Multi-agent system based sequential energy management strategy for Micro-Grid using optimal weighted regularized extreme learning machine and decision tree

Abstract

Renewable energies are fundamentally changing the traditional power grid. Their integration in micro grid constitutes the best way to produce clean energy in a large scale. However, classical control methods based centralized approaches are not efficient to manage and control the different operations in micro grid. In this paper, an intelligent energy management system is presented for micro grid power control based on the distributed paradigm of Multi-Agent System. Its main objective is to find the optimal control of a MG with grid-connected mode in order to control the amount of power delivered or taken from the Distribution Network so as to minimize the cost and maximize the benefit. We present also a photovoltaic and wind power prediction method using an Optimal Weighted Regularized Extreme Learning Machine algorithm in which the Particle Swarm Optimization method is used to optimize the regularization parameter. The algorithm is tested on real weather data and has shown a good generalization performance and better results than the basic Extreme Learning Machine algorithm while keeping its extremely fast training speed ability. To establish an efficient energy management strategy, a Decision Tree is used to ensure the availability of power on demand by taking a reasonable decision about charging batteries/selling electricity and discharging batteries/buying electricity in order to reduce the balance between cost and benefit.

Keywords

Renewable energies Micro-Grid multi-agent system extreme learning machine optimal weighted regularized extreme learning machine particle swarm optimization decision tree

1. Introduction

Growing energy demand, atmospheric pollution, climate warming, nuclear power risks and resource limits of fossil energies are the major considerations for the modern power industry. For this reason renewable energies constitute the best alternative and many countries tend to the new concept: Micro-Grid (MG) that has the potential to play a vital role to integrate renewable sources in large scale to produce clean energy. MG is a set of single electrical power subsystems associated with a small number of distributed energy resources, both renewable and/or conventional sources together with a cluster of loads and energy storage [1].

Energy management systems (EMSs) are designed to monitor, optimize, and control the smart grid energy market. They are used to optimally schedule the power resources in MG and to smartly maintain a balance between the distributed energy resources and the demand requirement in a user friendly manner. Furthermore, their objective is to minimize MG’s operating costs in the same time regarding the environment uncertainty introduced by renewable generation. Classical control methods are not efficient to control the different operations in MG because the failure of the entire system depends on unique point presented by the central controller [2]. In fact, in order to handle the complexity of such system, EMS requires the integration of innovative solutions and intelligent soft computations. For this reason, in the past few years the paradigm of Multi-Agent System (MAS) has been invented as distributed intelligence paradigm in power engineering [3], and used in order to ensure the more powerful results, thanks to the advantages which characterize this approach. MAS overcomes the centralized system drawbacks [4] by dint of communication between agents, where each agent is in charge of specific task to accomplish common goal. In published literature, MAS was applied to deal with three main problems in electricity power management system and especially in MG [3]: maximization of economic profit [5, 6], scheduling energy [7, 8], and grid stability [9, 10].

In this paper, considering scheduling approach for MG system to minimize the cost of non-green energy consumption, an intelligent EMS for MG is proposed as MAS based sequential control. The use of MAS leads the proposed EMS to find the best-integrated solution, taking into consideration the operating scenario and the system characteristics. Indeed, the main objective of this work is to find the optimal management of a MG with grid-connected mode in order to control the amount of power delivered or taken from the Distribution Network (DN) so as to minimize the cost and maximize the benefit. To achieve this goal, the approach is decomposed into two stages: The prediction stage and the decision making stage.

1.1 Prediction stage

Optimal control of MG is challenging due to uncertainties in generation amount of renewable generators, that’s why the integration of the forecast of weather data and output power is necessary, and there are many proposed works for predicting wind and solar power. For example [11], used time series to model the characteristics and behavior of wind speed as the autoregressive moving average. Some works use the artificial intelligence techniques like support vector machine (SVM) in [12] and artificial neural network (ANN) in [13]. However, most related works that use the cited algorithms have some problems, such as the slow convergence time, the weakness to find the global optimistic results, and the difficulty of calculating the quadratic convex program modeling the real problem [14]. Besides, these techniques are unable to cope with the strong fluctuation of observations. To overcome these drawbacks, a technique to predict the power produced by renewable generators was proposed in our previous works [14, 15] based on Extreme Learning Machine algorithm (ELM) because it overcomes the shortcomings of several other machine learning techniques due to its extremely fast training speed and its good generalization performance [16]. However, despite its attractive features, there are also some limitations for its solutions. Firstly, the ELM algorithm is still based on empirical risk minimization (ERM) principle and tends to over-fitting. Additionally, since ELM doesn’t consider heteroskedasticity in realistic applications, its performance will be affected seriously when outliers exist in dataset [17]. Finally, ELM provides weak control capacity since it directly calculates the minimum norm least-squares solutions [17]. To address these issues, Deng et al. was proposed Regularized Extreme Leaning Machine algorithm (R-ELM) based on structural risk minimization (SRM) principle and weighted least square. However, the performance of this algorithm depends on the regularization parameter which can be selected by experienced workers through trial and error or by optimization methods cited in the literature. For example, the classical Cross-Validation technique and the coordinate descent approach are two old optimization method and was used to choose the optimal regularization parameter in several works [18, 19]. Other methods have been proposed to select the appropriate $\gamma$ value such as the Nelder-Mead minimization approach in [20] and a method build on the Tikhonov regularization in [21]. The singular value decomposition based generalized cross-validation method is also used to estimate the regularization parameter [22, 23]. Nevertheless, this method increases the computational complexity, as it involves the repeated inversion of a large matrix. To address this issue, we propose an Optimal Weighted Regularized Extreme Learning Machine (OWR-ELM) algorithm in which the Particle Swarm Optimization (PSO) method is used to optimize the regularization parameter, for the prediction of power produced by renewable energy sources in the MG system for the next hour.

