A strategy to optimize the multi-energy system in microgrid based on neurodynamic algorithm

doi:10.1016/j.asoc.2018.06.053

Applied Soft Computing

Volume 75, February 2019, Pages 588-595

https://doi.org/10.1016/j.asoc.2018.06.053 Get rights and content

Highlights

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Using heat and power participants, a multi-energy management strategy is designed.
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A neurodynamic algorithm with fewer neurons is developed to regulate output.
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The convergence of the algorithm prove the effectiveness of management strategy.

Abstract

In this paper, we design multi-energy management strategy for power-supply participants, heat-supply participants and consumers in a microgrid. The objectives of the management strategy are to maximize the social welfare and to balance the energy supply and demands. With the transmission loss, the proposed social welfare model, subject to practical operation constraints, is formulated as a nonconvex optimization problem. Based on a sufficient condition, a equivalent problem transformed from the primary optimization problem is presented as a convex problem. A neurodynamic algorithm based Karush–Kuhn–Tucker(KKT) conditions and projection with fewer neurons is developed to regulate the resource output of each participant. The convergence of the applied algorithm is proved by Lyapunov function. Finally, numerical simulations are used to prove the effectiveness of the designed management strategy.

Introduction

The ongoing serious overreliance on traditional resources in recent energy consumption structure induces the global warming with the greenhouse gas emission and decreases the efficiency of energy utility [1]. Therefore, the vital issue is emphasized. Comprehensive resources supply and energy transformation can increase the energy utilization by recycling the by-product after generation and coordinate fossil fuel and renewable resources [2], [3], [4]. Based on smart grid, the key is to cope with the unbalanced resource structure and low converting efficiency. On the basis of the information sharing, the multi-energy management in smart grid highlights the integration of power production, processing, storage and transformation to find the efficient method for allocating the comprehensive energy source [5], [6], [7], [8].

Depending on the configuration by the shared information, multi-energy management in a microgrid offers an optimal output for minimizing total cost by using the different source inputs. The smart meter and central controller help to flexibly adjust the storage and outputs of heat and power in a practical and changing periods when the energy price and load fluctuate. Demand response strategy also has significant effects on minimizing system cost [9]. Based on the demand response strategy for load, [10] presents an extended energy hub model integrated with combining heat and power generators, heat storage units which maximizes the financial valuation. Optimal dispatch can be obtained finally through the inputs of price, system parameters and information processing. In residential energy hub, a mathematical model is provided to optimally control the residential loads, storage, and production components by [11]. The function of minimizing the energy consumption, total cost of electricity and gas, emission, peak load and combination of these objectives are formulated as a Mixed Integer Linear Programming optimization problem. In microgrids scenario, [12] proposes a hierarchical energy management for multiple sources and multiple products microgrids. The management system employs three layers, including a supervisory control layer, an optimization layer and an execution layer, which divides the control sub-layer of gas, heat, and power management into low, medium and fast. Demand response (DR) strategies can be considered as a method of “virtual power plant”. This objectives of this methods are accomplished by: $(1)$ peak-time load can be decreased. $(2)$ Large amounts of consumption can be scheduled to off-peak period [13]. Therefore, plenty of researches emphasize on the energy management with DR strategies [14].

Results in literatures have considered the multi-energy management strategy in microgrid. In [15], the electric and thermal energy management of a residential hub was formed as an integer linear programming problem. The transmission loss of electricity was omitted for model simplification, and the DR strategies only included the semi-flexible load. All of these methods above inevitably induces mismatch compared with practical situation and decreases the utility and efficacy of DR method. In [16], a simplified microgrid which integrated power supply, thermal supply and gas supply was given. Particle swarm optimization (PSO) algorithm was applied to solve the proposed model. PSO algorithm and other genetic algorithm(GA) work effectively in practical application, which performs great potential in system , multi-objective optimization, classification, information processing etc. However, the convergence and convergence rate of genetic algorithm have not been proved fully, which means the mathematical theory in this area is not enough [17]. Especially, the fact that PSO algorithm usually plunges into local optimum should be paid attention to. Therefore, for certain kinds of optimization problem like convex programming problems, neurodynamic algorithm has been used because of its developed mathematical theories and various of applications.

On the one hand, Recurrent neural network(RNN) which is inspired from their biological counterparts has shown great promises in improving computational efficiency and reducing model complexity of optimization problem. Among the applications of data classification, time series analysis and automatic control, the use of recurrent neural network has a continuous success in computational intelligence.

