MICROGRID ECONOMIC DISPATCH WITH STORAGE SYSTEMS BY PARTICLE SWARM OPTIMIZATION Sidney Cerqueira∗, Osvaldo Saavedra∗, Shigeaki Lima∗ ∗
Universidade Federal do Maranh˜ ao-UFMA Av. dos Portugueses s/n S˜ ao Lu´ıs, Maranh˜ ao, Brasil
Emails:
[email protected],
[email protected],
[email protected] Abstract— This paper presents the economic dispatch in a microgrid operating connected to main grid. This problem has nonlinear functions with equality and inequality constraints as well be dynamic and time dependent. The objective function takes into account the operation and maintenance costs of generators, state of charge (SOC) constraints for batteries, and includes wind and photovoltaic generation. The PSO algorithm is used to solve the problem to minimize the total system cost. Computer simulations are performed to show the effectiveness of proposed methodology and impacts of price and storage system on economic dispatch. Keywords—
Energy Storage, Microgrids, Economic Dispatch, PSO
Resumo— Este artigo apresenta o despacho econˆ omico de uma microrrede operando conectada ` a rede. Este problema possui fun¸co ˜es n˜ ao-lineares com restri¸co ˜es de igualdade e desigualdade, sendo dinˆ amico e dependente do tempo. A fun¸ca ˜o objetivo leva em conta os custos de opera¸ca ˜o e manuten¸ca ˜o dos geradores, restri¸ca ˜o dos estado de carga das baterias e inclui gera¸ca ˜o fotovoltaica e e´ olica. O algoritmo PSO foi utilizado para resolver o problema de minimizar o custo total do sistema. Simula¸co ˜es computacionais s˜ ao realizadas para mostrar a eficiˆ encia da metodologia proposta e a influˆ encia do pre¸co e sistema de armazenamento no despacho econˆ omico. Palavras-chave—
1
Sistema de armazenamento, Microrredes, Despacho Econˆ omico, PSO.
Introduction
The Electric Power Systems (EPS) has undergone significant changes over the last few years, for both: operational and organizational structure. These changes combined with the tendency for efficient production with less environmental impact, route us in search of new alternative sources for electricity generation. Some of these alternatives are the wind turbines and solar panels that has no pollution in the production of electricity. One effect of the deregulated environment of EPS, is the gradual introduction of Distributed Generation (DG). This allows a generation more decentralized, i.e. the generation close to the loads. The implementation of distributed generation has some benefits, such as: reduction of transmission and distribution power losses, reliability and security, among others. This creates new concepts that, associated with the increased use of renewable energy sources, introduces the idea of microgrids (Hatziargyriou, 2013). The microgrids are defined as part of distribution system and the basic structure has distributed energy resources, storage devices and flexible loads. These systems can operate connected to the main grid or isolated mode (Islanding mode) (de Souza Ribeiro et al., 2011). This concept of microgrids is a platform for integration of microgeneration, demand and storage units, that has some megawatts in a low-voltage system, to meeting a local load, and it can be seen as a part of a SmartGrid when added smart meters, data acquisition and communication system
between its components (Hatziargyriou, 2013). There are policies to encourage the implementation of microgrids, due to the benefits derived from these, such as low CO2 emission, increase reliability, low cost of implementation, diversification of power generation sources and power losses reduction. Other microgrids benefits can be found at (Hatziargyriou et al., 2009). The economic dispatch (ED) is an essential problem of short-term operation, and aims to determine the microgrid best optimal operation point at lowest cost. This problem is divided in two main types. A first one consider static, which solution is found for each period of time, and there’s no connection to others different periods. The other one is dynamic, which every decision made in a certain period of time, can influence future decisions, making time-dependent problem. In microgrid system, we need to add renewable energy resources, that due to their intermittent nature, are considered non-dispatchable , and thus, its production has priority to meet the demand. In the literature, some proposals can be found to solve Economic Dispatch problem. In (Logenthiran and Srinivasan, 2009), the authors proposed an efficient method based on three steps for microgrids optimal economic dispatch, considering unit commitment constraints into the objective function. In (Modiri-Delshad et al., 2013), the authors introduced a iterated-based algorithm to solve a microgrid economic dispatch without considering the losses, and compared with the solver CPLX. However they do not considered renewable energy sources and energy storage system in