1.2 Decision making stage

The optimal decision in MG when to buy or sell electricity from or to the DN, that is to say, when to charge and discharge batteries, is a complex problem of energy management. Its objective is to minimize the total energy costs with the principle of satisfying some constraint (fulfill load demands, guarantee a long lifetime of batteries and maximize the use of green energies $\ldots$ ). In the literature, some works have been broached the problem of decision making and optimal control of MG. For example in [24], an improved multi-agent reinforcement learning method was presented to minimize the electricity costs on the premise of satisfying the power balance and generation limit of units. In [25], a multi swarm optimization algorithm was used by a coordinator agent to find the best compromised solution to satisfy economical/environmental objectives. In [26], authors aim in decision making using data driven methods and present a model for price-directed demand response steered by market signals and expectation method. Other works have used the fuzzy control strategy based on the status of some criteria such as loads, renewable energy sources and electricity price in order to satisfy economic goals and reducing the balance between cost and benefit [27, 28, 14].

Certainly, decision-making process requires a special transparency, easiness to understand and explain. So, we need a way to demonstrate visually the rules under which the data are grouped into smaller, more specific parts. In the past two decades, Decision Trees (DTs) which have tremendous potential as a decision-making tool has been widely used for classification and prediction in many scientific fields due to their ability and supporting human decision-making in an easy to understand form. DTs are useful to show the routes by which the various possible outcomes are achieved. Using the DT, management can consider various courses of action with greater ease and clarity and there are several reasons behind its broad applicability. For example, its accuracy is comparable or higher than the accuracy of other classification methods [29]. In addition, due to its intuitively appealing topology, the resulting classification models become easy to comprehend [30]. Furthermore, it helps to make the best decisions on the basis of existing information and best guesses. For those attractive features, a decision support method based on DT for energy management is proposed in this paper, which aims to find an optimal decision taking into account the status of loads demands, renewable energy sources and the SOC of batteries in a MG with grid-connected mode.

The major contributions of this paper can be summarized as follows:

(i)
An intelligent EMS based on MAS is proposed. Each component of MG is treated as an autonomous agent able to interact with other agents according to its current state and specific goals.
(ii)
A wind and PV power prediction based on OWR-ELM algorithm is proposed to estimate the wind and solar power for the next hour from real weather data.
(iii)
To establish an efficient energy management strategy, decision is taken based on the status of loads, renewable sources and batteries in a MG with grid-connected mode. Decision tree is used to take a reasonable decision about charging batteries/selling electricity and discharging batteries/buying electricity in order to reduce the balance between cost and benefit.

This paper is then organized as follows: Section 2 describes the adopted MG and its MAS modeling; Section 3 explains the proposed MG control approach. Section 4 outlines the Wind and photovoltaic power prediction method adopted. Section 5 explains the proposed decision making method based DT. In Section 6 we present simulation and results. Lastly Section 7 draws the overall conclusions of this paper.
2. System model

2.1 Adopted Micro-Grid

MG can be considered as the ideal way to integrate renewable energies in the electricity production in a large scale to produce clean energy. It gives the consumer the opportunity to participate in the electricity market not just like a consumer but also like a producer. MG consists in general of different generation units (renewable generation and/or not), energy storage units and local demands. In this paper, we consider a MG with grid-connected mode which is presented in Fig. 1. Taking into account the unpredictable weather conditions and to assume a continuous availability of energy, PV panels are supplied with wind turbine in the proposed MG. The system also includes a number of batteries to store the excess of energy produced by renewable generators and provide the energy demanded by load when there is low renewable power produced. Thus batteries are used as a source added to renewable generators and the DN. In this paper, we consider the following classification of the different sources according to priority order; firstly renewable energies as primary source i.e. consume green energy produced in the first place; at the second batteries as auxiliary source i.e. if the renewable power produced is not enough to fulfill the load demanded we must consume first the energy stored in batteries when they are charged; at the third DN as the last source i.e. we purchase electricity only when batteries are discharged.

Figure 1.

Diagram overview of the adopted MG with renewable energy resources.

2.1.1 Wind turbine

A wind turbine is a power generating device that uses wind to produce energy. The wind power is considered as primary source since it is renewable. The output power generated is considered as function of the wind velocity and calculated as follows [31]:

$\displaystyle P_{w}=\left\{\begin{array}[]{ll}0&\text{if}\ V_{ac}<V_{ci}\\ aV_{ac}^{2}+bV_{ac}+c&\text{if}\ V_{ci}\leqslant V_{ac}<V_{r}\\ P_{wr}&\text{if}\ V_{r}\leqslant V_{ac}>V_{co}\\ \end{array}\right.$ (1)

where $P_{wr}$ , $V_{ci}$ , and $V_{co}$ are the rated power, cut-in wind speed, and cut-out wind speed, respectively. Furthermore, $V_{r}$ and $V_{ac}$ are the rated and actual wind speed, respectively. Constants a, b, and c depend on the type of the wind turbine. We assume AIR403 wind turbine model is used in this paper. According to the data from the manufacturer, their characteristics are as follows [31]:

$a=$ 3.4; $b=$ $-$ 12; $c=$ 9.2; $P_{wr}=$ 130 W; $V_{ci}=$ 3.5 sm/s; $V_{co}=$ 18 m/s; $V_{r}=$ 17.5 m/s.

2.1.2 PV panel

PV panel is a power generating device that absorbs sunlight to generate electrical energy during daylight hours. The solar power is considered as primary source in our MG. Its output power can be calculated using the following equation [31]:

$\displaystyle P_{\textit{PV}}=P_{\textit{STC}}\times\frac{G_{\textit{ING}}}{G_% {\textit{STC}}}\times\left[{1+k\left({T_{c}-T_{r}}\right)}\right]$ (2)

where $P_{\textit{PV}}$ is the output power of the module at irradiance $G_{\textit{ING}}$ , $P_{\textit{STC}}$ is the module maximum power at standard test condition (STC), $G_{\textit{ING}}$ is the incident irradiance, $G_{\textit{STC}}$ is the irradiance at STC (1000 W/m ${}^{2}$ ), k is the temperature coefficient of power, $T_{c}$ is the cell temperature, and $T_{r}$ is the reference temperature. We assume that Solarex, MSX-83 is used in this paper. Their output characteristics are as follows: peak power $=$ 83 W, voltage at peak power $=$ 17.1 V, current at peak power $=$ 4.84 A, short circuit current $=$ 5.27 A, and open circuit voltage $=$ 21.2 V at STC.

