www.ietdl.org Published in IET Generation, Transmission & Distribution Received on 20th August 2013 Revised on 25th November 2013 Accepted on 30th November 2013 doi: 10.1049/iet-gtd.2013.0541
ISSN 1751-8687
Multi-objective stochastic optimal planning method for stand-alone microgrid system Li Guo, Wenjian Liu, Bingqi Jiao, Bowen Hong, Chengshan Wang Key Laboratory of Smart Grid of Ministry of Education, Tianjin University, Tianjin 300072, People’s Republic of China E-mail:
[email protected]
Abstract: To achieve economic and environmental benefit for the stand-alone microgrid consisting of diesel generators, wind turbine generators, photovoltaic generation system and lead-acid batteries, a multi-objective stochastic optimal planning method and a stochastic chance-constrained programming model are presented. In the model, the optimal objective is to simultaneously minimise the total net present cost and carbon dioxide emission in life cycle; the type and capacity of distributed generation units have been selected as the optimal variables; the loss of capacity is adopted as probability index constraint; the coordinated operation strategies between diesel generators and battery, the multi-unit operation constraints of diesel generators and the reserve capacity have been considered in the hard-circle operation strategy. Considering the uncertainties of wind speed, clearness index and load demand, Markov process transition probability matrix is adopted to synthesise those time series data. Optimal planning for an island microgrid system has been carried out by the planning system for microgrid (PSMG), a self-developed optimal planning software based on the multi-objective stochastic optimal planning method for stand-alone microgrid system.
1
Introduction
With the world’s growing demand for energy and the increasing of greenhouse gases emission in the atmosphere, utilisation of solar and wind energy has become increasingly significant, attractive and cost-effective [1–2]. However, as we known, the solar and wind energy are closely dependent on the weather and climatic changes. In order to overcome this shortage, the stand-alone microgrid system including solar and wind power generators and other different kinds of distributed generation (DG) units are considered. The stand-alone microgrid system is a hybrid power system that integrates all types of DG units to take full advantage of their individual and complementary characteristics, thus increasing the energy efficiency, the energy utilisation rate and the power supply reliability of the system [3–5]. The optimal planning for stand-alone microgrid system is a process of searching the best result in a solution space, which must fulfill all the constraints. In addition, it usually takes economic performance, environmental performance and reliability as the optimisation objectives [4]. Meanwhile, the method for it can be divided into deterministic optimal planning method and stochastic optimal planning method [6]. In respect to deterministic optimal planning, based on accurate meteorological data and load data, quasi-steady state simulation method is adopted in the most studies of the field. According to the wind speed, solar radiation, temperature and load demand obtained, all the indicators
IET Gener. Transm. Distrib., 2014, Vol. 8, Iss. 7, pp. 1263–1273 doi: 10.1049/iet-gtd.2013.0541
are calculated for each combination schemes of the stand-alone microgrid system using the quasi-steady-state simulation program, which can simulate the fluctuation of renewable resource and load demand, as well as the process of the control strategies of stand-alone microgrid system. Based on recorded data of wind speed, solar radiation and load demand, in [7] a single-objective optimal planning model constructed for a stand-alone microgrid composed by wind turbines, PV, diesel generators and batteries, which takes minimisation of the total cost in life cycle as optimisation objective. For the same stand-alone microgrid system, literature [8] adopts the wind speed and solar radiation obtained from the website of NASA, and the capacity optimisation is carried out with the total net present cost (NPC) and carbon dioxide emission in life cycle to be minimised as the optimisation objective. Considering the influence of the control strategies on optimal results, in literature [9] a two-stage optimal design method was presented which investigates the combined optimisation of control strategy and system configuration. In this method, the capacity of DGs are optimised on the first stage, while some key control variables, such as state of charge (SOC) set point of battery, are optimised on the second stage. The year-round meteorological data and load data must be obtained while using the deterministic optimal planning method. However, it is difficult to acquire those relative dates on the practical planning and design stage. Meanwhile, a large number of uncertain factors will affect the optimal results [10], which cannot ensure all the
