Portal de Periódicos da CAPES

Double‐deck optimal schedule of micro‐grid based on demand‐side response

2018; Institution of Engineering and Technology; Volume: 13; Issue: 6 Linguagem: Inglês

10.1049/iet-rpg.2018.5495

1752-1424

Chunxia Dou, ChiHua Meng, Wenbin Yue, Bo Zhang,

Power Systems and Renewable Energy

IET Renewable Power GenerationVolume 13, Issue 6 p. 847-855 Special Issue: Demand Side Management and Market Design for Renewable Energy Support and IntegrationFree Access Double-deck optimal schedule of micro-grid based on demand-side response ChunXia Dou, Corresponding Author ChunXia Dou cxdou@ysu.edu.cn Institute of Electrical Engineering, Yanshan University, Qinhuangdao, 066004 People's Republic of China Institute of Advance Technology, Nanjing University of Posts and Telecommunications, Nanjing, 210023 People's Republic of ChinaSearch for more papers by this authorChiHua Meng, ChiHua Meng Institute of Electrical Engineering, Yanshan University, Qinhuangdao, 066004 People's Republic of ChinaSearch for more papers by this authorWenbin Yue, Wenbin Yue Department of Computer Science, Brunel University London, Uxbridge, Middlesex, UB8 3PH UKSearch for more papers by this authorBo Zhang, Bo Zhang Institute of Electrical Engineering, Yanshan University, Qinhuangdao, 066004 People's Republic of ChinaSearch for more papers by this author ChunXia Dou, Corresponding Author ChunXia Dou cxdou@ysu.edu.cn Institute of Electrical Engineering, Yanshan University, Qinhuangdao, 066004 People's Republic of China Institute of Advance Technology, Nanjing University of Posts and Telecommunications, Nanjing, 210023 People's Republic of ChinaSearch for more papers by this authorChiHua Meng, ChiHua Meng Institute of Electrical Engineering, Yanshan University, Qinhuangdao, 066004 People's Republic of ChinaSearch for more papers by this authorWenbin Yue, Wenbin Yue Department of Computer Science, Brunel University London, Uxbridge, Middlesex, UB8 3PH UKSearch for more papers by this authorBo Zhang, Bo Zhang Institute of Electrical Engineering, Yanshan University, Qinhuangdao, 066004 People's Republic of ChinaSearch for more papers by this author First published: 30 October 2018 https://doi.org/10.1049/iet-rpg.2018.5495Citations: 7AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract In order to fully consume renewable energies and schedule demand-side resources more hierarchically, a double-deck optimal schedule model of micro-grid, which connects to power grids and concludes battery energy storage system (BESS), is proposed. Unlike the original peak-valley time-of-use (TOU) price, in the upper layer optimal schedule, the improved TOU price which takes account into the user's satisfaction can express the adjusted loads accurately and the resulting net loads can be treated as a link between upper and lower layer scheduling. For the reason of having no precise model of BESS, the lower model for the goal of minimising the operation cost is solved by action dependent heuristic dynamic programming algorithm that is not relying on the accurate controlled object model. This algorithm is used to obtain the most optimal performance index function and control strategy by the optimal iterative process, which is based on the back propagation neural network used for evaluating the optimal performance index. Analysis of examples and results has been presented to show the effectiveness of the proposed strategies. Nomenclature Indices/sets number of wind turbine generators number of solar units number of scenarios t (s) index of time (scenario), running from 1 to 24 () Wk (Pk) index of wind turbine (photovoltaic, PV) units, running from 1 to () i (l) index of time or number of the external iteration (internal iteration), running from 1 (0) to the maximum number of iterations (23) j index of shiftable loads Parameters and constants probability of scenarios () lower (upper) limit value of the output power of the wind turbine () lower (upper) limit value of the output power of the PV unit () lower limit value of the user's comfort (the user's economy of electricity) coefficient of surrendering part of the profits () minimum (maximum) charge and discharge power of battery charging or discharging efficiency response period rated power output of the battery () smallest moment range of the allowable responding time () period to start (end) of the shiftable loads nominal power of the shiftable load comprehensive working cost of BESS ω inertia weight factor () acceleration constant () new velocity (position) of particles γ discount factor with Wc weight coefficient in critic network ε computational accuracy Variables () net load power (adjusted load power) of t time interval () wind power (PV power) of t time interval () electricity price after optimal (original electricity price) of the ith time interval () adjusted demand power (original demand power) of the ith time interval ratio of the change in demand to original demand ratio of the change in price to original price () change in electric quantity (user's electric charge) at t time interval after optimising () electric quantity (user's electric charge) at t time interval before optimising electric price of grid at t time interval interactive power between the micro-grid and the grid at t time interval power of all working shiftable loads at t time interval compensation cost of the shiftable loads charging or discharging cost of the BESS charging or discharging power of the battery power from the battery to the demand () power from grid (renewable energy) to the battery rest energy in the battery at time t working state of the jth shiftable load at t time interval 1 Introduction 1.1 Motivation Demand-side response, along