2.1.3 Energy storage

Batteries are used to store energy during peak production when output is in over-supply for subsequent use in the event that the energy produced is insufficient (at night or when wind stops). The SOC of battery is defined as its available capacity expressed as a percentage. It can be calculated using the following equation:

$\displaystyle\textit{SOC}=C\times\frac{100}{C_{\textit{REF}}}$ (3)

where $C$ is the capacity of battery and $C_{\textit{REF}}$ is the reference capacity of battery. In this paper the depth of discharge ( $\textit{SOC}_{\textit{min}}$ ) and the depth of charge ( $\textit{SOC}_{\textit{max}}$ ) are fixed at 20% and 80% respectively.

Figure 2.

MAS architecture of adopted MG.

2.2 Multi-agent system modeling

MG with renewable generators is affected by the site climatic data change. That is why an intelligent EMS must exist to optimally schedule the power resources of MG in a user friendly manner. One of the main objectives of the EMS is to achieve a high level of flexibility. Thus, we are obliged to call upon a distributed intelligence paradigm, because with centralized approach the entire system depends on unique point presented by the central controller. MAS has been invented as distributed intelligence paradigm in power engineering since it overcomes the centralized system drawbacks by allowing to the different generation units the possibility to collaborate to achieve a common goal.

A MAS is an architecture composed of a set of software autonomous entities called “agents” able to interact to accomplish a global goal. Also, it can be defined as a distributed system consisting of a set of agents working together to solve problems that are beyond their individual capacities or knowledge [32]. A MAS allows a better manner to design and implement complex control systems due its flexible autonomous action, showing the following characteristics:

•
Autonomy: agent is able to act without the intervention of a third party (human or agent) and controls its own actions as well as his internal state;
•
Pro-activeness: agent do not only act in response to their environment, but as it is led by its own function and goals, it must also exhibit proactive and opportunistic behavior, while being able to take the initiative at the right time;
•
Social ability: Placed in its environment, the agent must be able to interact, when appropriate, with other agents through agent communication language to perform its tasks or help these agents to accomplish theirs;
•
Reactivity: agent must be able to perceive its environment and develop a response in the required time [32].

The MG components are often distributed and the energy management system is tightly associated with the communications between stakeholders and entities to exchange information. The use of MAS ensures the information exchange. The integration of this technology provide a communication layer that allow the MG to exchange information among its components by sharing message between the different agents.

So to model our MG we use MAS. Each important and flexible entity in MG can be represented by an autonomous agent .The proposed distributed MAS architecture is presented in Fig. 2 with the illustrated communication between six agents as follow:

•
AgentPV: this agent estimates the PV power produced by solar panels at time $t$ . It uses the OWR-ELM algorithm to predict the PV power for the next hour;
•
AgentWindTurbine: it predicts the wind power produced at time $t$ by the wind turbine using the OWR-ELM algorithm;
•
AgentBatteryBank: it is the agent who is responsible for the storage of energy. Among its roles, it gives information on the SOC and provides power to the MG when a trigger request comes from the AgentController;
•
AgentLoad: it gives information of load demand-ed in MG at time $t$ ;
•
AgentMainGrid: this agent offers the different selling or purchase price of electricity over time, and provides power to the MG when a trigger request comes from the AgentController;

Figure 3.
Proposed energy management strategy.

•
AgentController: this agent is responsible for the coordination between the other agents and decision making.

3. Micro-Grid control approach

Solar and wind energies are not available all the time, and their performance is affected by unpredictable weather changes. Therefore, optimal control of MG with renewable units is challenging and considered as a complex problem because of the uncertainties in generation amount of renewable generators. Therefore, the integration of the forecast of weather data and output power is necessary to overcome problems related to complex mathematical modeling. In this paper, considering scheduling approach for MG system to minimize the utilization of non-green energy, an intelligent EMS is proposed that is based on sequential control concepts. Its main objective is to find the optimal management for MG with grid-connected mode in order to increase the use of green energy, reduce the electricity bill and make profit by selling the surplus of power produced by renewable generators in the energy market if there is. In other words, the goal of our EMS is to control the amount of power delivered or taken from the DN so as to maximize the benefits by selling electricity to the DN, as soon as possible, after filling the local requirement of MG and charging batteries; and minimize the costs by purchasing electricity from the DN only when batteries are discharged and the load demanded is greater than the produced energy. To achieve these goals, we divide the energy management strategy into two main phases: prediction phase and decision making phase (see Fig. 3).

The prediction phase is based on the OWR-ELM algorithm for the prediction of the PV and wind power produced for the next hour. Decision making phase is based on DT classifier to take a reasonable decision about charging batteries/selling electricity in case if there is excess energy, and discharging batteries/buying electricity in case if there is necessary energy in order to reduce the balance between cost and benefit. The step-by-step procedure for carrying out the energy management strategy is summarized in the flowchart of Fig. 4.

Figure 4.

Flowchart of proposed hierarchical operation of EMS system.

4. Wind and photovoltaic power prediction

4.1 ELM

Huang et al. [33] introduced a new approach, so called ELM, for single-hidden layer feedforward network (SLFN) where only the output weights needs to be determined. Contrary to the other approaches that require either a manual or a computationally very expensive parameter setting, the hidden neuron parameters of ELM are randomly assigned and the output weights can be determined analytically by Moore – Penrose generalized inverse. Thereby the parameters in the hidden layer can be independent of the training samples [33].

Suppose that there is a training set ${\{}(x_{i},t_{i}){\}}^{N}_{i=1}$ with N distinct instances, where $x_{i}=[x_{i1}$ ; $x_{i2}$ , $\ldots$ , $x_{in}]^{T}$ contains $n$ inputs(attributes) and $t_{i}=[t_{i1}$ , $t_{i2}$ , $\ldots$ , $t_{im}]^{T}$ contains $m$ outputs (classes). Assume that we have a SLFN with $l$ hidden neurons. In SLFN, the input layer and the hidden layer are interconnected by an $l\times n$ input weight matrix $\omega$ where the $i$ th row vector is $\omega_{j}=[\omega_{j1};\omega_{j2};\ldots;\omega_{jn}]^{T}$ , $b$ is an $l\times 1$ hidden bias vector for each hidden neuron and the output layer and the hidden layer are interconnected by an $l\times m$ output weight matrix $\beta$ where the $i$ th row vector is $\beta j=[\beta_{j1};\beta_{j2};\ldots;\beta_{jm}]^{T}$ .

