The design and dispatch strategy of renewable energy absorption facility on pelagic island

Electrical Power and Energy Systems 118 (2020) 105748

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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes

The design and dispatch strategy of renewable energy absorption facility on pelagic island☆

T

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Suyang Dinga, Xiangning Lina, , Zhe Chenb, Zhixun Wanga, Zhengtian Lia a

State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan 430074, China b Aalborg University, Depth Energy Technology, Aalborg DK-9220, Denmark

A R T I C LE I N FO

A B S T R A C T

Keywords: Renewable energy Energy consumption Hydrogen electrolyzer Decision tree pruning algorithm Reinforcement learning Monte-Carlo method

The peaceful development and utilization of pelagic island occupy vitally important position in the maritime development. For the rich resource islands that support the load center island by shipping, the efficient operation of off-shore renewable energy absorption facility (REAF) is of vital importance. Focusing on this issue, the hydrogen electrolyzer containing multiple energies (battery, hydrogen and cool) is designed in this paper. This design promotes the energy absorption efficiency of REAF significantly. On the other hand, the flexible-size decision tree pruning (FSP) and improved reinforced learning Monte-Carlo method (IRLMCM) are proposed in this paper, and the hierarchical dispatch strategy of REAF based on the above algorithms is designed. Case studies show that the dispatch strategies of REAF proposed in this paper can improve the energy absorption ability significantly. At last, the possible improvement methods of the dispatch strategies of REAF are discussed in this paper.

0. Introduction In recent years, the exploitation of seas and oceans (especially the less developed areas far away from the coast line) has become a global hotspot issue. During the process of exploitation, pelagic islands will act as main supporting bases. As a result, the development of pelagic islands, especially the construction of energy supply system on pelagic islands, is of great importance. Literature [1–4] discussed the basic topology, function and operation mode of pelagic islands, and proposed that the rich resource islands (equipped with renewable energy generators) should support the load center island (main location for human activity with little energy source) by energy packages that contain multiple energy forms. Under this supply-demand mode, the energy link can be constructed wirelessly with transportation. The REAF deployed on rich resource islands can produce electricity, cool, hydrogen and other energy forms, and these energies can be delivered to load center island by cargo ships. Under this circumstance, the boost of operation efficiency of REAF has been the key issue. The researches aiming at renewable energy consumption by multiple energies has been the hot spot in recent years. Literature [5] proposed a probabilistic energy balance analyses of tree-like user-mode

networks with a stochastic end-user population to investigate the energy reliability. Literature [6] established the model of combined heat and power (CHP) in the wind power integration; literature [7] proposed the dispatch strategy that can coordinate the power system and distributed CHP; literature [8–12] analyzed the topology, management and dispatch problems of CHP based on demand side response; literature [13–15] studied the flexibility, environmental friendliness, wind power compatibility and engineering application of electrical-gas combined network; literature [16,17] proposed the design and evaluation method for multiple energy network. These researches have great reference value to the study in this paper. However, they still have some limitations. The energy forms needed in the pelagic islands such as cool and hydrogen is rarely studied. Moreover, these researches assumed that the power production is controllable and the energy absorption facilities keep operating all the time. But on the isolated island where the generators are all based on renewable energy and the power output is hard to control, it is not efficiency or even feasible to keep the REAF operating all the time. The switch states as well as the power of REAF need to be controlled. These problems have not been solved well in the current studies. Focusing on the topic of renewable energy consumption with

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Project Supported by the National Natural Science Foundation of China (51537003); Guangxi Power Grid Corp “The effects and countermeasures of Guangxi grid against large-scaled wind power integration”. ⁎ Corresponding author. E-mail address: [email protected] (X. Lin). https://doi.org/10.1016/j.ijepes.2019.105748 Received 26 December 2018; Received in revised form 6 March 2019; Accepted 27 November 2019 0142-0615/ © 2019 Elsevier Ltd. All rights reserved.

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multiple energies on isolated rich resource islands, this paper proposed an improved design of hydrogen electrolyzer that can utilize the dissipated energy and promote energy efficiency significantly. Moreover, this paper has proposed flexible-size decision tree pruning algorithm, and improved the reinforcement learning Monte-Carlo method. These algorithms are used to construct the hierarchical optimal control and dispatch strategy of REAF in this paper. It is proved by theoretical analysis and case studies that the proposed hierarchical optimal control and dispatch strategy based on the FSP and IRLMCM performs well in coordinating the Boolean variable (switch states) and continuous variable (power) of REAF. This paper has presented effective methods to promote the operation level of renewable energy consumption with multiple energy forms from the aspects of facility design, control/dispatch scheme and algorithm efficiency.

Fig. 1. Schematic diagram of multi-energy hydrogen electrolyzer.

drive the turbine and generate power. The whole process can be seen as an adiabatic expansion since the time is too short for heat exchange. Take H2 as an example, according to state equation of ideal gas:

1. Design and modelling of combined REAF of battery-hydrogencool

(1)

PV = nRT

There are multiple energy forms that are needed on load center island, such as cooling and hydrogen. The preserve of fresh food, the fishery production and the air condition control require large amount of cooling load. The hydrogen can be used in the peak load dispatching power station, and can be directly used on hydrogen powered cars. The cooling facility and hydrogen electrolyzer can be set on rich resource islands. The development of phase change cool storage and hydrogen storage with high energy density has boosted the transmission efficiency of wireless energy link. Because the development of phase change cool storage and hydrogen storage will increase their energy density, thus it will increase the energy transported without influencing the energy expended. According to statistics, the energy storage costs of phase change cool storage and hydrogen storage are individually 37% and 51% lower than lithium battery. However, the low efficiency of hydrogen electrolyzer (usually less than 40%) limits the overall efficiency of energy supply system. Since the costs of hydrogen electrolyzer and storage are relatively low, simply removing hydrogen system from REAF will cause the increase of cost to achieve the same energy capacity. As the result, promoting the efficiency of hydrogen electrolyzer is important to the energy supply system. An improved design of hydrogen electrolyzer is proposed and modeled in this section. This design can utilize the mechanical energy and the heat energy that are wasted in the traditional hydrogen electrolyzer, and promote the consumption efficiency.

where P is the pressure, V is the volume, n is the molar quantity, R is ideal gas constant (R = 8.314J ·mol−1·K−1) and T is the temperature. According to equation of adiabatic expansion: (2)

PV γ = C Cp

where γ = C . Cp is the heat capacity at constant pressure and Cv is the v heat capacity at constant volume. For H2, γ = 1.41. C is a constant number. Solve equation (1) and (2), the result is: 1 − 1γ