with advanced communication and control technologies, has been considered to be a major means in micro-grid energy management for decreasing the operation cost [1]. Enhancing the development of demand-side resources and strengthening the connection of it in the scheduling become particularly important, which are conducive to transfer the renewable energy from the micro-grid with additional power generation to the load of peak periods [2, 3]. The integration of different types of energy resources can be a viable solution to enhance the performance of the existing demand response programs [4]. Due to different demand-side resources response in different ways for its characteristic, it should be dispatched more hierarchically and its effect should be represented more accurately. However, traditional peak-valley time-of-use (TOU) price regulating price-based load cannot express the adjusted load, which is detrimental to the later scheduling. Besides, battery energy storage systems (BESSs) as generalised demand-side resources have no precise charging and discharging model, which makes deviate from the calculation of operation cost [5]. Therefore, the most challenge for scheduling demand-side resources is improvement of TOU price and estimation of the impact of BESS on operating cost of micro-grid. 1.2 Literature review In [6], demand-side response as a load management program is an effective way for operator to shift the demand from peak time periods to valley period to obtain a smooth load curve. The effect of electricity price on load is fully considered in [7]. Real-time pricing is applied in the demand-side management to reduce peak load and save cost. In [8, 9], the responsiveness between demand and price has been largely formulated as the price elasticity matrix largely formulated as the price elasticity matrix which is used to compute the changes in demand of users under time of use price. A day-ahead energy optimal dispatch model is proposed in the condition of adopting TOU price and taking into account the user's comfort and economy of electricity for micro-grid in [10]. In [11, 12], a mathematical model is developed to obtain the optimal operation schedule that concludes demand response by the way of improved TOU price. It considers the impact of demand response program and uncertainty in demand and market price. Seeing from the previous literature, the way to adjust load under TOU price is improving incrementally. The energy storage system as generalised demand side response resource is essential for the micro-grid operation. It allows getting a number of benefits in micro-grid operation, attributing to its advantageous features that it can perform both as load (in charging state) and generators (in discharging state) [13, 14]. Guaranteeing a continuous and flexible power supply to the loads and reducing the operation cost for micro-grid are the objectives for the optimal operation of those storage systems in the micro-grid, which can be achieved by means of reasonable scheduling. In [15, 16], considering interactive of micro-source, energy storage system and loads, the optimal scheduling model is established. More methods that are proposed to optimise the micro-grid include photovoltaic (PV), wind and storage system. In [17-19], the main objective function for minimising the cost of that micro-grid is solved by using particle swarm optimisation (PSO). However, the optimisation result of these methods cannot have a good control effect on the energy storage system because it belongs to a complex non-linear system and has no precise charging and discharging efficiency model. Action dependent heuristic dynamic programming (ADHDP) is one of the adaptive dynamic programming (ADP) methods, proposed by Fan et al. [20]. It has demonstrated powerful self-learning capability for optimisation of complex non-linear systems by taking neural network as approximate structure of function [21-23]. In this algorithm, the optimal performance index function also called as Q-function depends on both the system state and control variables, and includes the information of both the system and the utility function. Therefore, the optimal control can be obtained directly by minimising the Q-function. However, owing to the demand and energy are presented as time-varying functions, it cannot availably approach the optimal Q-function and optimal control. To solve the problem, a dual iterative ADHDP algorithm is developed to optimise the battery operation in a small power system in [24, 25]. Inspired by Shi et al. [25], this algorithm is used for solving the optimal scheduling model of micro-grid that includes BESS. 1.3 Contributions The contributions of this paper are as follows: For increasing connection between scheduling demand-side resources and eliminating more renewable energy, upper optimal scheduling model is proposed with the objective function of minimising the square of net load which is closely linked to lower scheduling model. Different with original TOU price, the improved TOU price adopted in upper model can represent adjusted load accurately and ensure that users can actively participate in demand-side response and guarantee their interests. Unlike previous optimisation algorithms, the algorithm of ADHDP adopted in lower model can evaluate the impact of using BESS on operation cost and make BESS charge and discharge with more efficiency. 1.4 Paper organisation The remaining of this paper is organised as follows. In Section 2, upper optimal scheduling model is established. In Section 3, lower optimal scheduling model is proposed. Two solution algorithms of double-deck scheduling model are introduced in Sections 4 and 5, respectively. Analysis of example of a micro-grid is illustrated in Section 6. The conclusions are given in Section 7. 