The structure of ELM consists of an input layer; an output layer and a single hidden layer. More specifically, its structure can be defined as:

$\displaystyle t_{i}=\sum\limits_{j=1}^{l}{\beta_{j}}g\left({\omega_{j}.x_{i}+b% _{j}}\right);i=1,2,\ldots,N$ (4)

where $j$ $\in$ {1; 2; $\ldots$ ; $l$ }, $\omega_{j}.x_{i}$ indicates the inner product of $\omega_{j}$ and $x_{i}$ and $g(x)$ is an activation function that can be step function, sigmoid function $\ldots$

Equation (4) can be written as the following compacted form:

$\displaystyle H\beta=T$ (5)

where $H$ is called the hidden layer output matrix of the network. $T$ is the output matrix and $T=[t_{1};t_{2};\ldots;t_{N}]^{T}$ .

$\displaystyle H=\left[\begin{array}[]{l}g(\omega_{1}.x_{1}+b_{1})\ldots g(% \omega_{l}.x_{1}+b_{l})\\ g(\omega_{1}.x_{N}+b_{1})\ldots g(\omega_{l}.x_{N}+b_{l})\\ \end{array}\right]$ (6)

Since the Eq. (5) can be viewed as a linear system, then the training of SLFN can be achieved by solving this linear system. Training the SLFN is simply equivalent to finding the unique minimum norm least square solution $\beta$ of Eq. (5) as follow:

$\displaystyle\beta=H^{\dagger}T$ (7)

where $H^{\dagger}$ is the Moore – Penrose (MP) generalized inverse of matrix H [34].

4.2 R-ELM

ELM has recently increased popularity and has been successfully applied due to its extremely fast training speed and its good generalization performance but it still can be considered as empirical risk minimization theme and tends to generate over-fitting model [17]. Additionally, it might lead to less robust estimation, especially with respect to outliers on the data or when heteroskedasticity exists. Finally, ELM provides weak control capacity since it directly calculates the minimum norm least-squares solutions [17]. In order to address these drawbacks, Deng et al. was proposed a novel algorithm called R-ELM based on SRM principle and weighted least square. Generally, when we would like to train an SLFN, we should find $\omega_{i}$ , $b_{i}$ , $\beta$ ( $i=1,2\ldots l$ ) such that:

$\displaystyle\min\left\|\varepsilon\right\|^{2}$ $\displaystyle s.t\sum\limits_{j=0}^{l}{\beta_{j}g(\omega_{j}.x_{i}}+b_{j})-t_{% i}=\varepsilon_{i};$ (8) $\displaystyle\qquad i=1,\ldots,N$

where $\varepsilon_{i}=[\varepsilon_{i1},\varepsilon_{i2},\ldots,\varepsilon_{im}]$ is the resident between target value and real value of the $i$ -th sample, and $\varepsilon=[\varepsilon_{1},\varepsilon_{2},\ldots,\varepsilon_{N}]$ . However, a model with good generalization ability should have the best tradeoff between the two risks: empirical risk and structural risk that composes the real prediction risk of learning according to statistical learning theory. The proportion of them can be regularized by introducing a weight factor $\gamma$ for empirical risk which is represented by sum error square i.e. $||\varepsilon||^{2}$ and structural risk can be represented by $||\beta||^{2}$ which is derived from maximizing the distance of the margin separating classes [35]. Moreover, to obtain a robust estimate weakening outlier interference, the error $\varepsilon_{i}$ is weighted by variable $\nu_{i}$ . Thus, $||\varepsilon||^{2}$ is extended to $||$ D $\varepsilon||^{2}$ , where $D=\textit{diag}\left({\nu_{1},\nu_{2},\ldots,\nu_{N}}\right)$ . Therefore the proposed mathematic model of R-ELM algorithm can be described as:

$\displaystyle\text{min }\frac{1}{2}\left\|\beta\right\|^{2}+\frac{1}{2}\gamma% \left\|{D\varepsilon}\right\|^{2}$ $\displaystyle s.t\ \sum\limits_{j=1}^{l}{\beta_{j}g(\omega_{j}.x_{i}+b_{j})}-t% _{i}=\varepsilon_{i},$ (9) $\displaystyle\qquad i=1,2,\ldots,N$

We can adjust the proportion of empirical risk and structural risk by regulating $\gamma$ to obtain the optimal tradeoff between these two risks in order to have a model with best generalization performance. The Lagrangian function for Eq. (4.2) can be described as:

$\displaystyle L=(\beta,\varepsilon,\alpha)=\frac{\gamma}{2}\left\|{D% \varepsilon}\right\|^{2}+\frac{1}{2}\left\|\beta\right\|^{2}-\sum\limits_{i=1}% ^{N}{\alpha_{i}}\left(\sum\limits_{j=1}^{l}{\beta_{j}g(\omega{}_{j}.x_{i}+b_{j% })}-t_{i}-\varepsilon_{i}\right)=\frac{\gamma}{2}\left\|{D\varepsilon}\right\|% ^{2}+\frac{1}{2}\left\|\beta\right\|^{2}-\alpha(H\beta-T-\varepsilon)$ (10)

where $\alpha_{i}\in\mathbb{R}$ ( $i=1,2,\ldots,N$ ) is the Lagrangian multiplier with the equality constraint of Eq. (4.2) and $\alpha=[\alpha_{1},\alpha_{2},\ldots,\alpha_{N}]$ . Then setting the gradients of this Lagrangian with respect to ( $\beta$ , $\varepsilon$ , $\alpha$ ) equal to zero gives the following optimality conditions:

$\displaystyle\left\{\begin{array}[]{l}\frac{\partial L}{\partial\beta}\to\beta% ^{T}=\alpha H,\\ \frac{\partial L}{\partial\varepsilon}\to\gamma\varepsilon^{T}D^{2}+\alpha=0,% \\ \frac{\partial L}{\partial\alpha}\to H\beta-T-\varepsilon=0.\\ \end{array}\right.$ (11)

Substituting the last expressions of Eq. (11) in the second expression will give an explicit expression for $\alpha$ (Eq. (15)) and $\varepsilon_{i}$ can be calculated using $\alpha$ (Eq. (15)):

$\displaystyle\alpha=-\gamma({\bf H}\beta-{\bf T})^{T}$ (12) $\displaystyle\varepsilon_{i}=\frac{\alpha_{i}}{\gamma}$ (13)

By solving Eq. (11), we can obtain the solution of $\beta$ :

$\displaystyle\beta=\left({\frac{I}{\gamma}+H^{T}D^{2}H}\right)^{\dagger}H^{T}D% ^{2}T$ (14)

where $I$ is an unit matrix.