T1 P = ⎛ 1⎞ T2 ⎝ P2 ⎠ ⎜

⎟

(3)

where T1 and P1 are the temperature and pressure before expansion while T2 and P2 are those after expansion. The calculation shows that the temperature of H2 will be 194.05 K (about −79 °C) after the adiabatic expansion. The cool energy can also be absorbed by cool storage equipment. H2 and O2 after adiabatic expansion contain considerable cool energy that can be absorbed by phase change materials and transported to load center island. The “charged” phase change material can be directly used in the refrigeration warehouse, or even in the central air conditioners of some public places. This will reduce the cool load and the corresponding fuel consumption on load center island significantly. Since the gas temperature after is 194.05 K, it is suitable to use the phase change material of normal refrigeration temperature (around 255 K) to absorb the cool energy. According to literature [18], the material containing HOCH2CH2OH solution (15 wt%) and NH3CL solution (25 wt%) has the phase change temperature of 255.9 K (-17.10℃). The latent heat of phase change is I = 304.00 kJ·kg−1 and the heat capacity is C = 4.013 kJ·kg−1·K−1. So in the heat exchanger, the temperature of H2 and O2 will rise to 255.9 K. During the adiabatic expansion, since there is no heat exchange between hydrogen and the atmosphere, the energy of mechanical work equals the change of internal energy. According to internal energy equation:

1.1. An improved design of hydrogen electrolyzer In the hydrogen electrolyzer, the pure water is mixed with strong alkali (KOH), and resolved into H2 and O2 under DC current. H2 and O2 will be separated, washed, dried and cooled before exhausted. Take a commercial hydrogen electrolyzer as an example, the production rate of hydrogen is 0.05 mol/s. The efficiency is 0.05 mol/s × 284.7 kJ/ mol ÷ 40 kW = 35.59%. However, the temperature and pressure of H2 and O2 at the exhaustion port are very high. Since the gases are usually decompressed and cooled by pressure reducing valve in the traditional hydrogen electrolyzer, this part of energy is wasted. To utilize this part, an enhanced hydrogen electrolyzer scheme is designed as in Fig. 1: In Fig. 1, the electrolyzer part is the same as the traditional one. The complementary energy utilization attached to the traditional electrolyzer can produce electricity and cool energy using the internal energy of hydrogen and oxygen. What needs to be illustrated is that the electricity and cool energy is subjected only to the production of electrolyzer, and not related to the battery and specialized refrigeration machine in the whole REAF system. The production rates of H2 and O2 are individually 0.05 mol/s and 0.025 mol/s. At the exhaustion port, the temperature of the gases is 712.2 K and the pressure is 70 MPa. H2 will be put into hydrogen tank (0.8 MPa, 293 K), and O2 will be directly released into atmosphere. The energy of pressure release can be used to

Ein = 2.5nRT

(4)

where Ein is the internal energy. Considering the mechanical efficiency of turbine is high (ηturbine ⩾ 95%), the electric power is no less than: dEin ·ηturbine = 2.5·0.05(mol/s )· dt 8.314(J ·mol−1·K−1)·518.15K ·95\% = 511.6W

(5)

The cool power of heat exchanger is: dn Cp· dt ·ΔT

= 14.268(J ·g −1·K−1)·0.05(mol·s−1)·

2(g ·mol−1)·61.85K = 88.25W

(6)

Likewise, the electric power and cool power is only subjected to the 2

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For the phase change cool storage, only the dissipation of cool energy needs to be considered. Sponge rubber (thermal conductivity 0.031W/(m·K) ) material is commonly used as the filling material of cool storage. For tubular cool storage container, the thickness of sponge rubber should be [19]:

⎧ δ=

D0 (X − 1) 2 2λ (ts − t f )

⎨ X ln X = ⎩

production of hydrogen, and will not be influenced by the battery electric power and specialized refrigeration power of REAF. It can be seen from above that in the hydrogen exhaustion port, the proposed design can generate 600 W extra power. Similarly, the oxygen exhaustion port can also generate 410.5 W extra power. Take an actual operational hydrogen plant of 15 electrolyzers (annual hydrogen production 11,826 kmol) as an example, the total modification cost is no more than $25,000. However, the annual extra energy generation is about 66357 kW·h. Under the electricity price of 0.417$/kW·h in pelagic islands, this extra energy means $27,650 extra income. The profit of a single year is more than the modification cost. For pelagic islands with larger scale of hydrogen electrolyzers, the profit will be considerable.

q=

According to Section 1.1, the proposed hydrogen electrolyzer produces electricity and cool energy as well as hydrogen. So, it is coupled with battery and cool storage system. The topology of REAF is as Fig. 2. There is no regular load on rich resource islands. During the period when no electric ship is attached for charging, the renewable energy generation can only be consumed by REAF. The battery and cool storage can consume energy from renewable energy generator and hydrogen electrolyzer.

(8)

(12)

(13)

where, P hy (t ) is the real-time power of multi-energy composite hydrogen electrolyzer, P hy.min is the minimum operating power, P hy.rate is the rated power. The multi-energy composite hydrogen electrolyzer involves output in multiple energy forms, given by

⎧ P hy.hy (t )= ηhy.hy ·P hy (t ) ⎪ P hy.the(t )= ηhy.the ·P hy (t ) ⎨ ⎪ P hy.elec (t )= ηhy.elec ·P hy (t ) ⎩

(9)

where Δt is the step length and Eele.0 is the energy capacity of battery.

(14)

where P hy.hy (t ) , P hy.the(t ) and P hy.elec (t ) represent the equivalent output power of hydrogen, cool and electricity in the multi-energy hydrogen electrolyzer, respectively, ηhy.hy , ηhy.the and ηhy.elec represent the output efficiency of hydrogen, cool and electricity in the multi-energy hydrogen electrolyzer, respectively, and ηhy.hy + ηhy.the + ηhy.elec ⩽ 1, where ηhy.hy = 35.59%, ηhy.elec is determined according to the SOC(t) of the battery energy storage system, satisfying ⎧ ηhy.elec.rate (SOC (t ) < SOCup) ηhy.elec = , where ηhy.elec.rate represents the ⎨0 (SOC (t )⩾ SOCup) ⎩ standard generation efficiency of multi-energy hydrogen electrolyzer where absorption state is not considered. Similarly, ηhy.the is determined

1.2.2. Modelling of cool system The cool system contains refrigeration facility and phase change cool storage system. To simplify the analysis, the refrigeration power will be converted to the power of refrigeration machine. The power limit of refrigeration machine is:

Pthe . min ⩽ Pthe (t ) ⩽ Pthe . rate

1 αs XD0

P hy.min ⩽ P hy (t )⩽ P hy.rate

where Pele (t ) is the power of battery, Pele, max is the maximum power of battery. SOCele.down and SOCele.up are the upper and lower limits of the state of charge (SOC) of battery. The recursion formula of SOC is:

Eele.0 SOCele (t + Δt ) = Eele.0 SOCele (t ) + Pele (t )Δt

ln X +

1.2.3. Modelling of hydrogen electrolyzer The multi-energy hydrogen electrolyzer only works as a power load. In order to ensure the normal operation, the power of the hydrogen electrolyzer should meet the following constraint:

1.2.1. Modelling of battery The battery on rich resource island has 2 main functions: store energy and coordinating the operation of the entire REAF. The maximum power limit and state of charge limit of battery are:

SOCele.down ⩽ SOC (t ) ⩽ SOCele.up

π (tk − t f ) 1 2λ

Actually, the phase change cool storage container can operate under 2 conditions. The first is that the temperature of material is higher or lower than phase change temperature. Under this condition, the container can absorb the cool energy. However, since the heat capacity of phase change material is not high, the fluctuation of temperature will influence the operation of the container. In the actual application, this condition should be avoided. The second is at the phase change temperature. Under this condition, the latent heat capacity of phase change material is high enough. This is the normal operation condition of the container. As a result, 2 parameters, SOCthe (State of Cooling) and Tthe , are set to describe the states of phase change cool storage. SOCthe is the state of cooling under phase change temperature, and Tthe is the temperature of the material. Only when Tthe is at phase change temperature, SOCthe is meaningful. To avoid the operation under overcooling condition, when SOCthe = 100\% , the refrigeration machine should stop working. However, the cool energy from the hydrogen electrolyzer can still be absorbed by the container to compensate the cool loss.

1.2. Modelling of REAF

(7)

(11)

where δ is the thickness of material, λ is the thermal conductivity, X is the ratio of external/internal diameter, D0 is the internal diameter, ts is the surface temperature of material, tf is the internal temperature of the container, tk is the temperature of atmosphere, αs is the surface heat emission coefficient of material, αs = 8.14 W/(m2·K) . The cool loss per unit length of the container is:

Fig. 2. Topology of REAF with battery-hydrogen-cool.

|Pele (t )| ⩽ Pele, max

D0 αs (tk − ts )

(10)

where Pthe(t ) is the real time power, Pthe.min is the minimum operation power and Pthe.rate is the rated power. Since the refrigeration facility is not operational all the time, a Boolean value Sthe is needed to describe the switch statues. Sthe = 1 means the facility is operating and Sthe = 0 means the facility is shut down.

(Tthe ⩾ Tpc ) ⎧ ηhy.the.rate by Tthe of cool storage container, ηhy.the = ⎨ ηhy.the.rate ·p(Tthe) (Tthe < Tpc) ⎩ 3

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, where ηthe.rate represents the standard refrigeration efficiency of multienergy hydrogen electrolyzer where absorption state is not considered, p(Tthe ) = e−1 + Tthe/ Tpc is the penalty factor that represents the degree of how the temperature of the phase-change cool storage system is lower than that of the phase-change temperature, p(Tthe )⩽ 1. As described in Section 1.2.2, the penalty function is set to avoid the phase-change cooling system from working below the phase-change temperature. As the multi-energy composite hydrogen electrolyzer is operating all the time, the switch state should be represented by Boolean valueShy . Shy = 1means the facility is operating and Shy = 0 means the opposite.

⎧ ⎪ ⎪ ⎪

M

ηele · ∑ (Pele.j + ηhy.ele ·P hy.j ) j=1 M

M

⎫ ⎪ ⎪ ⎪

E0 = Δt· ∑ (Pthe.j + ηhy.the ·P hy.j) − ∑ Q (Tthe.j ) ⎬ ⎨ j=1 j=1 ⎪ ⎪ M ⎪ ⎪ η P · ∑ hy.j hy.hy ⎪ ⎪ j = 1 ⎭ ⎩

(15)

where line 1 is the energy increment of battery, and ηele is the charging/ discharging efficiency; line 2 is the energy increment of phase change cool storage system, and Q (Tthe.j) is the cool loss function defined as formula (12); line 3 is the energy increment of hydrogen storage. What needs illustration is that since the refrigeration can be seen as production process instead of energy storage process (because the cool energy is used directly and cannot be turned into electricity again), the efficiency of refrigeration can be seen as 100%. The objective function within dispatching interval can be defined as:

2. The hierarchical optimal control and dispatch strategy of REAF For rich resource islands, the renewable energy generation in the daytime can be consumed by the charging load of fish boats, public transportation ship and so on. However, during the night when the wind power is more adequate, there is no external charging load and the generated energy can only be consumed by the REAF on rich resource islands. This period can be defined as non-charging interval period. The produced energies will be transported to load center island by cargo ships in the morning. The control and dispatch of REAF during non-charging interval period are the key factors to promote the efficiency of energy supply system of pelagic islands. The main target of REAF should be using the limited amount of energy (produced by renewable generators) and limiting energy capacity within a certain period (non-charging interval period), so as to achieve the maximum amount of energy that can support the load center island. Since the refrigeration system and the multi-energy hydrogen electrolyzer contained in the REAF system have minimum power limits, they are not suitable to keep operating all the time. The renewable energy generators cannot ensure that their minimum power limits are satisfied at any time. Though the battery can be used to support the power requirement, the problems of poor economic efficiency and the limited energy capacity are hard to solve. The switching states of refrigeration system and the hydrogen electrolyzer need to be controlled too. However, the switching state should not be changed frequently to avoid the damage on the facility. Hierarchical tree topology has been proposed [20,21] to facilitate energy balance management and energy dispatching mechanisms for smart energy webs, as well as control the power regulated DC/DC drivers for power distribution. This kind of hierarchical structure can also be used to design the optimal control and dispatch strategy of REAF. The hierarchical optimal control strategy of combined REAF system is proposed in this section. Within each dispatching interval, only the powers of components in REAF system are controlled; between dispatching intervals, the switch states of components in REAF system are altered. Therefore, the switch states of hydrogen electrolyzer and refrigeration machine will keep unchanged for 15 min at least, thus the avoidance of frequent switching states of REAF can be achieved.

f = S · E0

(16)

The objective function represents the amount of effective energy consumption with a dispatching interval. The convention constraint condition is:

|Pele.j| ⩽ Pele, max ⎧ ⎪ Sthe·Pthe.min ⩽ Pthe.j ⩽ Sthe·Pthe.rate ⎨ Shy ·P hy.min ⩽ P hy.j ⩽ Shy ·P hy.rate ⎪ Pele.j + Pthe.j + P hy.j = Pge.j ⎩

(17)

where Pge is the real time power output of renewable energy. Once a component of REAF reaches its energy capacity limit, the component should quit operation. So the energy state should be calculated by recursion formula. There is only 1 energy state variable of battery, SOCele . The recursion formula is:

SOCele.j + 1 = SOCele.j + (Pele.j + ηhy.ele ·P hy.j)·Δt / Eele0

(18)

where Eele0 is the total capacity of battery. There are 2 energy state variables of phase change cool storage system, Tthe and SOCthe . The recursion formulas are:

Tthe.j + 1 =

⎧Tthe.j ⎨ Tthe.j + ⎩

(0% ⩽ SOCthe.j ⩽ 100%) (Pthe.j + ηhy.the·P hy.j − Q (Tthe.j))·Δt m·C

(SOCthe.j = Null) (19)

SOCthe.j + 1 =

⎧ Null ⎪ (Tthe.j ≠ Tpc ) ⎨ (P ·P +η − Q (Tthe.j))·Δt ⎪ SOCthe.j + the.j hy.the hy.j (Tthe.j = Tpc ) m·I ⎩ (20)

where m is the mass of phase change material. What needs illustration is that SOCthe makes sense only when Tthe = Tpc . If the material is at nonphase-change area, the temperature will be calculated by specific heat capacity. The recursion formula of hydrogen electrolyzer is:

2.1. Control strategy of REAF within dispatching interval The control strategy of REAF within dispatching interval mainly depends on the power output prediction of renewable energy. Since the precision of ultra-short term weather forecast is high enough, it is assumed that the weather forecast and the corresponding power output forecast in 15-minute dispatching interval have no bias compared to actual values. Unless the refrigeration system and the multi-energy hydrogen electrolyzer have reached their upper capacities, the switching state will not be changed; the battery is always operational. That is, Sbatt = 1; Sthe and Shy are 1 or 0. The switching state matrix of REAF can be defined as S = {Sbatt, Sthe, Shy } . Assuming that the total time of an interval can be equally divided into M parts, and each part is Δt, the inherent energy consumption of REAF can be described in matrix form as:

SOChy.j + 1 = SOChy.j + ηhy.hy ·P hy.j·Δt / Ehy0

(21)

The SOCthe and SOChy influence the switching state of REAF in the following dispatching interval. If SOCthe = 100%, the refrigeration system will be shut down in the following interval; if SOChy = 100\% the hydrogen electrolyzer will also be shut down. So the augmentation constraint condition is:

⎧ Pthe.j + 1, Pthe.j + 2, ...,Pthe.M = 0 (SOCthe.j = 100%) ⎨ P hy.j + 1, P hy.j + 2, ...,P hy.M = 0 (SOChy.j = 100%) ⎩ 4

(22)

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Table 1 Energy consumption under different algorithm. Energy consumption (kW·h) Improved Improved Improved Improved Improved

genetic algorithm particle swarm algorithm neural network algorithm simulated annealing algorithm fruit fly algorithm

51.2 51.1 49.7 50.5 51.2

As for the selection of optimal algorithm, the main algorithms include genetic algorithm, particle swarm algorithm, neural network algorithm, simulated annealing algorithm and fruit fly algorithm. Literature [22–26] have introduced and improved the above algorithms, boosted their convergence rate, global searching ability, robust performance and so on. The performances of these algorithms are tested by simulations (the simulation data are captured from some data in Section 3). The interval length is 15 min and the step length is 1 min. The switching state matrix is {1, 1, 1} . The maximum iteration number is 100. The initial value is to minimize the power of battery while all the constraint conditions are satisfied. The result is shown in Table 1. It can be seen from Table 1 that the performances of improved neural network algorithm and improved simulated annealing algorithm are slightly worse than others. The performances of improved genetic algorithm, improved particle swarm algorithm and improved fruit fly algorithm are almost the same. Fig. 3 shows the power distribution scheme of improved fruit fly algorithm. Actually, the control strategy of REAF is not limited to the above optimal algorithms, other algorithms are also available. However, since the energy consumption of REAF has little improvement room, and the performance of the above algorithms is satisfactory, the improved fruit fly algorithm is used to construct the control strategy of REAF within dispatching interval in the following content.

Fig. 4. A dispatch scheme of non-charging section.

The selection of optimization method highly depends on the scale of the decision tree. To the small-scaled decision tree, the exhaust method is suitable to find the optimal solution; for the medium-scaled decision tree, the random Monte-Carlo method can be used to reduce the complexity of decision tree and obtain the maximum likelihood optimal solution; but the optimization method for large-scaled decision tree has always been the difficult and high focused issue. For the dispatch strategy of REAF between dispatching intervals, the complexity of decision tree is 4N . Assuming that the non-charging section is 20:00 to 8:00 (next day), and the interval is 15 min, N = 48. So the scale of switching dispatch decision tree is too large to be solved by exhaust method or random Monte-Carlo method. In recent years, there are 2 kinds of ways to solve the optimal problem of large-scaled decision tree: the first is using proper pruning algorithm to reduce the scale of decision tree, and obtain the solution with the simplified decision tree; the second is setting additional functions in the process of random Monte-Carlo search to boost its performance. These 2 kinds of ways are both analyzed in the construction of dispatch strategy of REAF between dispatching intervals.

2.2. Dispatch strategy of REAF between dispatching intervals Once the control strategy of REAF within dispatching interval is determined, the key issue is to dispatch the switching state between dispatching intervals. That is, determining S = {Sbatt, Sthe, Shy } of each interval. The optimal objection of the dispatch strategy is maximizing the energy that can be delivered to load center island. The process of a dispatch scheme is shown in Fig. 4 In Fig. 4, each interval has its switching state, and a complete dispatch scheme is consist of N switching state matrix (assuming the noncharging section contains N intervals). The route marked in red arrow is a possible dispatch scheme. Under certain renewable energy power output condition, if the control strategy (described in Section 2.1) and the dispatch strategy are confirmed, the amount of energy that can be transported is also determined. Therefore, the dispatch strategy problem can be seen as optimization process of decision tree. The initial state of REAF is the root node and the final energy output is the leaf node.