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www.ietdl.org constraints met for the optimal results obtained by deterministic planning method. Hence, the stochastic optimal planning is presented to deal with the issue. At present, the study of stochastic optimal planning is usually converted to their definitive equivalents. Stochastic programming and Monte Carlo simulation (MCS) are common methods to carry out the stochastic optimal planning [11], which have been widely used in optimal power flow [12–13], distribution network planning [14–15], electric power market [16–17], distribution system expansion planning [18] and energy management for microgrid system [19]. Currently, the research of optimal planning for stand-alone microgrid system considering uncertainties is relatively scarce. Arun et al. [20] proposed a design space approach for optimal sizing of PV battery systems, with Chance Constrained Programming (CCP) and MCS incorporating the uncertainties of solar radiation and initial battery level; and coefficient of variation of loss of load (LOL) expectation terminating the MCS for system reliability estimation. Carpentiero et al. [21] developed probabilistic sizing method for hybrid wind-diesel stand-alone microgrid system with fuel price growth trend and the occurrence probability of each trend modelling the uncertainties of fuel price. However, for the research on deterministic optimal planning method, the combined optimisation of the equipment type and capacity, multi-units operation conditions of conventional generators (e.g. diesel generators), as well as reserve capability have not been taken into account. Meanwhile, among most of the literatures, uncertain data considered in stochastic programming are synthesised by MCS method or similar method. The MCS method is good adaptability as it can use the existing model and method of deterministic planning method. However, the adjacent uncertain data (e.g. wind speed, solar radiation) have some correlation with each other, the time series data synthesised by the MCS method cannot reflect the characteristic. In this paper, a stochastic chance-constrained programming model for stand-alone microgrid system with diesel generators, wind turbine, PV generation system and lead-acid batteries is presented. In the model, the optimal objective is to simultaneously minimise the total NPC and carbon dioxide emission in lice cycle; the coordinated operation strategies between diesel generators and batteries, the multi-units operation conditions of diesel generators, and the reserve capacity had been considered in operation strategy. The type and capacity of DG units had been selected as the optimal variables. Markov process transition probability matrix is adopted to synthesise time series data of wind speed, clearness index and load demand. Compared with MCS method, data synthesised by this method is sequence dependent, which is more favorable in practice. Optimal allocation of DG units and battery for an island microgrid system has been carried out by the PSMG, which is a self-developed optimal planning software. This work is organised as follows. In Section 2, an overview of the system is introduced. The optimal planning model and stochastic chance-constrained programming model of stand-alone microgrid system are presented in Sections 3 and 4, respectively. In Section 5, the solving algorithm based on non-dominated sorting genetic algorithm II (NSGA-II) is described. A case study for an island microgrid system is made in Section 6. Conclusion is given at the end of this paper. 1264 & The Institution of Engineering and Technology 2014
2
Stand-alone microgrid system
2.1
Overview of a stand-alone microgrid system
The system described in this paper can be shown as Fig. 1. Wind turbines, PV generation system and storage batteries are connected to the AC power grid through their respective converters. Diesel generating units are synchronous generators and directly incorporated into the microgrid system. Power losses caused by line impedance are ignored in this paper. Meanwhile, for the paper some assumptions are made as follows: 1. All of the equipments of the microgrid will not fail. Therefore the failure rate of each equipment is not considered. 2. The state (efficiency) of each kind of equipment remains constant during one simulation step. 3. As the network of the microgrid being very simple, the reactive power, power factor of diesel generator, power flow equation and the optimal allocation of each device are not considered in the model.
2.2
Operation control strategy
There are a variety of strategies to control diesel generators and storage batteries in coordinated operation. In this paper, the hard-circle control strategy, in which diesel generators and storage batteries take turns to be main power supply to meet the net load demand, is adopted and the net load demand is equal to the total load demand minus the output power of PV generation system and wind turbines. This strategy can reduce the running time of diesel generators as much as possible, and therefore make itself applicable where renewable resources are rich while diesel generators are limited because of environmental and energy problems. Under this strategy, diesel generators and storage batteries play a major role in turn to meet the net load demand, and the diesel generators are allowed to charge the storage batteries. Quasi-steady simulation in life cycle is a simulation flow that simulates in each hour under certain pre-determined strategies according to the variations of wind, solar radiation and load demand conditions in that area, which can help us to identify the number of started diesel generators, fuel consumption, charging and discharging power of batteries, LOL, or unmet load, loss of capacity (LOC, or capacity shortage) and excess power (EP) of the system. The flowchart of quasi-steady simulation for hard-cycle strategy is shown in Fig. 2. P1−P6 in the diagram refer to the real net load, net load of considering the reserve capacity, maximum charging and discharging power of batteries, maximum and minimum output of diesel generators, respectively.
