 Original article
 Open Access
Scenariobased stochastic optimal operation of wind/PV/FC/CHP/boiler/tidal/energy storage system considering DR programs and uncertainties
 Ehsan Jafari^{1},
 Soodabeh Soleymani^{1}Email author,
 Babak Mozafari^{1} and
 Touraj Amraee^{2}
https://doi.org/10.1186/s137050170142z
© The Author(s). 2018
 Received: 7 July 2017
 Accepted: 13 December 2017
 Published: 15 January 2018
Abstract
Background
Microgrid (MG) can be described as a group of controllable loads and distributed energy resources that can be connected and disconnected from the main grid and utilized in gridconnected or islanded modes considering certain electrical constraints.
Methods
The objective of this article are as follows: (1) predict the uncertainties through the hybrid method of WTANNICA and (2) determine the optimal generation strategy of a MG containing wind farms (WFs), photovoltaic (PV), fuel cell (FC), combined heat and power (CHP) units, tidal steam turbine (TST), and also boiler and energy storage devices (ESDs). The uncertainties include wind speed, tidal steam speed, photovoltaic power generation (PVPG), market price, power, and thermal load demand. For modeling uncertainties, an effort has been made to predict uncertainties through the hybrid method of wavelet transform (WT) in order to reduce fluctuations in the historical input data. An improved artificial neural network (ANN) based on the nonlinear structure is applied for better training and learning. Furthermore, the imperialist competitive algorithm (ICA) is applied to find the best weights and biases for minimizing the mean square error of predictions.
Result
The scenariobased stochastic optimization problem is proposed to determine the optimal points for the energy resources generation and to maximize the expected profit considering demand response (DR) programs and uncertainties.
Conclusions
In this study, three cases are assessed to confirm the performance of the proposed method. In the first case study programming, MG is isolated from grid. In the second case study, which is gridconnected mode, the WTANNICA and WTANN uncertainty prediction methods are compared. In the third case, which is gridconnected mode, the effect of DR programs on the expected profit of energy resources is assessed.
Keywords
 Microgrid
 Wind farm
 Photovoltaic
 Combined heat and power
 Tidal steam turbine
 Expected profit
Background
The microgrid (MG) concept has recently attracted significant public attention. Integration of renewable sources, combined heat and power (CHP) systems, and energy storage technologies in the MGs will result in environmental friendly, low cost, and reliable energy. Recently, using CHP systems in MGs has attracted more attention. The primary motivation for incorporating CHP units is providing electrical and thermal energy, simultaneously. During electricity generation process of CHP systems, waste heat is employed to provide thermal energy. This process will result in the improvement of overall system efficiency as well as a significant reduction in the cost of thermal energy generation. It should be mentioned that, in a CHP unit, the power generation boundaries depend upon the heat generation of unit and the heat generation boundaries depend on the power generation of the unit [1].
Owners of renewable resources need to predict the uncertainties for optimal planning such as photovoltaic voltage/power generation [2], market price [3], and load forecasting [4], wind farm power generation/wind speed (WS) [5–9]. In [7], firstly, historical data of WF is decomposed using wavelet transform (WT) and then WF power generation is predicted by artificial neural network (ANN). This method is tested in two regions of china. Afterwards, comparing WTANN, ANN, and auto regressive moving average (ARMA) methods revealed that WTANN can significantly reduce the error in spite of ANN and ARMA methods. In [8], the optimal weights and biases of ANN are determined by genetic algorithm (GA), imperialist competitive algorithm (ICA), and ICAGA methods; then, they are tested on six specified databases. In the end, the obtained results confirmed that ICA has higher capabilities. Similarly, ANN is employed to predict WF power generation, and then, ICA, GA, and particle swarm optimization (PSO) are chosen to determine the optimal weights and biases [9]. The prediction results were more satisfactory when ICA algorithm was utilized.