Therefore, the neurodynamic method has been applied to optimization problems of the smart grid in recent years. The different neurodynamic algorithms has been designed to address economic dispatch problem, PHEV charging problem and DR problem in smart grid, which is formed as the convex optimization problems [18], [19]. Hopfield and Tank pioneered the area by applying a neural network into the disposition of linear programming [20]. Kenney and Chua studied dynamics of the modified canonical nonlinear programming circuit which can be realized by network and applied the dynamic circuit to handle nonlinear problem [21]. Wang proposed a deterministic annealing neural network for convex programming problem [22]. Xia and Wang presented a neural network for solving the nonlinear projection formulation, and this model can solve a large amount of constraints optimization problems [23]. On another hand, recent advances in neurodynamic engineering offer availability of hardware implementation of neural network which expresses advantages of computing speed, such as the use of specialized integrated circuit to realize the parallel distributed computing. And the results have shown these proposed algorithms are effective in solving the problems. This paper aims to propose the multi-energy management strategy for heat and power scheduling in microgrid. Considering the integration with heat and power participants, we design a multi-energy management strategy with the power transmission loss formed as a nonconvex optimization problem, which aims to achieve the maximal social welfare. Heat balance, power balance and other practical operation constraints are taken into consideration. The DR schemes of residential consumers, which analyse and module household appliances in detail, are proposed to alleviate the power production in peak time.

The paper is organized as follows. A DR scheme model basis of the precise classification and the operation control of household appliances is proposed in Section 2. In Section 3, we focus on the mathematical model of maximal social welfare for the multi-energy management in a microgrid. In Section 4, the nonconvex optimization problem is formulated to a convex problem by a sufficient condition. Then in Section 5, a neurodynamic algorithm with fewer variances is developed to cope with this problem, and the convergence analysis of the neurodynamic algorithm is given in Section 6. In Section 7, we present some numerical simulations to validate the proposed strategy and algorithm. Finally, in Section 8, conclusion is presented.

Section snippets

A demand response strategy for residential consumers

The usage time and consumption of household load are the vital factors that should be taken into consideration when coping with the residential demand response. For all kinds of household load, we classify them as three elements, namely based load, semi-flexible load, and flexible load. Electricity lamps, television receivers and kettles belong to the first category, which denote this part of load cannot be scheduled by controlling the usage period or the usage amount. The semi-flexible load

Welfare model of energy hub

As for energy hub(EH), three elements constitute the system, mainly including energy transmission devices, energy conversion devices and energy storage devices. Fig. 1 shows the architecture of EH. Power-supply devices, such as renewable power generators(RPG), fuel power generators(FPG), power storage devices(PSD), combining power and heat generators(CPHG), transform prime sources into power. The heat-supply devices are renewable heat generators(RHG), fuel heat generator(FHG), heat storage

Problem transformation

For problem (12), the objection function is a convex function and the constraint (12b) is an equality linear constraint. However the equality constraint (12a) is non-convex. [24] proposes a sufficient condition for problem (12). Due to the condition (7) in [26], we can obtain the following condition.

Suppose that the lower bounds of all generation participants and upper bounds of all consumption participants satisfy $\sum_{i \in v_{p}} (p_{i, t}^{min} - \overset{̆}{ϱ} {(p_{i, t}^{min})}^{2}) + \sum_{m \in v_{p h}} p_{m, t}^{min} \leq \sum_{n \in v_{d}} p_{n, t}^{max}$ The optimal solution of the

Algorithm description

The Karush–Kuhn–Tucker conditions of problem (14) are described as, $\begin{matrix} \frac{\partial L}{\partial p_{i, t}} = \frac{\partial C_{i}}{\partial p_{i, t}} + μ (1 - 2 ρ p_{i, t}) - η_{i}^{-} + η_{i}^{+} \\ \frac{\partial L}{\partial p_{m, t}} = \frac{\partial C_{m}}{\partial p_{m, t}} + μ (1 - 2 ρ p_{m, t}) - ι_{m}^{-} + ι_{m}^{+} \\ \frac{\partial L}{\partial h_{j, t}} = \frac{\partial C_{j}}{\partial h_{j, t}} + λ - ζ_{j}^{-} + ζ_{j}^{+} \\ \frac{\partial L}{\partial h_{m, t}} = \frac{\partial C_{m}}{\partial h_{m, t}} + λ - φ_{m}^{-} + φ_{m}^{+} \\ \sum_{j \in v_{h}} h_{j, t} + \sum_{m \in v_{p h}} h_{m, t} - \sum_{n \in v_{d}} h_{n, t} = 0, \\ η_{i}^{-} (p_{i, t} - p_{i, t}^{min}) = 0, η_{i}^{-} \geq 0 \\ η_{i}^{+} (p_{i, t}^{max} - p_{i, t}) = 0, η_{i}^{+} \geq 0 \\ ι_{m}^{-} (p_{m, t} - p_{m, t}^{min}) = 0, η_{m}^{-} \geq 0 \\ ι_{m}^{+} (p_{m, t}^{max} - p_{m, t}) = 0, η_{m}^{+} \geq 0 \\ ζ_{j}^{-} (h_{j, t} - h_{j, t}^{min}) = 0, ζ_{j}^{-} \geq 0 \\ ζ_{j}^{+} (h_{j, t}^{max} - h_{j, t}) = 0, ζ_{j}^{+} \geq 0 \\ φ_{m}^{-} (h_{m, t} - h_{m, t}^{min}) = 0, φ_{m}^{-} \geq 0 \\ φ_{m}^{+} (h_{m, t}^{max} - h_{m, t}) = 0, φ_{m}^{+} \geq 0 \\ μ (\sum_{i \in v_{p}} (p_{i, t} - \overset{̆}{ϱ} p_{i, t}^{2}) + \sum_{m \in v_{p h}} (p_{m, t} - \overset{̆}{ϱ} p_{m, t}^{2}) - \sum_{n \in v_{d}} p_{n, t}) = 0 \\ \sum_{i \in v_{p}} (p_{i, t} - \overset{̆}{ϱ} p_{i, t}^{2}) + \sum_{m \in v_{p h}} (p_{m, t} - \overset{̆}{ϱ} p_{m, t}^{2}) - \sum_{n \in v_{d}} p_{n, t} \end{matrix}$