Fig. 1 Structure of a stand-alone microgrid system IET Gener. Transm. Distrib., 2014, Vol. 8, Iss. 7, pp. 1263–1273 doi: 10.1049/iet-gtd.2013.0541
www.ietdl.org batteries would discharge when the diesel generators operating at the rated power point cannot satisfy the load. If there is still power shortage in the system, the actual LOL is recorded.
3 Optimal planning model for stand-alone microgrid 3.1
Objective functions
The objective functions to be minimised are: NPC in life cycle and pollutant emissions. The problem is a multi-objective optimisation problem and the objective function can be expressed as min fi (X )
i = 1, 2
(2)
3.1.1 NPC in life cycle: NPC in life cycle is the objective function of costs, which includes the present value of the total cost and the salvage cost of all equipment and the total cost includes the initial investment cost, replacement cost, operation and maintenance cost, and fuel cost. The NPC can be expressed as follows f1 (X ) = Fig. 2 Flow chart of quasi-steady simulation for hard cycle strategy
Since the reserve capacity, Pres, is taken into account in the simulation process, P1 and P2 should be calculated, respectively. The relationship between them is as follows P2 = Pres + P1
(1)
Then, the number of started diesel generators nt at the current time can be obtained according to the P2, the number of started diesel generators and the maximum charging/ discharging power in the previous time step. All the diesel generators whose running time is over the minimum operating hour can be shut down if the others are able to meet the load demands. Otherwise, they need to be shut down one by one until the rest of the generators can satisfy the load demand and battery charging demand. However, if the load demand exceeds the power supplied by the system, more diesel generators are needed. It should be noted that the diesel generators only need to meet the load demand in the situation, so they do not need to charge the batteries. If the load demand cannot be fully satisfied with all the diesel generators on, then the batteries would discharge to complement the load capacity shortage and LOC would be recorded if the system still cannot meet the load demand with battery discharging power taken into account. After determining the number of started diesel generators at the current time step, various indices of the system (such as fuel consumption, charging/discharging power of batteries, unmet load demand and EP etc.) can be calculated according to the demand of real net load P1. All the diesel generators would run at minimum output power point if they can satisfy the load demand and battery charging on this condition, at the same time EP would be recorded. Otherwise the total output of diesel generators would be determined by load demand and battery power demand. The IET Gener. Transm. Distrib., 2014, Vol. 8, Iss. 7, pp. 1263–1273 doi: 10.1049/iet-gtd.2013.0541
K C(k) − Bsalvage k k=1 (1 + r)
(3)
where K is the lifetime of the entire stand-alone microgrid system, r is the discount rate, C(k) is the total cost of kth year and Bsalvage is the equipment residual value, which generates in the last year of the economic assessment. C(k) can be calculated as follows C(k) = CI (k) + CR (k) + CM (k) + CF (k)
(4)
where CI(k), CR(k), CM(k) and CF(k) are the initial investment cost, replacement cost, operation and maintenance cost, and fuel cost in the kth year, respectively. Those variables can be calculated as follows CI (k) = CI battery + CI pv + CI wind + CIDG + CI Converter
(5)
where CIbattery, CIpv, CIwind, CIDG and CIConverter are the initial investment cost of batteries, PV generation system, wind turbines, diesel generators and converter, respectively CR (k) = CR battery (k) + CR pv (k) + CR wind (k) + CRDG (k) + CR Converter (k)
(6)
where CRbattery(k), CRpv(k), CRwind(k), CRDG(k) and CRConverter(k) are the replacement cost of batteries, PV generation system, wind turbines, diesel generators and converter in the kth year CM (k) = CMbattery (k) + CMpv (k) + CMwind (k) + CMDG (k) + CMConverter (k)
(7)
where CMbattery(k), CMpv(k), CMwind(k), CMDG(k), CMConverter(k) are the operation and maintenance cost of batteries, PV generation system, wind turbines, diesel generators and converter in the kth year, respectively. 1265
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www.ietdl.org 3.1.2 Pollutant emissions: In order to measure the pollutant emissions, CO, CO2, unburned hydrocarbon, sulphur compounds and nitric oxide are considered, as diesel generators use diesel as primary fuel. The pollutant emissions are related to fuel consumption directly, which equal to the annual fuel consumption multiplied by the emission coefficient of different pollutants. It can be expressed as [18] f2 (X ) =
K
sCO2 + sCO + sHC + sNO + sS vfuel (k) (8)
where x is the n-dimensional decision variables, ξ is the probability density function of the random vector, f (x) is the objective function, gj (x, ξ) is the random constraint functions, Pr{gj (x, ξ) ≤ α, j = 1, 2, …, k} represents the probability that gj (x, ξ) holds and β is the confidence level. In this paper, to ensure LOC meets certain confidence level, LOC is used as a constraint. LOC, which is between 0 and 1, indicates the ratio of capacity shortage to the load demand. The smaller the value, the higher the reliability of power supply would be. It can be expressed as E Pr LOC = CS ≤ 0.01 ≥ 80% Etot