2.2.1. Dispatch strategy based on decision tree pruning algorithm The dispatch strategy based on decision tree mainly contains 2 parts, the decision tree pruning part and the dispatch scheme online evaluation part. For the decision tree pruning part, since the operation time of REAF in a day is fixed (take 20:00 to 8:00 of next day as example), and the connected renewable energy is fixed (to the pelagic island, only wind power), the power output during the operation time is only related to the wind condition. For a certain area, the wind condition follows relatively stable meteorological pattern, so the optimal dispatch strategy schemes also follow the corresponding pattern. As a result, for the complete decision tree of REAF dispatch strategy, there must be redundant brunches that will never be the optimal dispatch schemes under the meteorological pattern. These redundant brunches need to be pruned in advance to boost the online evaluate efficiency. The dispatch scheme online evaluation part is using the wind power prediction to exhaust the pruned decision tree and acquiring the optimal scheme. It is obvious that the decision tree pruning part is the key point in the dispatch strategy of REAF based on decision tree. The decision tree pruning algorithm has been studied deeply in recent years. The Minimax search algorithm [27] and the α-β pruning algorithm [28] have been widely used in the game problem. For example, the chess software Stockfish is constructed on the basis of α-β pruning algorithm and had been the best chess software until Alpha Go was released. However, these algorithms mainly focus on the issue of maximum winning probability instead of optimal result searching, and not suitable for being applied to the dispatch strategy of REAF. The decision tree pruning algorithms that focus on optimal result searching mainly include Cost-Complexity Pruning (CCP), Minimum-Error Pruning (MEP), Pessimistic-Error Pruning (PEP) and Reduced-Error

Fig. 3. Power distribution of optimized fruit fly algorithm. 5

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Pruning (REP). The CCP algorithm has relatively long training time and risk of ignoring the optimal pruning set, so the performance of CCP is worse than other algorithms [29]; the MEP algorithm can prune the decision tree depends only on training sample set (without independent pruning data set), but the searching efficiency will be affected since the size of MEP pruned decision tree is always too large [30]; the scale of training set required by PEP algorithm is relatively small, and the precision of PEP is high [31], but the top-to-down pruning process may lead to over pruning or pruning failure [32]; REP algorithm has the highest precision and always act as the criterion to evaluate other pruning algorithms, but the training set required by REP is too large, and the down-to-top pruning method (with poor efficiency) makes it hard to handle the pruning of large-scaled decision tree [33]. The principles of above pruning algorithms have high reference value, but cannot be directly applied in the decision tree pruning of REAF dispatching. Based on the basic principle of pruning and the requirement of REAF dispatching, the flexible-size pruning (FSP) algorithm is proposed. This pruning algorithm can adjust the size of decision tree according to the requirement and balance the precision and concision. The procedure of FSP is as followed: Assuming the decision tree contains N layers, ti.k is the k-th node in the i-th layer. For the original decision tree, there are 4i-1 nodes in the ith layer. First, an initial test set S0 is produced and used on the decision tree. The final energy outputs of every scheme in S0 are ranked. The medium energy output Eoutput.cri is used as the criterion to judge the performance of each leaf node. The leaf node with more energy output than Eoutput.cri is marked as “good” node; otherwise, marked as “bad” node. Second, all the “bad” nodes are traced back. If 2 or more “bad” nodes share the same non-leaf node with the most expansion depth (namely, the non-leaf node should be the farthest to the root node), and there is no “good” node generated from this non-leaf node, there are good reasons to suspect that this non-leaf node cannot produce “good” node. These non-leaf nodes are marked as “quasi-pruning node”. Third, all the quasi-pruning nodes are retested. A sub-test set S0.test is appended to each quasi-pruning node and further expand this node. If the leaf nodes of S0.test are all worse than Eoutput.0 , the quasi-pruning node will be pruned. The whole process is shown in Fig. 5. In Fig. 5, “bad” nodes tN.1 and tN.2 are all generated by ti.k , and ti.k is the farthest one from root node. Since there is no “good” node generated by ti.k , it is marked as quasi-pruning node. tN.3, tN.4 and tN.5 are contained in sub-test set S0.test. since they are all “bad” nodes either, ti.k is pruned. Repeat this procedure until all the qualified non-leaf nodes are pruned. Forth, add new test elements to S0 and form a new test set S1, update Eoutput.cri and repeat the above steps until the terminal condition is satisfied. The decision tree pruning process of REAF dispatch based on FSP is shown in Fig. 6

Fig. 6. Switch strategy of REAF based on FSP.

What need illustration is that the terminal condition has great influence on the size of decision tree. If it ends too early, the size of decision tree will be too large to satisfy the rapidity requirement of dispatching; if it ends too late, the decision tree may be over pruned and cut off some potential optimal brunches. In this particular case, the REAF will exhaust the pruned decision tree to find the optimal scheme corresponding to the wind condition, so the calculation time has direct ratio with the number of leaf nodes. Meanwhile, in the first dispatch interval, since the exhaustive calculation starts from the root node and corresponds to the maximum number of leaf nodes (all the leaf nodes), the calculation time of first dispatch interval is the longest. So if the calculation time of the first dispatch interval is satisfied, and the corresponding number of leaf nodes is set as terminal condition, the optimization performance will be the highest on the premise of rapidity requirement. The REAF will decide the switch states of all the following intervals based on the control strategy of REAF within dispatching interval proposed in Section 2.1 and the power output prediction. Since the power output prediction of renewable energy keeps updated, the switch states will be updated accordingly. When the season or the local climate changes, the decision tree should be regenerated to guarantee the effectiveness. 2.2.2. Dispatch strategy based on reinforcement learning Monte-Carlo algorithm Except for the pruned decision tree, improved Monte-Carlo method also can be used in the dispatching of REAF. Literature [34] proposed a dimension reduction method to discontinuous optimization function based on Quasi-Monte Carlo search; literature [35] proposed a Monte Carlo search combined with importance sampling to avoid missing small probability events; literature [36] introduced a reversible proposal transition kernel to boost the convergence rate of Markov chain Monte Carlo method. Among these researches, Reinforcement Learning Monte-Carlo Method (RLMCM) is one of the most effective methods dealing with optimal issue of high-dimensional decision tree. RLMCM was used to construct the core algorithm of AlphaGo Zero [37] in the first place, and defeated the original AlphaGo [38] in the test. RLMCM is classified as self-gaming optimal algorithm, which does not need human knowledge to instruct the searching process. There are 4 parameters of each non-leaf node, profit function W (ti.k ) , search times N (ti.k ) , value function V (ti.k ) and search preference function SP (ti.k ) . W (ti.k ) is the accumulated profit of all the brunches generated from ti.k ,

Fig. 5. Decision tree pruning of FSP. 6

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3. Simulation analysis

and N (ti.k ) is the number of brunches generated from ti.k . V (ti.k ) and SP (ti.k ) need further definition. Literature [34] define V (ti.k ) as W (t ) V (ti.k ) = N (t i.k ) , which means the average profit of ti.k . The purpose of i.k this definition is to expand the evaluation range in the game of go, and avoid being defeated by “unconventional” moves. However, for the dispatching of REAF, this definition is not proper. The training samples in the early period might have random low profit, and will continuously affect V (ti.k ) under this definition. This may have bad influence on the optimization searching process. In this paper, the value function is defined as:

W (ti.k )/ N (ti.k ) V (ti.k ) = ⎧ W ⎨ ⎩ Nmax (ti.k )/ Nmax

(N (ti.k ) ⩽ Nmax ) (N (ti.k ) > Nmax )

The simulation cases are all based on the actual configuration and meteorological data in a pelagic island in Pacific Ocean during consumption time (20:00 to 8:00). According to Section 2.1, the improved fruit fly algorithm has been chosen to control REAF within the dispatch interval. Therefore, the case studies mainly focus on the comparison of dispatch strategies between intervals. The simulation platform is 4-core Intel X3440 processer with standard frequency of 2.53 GHz. The maximum allowed calculation time is 5 min. Since the actual project will adopt computers far more powerful than personal computer, the equivalent calculation time is far less than 5 min and can satisfy the time requirement of dispatch. Since the meteorological condition of the island changes from season to season (spring-summer season and autumn–winter season), the dispatch strategy based on decision tree pruning algorithm will be modified accordingly. Only the meteorological data of autumn-winter season (September 1st to February 28th) of 2015 and 2016 are used to simplify the analysis. The basic parameters are shown in Table 2 (the photovoltaic generators are not listed).

(23)

where Nmax is the maximum number of samples. When the access time of ti.k is large, V (ti.k ) will only take the latest Nmax samples to evaluate ti.k and avoid the above problem. The search preference function SP (ti.k ) represents the visit preference of ti.k . Theoretically, the node with higher V (ti.k ) should be visited more often to gain higher result. However, the greedy search of a node with highest V (ti.k ) is inevitable if SP (ti.k ) = V (ti.k ) , and the Monte-Carlo search will fall into premature convergence. To prevent the above problem, SP (ti.k ) can be set as:

SP (ti.k ) = cV (ti.k ) +

log (N (∑ ti.k )) N (ti.k )

Strategy 1: The switch state is altered according to the average wind power of each interval, as shown in Table 3. Strategy 2: Prune the decision tree based on PEP algorithm and produce simplified decision tree. When the consumption begins, use the exhaustion method to find the optimal leaf node. The training set is the meteorological data of 2015, and the trained decision tree is used to dispatch the REAF in 2016. After the pruning, the number of leaf nodes is 3314. What needs further illustration is that the CCP, MEP and REP algorithms cannot prune the decision tree to satisfy the requirement of calculation time. Strategy 3: Produce the simplified decision tree based on the FSP pruning algorithm proposed in this paper. Other methods are the

(24)

where N (∑ ti.k ) is the total number of training samples, c is a constant value that can be used to adjust the influence of V (ti.k ) . It can be seen that the less a node has been visited, the larger

log (N (∑ ti.k )) N (ti.k )

will be.

This design is to guarantee that even if the value function is not large, the corresponding node will be visited several times to avoid greedy search. The new algorithm is defined as improved reinforcement learning Monte-Carlo method (IRLMCM). To sum up, the dispatch strategy of REAF based on IRLMCM is shown in Fig. 7. Theoretically, the more time IRLMCM searches, the more precise the optimal result will be. As a result, the searching time should be as much as possible within the limitation. So, the terminal condition can be set as the maximum calculation time allowed. Similar to the dispatch strategy based on decision tree pruning algorithm, as the dispatch interval moving forward, the calculation complexity will reduce accordingly. However, the IRLMCM does not need a particular calculation time to output the optimal scheme like the pruned decision tree. Instead, it can output a result anytime based on the current value functions (though the result may not be the real optimal one if the calculation time is too short). Moreover, since IRLMCM does not require human knowledge or precondition, it is unnecessary to adjust the dispatch strategy when the season or the climate changes. This feature makes the algorithm more flexible and universal.

Table 2 Relative parameters for case study. Facility

Index

Parameter

Wind turbine

Rated power Number Cut-in speed Rated speed Cut-out speed Charge/discharge efficiency SOC limit Energy dendity Rated capacity Maximum power Rated power Minimum power Production speed of hydrogen Hydrogen efficiency Electricity efficiency Cooling efficiency Weight Rated capacity Operation temperature Energy capacity Number Rated power Minimum power Phase change latent heat Phase change temperature Non-phase change heat capacity Weight Power of cool loss

20 kW 40 2.5 m/s 10 m/s 45 m/s 0.9

Battery

Multi-energy hydrogenelectrolyzer

Hydrogen storage

Cooling machine Phase change cool storage

Fig. 7. Switch strategy of REAF based on IRLMCM. 7

10%–90% 110Wh/kg 1.4 MW·h 350 kW 200 kW 100 kW 0.25 mol/s 35.59% 2.1%/0% 0.5% p(Tthe) 50 kg 1123.15 mol 300 K 88.83 kW·h 10 500 kW 150 kW 84.44Wh/kg 255.9 K 1.2Wh·kg−1·K−1 31.4 t 1219.3 W

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Table 3 Switch states of strategy 1.

Table 4 Switch dispatch of a regular day.

Wind power/kW

Sbatt

Sthe

Shy

Strategy

Interval 1

…

Interval 25

…

Interval 48

0–100 100–200 200–500 500–800

1 1 1 1

0 0 1 1

0 1 0 1

1 2 3 4 5

(1,1,0) (1,0,1) (1,0,1) (1,0,1) (1,0,1)

… … … … …

(1,1,0) (1,1,0) (1,1,0) (1,0,1) (1,1,0)

… … … … …

(1,0,1) (1,1,0) (1,1,0) (1,1,0) (1,1,0)

same as strategy 2. Limited by calculation time, the number of leaf nodes is 5831. Strategy 4: Based on the Monte-Carlo searching method containing reversible proposal transition kernel proposed in literature [36], and dispatch REAF only according to the meteorological data of 2016. Strategy 5: Based on the IRLMCM proposed in this paper, and dispatch REAF only according to the meteorological data of 2016.

Table 5 State of energy of REAF of a regular day.

3.1. Case of regular day Regular day can represent most of the meteorological conditions of the season. The wind pattern is relatively constant during the consumption time. Take November 10th, 2016 to November 11th, 2016 as an example, the timely wind power output is shown in Fig. 8: It can be seen that the peak of wind power output mainly locates between 0:00–4:00. During the 182 days of autumn-winter season, there are 151 days that follows the similar pattern. Strategy 1–5 are individually used to dispatch REAF under this condition, and the results are shown in Table 4: After the non-charging consumption section, the states of energy of REAF are shown in Table 5. It can be seen from Table 5 that the performances of strategy 2, 3 and 5 are the same. They achieve the same dispatch scheme and energy output. It can be speculated that they all find the optimal leaf node of the decision tree. Due to the weak search ability, strategy 4 did not find the optimal leaf node, resulting in less energy consumption. Strategy 1 has the worst performance among all the strategies. Run the simulation to all 151 regular days, the average energy consumption of different strategies is shown in Table 6: It can be seen from Table 6 that strategy 3 and 5 always keep the same highest dispatch performance. The decision tree of strategy 2 is over pruned and may not find the optimal dispatch scheme occasionally, but the overall performance is acceptable. Strategy 1 and 4 have the worst performances.