this study. A multiobjective optimal generators allocation was proposed in (Meiqin et al., 2010), where the customer outage cost, emission pollution and production cost was considered into objective function. The solution technique is a hybrid algorithm using fuzzy system and particle swarm optimization. In the microgrid formulation proposed by (Mohamed and Koivo, 2010) its take in a count objective function consider operation, start-up and emissions cost into the formulation, and for the solution technique, was use the algorithm Mesh Adaptive Direct Search. Applications of multiagent systems in microgrids operation and control can be found in (Dimeas and Hatziargyriou, 2005), (Logenthiran et al., 2011). In this paper is proposed the solution to the Economic Dispatch in a microgrid with renewable energy sources, diesel generators and energy storage systems (batteries). The Particle Swarm Optimization algorithm is used to find optimal scheduling, meeting the constraint imposed and limits of battery power and energy, that makes the problem dynamic. The rest of this paper is organized as follows. In section 2, will be presented the problem formulation for a microgrid economic dispatch and detail power generation sources and its constraints. In section 3, the particle swarm optimization technique is explored, and in section 4, simulations and results will be discussed. Finally in section 5 will be presented the conclusions of this paper. 2
Problem formulation
Figure 1 shows a typical microgrid thats contain renewable sources, loads, diesel generator and energy storage system (ESS), etc. There are a variety of loads, and can be classified into three types: controllable, shiftable and critical. For storage systems, the main technologies are ultracapacitors, SMES, flywheels, hydro pumping and batteries. In this paper, batteries are used for ESS.
tors, given all the technical constraints and meet their local demand. Mathematically, it is a nonlinear problem and can be formulated as follows:
min
CT =
T X t=1
"
NG X
!
(CFi (Pi,t ) + OMi (Pi,t ))
i=1
+Pgrid, t · πR,t + CB (PB,t )
]
where CFi (Pi,t ) is the production cost of diesel generator i at hour t, OMi (Pi,t ) is the operation and maintenance cost of generator i; Pi,t is the output power generator i at hour t. Pgrid and πR,t is grid power output and the grid energy price, respectively. The battery power at hour t is represented by PB,t . Positive values for grid power, indicate purchasing power at time t, while negative values indicate sale to the grid, that resulting in profit for microgrid. The operation and maintenance cost, will be given in terms of output power as follows: OM (Pi ) = λOP · Pi
(2)
onde λOP is a proportionality constant in terms of output generator power i. 2.1
Constraints
The objective function (1), is subjected to several constraints, like a power generators limits, power balance, SOC constraint, among others. The instantaneous demand must be met and therefore the power supplied by renewable sources enter as negative charges, given as follows: NG X
Pi,t +PB,t +PV,t +PW,t +Pgrid,t = PD,t +Ploss,t
t=1
(3) sendo PD is the demand power. Ploss are the systems losses. In this paper, losses will be considered equal to zero. 2.2
Generators Modelling
2.2.1
Wind power
The output power of wind turbines are modeled as a function of wind speed. In this paper, the output power of wind turbines is calculated as follow (Mohamed and Koivo, 2011): 0, Vw < Vci aW Vw2 + bW Vw + cW , Vci ≤ Vw ≤ VN VN ≤ Vw > Vco PWN , (4) where PW is the output power, Vci is the cut-in wind speed, Vco is the cut-out speed, VN is the rated speed and Vw wind speed. The power curve coefficients are represented by aW , bW and cW . PW =