When $D$ is the unit matrix $I$ , $\beta$ can be calculated by the following expression:

$\displaystyle\beta=\left({\frac{I}{\gamma}+H^{T}H}\right)^{\dagger}H^{T}T$ (15)

In this case, the algorithm is called as unweighted Regularized ELM (UWR-ELM). In fact, the traditional ELM is just the special case of UWR-ELM when $\gamma\to\infty$ . To find the weights $\nu_{i}$ there are many kinds of computing method such as [36]:

$\displaystyle\nu_{i}=\left\{\begin{array}[]{ll}1&\left|{\frac{\varepsilon_{i}}% {\hat{s}}}\right|\leqslant c_{1}\\ \frac{c_{2-}\left|{\frac{\varepsilon_{i}}{\hat{s}}}\right|}{c_{2}-c_{1}}&c_{1}% \leqslant\left|{\frac{\varepsilon_{i}}{\hat{s}}}\right|\leqslant c_{2}\\ 10^{-4}&\text{otherwise}\\ \end{array}\right.$ (16)

where the constant $c_{1}$ and $c_{2}$ are typically set as 2.5 and 3 respectively [37]. $\hat{s}$ is a robust estimate of the standard deviation of the unweighted error variables $\varepsilon_{i}$ , and can be calculated as:

$\displaystyle\hat{s}=\frac{\textit{IQR}}{2\times 0.6745}$ (17)

where IQR is the inter quartile range which is the difference between the 75th percentile and 25th percentile.

Therefore the algorithm of R-ELM can be described as [17]:

Algorithm 1:
Given a training set $N=\{(x_{i},t_{i})\|x_{i}\in\mathbb{R}^{n},t_{i}\in\mathbb{R}^{m},i=1,\ldots,N{\}}$ , activation function $g(x)$ , and hidden node number $l$ .
Step 1:	Randomly assign input weights $\omega_{j}$ and bias $b_{j}(j=1,\ldots,l)$ and calculate the hidden layer output matrix $H$ by Eq. (6);
Step 2:	Calculate $\alpha$ by Eq. (12) and calculate $\varepsilon_{i}$ by Eq. (13) ( $i=1,\ldots,N$ );
Step 3:	Calculate $\hat{s}$ by Eq. (17) and calculate the weights $\nu_{i}$ by Eq. (16);
Step 4:	update $\beta$ by Eq. (14);
Step 5:	End.

Figure 5.

Illustration of OWR-ELM’s predictors.

4.3 OWR-ELM

The selection of regularization parameter $\gamma$ plays a vital role in the generalization performance. In this paper we present an OWR-ELM for the prediction of solar and wind power based on PSO algorithm that allows to obtain the optimum value of regularization parameter. PSO is a stochastically global optimization method based on swarm intelligence that optimizes a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality. It uses a population of candidate solutions, called particles, to develop an optimal solution to the problem. The particles move in the search-space according to mathematical formulae in terms of particle’s position (Eq. (18)) and velocity (Eq. (19)).

$\displaystyle x_{i,d}(t+1)=v_{i,d}(t+1)+x_{i,d}(t)1\leqslant i\leqslant n;1% \leqslant d\leqslant D$ (18) $\displaystyle v_{i,d}(t+1)=v_{i,d}(t)+c_{1}r[p_{i,b}(t)-x_{i,d}(t)]+c_{2}r[g_{% i,b}(t)-x_{i,d}(t)]$ (19)

where $c_{1},c_{2}$ are the acceleration constants with positive values; $r$ is a random number between 0 and 1, $g_{i,b}$ is the best position of the neighbors, $p_{i,b}$ the best position of the ith particle, $D$ is the dimension for a searching space and $n$ is the total number of particles.

To use PSO technique, two main points have to be considered: First one is how to represent the particles and the second one is how to select the fitness function. Since we try to find an optimal weight factor value, then particles are initialized by candidate solutions of logarithmic values from the set {2- ${}^{50}$ , $\ldots$ , 2 ${}^{50}$ } [17]. To define the fitness value, the mathematic model of R-ELM (represented by Eq. (4.2)) is taken as objective function to be optimized.

The procedure of our proposed algorithm OWR-ELM can be summarized by the following steps:

Algorithm 2:
Given a training set $N={\{}(x_{i},t_{i})\|x_{i}\in\mathbb{R}^{n}$ , $t_{i}\in\mathbb{R}^{m}$ , $i=1,\ldots,N$ }, activation function $g(x)$ , and hidden node number $l$ .
Step 1:	Randomly assign input weights $\omega_{j}$ , bias $b_{j}$ ( $j=1,\ldots,l$ ) and regularization parameter $\gamma$ from the set {2 ${}^{-50}$ , $\ldots$ , 2 ${}^{50}$ };
Step 2:	2.1. Calculate the hidden layer output matrix $H$ by Eq. (6);
	2.2. Calculate $\alpha$ by Eq. (12);
	2.3. Calculate $\varepsilon_{i}$ by Eq. (13);
	2.4. Calculate the weights $\nu_{i}$ by Eq. (16);
	2.5. Calculate $\hat{s}$ by Eq. (17); ( $i=1,$ … $, N$ );
Step 3:	Update $\beta$ by Eq. (14);
Step 4:	Set parameters $c_{1}$ and $c_{2}$ of PSO algorithm;
Step 5:	Initialize population of $n$ particles from the set {2 ${}^{-50}$ , $\ldots$ , 2 ${}^{50}$ } having positions $X$ and velocities $V$ ;
Step 6:	Set iteration $t=$ 1;
Step 7:	Compute the fitness of each particle according to Eq. (4.2);
Step 8:	Initialize $p_{i,b}$ of each particle by its fitness value and $g_{i,b}$ by the particle with the minimum fitness value;
Step 9:	For each particle update position and velocity using Eqs (19) and (20);
Step 10:	For each particle compute the new fitness to update $p_{i,b}$ and $g_{i,b}$ ;
Step 11:	If $t<$ Maximum iteration, then $t=t+1$ and go to step 9 else go to step 12;
Step 12:	Conclude the optimum regularization parameter as $g_{i,b.}$ in order to select the optimal prediction model.

