced control. The central controller also plays an important role as a load dispatch control center in bulk power systems, which is in charge of distributed generator operations installed in MG [8]. 3. Optimization model The power optimization model is shown in Fig. 2 highlighting the following points. The output is the optimal configuration of a MG that takes into account technical performance of supply
MicroGrid Central Controller
PCC
SD
Feeder 3
Feeder 2
Feeder 1
Load
LC
LC LC
Load
Load
Wind Turbine
Load
Diesel Engine
Load
LC
LC Fuel Cell
Charger Controller LC
Load
Micro Turbine
Battery
Fig. 1. MicroGrid architecture.
Load
Heat load
Load
Load
PV array
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Fig. 2. Power optimization model structure.
options, locally available energy resources, demand characteristics, and system reliability. To use the model, the following have to be defined: The power demand by the load. Locally available energy information: This includes solar irradiation data (W/m2), temperature (°C), wind speed (m/s), as well as cost of fuels ($/l) for the DG and natural gas price for supplying the FC and MT ($/kW h). Daily purchased and sold power tariffs in ($/kW h). Start-up costs in ($/h). Technical and economic performance of supply options: These characteristics include, for example, rated power for PV, power curve for WT, fuel consumption characteristics DG and FC. Operating and maintenance costs and the total emission: Operating and maintenance costs must be given ($/h) for DG, FC, and MT. Emission level must be given in kg/h for DG, FC, and MT. 4. Proposed objective function The major concern in the design of an electrical system that utilizes MG sources is the accurate selection of output power that economically satisfy the load demand, while taken into account the environmental externality costs by minimizing the emissions of oxides of nitrogen (NOx), sulfur oxides (SO2), and carbon oxides (CO2). The objective function is developed according to the above mentioned assumptions to minimize the operating cost of the MG in the following form[9]: N X CFðPÞ ¼ ðC i F i ðPi Þ þ OMðPi Þ þ STC i þ DCPEi þ DCPGi IPSEi
of emission type k, EFik the emission factor of generating unit i and emission type k, N the number of generating units i, M the Emission types (NOx or CO2 or SO2), DCPEi the daily cost of purchased electricity if the load demand exceeds the generated power in $/h, DCPGi the daily cost of purchased gas for residential application if the produced thermal power in the MG is not enough to meet the thermal load demand in $/h, IPSEi is the daily income for sold electricity if the output generated power exceeds the load demand in $/ h. The solution of the optimization procedure produces the optimal decision variables:
fPi ¼ PFC i ; Pj ¼ P MT j ; Pk ¼ P DGk : j ¼ N þ 1; . . . ; N2 ;
þ
ak ðEF ij P i Þ
T off ;i STC i ¼ ri þ di 1 exp
si
i¼1 k¼1
where Ci is the fuel costs of generating unit i, Fi(Pi) the fuel consumption rate of generator unit i, OMi(Pi) the operation and maintenance cost of generating unit i, Pi the decision variables, representing the power output from generating unit i, P the decision variable vector, STCi the start-up cost in $/h, ak the externality costs
ð2Þ
ri is the hot start-up cost, di the cold start-up cost, si the unit cooling time constant and Toff,i is the time a unit has been off. The operating and maintenance costs OM are assumed to be proportional with the produced energy, where the proportionally constant is K OMi for unit i. OM ¼
ð1Þ
k ¼ N2 þ 1; . . . ; Ng:
where P FC i is the output power of fuel cell i [kW],i = 1, . . . , N1, PMT j the output power of microturbine j [kW],j = N + 1, . . . , N2, P DGk is the Output power of diesel generator k [kW], k = N2 + 1, . . . , N. The generator start up cost depends on the time the unit has been off prior to the start up. The start up cost for unit i in any given time interval can be represented by an exponential cost curve:
i¼1 N X M X
i ¼ 1; . . . ; N 1 ;
N X K OMi P i
ð3Þ
i¼1
The values of K OMi for different generation units are as follows [10]: where
K OM ðDEÞ ¼ 0:01258 $=kW h K OM ðFCÞ ¼ 0:00419 $=kW h K OM ðMTÞ ¼ 0:00587 $=kW h:
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ð4Þ
IPSE ¼ C s maxðP i PL ; 0Þ
where Cp and Cs are the tariffs of the purchased and sold power respectively in ($/kW h), and PL is the load demand. The thermal output power depends on the electrical power, and can be described by a nonlinear equation [11]. The daily cost of the purchased fuel for residential applications when the produced thermal power is not enough to meet the thermal load demand is given by:
DCPG ¼ cF maxðLth Pi ; 0Þ
ð6Þ
i¼1
where PL is the total power demanded in kW, PPV the output power of the photovoltaic cell in kW, PWT the output power of the wind turbine in kW, Pbatt the output power of the battery storage kW. Generation capacity constraints: For stable operation, real power output of each generator Pi is restricted by lower and upper limits as follows:
i ¼ 1; . . . ; N
ð7Þ P max i
where is the minimum operating power of unit i, is the maximum operating power of unit i. Each generating unit has a minimum up/ down time limit (MUT/MDT) time limits. Once the generating unit is switched on, it has to operate continuously for a certain minimum time before it is switched off again. On the other hand, a certain stop time has to be terminated before starting the unit. The violation of such constraints can cause shortness in the life time of the unit. These constraints are formulated as continuous run/stop time constraint as follows [9]:
ð8Þ
on Time t 1 T off t1;i =T t1;i denotes unit i off/on time, while ut1,i denotes the unit off/on [0, 1] status. The number of starts and stops (estart–stop) should not exceed a certain number (Nmax).