Figure 1: Typical microgrid system. The microgrid optimal operation aims to minimize the total production cost of diesel genera-
(1)
2.2.2
Photovoltaic panels
The power supplied by a solar panel is limited by technical issues and climate factor. Among the technical factors are efficiency, nominal installed capacity and the rated temperature of each cell. Considering the climatic factors, has solar radiation and ambient temperature. The advantages of the implementation of a photovoltaic system are in practical assembly shortly to design, no moving parts (no noise during the operation), easy installation in urban environments, long life and low maintenance (Mohamed and Koivo, 2011). Considering all these factors, the output power is calculated by the equation:
PV = PST C
GIN G [1 + kP V (Tc − Tr )] GST C
Diesel generator
Diesel generators are important components of a microgrid and its cost curve as a function of output power represented by a quadratic function, as follows: C(Pi ) = aPi2 + bPi + c
(6)
where a, b and c are generator coefficients. The diesel generators are subjected to a constraint given below: Pimin ≤ Pi ≤ Pimax 2.3
(7)
Batteries
Batteries are devices that convert chemical energy into electrical energy. Together with distributed generation, are used to store energy so it can be used later, when the microgrid distributed generation is not sufficient to meet local demand (islanding mode). Otherwise, serves as reserve and can store excess energy from wind turbines and solar panels until they are fully charged. Is also used to minimize the cost production, when the grid price and production cost of diesel generators increase. An important factor to increase the battery life time is the state of charge (SOC). There are energy limitation in batteries, where the measuring the SOC, prevents battery from overcharging and deep discharge, or even to be discharged for a long time. Thus, the energy in each time interval t is calculated as follows: SOCt = SOCt−1 − PB,t · ∆t
SOCmin ≤ SOCt ≤ SOCmax
(8)
(9)
Its assumed the SOC for final planning period equal to initial SOC value. To calculate the battery output power, the storage system conversion efficiency must to be considered according to (Hoke et al., 2013). In this case, defining Pin and Pout , as the input and output power for energy storage respectively, we get:
(5)
where GIN G is the solar irradiation, GST C is the irradiation in standard test condition, Tc is the cell temperature, Tr is reference temperature and kP V is the coefficient temperature. PV is the photovoltaic output power and PST C is the maximum output power in standard test condition. 2.2.3
where SOCt is the energy stored at time t and ∆t is the time interval. It is considered. For positive values, is consider battery discharge mode and negative for charge. The batteries must to be used into energy limits range. Thus:
Pout =
Pin =
PB /ηo , if PB ≥ 0, 0, if PB < 0
(10)
0, se PB ≥ 0, −PB ηi , se PB < 0
(11)
where ηi and ηo are the efficiency conversion for Pin and Pout . Thus, the new battery power is calculated as follow: PB = ηo · Pout − 3
Pin ηi
(12)
Particle Swarm Optimization - PSO
Particle Swarm Optimization (PSO) was introduced by (Kennedy and Eberhart, 1995) through studies on the social behavior of populations of birds and fish (Cerqueira et al., 2011). Its a natured-inspired algorithm for global optimization. Each particle j, has a position Xj and velocity vj , and flying through on the search space, and optimized at each iteration their positions and velocities (Shi and Eberhart, 1998). In the iterative process, the best individual position (PBest ) of each particle and global position (GBest ) are stored, and will later be used in the process of update their speeds and positions. The following equations, described the update process, for velocity and position, respectively: k vjk+1 = ω · vjk + c1 · rand1 () · (PBest,j − Xjk )
+c2 · rand2 () · (GkBest − Xjk ) (13) Xjk+1 = Xjk + vjk+1
(14)
where c1 are c2 are cognitive factors, that represent the trust for each particle in it and the swarm, rand1 are rand2 random numbers in the range [0,1]. For each step,the fitness function of individuals particles will be valued.