4.4 Proposed prediction method based OWR-ELM

Having regard to the fluctuation of weather data and the shortcomings mentioned above of many machine learning techniques in the prediction field of solar and wind output power, an algorithm based OWR-ELM is proposed.

Therefore, we use one predictor trained by OWR-ELM algorithm for each renewable energy source (see Fig. 5) one for PV power and another for wind power. To choose the parameters of the two networks, we are based on mathematical models of output power generated by each renewable energy source which are represented in Eqs (1) and (2). The output power produced by PV panel can be considered as a function of irradiation and temperature, when the output power produced by wind turbine can be considered as a function of wind velocity. The other parameters mentioned in Eqs (1) and (2) depend only on the characteristics of materials model installed in MG (model of PV panel and wind turbine). Therefore, for PV power, the proposed network has two inputs: irradiation and temperature and one output: the amount of PV power produced ( $P_{PV}$ ) at each time scale $t$ . For wind power, we propose a predictor that takes as input the wind speed and gives as result the wind power produced ( $P_{W}$ ). After obtaining both estimated values $P_{PV}$ and $P_{W}$ , we sum them to get the total power produced ( $P_{T}$ ) by renewable energy sources in MG at each period of time $t$ .

$\displaystyle P_{T}\left(t\right)=P_{PV}\left(t\right)+P_{W}\left(t\right)$ (20)

After that, we calculate $\Delta P$ , the difference between the total power produced $P_{T}$ and load demanded $P_{L}$ as follow:

$\displaystyle\Delta P\left(t\right)=P_{T}\left(t\right)-P_{L}\left(t\right)$ (21)

According to $\Delta P^{\prime}s$ sign we can know if we still need another amount of energy that can be taken from batteries or from the DN according to SOC of batteries to fulfill the required demand ( $\Delta P$ negative) or we have an excess power produced that should be used in charging batteries or injected in the DN instead of to be wasted ( $\Delta P$ positive).

Figure 6.

Adopted DT for decision making.

Figure 7.

PV and wind Power Predicted by OWR-ELM (blue), R-ELM (green), ELM (yellow) and Calculated by Mathematical Formulas (red).

5. Proposed decision making method based decision tree

Rules-based system (RBS) is a deterministic type of artificial intelligence, which use a set of IF-THEN statements (created by an expert) to make a decision. Despite it still has its place, but also it has some weaknesses. The wrong choice of rules can lead to the wrong result. In addition the system can begin quite simple and become rather unwieldy as more as changes are added. Machine learning is probabilistic and uses statistical models rather than deterministic rules. Therefore, it constitute an alternative approach which can help to address the RBS’s issues. There are many possible machine learning models out there, some algorithms are easier to explain and understand than other. DT can visualize its decision in a way not unlike RBS. The rules in RBS come from human experts, whereas the decisions in a DT are produced by the machine learning process. For this reason, we considered using DT; which has tremendous potential as decision-making tool; to make a suitable and reasonable decision about charging batteries/selling electricity and discharging batteries/buying electricity in order to reduce the balance between cost and benefit. DTs are a non-parametric supervised learning method used for classification and regression. Their goal is to create a model that predicts the value of a target variable by learning simple decision rules inferred from the data features. The elements of DT are called nodes. They are connected together by hierarchy relationships. Thus we say that the node which is superior to another in this hierarchy is his father. In addition, it possesses possibly one or more son. A node that has no father is the root of DT. A node that has no son is called a leaf. Any other node in DT will be called an internal node.

DTs are at their heart a fairly simple type of classifier for data represented by ‘attribute/value’ sets. They are easy to explain because they can be visualized, and this is one of their advantages. DTs have many other advantages. They can be useful with or without hard data, and any data requires minimal preparation. They are able to handle both numerical and categorical data. Other techniques are usually specialized in analyzing datasets that have only one type of variable. They are able to handle multi-output problems. New options can be added to existing trees. In short, they follow the same approach as humans generally follow while making decisions.

Figure 8.

Profile of Load Power demanded of the Adopted MG for one day.

Figure 9.

PV power predicted during one day from four different seasons.

Figure 10.

Wind power predicted during one day from four different seasons.

Considering the adopted MG with grid-connected mode, our goal is to predict the decision that we should take at each period of time. To establish an efficient decision making strategy, decision is taken based on the status of loads, renewable energy sources and batteries. The status of loads and renewable energy sources are presented by $\Delta$ P, where the status of batteries is presented by its SOC. The construction of our DT is not done randomly. Our goal is to determine the best attributes to place at each node so that the constructed tree is as small as possible (more the tree is small, more the prediction will be easy to obtain) and at the same time the tree is able to make good prediction. The best attribute for our DT is $\Delta$ P which is considered as the root. Starting from $\Delta$ P we should answer the question “what is the sign of $\Delta$ P?” it could be two responses: negative or positive and according to each answer we must examine the value of the SOC of batteries which is considered as an internal node. Since the batteries depth of charge is between 20% and 80% then they cannot be discharged if the SOC is below 20% and they cannot be charged if the SOC is over 80%. Therefore, when $\Delta$ P is positive we must answer the question “is SOC over or under 80%?” According to the answer we make decision about charging batteries or selling excess power to the DN. When $\Delta$ P is negative we must answer the question “is SOC over or under 20%?” According to the answer we make decision about discharging batteries or buying necessary power from the DN.

Table 1

Skill metric in terms of the overall rmse and training time

Skill	OWR-ELM	R-ELM	ELM	BP	FFNN
PV power
RMSE	0.0907	0.0951	0.1054	0.8679	0.9025
Training time(s)	1.1914	1.1521	1.0112	7.1821	9.3452
Wind power
RMSE	0.1192	0.1214	0.1391	0.9125	0.9217
Training time(s)	1.0611	0.9891	0.9044	6.9961	8.2493

Figure 11.

SOC of batteries during the period test.

Figure 12.

Comparison between benefits and costs.