The second solution for uncertainty reduction in renewable units including renewable resources is to coordinate other energy resources which are quite expensive, but available and more reliable, such as pumpstorage unit, hydro unit, gas turbines, combined cycle power plants, and energy storage batteries [10–21]. However, the share of these energy sources should diminish for many reasons [10]. In [11], the coordinated planning of WF, pumpstorage unit, and thermal units is presented by the multistage stochastic planning and solved by scenario decreasing algorithm of PSO. In [12], the required reserve level is estimated in the presence of highlevel WF penetration. In [13], the optimal strategy of WF is determined in the realtime market. The wind speed and market price are predicted by ARMA. Moreover, the expected profit is limited by FR and the required reserve is determined due to the error prediction in WF power generation. In [14], the coordinated planning problem of WF and thermal power plants are solved by artificial immune optimization method. This optimization method is implemented on a system including ten thermal power plants and two wind farms (WFs). A mixed integer programming algorithm is adopted for period planning of operation startup/shutdown and generating/pumping mode of pumpstorage unit to maximize the profit in coordinated operation of WF and pumpstorage unit [15]. A scenariobased and chance constrained optimization method is hired to consider the WF power generation prediction error. A rolling optimization method for WF coordination with the energystorage systems in the dayahead market is presented to increase the profit of these power plants.
The optimal scenariobased operation management of MG including WF, photovoltaic, microturbine/fuel cell, and energy storage devices are studied in [16]. In this paper, the considered uncertainties are load, WF power generation, photovoltaic power generation, and market price. In [17], the optimal biding strategy model in an electricity distributed company is considered in order to make the maximum profit in the dayahead market. In [18], the modified particle swarm optimization algorithm is used to optimize energy in MG. Moreover, in this study, uncertainty of data is checked using Hong method. In [19], like [18], Hong method is applied for covering uncertainties; however, the modified firefly algorithm is utilized for optimization. In [20], studies on utilization of micronetwork are made in the presence of generating resources of thermal and electrical energy and also Proton Exchange Membrane Fuel cell power plant along with the hydrogen storage. The modified algorithm of selfadaptive charge search algorithm is applied for optimization. In [21], the objective function is considered to maximize the profit of wind farm, fuel cell, boiler, CHP units, electrical power generation unit, and energy storage devices (ESDs) connecting to a MG regarding uncertainties. The uncertainties are predicted by time series methods.
 1.
Prediction of uncertainties via hybrid method (HM) of WTANNICA. According to the studies in [7–9], prediction of uncertainties using the proposed method can lessen errors of prediction of WS in comparison to ARMA, ANN, WTANN, WTANNPSO, and WTANNGA methods. Therefore, this approach may generate scenarios closer to reality and lead to the optimal programming.
 2.
Generating the scenarios of WS, tidal steam speed (TSS), photovoltaic power generation (PVPG), market price, and power/thermal load demand, decreasing the scenarios with the scenarioreduction backward method, and modeling them through the tree scenario method.
 3.
The programming of MG, including WFs, photovoltaic (PV), tidal steam turbine (TST), fuel cell (FC), CHP units, boiler, and electrical and thermal ESDs, considering constraints and the uncertainties of WS, TSS, PVG, market price, and power/thermal load demand.
 4.
Studying the expected profit of energy resources with and without DR program.
Methods
Scenariobased stochastic modeling
As a result of extending renewable resources and uncertainty in the nature of such resources, the modern complicated power systems should be analyzed in uncertain environment so that operating point and reliability of energy supply occur in approximation with the optimal point in reality. Therefore, having access to powerful tools is necessary for transition from uncertain environments with random variables, including their probability contributions, to the certain problems with certain variables. In the modern deregulated power supply markets, the most important random variables are load demands, wind speed, PVPG, and market price. The origin of the abovementioned uncertainties are found in issues like weather conditions, temperature variations, and government decision.
This proposed method for prediction of uncertainties is proposed in Fig. 1 as a flowchart. As observe here, it is assumed that the prediction for dth day can be made and the historical data extracted for every single hour of 24 h beginning 100 days ago.
Stage 1: data homogenization
The historical data are recalled and normalized to improve data homogenization.
Stage 2: data processing using wavelet theory
Stage 3: ANN
McCulloch and Pitts tried to simulate the ANN by a logical model for the first time which now is widely applied in many fields. Here, the chosen ANN consist of three perception layers: the output layer with one neuron, the input layer with five neurons, and the hidden layer with three neurons. This ANN can predict the information of hours d (t + 1,…,t + 24) for the output signals of WT as the initial data.
Stage 4: ICA