estart—stop 6 Nmax
Emission factors for FC (lb/MW h)
Emission factors for MT (lb/MW h)
NOx SO2 CO2
4.2 0.99 0.014
21.8 0.454 1.432
0.03 0.006 1.078
0.44 0.008 1.596
MICROTURBINE
0.06 0.04 0.02
0
5
10
15
20
15
20
15
20
FUEL CELL
0.2 0.1 0
0
5
10 DIESEL GENERATOR
6 4 2
0
5
10
Iteration
N X Pi PL þ ðPPV þ PWT þ Pbatt Þ ¼ 0
T on t1;i MUT i ðut1;i ut;i Þ P 0 T off t1;i MDT i ðut1;i ut;i Þ P 0
Emission factors for DE (lb/MW h)
Cost [$/h]
Power balance constraints: To meet the active power balance, an equality constraint is imposed
P min i
Externality costs ($/lb)
ð5Þ
4.1. Objective constraints
Pmin 6 Pi 6 Pmax ; i i
Emission type
Cost [$/h]
DCPE ¼ C p maxðPL Pi ; 0Þ
Table 1 Externality costs and emission factors for NOx, SO2, and CO2.
Cost [$/h]
As shown in Fig. 1, the main utility balances the difference between the load demand and the generated output power from microsources. Therefore there is a cost to be paid for the purchased power whenever the generated power is insufficient to cover the load demand. On the other hand, there is income because of sold power when the power generated is higher than the load demand but the price of the sold power is lower than the purchased power tariff. It is possible that there will be no sold power at all. Therefore, to model the purchased and sold power, two different conditions are considered. The following equations define these conditions [11]:
ð9Þ
Externality costs and emission factors of the DG, FC, and MT used in this paper are stated in [12], and summarized in Table 1. In order to explore the minimum costs of the DG, FC, and MT, we used the well known golden search technique which is an elegant and robust method of locating a minimum for all the three cost functions individually as shown in Fig. 3.
Fig. 3. Minimization of the MT, FC, and DG costs.
5. Implementation of the algorithm When designing MGs, several goals could be set, including reduction in emissions and generation cost. To achieve this, it is important to highlight all factors influencing the main goal.The key characteristics of the implemented strategy is summarized in the following items: Power output of a WT is calculated according to the relation between the wind speed and the output power. Power output of a PV is calculated according to the effect of the temperature and the solar radiation that are different from the standard test condition. There will be income whenever the power from the wind and PV are greater than the load. Since the WT and PV deliver free cost power (in terms of running as well the emission free), the output power is treated as a negative load, so the load which is the difference between the actual and microsource output can be determined if the output from the PV and WT is smaller than the load demand. The power from the battery is needed whenever the PV and the WT are insufficient to serve the load, meanwhile the charge and discharge of the battery are monitored. Calculate the net load. Choose serving the load by other sources (FC or MT or DG) according to the objective functions. If the output power is not sufficient then purchase power from the main gird, and if the output power is more than the load demand, sell the exceed power to the main grid 6. Genetic algorithms Genetic algorithms are probabilistic search algorithm. They combine solution evaluation with randomized, structured exchanges of information between solutions to obtain optimal solution.