Figure 6 describes the proposed DT that indicates the way for selecting the appropriate decision depending on the available data $\Delta$ P and SOC. We assume that the batteries are considered as one entity and lumped together to form an energy storage system.

6. Simulation and discussion

We present in this section the obtained results to discuss the performance of the proposed EMS. The adopted MAS was developed using Java Agent Development Framework (JADE) platform [38]. Concerning the interoperation, we used Agent Communication Language (ACL) which plays a vital role in facilitating the communication amongst agents operating in a MAS.

As regard to the prediction phase, the OWR-ELM network applied for PV power prediction has two neurons in the input layer represented by irradiation and temperature, and one neuron in the output layer which is the power produced by PV panels. For the wind power, the OWR-ELM predictor applied has one input which is the wind speed and one output which is the amount of power produced by wind turbine.

To learn and test the OWR-ELM algorithm, we used real observations of irradiation, temperature, and wind speed of Tetouan city of northern Morocco. Figure 7 present four curves, in both cases PV power and wind power respectively, comparing the predicted power using OWR-ELM algorithm (blue), predicted power using R-ELM algorithm (green), predicted power using ELM algorithm (yellow) and results calculating by Eqs (1) and (2) (red).

To select the regularization parameter of R-ELM, $\gamma$ is suitably chosen to achieve good generalization performance in the interval [2 ${}^{-20}$ , $\ldots$ , 2 ${}^{20}$ ]. Here 40 different values of $\gamma$ are chosen and the best value is the one corresponds to lower prediction errors. After several tests we opt for $\gamma=2^{-2}$ .

On the other hand, to implement OWR-ELM algorithm the regularization parameter $\gamma$ is also selected in the range [2 ${}^{-20}$ , $\ldots$ , 2 ${}^{20}$ ]. The population size and number of iteration are selected as 10 and 40 respectively for PSO method. The algorithm give 0.2191 as optimal value obtained after 40 iterations. The final accuracy of the proposed algorithm is measured based on the test data set. Therefore, the profile of load for 24 hours is chosen as in Fig. 8. And the results obtained for one day from four different seasons are summarized in Figs 9 and 10.

In order to evaluate the potential of the proposed prediction models, we compared results of OWR-ELM with other obtained by R-ELM algorithm, ELM algorithm, the conventional neural network model trained by BP (back-propagation) algorithm and the simple feed forward neural network (FFNN) in which we adjust the connection weights by iterative process. We run these algorithms on the same data sets. The performance comparison is based on training time and estimation capability using the root mean square error (RMSE) as a numerical tool for comparison. RMSE could be represented as the following equation where $y_{i}$ is the predicted value, $x_{i}$ is the measured value, and N is equal to the number of observations.

$\displaystyle\textit{RMSE}=\sqrt{\frac{\sum\limits_{i=1}^{N}{(y_{i}-x_{i})^{2}% }}{N}}$ (22)

It can be seen from Table 1 that OWR-ELM obtains the lower RMSE than R-ELM and the basic ELM while the training time increase very slightly, and it is significantly better than RMSE of BP and FFNN while training speed is very faster. On the basis of this analysis, the obtained results are quite acceptable, and we can resume that the proposed models can predict the power produced by PV and wind generators for the next hour with high accuracy taking into account meteorological data. This is shown also in Fig. 7 since the curve presenting the OWR-ELM results is the one closest to the curve presenting the calculated results for the overall test.

On the other hand, using DT for decision making gives more capability to control the different operations as storage or selling and allows the possibility to reduce the balance between the cost and benefit in the MG. The lifetime of batteries is taking into consideration by setting the SOC as much as possible between 20% and 80%. DT adopted allowed to obtain this level of guard. Figure 11 presents the SOC of the batteries during the period test of 1000 hours. The variation of SOC remains between 20% and 80% with only one deep discharge in all the test period.

Another simulation over the test period was performed to compare benefit and cost (Fig. 12). When we had a benefit, this appears in red; otherwise, the cost appears in blue. In the case, where the two curves are at zero, this means that we had discharged or charged the batteries and we did not need the intervention of DN. It is clear that we had managed to achieve more benefits than costs according to the test period.

7. Conclusion

A novel strategy to optimally schedule the power resources in a MG with grid-connected mode through MAS has been proposed in this paper. The components of MG are represented by a set of agents able to interact between them. The use of MAS has ensured an economic and environmental operation even though we have a randomized natural behavior of wind and solar energy sources. This is allowed thanks to the proposed intelligent EMS based sequential control which consider scheduling approach for MG system to minimize the cost of non-green energy consumption through two-stage: prediction and decision making stages.

The PV and wind power produced by renewable generators has been predicted using OWR-ELM algorithm that hade the advantages of reduced randomness, reduced computational complexity and better generalization than the basic ELM algorithm while keeping its extremely fast training speed ability. OWR-ELM compared with R-ELM, ELM, BP and FFNN algorithms was capable of predicting with high accuracy and fast convergence speed. The results of the case study confirmed that the proposed models can be applied in a very flexible way and yielded lower prediction errors.

For decision making stage, a decision based DT was taken based on the status of loads, renewable sources and batteries. DT adopted gave more capacity to take a reasonable decision about charging batteries/selling electricity in case if there is excess power produced by renewable sources, and discharging batteries/buying electricity in case if there is necessary energy so as to increase the use of the green energies and satisfy economic goals by reducing the balance between cost and benefit. The simulation results highlight the performance of the proposed DT as the SOC remains over 20% and under 80% with only one deep discharge in the overall test to ensure their proper use and their long lifetime.

References

Lasseter

Paigi

. Microgrid: a conceptual solution. Proceedings of the IEEE 35th; Annual Power Electronics Specialists Conference (PESC 04), 2004; 4285-4290.

Ambia

Al-Durra

Caruana

Muyeen

. Power management of hybridmicro-grid system by a generic centralized supervisory control scheme. Sustain Energy, Technol Assess. 2014; 8(3): 57-65.

McArthur

Davidson

Catterson

Dimeas

Hatziargyriou

Ponci

, et al. Multi-agent systems for power engineering applications – Part II: Technologies, standards, and tools for building multi-agent systems. IEEE Transactions on Power Systems. 2007; 22(4): 1753-1759.

Siljak

. Decentralized control of complex systems. Dover Publications, 2012.