1. Developing initial colonies: the ANN consist of input signals (Ah, Dh1, Dh2, and Dh3), the five neurons in the input layer (IL), the three neurons in hidden layer (HL), and the one neuron in output layer (OL). The matrixes of wrights (W) and biases (B) consist of ILW = [5 × 4], ILB = [5 × 1], HLW = [5 × 3], HLB = [3 × 1], OLW = [3 × 1], and OLB = [1 × 1]. Hence, each colony constitutes 47 variables. Initial colonies are selected through specific range based on initial training of ANN on a random basis. Regarding the cost function based on decreasing the prediction error, the optimization of weights and biases are performed within the neural network for better training. The cost function here is the mean square error which is proposed as Eq. (3).

2. Selecting the imperialist: in this stage, the colonies with minimum cost are selected as the imperialists.

3. Allocating the other countries as the colony to the imperialists: in this step, some colonies are allocated to each of imperialists and empires. This allocation is done according to imperialists fitness (fewer cost) by stochastic universal sampling method. The stages of 1–3 are the initialization stages of ICA.

4. Performing the act of assimilation or absorption policy: in this stage, each of the colonies is moved towards the imperialist in each empire. This stage proceeds to improve the exploitation of algorithm.

5. Performing the act of revolution: in this stage, the random changes are applied on each of the colonies. This action can improve the exploration of algorithm and prevent from involving the optimization in the local optimal points.

6. Computing the cost of colonies and imperialists.

7. Comparing the cost of colonies with imperialist in each empire: if a colony holds a lower cost than the imperialist, it will take its place.

8. Evaluating the empires: the cost for each empire is computed according to Eq. (4).

9. Decreasing the colonies: in this stage, a colony is omitted from the weakest empire and transmitted to another empire by roulette wheel method. According to this method, the empire with the lower cost has more chance to seize the colony.

10. Omitting the empire: if the weakest empire has no colony, the related imperialist will be transmitted to another empire as a colony.
Stage 5
Mean square error of four prediction method of WS
Method  1 h ahead(m/s)  3 h ahead(m/s) 