k=1 CO2
CO
HC
NO
S
where s , s , s , s and s are the coefficients of different pollutants, v fuel(k) is the diesel consumption of the kth year. 3.2
Optimal variables
Here, the type and the number of wind turbines (Windtype, WindNum), the type and the number of diesel generators (Dieseltype, Dieselnum), the capacity of PV generation system (PVcap), the type and the parallel branch number of batteries (Battype, Batparrel), and the capacity of bidirectional converter used by batteries (Concap) are selected as optimal variables, which can be expressed as X = Windtype , WindNum , Dieseltype , Dieselnum , PVcap , Battype , BatParrel , Concap 3.3
4 Stochastic chance-constrained programming model
Considering that in some extreme conditions some constraints may be violated with a very small probability, using strict constraints may result in an optimal solution that is too conservative (e.g. cost is too high). To handle this problem, CCP, proposed by Charles and Cooper in 1959 [23], is executed with permission for the solutions to violate the constraints to some extent, while the probability to meet these constraints is above a certain confidence level. This means that the solutions are optimal in probabilistic sense. Hence, CCP is mainly used to solve the optimisation problem that contains random variables in constraints. A common form of CCP can be expressed as
j = 1, 2, . . . , k} . b
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4.2.1 Probabilistic modelling: The uncertainties considered in this paper include wind speed, cleanness index and load disturbance factor.
Suppose that the wind speed follows a Weibull distribution with the following probability density function k−1 k
k W W p(W , c, k) = exp − c c c
(10)
(12)
with scale facer, c, and shape factor, k, can be calculated as −1.086 s k= W
(13)
W G(1 + 1/k)
(14)
c=
Chance-constrained programming
min f (x) s.t Pr{gj (x, j) ≤ a,
Markov process transition probability matrix
1. Weibull distribution of wind speed
Model of system components
Model of diesel generator, PV generation system, wind turbine and battery have been studied in lots of researches. In this paper, the models of system components mainly refer Lambert et al. [22], but are not presented in this paper to keep the paper reasonably concise. The technical constraints and energy balance constraints can also find in the reference. For example, it includes power balance constraint, diesel generator technical constraint, battery technical constraint and so on.
4.1
where ECS is the total capacity shortage and Etot is the total electrical load demand. Here must note that capacity shortage is a shortfall that occurs between the actual amount of operating capacity the system the can provide and the load considering the reserve capacity. Considering the chronological time correlated nature of wind speed, load and cleanness index (i.e. the state at the next time step has some relevance with the current state), Markov process transition probability matrix is used to generate sequences of random numbers, which are introduced as follows. 4.2
(9)
(11)
where W and s are the average value and standard deviation of wind speed, respectively, Γ(·) is the gamma function. 2. Normal distribution of load disturbance factor Load is obtained by the original data multiplying the load disturbance factor. The input data is hourly average load demand for all the months over a year, so the total number is 12 × 24. Disturbance coefficient is expressed as follows
a = 1 + dd + dh
(15)
where δd is the daily disturbance factor, δh is the hourly disturbance factor and α is the disturbance coefficient. Both of them follow normally distribution with the mean value of zero. IET Gener. Transm. Distrib., 2014, Vol. 8, Iss. 7, pp. 1263–1273 doi: 10.1049/iet-gtd.2013.0541
www.ietdl.org 3. Cleanness index As the solar radiation has a significant diurnal and nocturnal mode, it cannot be directly obtained from the probability density function. The uncertainty of solar radiation is mainly because of the stochastic nature of weather condition. In this paper, cleanness index is used to represent the uncertainties of weather condition, namely the solar radiation and the relationship between the cleanness index and the solar radiation can refer Lambert et al. [22]. The distribution function of cleanness index can be expressed as [24] (k − kt ) P(kt ) = C tu exp (lkt ) ktu
C = l2 ktu / elktu − 1 − lktu
(18)
(22)
2. Second, revise the initial probability vector {P} iteratively {P} = {P} + 0.9 × {R} − {Rt }
(23)
3. The iterations are terminated when the difference between steady-state distribution vector {R} and transition steady-state vector {Rt} is less than a certain threshold. At this point, {P} is the desired initial probability vector, which is composed by the diagonal elements of [P]. Then the required transfer matrix [T] can be generated from [P]
(19)
4.2.2 Markov process transition probability matrix [25]: The transition probability matrix [T] consists of three matrices: standardised matrix [N], attenuation matrix [G] and initial probability matrix [P]. Where [N], [P] are the diagonal matrices. If the current state is i, the probability of making a transition from state i to state j is Ti, j. Since the state i is bound to be transferred to certain state in the ith row of [T], the sum of elements in each row of [T] is 1. 1. Attenuation matrix [G] Take wind speed as an example. If it is 5 m/s at state i, then the probability that the wind speed is 5 m/s should be the maximum at next state. Hence centred around Ti,i, the transition probability is reduced gradually. Using Gi, j to achieve this effect Gi, j = (gbase )i−j