Pinto

Morais

Oliveira

Vale

Praça

Ramos

. A New approach for multi-agent coalition formation and management in the scope of electricity markets. Energy. 2011; 36(8): 5004-5015.

Zhou

Zhao

Wang

. Agent-based electricity market simulation with demand response from commercial buildings. IEEE Transactions Smart Grid. 2011; 2(4): 580-588.

Khan

MRB

Razali

Pasupuleti

. Multi-agent based distributed control architecture for microgrid energy management and optimization. Energy Conversion and Management. 2016; 212: 288-307.

Karavas

Kyriakarakos

Arvanitis

Papadakis

. A multi-agent decentralized energy management system based on distributed intelligence for the design and control of autonomous polygeneration microgrids. Energy Conversion and Management. 2016; 103: 166-179.

Zhang

. Distribution service restoration with DGs based on multiagent immune algorithm. The 2nd; International Conference on Power Electronics and Intelligent Transportation System Shenzhen, China, 2009; 1-4.

10.

Yuqin

Zengping

. Research on service restoration for large area blackout of distribution system with distributed generators. International Conference on Sustainable Power Generation and Supply. Nanjing. 2009, pp. 1-6.

11.

Juan

Jos

Rodolfo

Jos

. Forecast of hourly average wind speed using ARMA model with discrete probability transformation. Electrical Engineering and Control. 2011; 98: 1003-1010.

12.

Han

Zhai

. Wind speed forecasting based on support vector machine with forecasting error estimation. The 6th International Conference on Machine and Cybernetics. China. 2007; 2745-2739.

13.

Di Piazza

Vitale

. Estimation and forecast of wind power generation by FTDNN and NARX-net based models for energy management purpose in smart grids. International Conference on Renewable Energies and Power Quality. Spain. 2014.

14.

El Bourakadi

Yahyaouy

Boumhidi

, Multi-agent system based on the extreme learning machine and fuzzy control for intelligent energy management in microgrid, Journal of Intelligent Systems. 2018; doi: 10.1515/jisys-2018-0125.

15.

El Bourakadi

Yahyaouy

Boumhidi

, Multi-agent system based on the fuzzy control and extreme learning machine for intelligent management in hybrid energy system. The 2nd International Conference on Intelligent Systems and Computer Vision. Morocco. 2017.

16.

Huang

. Zhu

Siew

. Extreme learning machine: theory and applications. Neurocomputing. 2006; 70: 489-501.

17.

Deng

Zheng

Chen

. Regularized extreme learning machine. IEEE Symposium on Computational Intelligence and Data Mining Conference. USA, 2009.

18.

Friedman

Hastie

Tibshirani

. Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software. 2010; 33(1): 1-22.

19.

Miche

Van Heeswijk

Bas

Simula

Lendasse

. TROP-ELM: a double regularized ELM using LARS and Tikhonov regularization. Neurocomputing. 2011; 74(6): 2413-21.

20.

Miche

Eirola

Van Heeswijk

SéVerin

Lendasse

. Regularized extreme learning machine for regression with missing data. Neurocomputing. 2013; 102: 45-51.

21.

Cancelliere

Gai

Gallinari

Rubini

. OCReP: an optimally conditioned regularization for pseudoinversion based neural training. Neural Networks 2015; 71: 76-87.

22.

Naik

Jagannath

. Accurate validation of GCV-based regularization parameter for extreme learning machine. International Conference on Advances in Computing, Communications and Informatics. India, 2017.

23.

Feng

Zhuang

. Improving ESVM with generalized cross-validation. International Joint Conference on Neural Networks. Ireland, 2015.

24.

Chen

. Optimal control in microgrid using multi-agent reinforcement learning. ISA transactions. 2012; 51(6): 743-751.

25.

Serraji

Didi

Boumhidi

. Multi swarm optimization based adaptive fuzzy multi agent system for microgrid multi-objective energy management. International Journal of Knowledge-Based and Intelligent Engineering Systems. 2016; 20(4): 229-243.

26.

Alamaniotis

Gatsis

Tsoukalas

. Virtual Budget: Integration of electricity load and price anticipation for load morphing in price-directed energy utilization. Electric Power Systems Research. 2018; 158: 284-296.

27.

Zhang

Davigny

Colas

Poste

Robyns

. Fuzzy logic based energy management strategy for commercial buildings integrating photovoltaic and storage systems. Energy and Buildings. 2012; 54: 196-206.

28.

Abadlia

Bahi

Bouzeria

. Energy management strategy based on fuzzy logic for compound RES/ESS used in stand-alone application. International Journal of Hydrogen Energy. 2016; 41(38): 705-717.

29.

Lim

Loh

Shih

. An Empirical Comparison of Decision Trees and Other Classification Methods. Technical Report, 979; 1998.

30.

Manwani

Sastry

. Geometric decision tree. IEEE Transactions on Systems, Man, and Cybernetics, Part B Cybernetics. 2012; 42(1): 181-192.

31.

Netto

Ramalho

Bonatto

Carpinteiro

OAS

Zambroni de Souza

Oliveira

D.Q

, et al. Real-time framework for energy management system of a smart microgrid using multiagent. Systems, Energies. 2018; 11(3): 656.

32.

Chedid

Akiki

Rahman

. A decision support technique for the design of hybrid solar-wind power systems. IEEE Transaction on Energy Conversion. 1998; 13(1): 76-83.

33.

Huang

Zhu

Siew

. Extreme learning machine: a new learning scheme of feedforward neural networks. IEEE International Joint Conference on Neural Networks. Singapore. 2004; 985-990.

34.

Rao

Mitra

. Generalized Inverse of Matrices and Its Applications. Probability and Statistics Series. 1971; 1: 601-620.

35.

Glenn

Mangasarian

. Proximal support vector machine classifiers. 7th ACM SIGKDD international conference on knowledge discovery and data mining. California. 2001; 77-86.

36.

David

. Early sample measures of variability. Statistical Science. 1998; 13(4): 368-377.

37.

Rousseeuw

Leroy

. Robust regression and outlier detection. Wiley Series in Probability and Statistics. 1987.

38.

Bellifemine

Caire

Greenwood

. Developing Multi-Agent Systems with JADE. Wiley Series in Agent Technology, 2007.