ARMA  0.61  0.995 
WTANN  0.585  0.981 
WTANNPSO  0.570  0.975 
WTANNICA  0.540  0.968 
Generating scenarios and backward method scenarios reduction
According to the stated issues, the determination of optimal strategy for resources connected to the MG is analyzed randomly. To reach this goal, at first, a probability density function is defined for each variable. In this study, the applied probability density function is adopted for power/thermal load demand, TSS, PVPG, and market price with normal distributed functions. In the case of WS, the statistical model is not coordinated with the normal distribution but more harmonized with Weibull distribution function.
The rate of each scenario is obtained by the sum of the error and predicted amount of variable [16]. Eq. (5) shows the amount of scenario for the WS. Consequently, 500 scenarios are generated for each uncertainty.
Objective function of WFs, PV, TST, FC, CHP units, boiler, and ESDs
In this study, the optimal scheduling of MG including WFs, PV, TST, FC, CHP units, boiler, and ESDs is examined with the 24hour time horizon as well as considering uncertainties and DR programs in order to maximize the expected profit. The multistage stochastic programming is applied to deal with uncertainties. Since the generation power of units should be determined before applying stochastic processes, they are the first stages or hereandnow decisions and are not dependent to the scenarios. Other variables such as buy or sell power from the market and charge or discharge of storage devices are at the second stage or waitandsee decisions. This mixed integer nonlinear optimization problem is solved through GAMS/COUENNE software. GAMS/COUENNE is a GAMS solver that allows users to combine the high level modeling capabilities of GAMS with the power of COUENNE optimizers which are designed to solve large and difficult problems quickly and with minimal user intervention. This solver is a general one which can be used to solve all scheduling problems. In these conditions, COUENNE solver can be used to solve the proposed optimization problem. COUENNE uses a branch and cut algorithm which solves a series of linear programming and subproblems [24].
Problem modeling
where i is the index of each energy resources; W, CHP, PV, FC, TST, K, and B are the index of wind farm, combined heat and power, photovoltaic, fuel cell, tidal steam turbine, electrical energy storage device, and boiler; A_{ W }, A_{ TST }, A_{ PV }, A_{ CHP } − F_{ CHP }, A_{ FC }, and B_{ FC } are the cost coefficients of wind farm, tidal steam turbine, photovoltaic, combined heat and power, and fuel cell; T/t is the total number/index of time intervals; S_{ P }, S_{ TSS }, S_{ W }, S_{ PV }, S_{ PL }, and S_{ HL } are the index of scenarios for market price, tidal steam speed, wind speed, photovoltaic power generation, power, and thermal load demand, respectively; Y is the sufficient large number; U_{COST}(i, t) and D_{COST}(i, t) are the startup/shutdown cost of ith generation unit at hour t; M(i, t) is the commitment state of ith generation unit at hour t; ρ_{ s } is the probability of the s_{ W }th wind speed; s_{ TSS }th is the tidal steam speed; s_{ PV }th is the photovoltaic generation; s_{ p }th is the scenario of market price; s_{ PL }th is the scenario of power load demand; s_{ HL }th is the scenario of thermal load demand; C_{ T }(i, t) is the value of total generation cost of ith generation unit at hour t; E_{ P }(s_{ p }, t) is the price of the market ($/MW) for energy for s_{ p }th scenario of price at hour t, respectively; P_{sale}(s, t) and P_{buy}(s, t) are the amount of power sold and bought to/from the market at hour t in MW; \( {P}_G^W\left({s}_W,t\right) \), \( {P}_G^{TST}\left({s}_{TSS},t\right) \), P_{G, CHP}(t), and \( {P}_G^{FC}(t) \) are the power generation of wind farm, tidal steam turbine, heat and power, and fuel cell at hour t in MW, respectively; SU(i, t)/SD(i, t) is the startup/shutdown status of ith unit at hour t.
Demand response program constrains
The aim of demand response programs is shifting the load of MG from high consumption hours (where the energy prices are high) to the low consumption hours. It should be noted that planning for load shifting is just able to change a part or percentage of load from an hour to another [21].
The final load after applying DR program:
CHP units constraints
Heat energy storage device constraints
Fuel cell constraints
WFs constraints
Characteristics of power generation for wind farms are nonlinear according to the wind speed which varies under the influence of type, dimension, and design of turbine. Generally speaking, the generation power of wind unit can be obtained by Eq. (39).
where WS(s_{ W }, W, t), P_{ WN }(W), WS_{ ci }(W), WS_{ n }(W), and WS_{ co }(W) are the amounts of wind speed of Wth wind farm for s_{ W }th wind speed scenario at time t, rated power of Wth wind farm, the minimum wind speed required to start power efficiency in wind farm (cutin speed), rated speed, and the cutout wind speed (the wind speed by which turbine puts the blades parallel to wind to prevent damages), respectively.
PV constraints
Electrical energy storage device constraints
The constraints of electrical energy storage devices correspond to Eq. (42–47). This difference is in charging and discharging of these devices and other constraints depend on scenarios pertaining to WS, PVPG, power/thermal load demand, while the PV constraints are just affected by PVPG.
Tidal turbine
 1.
Tidal stream system where kinetic energy of the freeflowing water is consumed and
 2.
Tidal barrage system that consumes potential energy of the ocean at ebb and flow. Usually, this method is not adopted due to the environmental conditions [27].
TSS(s_{ TST }, TST, t), \( {P}_{TST}^N(TST) \), TSS_{ ci }(TST), TSS_{ n }(TST), TSS_{ co }(TST), ρ_{water}, A, and C_{ P } are the amounts of steam speed of TSTth tidal steam turbine for s_{ TST }th steam speed scenario at time t, the rated power of TSTth tidal steam turbine, cutin steam speed, rated steam speed, cutout speed of tidal steam turbine, fluid density (\( \raisebox{1ex}{$\mathrm{kg}$}\!\left/ \!\raisebox{1ex}{${\mathrm{m}}^2$}\right. \)), the crosssectional area of the tidal steam turbine (m^{2}), and the power coefficient, respectively.
Results and discussions
In this part, firstly, the structure of MG and numerical data concerned with energy resources are studied, and then, simulation results of optimal operation for the stochastic problem are analyzed.
Configuration of MG
 1.
Planning isolated MG by predicting uncertainties by hybrid method of WTANNICA
 2.
Planning and determining the optimal strategy of MG energy resources connected to grid and comparing hybrid prediction methods of WTANN and WTANNICA, in order to examine the influence of predicting uncertainties upon the profit amount of MG
 3.
Programming and determining the optimal strategy of MG connected to the grid and applying hybrid prediction method of WTANNICA for predicting uncertainties and exploring the effect of DR problem on the profit of MG
The startup and shutdown cost of units
CHP units  A_{CHP} = 0.0435  B_{CHP} = 36  C_{CHP} = 12.5  D_{CHP} = 0.027  E_{CHP} = 0.6  F_{CHP} = 0.011 

Heat buffer tank  η_{loss} = 0.6  η_{gain} = 0.3  σ = 1%  \( {\displaystyle \begin{array}{l}{AH}_{\mathrm{discharde}}^{\mathrm{max}}=\\ {}{AH}_{\mathrm{charge}}^{\mathrm{max}}=2\end{array}} \)  AH_{max} = 7  AH_{min} = 0 
The heat buffer tank data and cost coefficients of CHP units
Unit  U _{COST}  D _{COST} 