7. Results and discussion The optimization model described in the previous section is applied to a load demand at different electricity and fuel prices. The available power from the PV and the wind generators were used first. The inputs to the wind turbine model and the model of the photovoltaic were measured data. The load demand is served with the battery storage and at the same time the SOC is monitored and in the end of the simulation the battery should be charged. From the results obtained we can see that the battery capacity was not large enough to supply the load for the period of time. The charged values of the battery power are added to the power demand. Then the algorithm calculates the needed power to charge the battery and serve the load. To evaluate the effect of varying the tariffs on the optimal settings, some comparisons are given in Figs. 4 and 5 for load curve. One tariff is changed each time, while the other is held constant. Fig. 4 shows the effect of varying the sold tariff US $ 0.0/kW h in first case and 0.1/kW h in second case, while purchased tariff is kept constant at $ 0.16/kW h. Varying varying the purchased tariff is illustrated in Fig. 5, where US $ 0.12/kW h in first case and 0.18/kW h in second case, while sold tariff is kept constant at $ 0.04/kW h.
Thermal power (kW)
15 10 5 0
0
5
10
15
20
10
15
20
15 10 5 0
0
5
Time [h] ____ load demand
....... 0.0$/kWh
−−o−−o 0.1$/kWh
Fig. 4. Effect of sold power tariffs on the MG optimal operation.
Thermal power (kW) Electrical power (kW)
Genetic algorithms are considered to be robust methods because no restrictions on the solution space are made during the process. The power of this algorithm comes from its ability to exploit historical information structures from previous solution guesses in an attempt to increase performance of future solution structures. GAS evaluate encodings of the original parameters instead of the actual parameters. The parameter set is reduced to a series of representative symbols from an arbitrary yet effective alphabet and solutions are evaluated based on certain symbol structures. GAS maintain a population of solution structures throughout the process, therefore they are not limited by the selection of initial single point solution guesses. In this way the entire solution space may be considered and multiple solutions detected. GAS incorporate probabilistic transition rules rather than simple deterministic rules. The programmer only has to define the objective function and the encoding technique. The GA is implemented in this paper to define the optimal settings by minimizing the cost function (1) subjected to the given constraints (6)–(9), were Population Size = 20 Crossover Fraction = 0.8 Generations = 100. The operation cost model of the MG is discrete and comprises many constraints. In case of tightly constrained problems, the infeasible solutions are known to cover the search space at the initial generations. Complete avoidance of infeasible solutions in this case leads to a high possibility of missing the area of global minimum. Also, moving the infeasible individuals to the nearest feasible area would be too complex and an extremely timeconsuming process. Therefore, a penalty function approach is applied to convert the constrained problem to an unconstrained one by augmenting additional cost terms with the main cost function. The additional terms assign nonlinear costs for solutions that do not satisfy constraints depending on their location relative to the feasibility boundary. The adequate choice of the penalty functions and their parameters is an essential factor in the evolution process. A higher additional cost value has to be assigned to any infeasible solution to ensure the rejection of all individuals that violate the constraints. Exponential penalty factors are used for ramp rate violation, while quadratic ones are applied when violating either minimum up/down time limits or maximum number of daily start–stop times constraints. This choice of penalty functions is found to achieve fast rejection of the infeasible members.
Electrical power (kW)
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15 10 5 0
0
5
10
15
20
0
5
10
15
20
15 10 5 0
Time [h] ___ load demand ......... 0.12 $/kWh
..o...o 0.18$/kWh
Fig. 5. Effect of purchased power tariffs on the MG optimal operation.
Thermal power (kW) Electrical power (kW)
566
15 10 5 0
0
5
10
15
20
0
5
10
15
20
15 10 5 0
Time [h] ___ Load demand ...... 0.02$/kWh −o−o−o 0.05 $/kWh Fig. 6. Effect of fuel tariffs for thermal residential applications on the MG optimal operation.
Fig. 6 illustrate the effect of the fuel tariff for thermal residential applications on the MG optimal operation, with two cases applied US $ 0.025/kW h in first case and 0.05/kW h in second case.
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Case Case Case Case Case Case
1 2 3 4 5 6
PE (kW/day)
PT (kW/Day)
Cp ($/kW h)
Cs ($/kW h)
CF ($/kW h)
Th. Opt. Gen (kW/D)
El-Opt. Gen (kW/D)
329.9725 329.9725 329.9725 329.9725 329.9725 329.9725
508.9320 508.9320 508.9320 508.9320 508.9320 508.9320
0.16 0.16 0.12 0.18 0.16 0.16
0.0 0.1 0.04 0.04 0.04 0.04
0.05 0.05 0.05 0.05 0.02 0.05
536.9814 572.0691 574.300 568.3191 568.700 571.0927
364.1601 359.1087 360.0957 366.1765 368.4700 359.0400
Table 3 Cost savings and average difference with respect to optimal case.