The inertial factor ω control the step size. If the inertia weight is larger, facilitates a global search while a small facilitates a local search. For this reason, a linearly decreasing is used and can be calculated as a function in the iterative process: ω = ωmax − (ωmax − ωmin ) · iter/itermax
(16)
For handling constraints, a most common approach for meta-heuristics algorithm is to apply penalty functions into the objective function. In this case, for a minimization problem, the objective function is modified and add penalties, as follow equation: f = CT + penalty
12. Print Gbest Values; 13. End
(15)
where ωmax and ωmin the inertial weight maximum and minima ; iter e itermax iteration and maximum iteration number, respectively. There are many different strategies for inertia weight to providing balance between exploitation and exploration of PSO. A comparative study for inertia weight strategies can be found in (Bansal et al., 2011). The particle velocity is controlled by the following constraint: vjk ∈ [−vmax , vmax ]
11. Repeat 7, 8 and 9 for each iteration, until the stop condition;
(17)
where f ´e the new cost function. The penalty is a violated constraint multiplied by a coefficient. The penalties coefficients is a value that has the same size of objective function value. The algorithm steps is showed:
4
Simulations and Results
For the simulations, renewable generations have priority because they are non-dispatchable sources, free delivery cost and has zero emissions, contributing to the environmental issues. In mode connected to the grid, the economic dispatch of microgrid depends on the generation costs of each source, as well as the purchase or sale price of energy from the upstream network and the demand to be meet. In this case, PW, PV and batteries, has priority in the dispatch, meanwhile battery SOC must be monitored. If this sources can’t supply the load, main grid and diesel generators, must to be used to complete. The generations costs and energy price from main grid is compared. If the external grid price is lower than generation, its use to complete the demand, otherwise we use the diesel generators. If baterry SOC is above of minimal SOC, the excess can be sale to main grid. Figure 2 shows the microgrid load profile for a typical day and ranges from 52kW to 90kW. The available power from PW and PV can be seen in figure 3. Its assumed that the data of wind and solar generation as deterministic. Simulations data can be found in (Cai et al., 2012), (ModiriDelshad et al., 2013). 90
1. Initialize the swarm positions with random values as follows: (18)
2. The speed must to be initialized with random values: vi = rand(.) ×
(vimax
−
vimin )
+
vimin
(19)
70
Demand (kW)
Xi = rand(.) × (Ximax − Ximin ) + Ximin
80
60 50 40 30 20 10
3. Calculate the objective function (1) for each particle; 4. Consider the initial population as local best position Pbest; 5. From Pbest, select the best values for global best position (Gbest) and store; 6. Start PSO loop and iteration counter; 7. Calculate the inertia weight, particle speed (13) and position (14); 8. Apply penalty conditions, if necessary; 9. Evaluated equation 1; 10. Update Pbest and Gbest;
0 2
4
6
8
10
12
14
16
18
20
22
24
hours
Figure 2: Microgrid load profile. In table 1, the maximum and the minimum power capacity of diesel generator unit and battery limits are shown. Price for the main grid is found on the table 2 (Sobu and Wu, 2012), (Cai et al., 2012). The PSO parameters is considered the same for all simulations. The parameters are itermax = 2000, npar = 40, ωmax = 0.9, ωmin = 0.4, c1 = 2.0 e c2 = 2.0. In all cases, simulations are performed 30 times to insure quality solutions and the non-dependence of initial solution by the algorithm PSO.
case is $ 283.14. Its observed that, between 1h to 8h and 17h to 23h, the system buy energy from the grid, because these intervals the grid energy price is low reducing the output power from diesel generator. Its also important to note that the batteries are charging during the first hours, to be used later, when the grid price increases. Batteries are charged when the grid power price is low and energy from renewable is available.