CHP units  20  20 
Fuel cell  0.0207  0.0207 
Boiler  9  9 
The tidal steam turbine data
Rated speed  2.4(m/s) 

Cutin speed  0.7(m/s) 
Cutout speed  4.2(m/s) 
Power coefficient  0.47 
Crosssectional area  3.006(m^{2}) 
Case studies
Case study 1: planning of MG in the gridisolated mode
Case studies results
State  Prediction method  Cost of buying energy ($)  Revenue from the sale of energy ($)  Generation cost ($)  Value of OF ($)  Expected profit ($) 

Case 1  WTANNICA  –  –  2032.76  −2032.76  – 
Case 2  WTANN  281.6  1295.78  2254.30  −1240.12  792.64 
WTANNICA  266.93  1456.96  2312.86  −1122.83  909.93  
Case 3  WTANNICA  387.57  1228.45  2161.59  −1320.71  712.05 
2. Case study 2
The effect of exchanging electrical energy with grid in connected mode and also the effect of more accurate prediction of random parameters on MG planning are studied by comparing the hybrid methods of WTANNICA and WTANN. The MG planning problem in the presence of all economic and technical constraints and the DR problems will be solved. The results are tabulated in Table 5, where, by WTANNICA prediction method, the generation cost increases by 13.77% in comparison with the first case. The profit of MG resulted from taking part in the market is $792.64 and $909.93 for WTANN and WTANNICA, respectively. This profit is due to the sale of power to the main grid.
Due to the stochastic nature of WFs, TST and PV power generations, market price, and power/thermal load demand, more accurate prediction of these random parameters led to generating scenarios proximate to reality and with greater possibility. Consequently, a more detailed planning can be achievable. In Table 5, the obtained results of MG planning are compared by prediction hybrid method of WTANN and WTANNICA. The results indicate 14.79% increased profits of MG in WTANNICA method in comparison with WTANN method.
Case study 3: to explore the effect of DR program on determination of generation strategy of MG
In the third case, the MG planning is studied without DR program in order to investigate its effects on the expected profit of MG by hybrid prediction method of WTANNICA. Table 5 shows the results of case study 3 versus 2. The expected profit decreased while the cost of generation dropped slightly. According to Table 5, the expected profit of MG in the third case study is $712.05 which approximately decreased 27.7% as compared to the second case study (applied DR program). This reduction in profit of MG indicates the efficacy of DR program on the optimal planning of these units.
Regarding Table 5, the objective function values of both cases 2 and 3 are negative. That is because of high energy demand inside the MG and lack of possibility to offer excess power to the main grid.
The difference between energy generation of resources with and without DR is illustrated in Fig. 8. The received and delivered power to grid with and without DR is depicted in Fig. 8a. Regarding this figure, the movable loads can be shifted from peak time to other hours when the energy price is lower and makes profit.
Conclusions
In this paper, an algorithm was suggested to ascertain optimal strategy of a MG including WFs, PV, TST, fuel cell, CHP units, boiler, and ESDs, by considering economic and technical constraints and DR program. This research aimed to present an optimization program to maximize the profit of MG in grid–connected mode, and to minimize the cost of energy resources in grid isolated mode. The uncertainties are WS, TSS, PVPG market price and power/ thermal load demand which are predicted by hybrid prediction methods of WTANN and WT ANNICA, and related scenarios are generated by probability density functions appropriate to each uncertainty and scenario reduction method. The simulation results represent that applying more accurate prediction method, some scenarios proximate to reality and with greater possibility are generated. Hence, a more detailed and precise planning is achieved and the expected profit of MG might be increased. If the method of WTANNICA is used rather than WTANN, the expected profit of MG will be increased by 14.79%. Furthermore, the expected profit can be raised by applying DR program. According to the studied cases, although the DR program increases the generation cost by 7%, the expected profit rises more than 27.7% and it goes to $909.93, while without considering DR program, this profit would be $712.05.
In addition, the outcome of case studies illustrate that by implementing this proposed framework, the MG can obtain a meaningful profit in the gridconnected mode in comparison with the isolated mode, as well as supplying total electrical and heat demand.
Declarations
Acknowledgements
The study was possible through financial assistance from the Department of Electrical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran.
Authors’ contributions
Dr. J analyzed data and simulated numerical example. Dr. S is the lead author and made a substantial contribution to the conception and design of the manuscript. DR. M and Dr. A revised the manuscript for important intellectual content. He also formatted the paper to conform to the specifications of the journal. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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