Rt = [P][G]{P}
(17)
with
l = (2t − 17.519 exp (−1.3118t) − 1062 exp (−5.0426t))/ktu t = ktu / ktu − k t
1. First, assume that the initial probability vector {P} is equal to the steady-state distribution vector {R}, transition steady-state vector {Rt} can be expressed as
(16)
where k t indicates the mean value of cleanness index, its maximum value and ktu is the 0.864 theoretically. C is expressed as
Definition: If all of the elements Rj in the vector {R} are non-negative and satisfy Rj = i[S Ri Ti, j , then {R} is called steady-state distribution vector of matrix [T] and the sum of all the elements in {R} is 1. The first step is to obtain {R} according to the probabilistic model: the element of {R} is the probability of different values. Then use the following methods to obtain initial probability matrix [P]:
(20)
[T] = [N][G][P]
(24)
4. Cumulative probability matrix. According to matrix [T], cumulative probability matrix [C] is obtained, and then time series data is generated. Ci,j represents the element of matrix [C ] and can be expressed as Ci,1 = Ti,1 ,
Ci, j = Ci, j−1 + Ti, j
(25)
At state i, generate a random number x between 0 and 1 following uniform distribution. If x ≥ Ci,j and x < Ci,j + 1, then the next state is transferred to state j. 5. Autocorrelation coefficient Autocorrelation coefficient is used to determine the linear correlative of the time series data before and after a certain time interval R(rDt) =
where gbase is the initial value, which is less than 1.
N −r 1 xx sx (N − r) i=1 i i+r
(26)
2. Standardised matrix [N] Standardised matrix [N] is a diagonal matrix, whose role is to make the sum of elements in each row of [T] to be 1. Ni,i can be expressed as K
1 pk gk−i
(21)
where N is the total number of generated data, r is the selected time interval and σx is the variance of data. If the autocorrelation coefficient obtained is too small, increase gbase, so that the probability of state i transferring to another state at the next time step will increase. Otherwise, decrease the value of gbase.
5 where K is the dimension of matrix [P], pk and gk−i are the elements of matrix [P] and [G], respectively. 3. Initial probability matrix [P] IET Gener. Transm. Distrib., 2014, Vol. 8, Iss. 7, pp. 1263–1273 doi: 10.1049/iet-gtd.2013.0541
Solving algorithm
Here, NSGA-II, a multi-objective evolutionary algorithm, is adopted to solve the multi-objective problem [26]. The flowchart of the optimisation method for stand-alone 1267
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Fig. 3 Flowchart of NSGA-II optimisation
microgrid system is shown in Fig. 3, in which the deterministic optimal planning method and stochastic optimal planning method are described together. The two methods are the same except the difference in quasi-steady state simulation module: the left dashed box describes the sub-module of stochastic optimal planning method, while the right dashed box represents the sub-module of deterministic optimal planning method. The detailed procedures are illustrated as follows: Step 1: System initialisation. It is the first step to read the parameters of the system, genetic algorithm, equipment, as well as the probability distribution function of wind speed, cleanness index and load demand. Step 2: Population initialisation. In this step, a random set of N possible individuals are generated, which act as the initial population P0. Meanwhile, the iteration of the algorithm is set to be 0. Step 3: Evaluate the fitness of the population Pt. a. Stochastic chance-constrained programming. Firstly, time series data (wind speed, cleanness index and load demand) of the whole year is synthetised using the Markov process transition probability matrix method. Then, quasi-steady state simulation strategy is called, and the objective values of each individual and the number that LOC satisfies the CCP constraint are recorded. Finally, the cycle are terminated when it reaches the maximum iteration, and the Fitness =
final objective values are obtained by averaging the objective values calculated in each iteration of the stochastic chance-constrained programming. b. Fitness calculation. The fitness value of each individual is evaluated according to the following equation (see (27)) where f1,max(X ) and f2,max(X ) are the maximum value of the first objective value and second objective value among all the individuals, Δ is the absolute value of constraint value of the individual which does not satisfy the constraint. Step 4: Application of selection, crossover and mutation operators. 1. Selection. The population Ps is selected from the current parent population Pt by the roulette wheel method. 2. Crossover and mutation operators. To obtain the offspring population Qt, the individuals in population Ps are updated by crossover and mutation operators. The single-point crossover operator and the uniform mutation operator are adopted. Step 5: Evaluate the fitness of the population Qt. Step 6: Sorting out the population Rt = Pt ∪ Qt. 1. Domination relationship calculation individual. 2. Crowding-distance calculation.