Wind and phovoltaic output power profile in kW
60
50
40
30
20
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0
2
4
6
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10
12 14 hours
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80 Battery Generator Microturbine Grid
Figure 3: Wind and Photovoltaic forecasted power profile. Table 1: Diesel generator and battery data. Pmin 0kW 0kW SOCmin 60 kWh
Diesel generator Pmax a 40 kW 0.0074 30 kW 0.01 Battery data SOCmax SOC0 300 kWh 100 kWh
b 0.3203 0.3333
4.1
20
0
-20
-40
grid ($/kW ) Price 0.9900 1.090 0.9900 0.7900 0.4000 0.3647 0.3585 0.4130 0.4448 0.3480 0.3000 0.2250
Results
4.1.1
40
PB -20/20 kW
The battery efficiency for charging and discharging are the same and equal to 0.95. Table 2: Price for the main Hour Price Hour 1 0.2400 13 2 0.1770 14 3 0.1301 15 4 0.0969 16 5 0.0300 17 6 0.1701 18 7 0.2710 19 8 0.3864 20 9 0.5169 21 10 0.5260 22 11 0.8100 23 12 1.000 24
Power output in kW
60
Case 1
For case 1, its considered that a microgrid can sell to main grid, and the system includes storage system, diesel generator, wind and solar power. Battery bank has operating and maintenance cost fixed and equal to $/kW 0.18. Figure 4 shows the results for case 1. All units operate into their limits and satisfy the load demand during planing period. The renewable sources and battery reduce the total operation cost, because their operation cost are considered zero. The total cost for this
5
10
15
20
hours
Figure 4: Optimal generation scheduling for case 1. Microgrid sell energy to the grid between 11h to 17h, because maximum renewable power is available and the battery bank is discharging, its also used power from diesel generators. Table 3: PSO best results with storage Total operation cost in ($) Mean Minimum Std. D 289.64 283.14 2.9063 The results obtained of the PSO performance can be seen in Table 3. Results show standard deviation of 2.9063, best solution is $ 283.14 and average value of $ 289.64. The convergence curve is shown in the Figure 5. 4.1.2
Case 2
For the case 2, the battery operation tariff cost is $0.28 and the price for sale energy to the grid is assumed 70% of purchase price. Its also considered a fixed price for grid of $ 0.7. This case shown the sensibility to the price, when the microgrid is connected to main network. In this case, the scheduling was changed due to the fixed grid price and battery tariff. For this reason, figure 6 shows that the grid has insignificant participation due to its high cost. Thus, microgrid used more diesel generator and battery energy to meet the demand. Batteries participate
1000
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950 900
900 850 800
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Cost in $
Cost in $
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population average
400
550
best population
300 0
population average best
500 500
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Generation
Figure 5: Convergence curve for case 1
Figure 7: Pso convergence curve for case 2.
to supply the demand during the peak hour and charging in another time.
making in the optimal management of a microgrid. 5
80 Battery Generator 1 Generator 2 Grid
Power output in kW
60
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0
-20
-40 5
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15
Conclusion
In this paper, the PSO algorithm was applied to solve the economic dispatch of a microgrid with renewable sources, diesel generators and energy storage system. The proposed model taken into account constraint for variety of sources, that make a non-linear and dynamic problem. The results shown satisfactory performance and stability of PSO algorithm. This study shown the relevance of storage system in the economic operation of microgrid allowing the displacement of cheaper energy supply to peak demand period.
20
hours
Figure 6: Optimal scheduling for case 2
Acknowledgment The authors would like to thank to CAPES and CNPq for the financial support.
The fixed price caused the PSO did not choose to buy power from the grid and not sell too, because the price is only 70% of the purchase price. This led to increased cost around 59% compared to the case 1. The best value was found to be $ 483.56. The mean value and standard deviation can be seen in Table 4. Convergence curve is shown in Figure 7 and its seen close average and best solution.
Bansal, J., Singh, P., Saraswat, M., Verma, A., Jadon, S. S. and Abraham, A. (2011). Inertia weight strategies in particle swarm optimization, Nature and Biologically Inspired Computing (NaBIC), 2011 Third World Congress on, IEEE, pp. 633–640.
Table 4: PSO results for case 2 Total operation cost in ($) Mean Minimum Std. D 487.1327 483.56 1.3054
Cai, N., Nga, N. T. T. and Mitra, J. (2012). Economic dispatch in microgrids using multiagent system, North American Power Symposium (NAPS), 2012, IEEE, pp. 1–5.
This case shows the sensitivity to price policy adopted in the realization of the economic dispatch when the microgrid is operating connected to the grid. It is an important issue in decision
Cerqueira, S., Trovao, S. A. and Saavedra, O. R. (2011). Pr´e-despacho hidrot´ermico em ambiente competitivo via otimiza¸ca˜o por enxame de part´ıculas, Vol. X, Simposio Brasileiro de Automa¸ca˜o Inteligente, pp. 749–756.
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