Strategy

Battery/kW·h

Hydrogen/kW·h

Cool/kW·h

Sum/kW·h

1 2 3 4 5

1009.6 1251.2 1251.2 1204.9 1251.2

659.0 370.8 370.8 544.8 370.8

2186.1 2647.5 2647.5 2276.4 2647.5

3854.7 4269.5 4269.5 4026.1 4269.5

Table 6 Average energy consumption of regular days. Strategy

1

2

3

4

5

Energy Consumption/kW·h

3771.8

4147.5

4147.9

4050.7

4147.9

Fig. 9. Power output of Wind energy. Table 7 Switch dispatch of a irregular day.

3.2. Case of irregular day During the whole autumn-winter season, there are some days with abnormal wind conditions. The wind distribution of these days does not have a certain pattern. Take February 8th, 2017 to February 9th, 2017 as an example, the timely wind power output is shown in Fig. 9: It can be seen that the overall wind power output is low and the distribution is different from Fig. 8. Dispatch the REAF with strategy 1–5 and the results are shown in Table 7. After the non-charging consumption section, the states of energy of

Strategy

Interval 1

…

Interval 25

…

Interval 48

1 2 3 4 5

(1,1,1) (1,1,1) (1,1,1) (1,0,1) (1,0,1)

… … … … …

(1,0,0) (1,0,0) (1,0,1) (1,0,1) (1,0,1)

… … … … …

(1,0,0) (1,0,1) (1,1,0) (1,0,1) (1,1,0)

REAF are shown in Table 8. It can be seen from Table 8 that for irregular wind distribution, strategy 5 is not influenced and keeps the highest amount of energy consumption. Limited by its search ability, strategy 4 cannot achieve enough energy consumption. For strategy 2 and 3, since most of the elements of train set are regular wind conditions, the performances in irregular days are heavily influenced, especially for strategy 2, which is Table 8 State of energy of REAF of an irregular day.

Fig. 8. Power output of Wind. 8

Strategy

Battery/kW·h

Hydrogen/kW·h

Cool/kW·h

Sum/kW·h

1 2 3 4 5

975.3 1017.6 1095.8 996.7 1240.3

157.6 268.1 127.8 131.7 30.8

1503.4 1558.2 1821.5 1906.4 2002.9

2636.3 2843.9 3045.1 3034.8 3238.0

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current day. Specifically speaking, assuming a node of historical day has the value function V ′ (ti.k ) , the initial value of the corresponding node of current day can be set as V (ti.k ) = (1 − H ) V ′ (ti.k ) . This method can reduce the calculation time significantly. Case studies shows that compared to the original strategy based on IRLMCM, the one with initialized decision tree can converge to the same optimal result within 1/ 10 or less time.

Table 9 Average energy consumption of irregular days. Strategy

1

2

3

4

5

Energy Consumption/kW·h

2719.5

3095.4

3351.2

3417.8

3523.6

Table 10 Average energy consumption of REAF.

5. Summaries

Strategy

1

2

3

4

5

Energy Consumption/kW·h

3592.6

3968.3

4012.2

3942.9

4041.6

Focusing on the issue of renewable energy consumption of noncharging interval time in rich resources island, those works are accomplished in this paper:

over pruned and has less leaf nodes. Strategy 1 remains to be the worst. Run the simulation to all 31 irregular days, the average energy consumption of different strategies is shown in Table 9: The similar conclusions can be summarized from the results of Table 9

1) Design an improved hydrogen electrolyzer that can utilize the complementary energy to produce electricity and cool energy; 2) Construct the control strategy of REAF within dispatching interval based on intelligent algorithm (improved fruit fly algorithm); 3) Propose FSP algorithm and IRLMCM algorithm, and construct the dispatch strategy of REAF between dispatching intervals based on those algorithms; 4) Verify the superiority of the proposed dispatch strategies based on FSP algorithm and IRLMCM algorithm, and analyze the potential ways to further improve the performances.

3.3. Simulation summaries The complete analysis of 182 days of autumn–winter season is shown in Table 10. It can be seen that strategy 5 has the best consumption performance, and is less influenced by the change of meteorology. The superiority of the IRLMCM proposed in this paper is proved. The overall performance of strategy 3 is fulfilling and the effectiveness of FSP is also proved. But the irregular wind condition will influence the amount of energy consumption. Strategy 2 with PEP algorithm has similar but more severe problems as strategy 3. The performance of strategy 4 is not satisfying because of the weak search ability, but still better than strategy 1. To sum up, the strategies based on IRLMCM or FSP have better performance than others. The adaptive ability of IRLMCM is higher than that of FSP