[f 1 (X ), f2 (X )], X is a feasible solution f1, max (X ) + D, f2, max (X ) + D , X is not a feasible solution
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between
each
(27)
IET Gener. Transm. Distrib., 2014, Vol. 8, Iss. 7, pp. 1263–1273 doi: 10.1049/iet-gtd.2013.0541
www.ietdl.org 3. Sorting out according to the number of solutions they are dominated by and the crowding-distance. Step 7: Generating new population. A new population Pt + 1 is generated as paternal population, which are selected from population Rt based on the Pareto sort order. Step 8: Stopping criterion. If the maximum number of generations indicated by the user has been reached, execution stops. Otherwise, it is needed to restart from step 4. Different from the stochastic optimal planning method, the deterministic optimal planning method calls quasi-steady state simulation strategy directly with no need to synthetise time series data, as it adopts the existing wind speed, solar radiation as well as load demand data.
6
Case study and results
An island microgrid on China’s eastern coastal island (east longitude 122.40°, latitude 30.10°) is adopted as a test case. The simulation step is 1 h, and the lifetime of this project is 20 years. Table 1 shows the parameters of diesel generators, PV generation system, wind turbines, lead-acid batteries and inverters, respectively. The discount rate is 3%. The reserve factors are rload = 0.1, rpeakload = 0, rwind = 0.25 and rsolar = 0.25 and for the multi-objective genetic algorithm, the population size is 40, the number of iterations is 400, the crossover rate is 0.9 and the mutation rate is 0.2. The number of iterations in stochastic chance-constrained programming is 50. Table 2 shows the average monthly value of cleanness index and wind speed, and variation of wind speed according to the year-round forecasted data. In the process
of synthesising time series data of wind speed and cleanness index, a 20 × 20 and 8 × 8 Markov process transition probability matrix are adopted, respectively. The correlation coefficient is 0.9. For the load demand, the standard deviation of daily disturbance factor and hourly distribution factor are 0.05 and 0.01, respectively. 6.1 Results of stochastic chance-constrained programming 6.1.1 Analysis of the programming process: The Pareto fronts of the 1st, 100th, 200th and 400th generation of offspring and paternal population are shown in Figs. 4 and 5. Fig. 4 depicts the evolutionary process of offspring population after the operation of selection, crossover and mutation. As the number of iterations of genetic algorithm increases, the number of individuals that satisfy the chance constraint increases, which means that the confidence level has been improved. In each generation there are individuals that fail to meet the confidence level described by chance constraint, which is caused by the operation of mutation and thus can help to increase the diversity of population. Fig. 5 illustrates the evolutionary process of parent population. According to (27) and selection regulation in genetic algorithm, individuals that violate the constraints have larger probability of being eliminated. From Fig. 5, it can be seen that all of the individuals in parent population meet the confidence level and the population has converged in the 400th iteration. 6.1.2 Simulation results: With the Pareto front of stochastic optimal planning shown in Fig. 5d, which is the Pareto front of stochastic optimal planning, it is easy to learn that pollutant emissions and net costs are two
Table 1 Parameters of system components Diesel generator single rated power, kW 50 life, h 20 000 minimum load rate, % 40 minimum running time, h 3 emission coefficient 2633.3 CO2, g/L CO, g/L 6.5 hydrocarbon, g/L 0.72 particulate matter, g/L 0.49 2.2 NOx, g/L 58 SO2, g/L fuel curve intercept coefficient, L/h/kW 0.011 initial investment cost, $ 10613 replacement cost, $ 10613 operation and maintenance cost, $/h 0.16 fuel cost, $/L 1.2 Wind turbine generator single rated power, kW 30 life, years 15 hut height, m 15 cut in wind speed, m/s 3 cut out wind speed, m/s 24 initial investment cost, $ 2776 replacement cost, $ 2776 operation and maintenance cost, $/year 327 PV derating factor rated power surface inclination angle, deg. surface azimuth, deg. surface reflectance the efficient of MPPT under STC
0.88 1 kW 22° 0 0.2 0.13
100 20 000 40 3 2633.3 6.5 0.72 0.49 2.2 58 0.034 21226 21226 0.24 1.2
Battery cell single rated voltage, V K C rated capacity, Ah series number maximum SOC minimum SOC maximum charging SOC floating charge life, years maximum charge rate maximum charge current, A charge and discharge efficiency output capacity in life cycle, kWh initial investment cost, $ replacement cost, $ operation and maintenance cost, $/year Converter rated capacity, kW life, years inversion efficiency rectification efficiency initial investment cost, $ replacement cost, $ operation and maintenance cost, $/year