2 Upper scheduling model Considering the condition that the maximum power generation period of PV is inconsistent with the peak period of load and the anti-peak regulation character of wind power, demand-side resources are used for improving this condition. Thus, the upper optimal scheduling model of micro-grid is established based on demand-side response. From the framework of the proposed double-deck scheduling model (see Fig. 1), it is distinct to see the effect of upper model and the relation of double-deck model. Fig. 1Open in figure viewerPowerPoint Framework of the proposed double-deck scheduling model 2.1 Upper optimal scheduling objective function Taking the characteristic of demand-side response into account, upper optimal dispatching model adopts the way of TOU price. In order to achieve peak-load shifting, and absorb wind power and PV power more, the square of the net load power which is the difference between the adjusted load power and that wind and PV power should be minimised, so the objective function is (1) (2) Inequality constraint conditions (3) (4) (5) (6) (7) (8) 2.2 Wind-turbine model At each time interval, the output power of per wind turbine generator can be shown as (9) according to [26] (9) 2.3 PV system model At each time interval, the output power of PV system can be presented by (10) according to [27] (10) 2.4 Model of TOU price The purpose of adopting the TOU price is to absorb more renewable energy and to reduce the operation cost of micro-grid by shifting responsive loads from peak hours to valley hours and preventing the commitment of expensive generation units. The relation between electricity price and demand has been discussed in [12]. The elasticity coefficient of demand is defined as the ratio of the relative change in demand to the relative change in price, including self-demand elasticity coefficient and cross-demand elasticity coefficient. The first represents the ratio of the ith time interval change in demand to its change in price. It is formulated as follows: (11) In the function, represents the ratio of the change in demand to original demand, represents the ratio of the change in price to original price. The cross-demand elasticity coefficient represents the ratio of the ith time interval change in demand to jth the time interval change in price. It is formulated as follows: (12) By analysing the characteristic of the different demand, the demand elasticity matrix can be known. Then according to the new electricity price, the adjusted load can be computed. It is formulated as follows: (13) 2.5 Satisfaction of user model The user's satisfaction comes from electricity marketing, having great impact on the result of TOU price. By considering the user's satisfaction enough, the optimal result can both keep the interest of user and achieve the aim that the demand adapt to the grid-connected operation of wind power and PV power. The relation between the time of use price and the user's satisfaction is researched in [10]. Two users' satisfaction index are adopted to describe, consisting of the user's comfort and economy of electricity. The user's comfort is formulated as follows: (14) The user's economy of electricity is formulated as follows: (15) The greater the user's comfort and economy of electricity is, the higher the user's satisfaction is. 3 Lower scheduling model The lower dispatching model diagram is shown in Fig. 2. By reasonably dispatching the interruptible load, the exchange power with grid and the BESS, the source-grid-load-storage optimal scheduling model is established to minimise the operation cost. Fig. 2Open in figure viewerPowerPoint Lower micro-grid scheduling model diagram 3.1 Lower optimal scheduling objective function A coordinative micro-grid optimal scheduling model is proposed, more economically improving the ability of balancing the supply-demand power. Taking into account the run mode of BESS and the character of other dispatch resources, the objective function that minimises the operation cost is formulated as follows: (16) The net load obtained from the upper scheduling model is used as the constant of the power balance formula of the lower scheduling mode. The supply-demand power balancing equation is (17) The objective function should be optimised under these following constraints: (18) (19) (20) 3.2 Battery model Battery energy storage units are essential for micro-grid operation [25, 28]. To increase battery efficiency and extend the battery's working life, some constraints need to be considered (21) The battery capacity constraint prevents the overcharging or undercharging of battery with the following constraints: (22) (23) The capacity of battery is formulated as follows: (24) (25) 3.3 Shiftable loads model Owing to the responding time of the interruptible loads can be controlled, a mathematical model is established. This model which uses 1 h as a dispatching interval is formulated as follows: (26) (27) (28) 4 Solution of the upper scheduling model 4.1 PSO algorithm PSO is an iterative optimisation algorithm for simulating bird predator behaviour [29]. For its characteristics of high precision and easy to implement, this algorithm is used for seeking optimal solution of the upper scheduling model. Besides, the number of variables in the model can be presented as dimension of particles, which is a simple and clear process. The stepwise procedure of PSO is shown as below [30]. First, initialise the particles. For the initial iteration, store all values of initial particles as P-best. The best value which has the minimum fitness among the set of initial particles is stored in the whole memory scheme as G-best. Second, update the velocity and position. For the next iteration, the new velocity and position are calculated as follows: (29) (30) (31) Third, revise the values of P-best and G-best. If the fitness value of the next iteration is smaller than the former individual best fitness value, then P-best is replaced by it. Subsequently, the beat value with minimum fitness among the revised set of P-best is stored in the whole memory scheme as G-best. The optimisation process from the second step to the third step is repeated until the maximum number of iterations is reached. The value of G-best after the last iteration corresponds to the whole optimal solution. 