Case A Case B Case C SQP GA
Average cost
Average difference with respect to the optimal case
Cost $/Day
Cost $/Day
Cost%
23,400 2760 633 2630 2610
20,790 150 1977 20 00.0000
796.5500% 5.7500% 75.7500% 0.7700% 00.0000
Table 2 summarizes the six cases applied. In the first two cases the changes in the sold tariffs, when the purchase and fuel tariffs are kept constant. It is noticeable from the table and the figure with the 0.1$/kW h tariff that the optimal setting is generate the required electrical power in the MG itself and sale the extra power to the main grid. In the third and fourth cases we change the purchase tariffs and keep the two other tariffs constants, finally in the tow last cases the fuel tariffs were changed, in all cases there is a power sold back to the main grid. From the results we can see there is a reduction in the total cost per day comparing to the results obtained in [7]. To investigate the effective of the optimal setting we applied in the reduction of the total daily operating cost. The results of optimization process is applied to the MG, are compared with three convectional settings. The first case is to operate the MG units always as their rated power. The second and third cases are to follow up the electrical or thermal load demands respectively. Table 3 presents a direct comparison of the outcomes achieved by the different cases. The results obtained using our proposed technique to minimize the total cost are compared with the different strategies of settings. The result obtained for Case A shows how uneconomical it is to let the generators work at their rated power for the whole day. In the second case, the cost is reduced somewhat, but still high. In Case C, the cost decreased compared to Case B and the optimal choice is to purchase more power from the main grid. For achieving the completeness and checking the effectiveness of the proposed cost function and proposed solution, the problem is solved with Sequential Quadratic Programming (SQP), With the proposed GA method, the total operating cost is 2610 $/day. It can be noticed that the GA is more capable of handling the optimization problem of the MG when the problem becomes more complex. Furthermore, the proposed technique produces better results in reducing the operating cost compared with SQP. The proposed approach is general in that multiple fuels, multiple pollutants and a highly nonlinear cost function can be dealt with. The effectiveness of the approach has been demonstrated throughout different scenarios. The total electrical output power from the three microsources together for GA is similar in the three last cases. However, the contributions from individual units vary depending on the load,
the operating tariffs and the operating cost of each one. In some cases, one or two units are not used. In other cases, one or two units are used only for short periods, particularly at peak-load time. Switching on one or two units increases the total operating cost as a result of the start-up costs. In addition, the utilization of the three units in parallel results in operating the units at lower efficiencies compared to a single unit since they generate a higher percentage of power based on their ratings. The result from GA reflects the high accuracy of finding the minimum and ensures the high capability of the GA to extract the features of the optimal performance. The GA outputs show good performance to meet the load demand, which demonstrates the capability of the GA and the effectiveness of the presented approach. It is expected that including more constraints, such as the starting costs leads to a significant increase in the operating cost. 8. Conclusion This paper has presented the GA approach to solve the problem of electric power dispatch optimization of MG. A model to determine the optimum operation of a MG with respect to load demand and environmental requirement is constructed and presented. The optimization problem includes a variety of energy sources that are likely to be found in a MG: a fuel cell, a diesel engines, a microturbine, PV arrays, and wind generators. Constraint functions added to the optimization problem to reflect some of the additional consideration are often found in a small-scale generation system. From the results obtained, it is clear that from the optimal power curves for the MG that the optimization works in good manner and assigns optimal power to the generators after taking into account the cost function for each of them. These results reflect the success of the GA to capture the optimal behavior of the MG with high accuracy even with new six different cases. The responses are effected by several variables including weather conditions, emissions operation and maintenance costs and, of course, the actual power demand. References [1] Hernandez-Aramburo CA, Green TC, Mugniot N. Fuel consumption minimization of a microgrid. IEEE Trans Ind Appl 2005;41(3):673–81. [2] Ramanathan D, Gupta R. System level online power management algorithms. In: Proc design, automation, test Eur; March 2000. p. 606–11. [3] Lasseter R. MicroGrids. IEEE power engineering society winter meeting, New York, NY; 2002. p. 305–8. [4] Patra Shashi B, Mitra Joydeep, Ranade Satish J. Microgrid architecture: a reliability constraind approach. IPower engineering society general meeting. IEEE,12-16, vol. 3; June 2005. p. 2372–7. [5] wMohamed F, Koivo H. System modelling and online optimal management of MicroGrid with battery storage. In: 6th International conference on renewable energies and power quality (ICREPQ’07), Sevilla, Spain, 26–28 March; 2007. [6] Basu M. Dynamic economic emission dispatch using nondominated sorting genetic algorithm-II. SIAM Electr Power Energy Syst 2008;30(2):140–9. [7] Mohamed Faisal A, Koivo Heikki. Solving economic power dispatch problem of microgrid using genetic algorithms for residential application. In: Proceedings of the international renewable energy congress – IREC 2011, Hammamet, Tunisia: CMERP; 2011. p. 102–7.
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