50 15 18 3 24 57148 57148 1494 Photovoltaic cell temperature coefficient life, years initial investment cost, $ replacement cost, $ operation and maintenance cost, $/year
IET Gener. Transm. Distrib., 2014, Vol. 8, Iss. 7, pp. 1263–1273 doi: 10.1049/iet-gtd.2013.0541
2 1.101 0.332 800 240 0.9 0.5 0.9 10 1 162 0.86 2817 163 163 0
2 1.22 0.317 1500 80 0.9 0.5 0.9 10 1 306 0.86 5279 490 490 0
1 20 0.95 0.95 816 816 0
−0.005 25 1011 1011 0
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www.ietdl.org Table 2 Average monthly value of clearness and wind speed Month
1 2 3 4 5 6 7 8 9 10 11 12
Mean of cleanness index
Mean of wind speed, m/s
Standard deviation of wind speed, m/s
0.37 0.43 0.39 0.44 0.44 0.41 0.54 0.53 0.46 0.44 0.47 0.45
6.06 6.31 6.74 7.92 6.07 7.27 7.24 4.06 4.83 5.24 5.11 4.04
2.87 2.99 3.20 3.75 2.88 3.45 3.43 1.92 2.28 2.48 2.42 1.91
conflicting objectives. Namely, the investment of stand-alone microgrid is to choose a way which can make maximum benefits based on the balance of economic performance and environmental performance. Three individuals (or three configurations) corresponding to three points in Fig. 5d are selected in random and their detailed information is listed in Table 3. Here must note that date including sum of PV output power, wind turbine output power, diesel generator output power, battery output power and load, total output power, wasted energy are obtained from one iteration of stochastic chance-constrained programming. As can be seen from the results, confidence level of LOC is greater than or equal to the set value of 0.8 when taking LOC as the constraint in the stochastic chance-constrained programming. By allowing the batteries acting as the main power supply and making more investment to enhance the proportion of renewable energy generation, the running time of diesel generators decreases greatly and thus
substantially reduce pollution emissions. With the increase of the total capacity of wind turbine, battery and PV generation system, the pollutant emissions and the fuel consumption of the system decrease quickly, while the NPC in lice cycle of the system increase sharply. For all of the three configurations, the battery capacity is relatively small, as it is not economic for stand-alone microgrid under the current price level. Compared with configurations 1 and 2, confidence level of LOC of configuration 3 is relatively low, as the fewer number of diesel generators, which means that by increasing the number of diesel generators, the reliability of the system can be also increased. Furthermore, with the increase of the total capacity of wind turbine, the waste energy of configuration 3 is much more than the other two configurations. Contrasting the wasted energy of the three configurations, it is easy to learn that even though the total capacity of wind turbines is relatively big, lots of the energy will be wasted, because of the fluctuation of wind speeds and the small capacity of battery. 6.2 Comparison between deterministic planning and stochastic programming To compare the difference between the stochastic optimal planning method and the deterministic planning method, the Pareto fronts of the two methods are shown in Fig. 6a. For the deterministic optimal planning method, the year-round data of wind speed, cleanness index and load demand are the forecast data. As Fig. 6a shows, both the NPC and pollutant emissions increase generally after taking uncertainties into account. However, when the NPC is high enough, the pollutant emissions obtained by the two methods will be nearly equality. This is because for the stochastic optimal planning method, when uncertainties of wind speed, cleanness index and load demand are
Fig. 4 Evolutionary process of the population of offspring generation a Optimal results for the 1st generation b Optimal results for the 100th generation c Optimal results for the 200th generation d Optimal results for the 400th generation 1270 & The Institution of Engineering and Technology 2014
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Fig. 5 Evolutionary process of the population of paternal generation a Optimal results for the 1st generation b Optimal results for the 100th generation c Optimal results for the 200th generation d Optimal results for the 400th generation
considered, the number and running time of diesel generators are increased, resulting in total output of diesel generators and costs of purchasing diesel fuels will be increased. And when the NPC is high enough, the installed capacity of wind turbine, PV generation system and battery will be practically enough to meet load demand, and the total installed capacity of diesel generators and the consumption of fuel are fairly low, which will lead to the nearly equality of the pollutant emissions.