4.2 Solution of the upper scheduling model The upper scheduling model needs to determine the electric price of 24 h and the net load each hour. Thus, the electric price is treated as particle and the upper scheduling model objective function is treated as the fitness function. By selecting the appropriate parameter, inputting those predictive values and adding constraints into the algorithm, the minimum fitness could be obtained after the optimisation process. The electric price of 24 h corresponding to the G-best value is the adjusted price. At the same time, the net load each hour could be computed by the demand elastic matrix. 5 Solution of the lower scheduling model 5.1 ADHDP algorithm Regarding the micro-grid optimal scheduling system as the discrete-time non-linear system in finite time interval, the ADP algorithm is adopted to minimise the operation cost. This algorithm is made to search on optimising multistage decision, making the decision of the current stage best for the whole goal. Another advantage of ADP is avoiding the problem of curse of dimensionality which usually appears in dynamic programming of the practical application. Due to the precise model of the charging and discharging efficiency of BESS is difficult to get, it would have a significant influence on the decision. Thus, the ADHDP algorithm as one of the ADP algorithm is adopted, consisting of action network and critic network and suiting for the condition of having no precise model. Its structure diagram is shown in Fig. 3. Fig. 3Open in figure viewerPowerPoint ADHDP structure diagram A brief introduction to ADHDP is presented in [31]. The system state is defined as follows: (32) where u(t) is the control action, is the system function. In the ADHDP algorithm, and are the inputs of the critic action, the performance index function corresponding to the system is defined as (33) where is the utility function. The output of the critic network approximates the cost function by minimising the following error function: (34) where . While at all times, is easy to obtain. Thus, a neural network is well trained by minimising this error function. Action network is well trained by minimising the output of the critic network. A neural network is obtained to produce the most optimal or suboptimal control signal. 5.2 Lower scheduling model transformation The micro-grid optimal scheduling system consists of 24 dispatching periods. Considering the changing and discharging efficiency of BESS have no accurate model, the rest energy in the battery at time t is put as the system state: , the input variable is defined as that: , , . Thus, the control action is represented as (35) The system state of the next time interval is represented as (36) The utility function is defined as (37) From the previous equation to see, objective function of the lower optimal scheduling model is transformed into the performance index function (38) where represents the control sequence from time t to time 23. The most optimal performance index function is presented as that: . 5.3 Parameter selection and the training strategy of ADHDP algorithm Before the process of optimising the performance index, the critic network and the action network should be well trained. Radial basis function neural networks have the ability of universal function approximation and less computation time, but it does not calculate partial derivatives which are often used in the ADHDP algorithm [32, 33]. Thus, back propagation neural network is more suitable for training critic network and action network now, which adopts the method of grads-descending. The detailed introduction of this training process has been presented in [34, 35]. In ADHDP, relevant parameters contain the node number of hidden layer between two network, learning rate and discount factor. The node number of hidden layer is always obtained by the experimental trial and error, starting from the smaller node number and stepping up. Training by the same sample, the node number is always obtained when the network error is the least. The higher the learning rate, the faster the learning speed, but brings the shock easily. On the contrary, the low learning rate needs two much time to study. Thus, the learning rate decreases gradually with the bigger initial value, in order to speed up training while reducing shock. For the structure of ADHDP, the critic network evaluates the value of function . Therefore, it is essential for critic network convergence to choose reasonable . Generally speaking, the smaller the discount factor, the easier the experiment is to succeed; the larger the discount factor, the better the control effect. Thus, is usually trained from a low value, and then increasing gradually. The training strategy of ADHDP is expressed as below. First, determine the structure of action network and critic network, the node number of each layer, transfer function type and the other related parameters. Second, build the model of micro-grid resources as controlled