References [1] Lin X, Chen C, Zhou X. Integrated energy supply system of pelagic clustering islands. Proc CSEE 2017;37(01):98–110. [2] Ding S, Yu Z, Lin X. The optimum strategy of renewable energy generation configuration schemes in pelagic islands based on gray matching algorithm of probabilistic image. Proc CSEE 2018;38(19). 5653-5667+5923. [3] Wang Z, Lin X, Ding S. Hybrid AC/DC wind energy system in an independent island microgrid and its optimal dispatching strategy. Proc CSEE 2018;38(16). 46924704+4974. [4] Zhang Z, Lin X, Ding S. (2018/OL) A dual-standby power source planning scheme for a micro grid in pelagic island. Proc CSEE: 1–12. [5] Alagoz BB, Kaygusuz A, Karabiber A. A user-mode distributed energy management architecture for smart grid applications. Energy 2012;44(1):167–77. [6] Chen X, Kang C, O'Malley M, et al. Increasing the flexibility of combined heat and power for wind power integration in China: modeling and implications. IEEE Trans Power Syst 2015;30(4):1848–57. [7] Li Z, Wu W, Shahidehpour M, et al. Combined heat and power dispatch considering pipeline energy storage of district heating network. IEEE Trans Sustain Energy 2015;7(1):12–22. [8] Sheikhi A, Rayati M, Bahrami S, et al. Integrated demand side management game in smart energy hubs. IEEE Trans Smart Grid 2015;6(2):675–83. [9] Bahrami S, Sheikhi A. From demand response in smart grid toward integrated demand response in smart energy hub. IEEE Trans Smart Grid 2016;7(2):650–8. [10] Patteeuw D, Bruninx K, Arteconi A, et al. Integrated modeling of active demand response with electric heating systems coupled to thermal energy storage systems. Appl Energy 2015;151:306–19. [11] Mancarella P, Chicco G. Real-time demand response from energy shifting in distributed multi-generation. IEEE Trans Smart Grid 2013;4(4):1928–38. [12] Good N, Karangelos E, Navarro-Espinosa A, et al. Optimization under uncertainty of thermal storage-based flexible demand response with quantification of residential users’ discomfort. IEEE Trans Smart Grid 2015;6(5):2333–42. [13] Bailera M, Lisbona P, Romeo LM, et al. Power to Gas projects review: Lab, pilot and demo plants for storing renewable energy and CO2. Renew Sustain Energy Rev 2017;69:292–312. [14] Clegg S, Mancarella P. Integrated electrical and gas network flexibility assessment in low-carbon multi-energy systems. Power and Energy Society General Meeting. IEEE; 2016. 1–1. [15] Yang J, Zhang N, Kang C, et al. Effect of natural gas flow dynamics in robust generation scheduling under wind uncertainty. IEEE Trans Power Syst 2018;33(2):2087–97. [16] Shahmohammadi A, Moradi-Dalvand M, Ghasemi H, et al. Optimal design of multicarrier energy systems considering reliability constraints. IEEE Trans Power Delivery 2015;30(2):878–86. [17] Shabanpour-Haghighi A, Seifi AR. An integrated steady-state operation assessment of electrical, natural gas, and district heating networks. IEEE Trans Power Syst 2016;31(5):3636–47. [18] Wang H, Liu Z, Chen X. Application research of refrigerator with cool storage materials. Refrigeration 2014;33(03):26–9. [19] Sun J. The selection and thickness calculation of cold insulation materials in freezing station. Mine Constr Technol 2012;33(01):37–9. [20] Alagoz BB, Keles C, Kaygusuz A. Towards energy webs: Hierarchical tree topology

4. Possible improvement of the dispatch strategy of REAF This section mainly focuses on the further improvement of dispatch strategy based on FSP and IRLMCM proposed in this paper. For the FSP algorithm, since the size of the pruned decision tree is flexible according to the requirement, the promotion of optimizing performance will surely increase the time of calculation. As a result, there are 2 main ways. The first is promoting the calculation ability (by improve hardware level) during the searching process. This method will allow the decision tree to preserve more leaf nodes to extend searching range, thus has higher opportunity to get the actual optimal result. The second is to start the searching earlier to gain more calculation time, and preserve more leaf nodes too. However, since this method uses the earlier weather forecast than the latest one, it is highly influenced by the precision of meteorology forecast. For the IRLMCM algorithm, though the current performance is satisfying, there is still room for improvement to meet the future requirement. Since the optimal dispatch schemes should be similar under similar wind conditions, the history data can be used to initialize the V (ti.k ) of the decision tree. Literature [39] proposed a method to compare the similarity between 2D images using standardized Hausdorff distance, and uses the index H to describe the similarity (H ∈ [0, 1]). When H = 1, the 2 images are completely dissimilar; when H = 0, the 2 images are the same. To the dispatch strategy of REAF, when the wind condition forecast comes out, the historical wind condition can be searched immediately. If there is a historical day that has the similar average wind speed (for example, the difference is less than 5%) and the similar time-domain wind power sequence (for example, the H between 2 wind speed sequences is lower than 0.2) with current day, the V (ti.k ) s of the historical day can be used to initializing that of 9

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[21]

[22] [23]

[24]

[25]

[26]

[27] [28] [29]

Knowl Inf Syst 2001;3(4):449–69. [30] Cestnik B, Bratko I. On estimating probabilities in tree pruning. Berlin Heidelberg: European Working Session on Learning. Springer; 1991. p. 38–150. [31] Quinlan JR. Simplifying decision trees. Int J Man Mach Stud 1987;27(3):221–34. [32] Breslow LA, Aha DW. Simplifying decision trees: A survey. Knowl Eng Rev 1997;12(1):1–40. [33] Elomaa Tapio, Kääriäinen, et al. An analysis of reduced error pruning. J Artif Intell Res 2011;15(1):163–87. [34] Xiao Y, Wang X. Conditional Quasi-Monte Carlo methods and dimension reduction for option pricing and hedging with discontinuous functions. J Comput Appl Math 2018;343:289–308. [35] Sun Y, Xu C. A hybrid Monte Carlo acceleration method of pricing basket options based on splitting. J Comput Appl Math 2018;342:292–304. [36] Kamatani K. Efficient strategy for the Markov chain Monte Carlo in high-dimension with heavy-tailed target probability distribution; 2018. Eprint Arxiv, preprint arXiv:1412.6231. [37] Silver D, Schrittwieser J, Simonyan K, et al. Mastering the game of Go without human knowledge. Nature 2017;550(7676):354–9. [38] Silver D, Huang A, Maddison CJ, et al. Mastering the game of Go with deep neural networks and tree search. Nature 2016;529(7587):484–9. [39] Ding S, Lin X, et al. A novel hausdorff distance based restrain criterion for zerosequence differential protection of converter transformer. Int J Electr Power Energy Syst 2019;105:753–64.

for future smart grids. 2015 3rd International Istanbul Smart Grid Congress and Fair (ICSG). IEEE; 2015. p. 1–4. Alagöz BB, Keleş C, Kaygusuz A, Kaplan Y, Karabiber AK. Power regulated DC/DC driver design by hierarchical control. Turkish J Electr Eng Comp Sci 2016;24(3):1325–39. Hermawanto D. Genetic algorithm for solving simple mathematical equality problem. Comput Sci; 2013. preprint arXiv:1308.4675. Lin GH, Zhang J, Liu ZH. Hybrid particle swarm optimization with differential evolution for numerical and engineering optimization. Appl Soft Comput J 2018;10(2):629–40. Zhang P, Guo Q, Zhang S, et al. Pattern mining model based on improved neural network and modified genetic algorithm for cloud mobile networks. Cluster Comput 2017;2:1–10. Jiang P, Ge Y, Wang C. Research and application of a hybrid forecasting model based on simulated annealing algorithm: A case study of wind speed forecasting. J Renew Sustain Energy 2016;8(1):226–39. Wang L, Zheng XL, Wang SY. A novel binary fruit fly optimization algorithm for solving the multidimensional knapsack problem. Knowl-Based Syst 2013;48(2):17–23. Korf RE, Chickering DM. Best-first minimax search. Artif Intell 1996;84(1–2):299–337. Althöfer I, Balkenhol B. A game tree with distinct leaf values which is easy for the alpha-beta algorithm. Artif Intell 1991;52(52):183–90. Prodromidis AL, Stolfo SJ. Cost complexity-based pruning of ensemble classifiers.

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