Fig. 6b shows the simulation results that put the solution obtained from deterministic optimal planning method into the proposed stochastic chance-constrained programming framework. As the figure shows, the LOC of lots of individuals cannot satisfy the confidence level after considering the uncertainties associated with the system, which means that those individuals cannot meet the probability constraint of chance constrained programming. Hence, the solution of deterministic planning may result
Table 3 Optimal results of three configurations Configuration 1
Configuration 2
Configuration 3
3 090 705 87.79 1044846 545411.1 608758.3 615109.8 264403.6 30 26 800 9 50 3 374.03 323.87 474 738 2 425 640 115091.7 3 015 470 1 325 620 1 645 210 1 31 867 168 013
3 299 189 47.15 1165406 557549.2 375637.2 956838.9 279942.9 30 29 800 14 50 3 382.35 342.90 490 299 2 779 850 69951.24 3 340 100 1 325 270 1 965 930 0.975 19409.9 178 255
5 346 785 6.21 2658911 573313.7 84483.47 1776978 285262.5 50 28 800 26 50 2 393.162 349.42 483 842 4 918 180 14506.67 5 416 529 1 324 980 4 044 760 0.95 4031.39 170 499
Net cost, $ pollutant emission, t wind turbine cost, $ PV cost, $ diesel generator cost, $ battery cost, $ inverter cost, $ wind turbine single rated power, kW wind turbine number battery capacity, Ah battery parallel number diesel generator power, kW diesel generator number PV capacity, kW inverter capacity kW sum of PV output power, kWh/y sum of wind turbine output power, kWh/y sum of diesel generator output power, kWh/y total output power, kWh/y sum of load, kWh/y waste energy, kWh/y confidence level of LOC fuel consumption, L/y sum of battery output power, kWh/y
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Fig. 6 Results of deterministic optimal planning method a Comparison with stochastic chance-constrained programming results b With uncertainties considering
in a less reliable system. Thus, it can be concluded that by stochastic chance-constrained programming, the optimisation results can achieve a more reliable system. Also, since it is more in line with the actual situation, the decisions are more reasonable.
demonstration project of island grid with intermittent renewable energy power generation of State Grid Corporation of China and Tianjin university, during the study.
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Conclusion
In this paper, considering the uncertainties of wind speed, solar radiation and load demand, a stochastic optimal planning model for stand-alone microgrid system is presented based on the chance-constrained programming algorithm. Based on multi-objective genetic algorithm of NSGA-II, optimal planning for an island microgrid system has been carried out, which has verified the model. As the adopted of uncertainties, the optimisation process of stochastic optimal planning method has become more complicated than the deterministic planning method. For the stochastic optimal planning method, it will lead to the generally increasing of the system’s NPC in life cycle and pollutant emissions compared with deterministic planning method. However, it can ensure all of the individuals meet the probability constraint of chance constrained programming, which can guarantee to achieve a more reliable system, and it is more in line with the actual situation. Meanwhile, the optimal objectives of minimisation of the total NPC and carbon dioxide emission in lice cycle are two conflicting objectives, which must be balanced during the actual planning process. For the hard-circle strategy, the coordinated operation between batteries and diesel generators, the multi-unit operation constraints of diesel generators and the system reserve capacity have been considered. As it allows the diesel generator and battery to be main power supply in turn, the running time of diesel generator decreases greatly and thus substantially reduce pollution emissions.
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Acknowledgments
The authors greatly appreciate the financial supports provided form the National High Technology Research and Development Program (863 Program) of China (2011AA05A107), National Nature Science Foundation (Project No. 51207099), the Technical Operations study and 1272 & The Institution of Engineering and Technology 2014
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