object. Third, initialise the weight coefficient of two networks and define the discount factor and the learning rate l. Fourth, set the initial quantity of state of micro-grid energy management system. Fifth, input the system state and controlled variable of current period into the controlled object and obtain the system state of next period. Sixth, treat the system state and the controlled variable of next period as the input of the critic network and obtain the estimated value of performance index function for next period. Seventh, compute the error of action network, adjust the network weight and train the action network. Eighth, compute the error of critic network, adjust the network weight and train the critic network. Ninth, return to the fourth step after finishing a session. The whole system training is over until the number of iterations comes to the maximum cycle times. The training flow chart of ADHDP algorithm is shown in Fig. 4. Fig. 4Open in figure viewerPowerPoint Training flow chart of ADHDP algorithm 5.4 Optimal iterative process Inspired by the authors in [24, 25], the iterative process is derived to find the optimal function, consisting of the external iteration and the internal iteration. The external iteration aims to obtain the most optimal performance index function by comparing with other suboptimal function. Choosing a random positive definite function as the initial performance index function (39) The initial control sequence is calculated as (40) The performance index function is updated as (41) For i = 1, 2,. .., the external iteration advances between (42) and (43) While the following equation is eligible, the iteration is stopped (44) This is the external iteration. However, the iterative control sequence cannot be obtained directly by previous equations. Thus, the internal iteration is necessarily required. While the initial performance index function is presented as (45) While the internal iteration advances between (46) and (47) For the internal iteration advances between (48) and (49) The internal iteration is aimed to obtain the control action of per time interval, so the number of the iteration is certain. The external iteration is to get the most optimal cost value, so the number of the iteration is uncertain. 6 Analysis of examples This proposed strategy is applied on a micro-grid system consisting of four power sources, i.e. wind energy, PV, power from grid and battery energy storage, which is in southern China. The diagram of this system is similar to Fig. 2. Demand response program is essential for transferring interrupt load. Simulation and result analysis are carried out from the following two parts. 6.1 Upper model simulation According to these predicted values, demand elastic matrix and the original electricity price shown in Table 1, the adjusted net load can be obtained by adopting the PSO. Fig. 5 shows the load forecast value of 24 time intervals before adopting improved TOU price and the predicted value of power generation from the PV units and wind generating sets. Table 1. Original electricity price of micro-grid Electricity price, RMB/kWh Time interval 0.4 24:00–6:00 0.7 7:00–9:00 13:00–16:00 22:00–23:00 1.2 10:00–12:00 17:00–21:00 Fig. 5Open in figure viewerPowerPoint Wind power generation, solar power generation and load curve The electricity price of 24 h (see Fig. 6) is obtained from the upper scheduling model solved by PSO algorithm. Comparing with the original price, the regulation of it is more close and logical. Users can arrange their own electricity reasonably. Its effect would be presented on the net load curves. Fig. 6Open in figure viewerPowerPoint Electricity price of 24 time intervals with improved TOU price The net load curve under two conditions is shown in Fig. 7. The improved TOU price more effectively plays a role of peak shaving and valley filling, embodying in period 2 and 18 particularly. It is obvious to see that the improved TOU price makes the net load curve more flat than the original, which is conducive to the lower dispatch. Fig. 7Open in figure viewerPowerPoint Net load curves (with improved TOU, with original TOU) The value of the user's satisfaction is shown in Table 2. It is obtained that a small amount of part load is changed and the interests of the user are not lost. Those values meet the constraints, which assure that users actively participate in demand-side response. Table 2. User's satisfaction index of TOU pricing scenarios Satisfaction index Improved TOU program comfort of users 0.9021 economy of users 0.9973 satisfaction of users 0.9497 6.2 Lower model simulation The lower economic power dispatch for the micro-grid needs to be satisfied the net load is obtained from the upper scheduling model. Table 3 shows some parameters of three scheduling resources which contain the exchange power with grid, the shiftable load and the battery. The compensation cost of interruptible loads is introduced in detail in literature [36]. The lowest quoted interruptible load at different period is defined in Table 3. There, in order to simplify the simulation operation, the interruptible load per is set as ¥1.2, which is the average value of invoke price at each time. Table 4 shows the electricity price of grid at previous periods. Thus, dispatching cost can be calculated by these basic data. Table 3. Parameters of the simulation system Module of simulation model Parameters maximum value of the SOC of battery 0.95 minimum value of the SOC of battery 0.25 capacity of the battery, kW 200 comprehensive cost of the battery, RMB/kW 1.01 upper limit value of exchange power with grid, kW 50 upper limit value of shiftable load, kW 10 lower limit value of shiftable load, kW 3 Table 4.