Convergence analysis of the algorithm

Theorem 1

Let $(P_{o u t}^{*}, χ^{*})$ be an equilibrium point of (18), the Lyapunov function is proposed as, $V (P_{o u t}, χ) = u (P_{o u t}, χ) - u (P_{o u t}^{*}, χ^{*}) - {(P_{o u t} - P_{o u t}^{*})}^{T} \nabla u_{P_{o u t}} (P_{o u t}^{*}, χ^{*}) - (χ - χ^{*}) \nabla u_{χ} (P_{o u t}^{*}, χ^{*}) + \frac{1}{2} ‖ P_{o u t} - P_{o u t}^{*} ‖^{2} + \frac{1}{2} ‖ χ - χ^{*} ‖^{2}$ where $u (P_{o u t}, χ) = C (P_{o u t}) + \frac{1}{2} ‖ {(χ - g (P_{o u t}))}^{+} ‖^{2}$ .

Then $(a) V (P_{o u t}, χ) \geq \frac{1}{2} ‖ P_{o u t} - P_{o u t}^{*} ‖^{2} + \frac{1}{2} ‖ χ - χ^{*} ‖^{2} (b) \frac{d V}{d t} < 0, \forall (P_{o u t}, χ) \neq (P_{o u t}^{*}, χ^{*})$

Proof

Because $u (P_{o u t}, χ)$ is continuously differentiable and $C$ is convex, the following inequality can be satisfied. $u (P_{o u t}, χ) - u (P_{o u t}^{*}, χ^{*}) \geq ({(P_{o u t} - P_{o u t}^{*})}^{T}, {(χ - χ^{*})}^{T}) {(\nabla u_{P_{o u t}} (P_{o u t}^{*}, χ^{*}), \nabla u_{χ} (P_{o u t}^{*}, χ^{*}))}^{T}$ $\nabla u (P_{o u t}, χ) = [\begin{matrix} \nabla C - \nabla g {(P_{o u t})}^{T} {(χ - g (P_{o u t}))}^{+} \\ {(χ - g (P_{o u t}))}^{+} \end{matrix}]$

Thus, $u (P_{o u t}, χ) - u (P_{o u t})$

Numerical investigations

In this section, two numerical cases are presented to validate the effectiveness of the proposed DR strategy and energy management strategy. In case 7.1, for DR strategy, we plan to compare the amount each kind of appliance consumes after scheduled with that before scheduled. A test cycle is closed a 24 h, and each period is define as one hour. We chose one hundred domestic consumers with six common household appliances, including two basic appliances, two semi-flexible appliances and two

Conclusion

In this paper, a strategy to optimize the multi-energy in microgrid is proposed. The proposed strategy aims to maximize the social welfare of all participants in microgrid and to balance the energy supply and demand for power and heat. Since the proposed welfare model is a non-convex problem with a non-convex inequality constraint. This paper proposes a sufficient condition to transfer the prime problem to another convex function. Numerical simulations and the analysis of the applied algorithm

Acknowledgements

This work is supported by Natural Science Foundation of China (Grant No: 61773320), and also supported by the Natural Science Foundation Project of Chongqing CSTC (Grant no. cstc2018jcyjAX0583, cstc2018jcyjAX0810), and also supported by Research Foundation of Key laboratory of Machine Perception and Children’s Intelligence Development funded by CQUE(16xjpt07), China, and also supported by the Foundation of Chongqing University of Education (Grant No. KY201702A).

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A strategy to optimize the multi-energy system in microgrid based on neurodynamic algorithm

Highlights

Abstract

Introduction

Section snippets

A demand response strategy for residential consumers

Welfare model of energy hub

Problem transformation

Algorithm description

Convergence analysis of the algorithm

Numerical investigations

Conclusion

Acknowledgements

Energy

Appl. Soft Comput.

IEEE Trans. Neural Netw. Learn. Syst.

Renew. Energy

Appl. Soft Comput.

Energy Build.

Neural Netw.

Neural Netw.

Distributed event-triggered scheme for economic dispatch in smart grids

IEEE Trans. Ind. Inf.

CHP Optimized Selection Methodology for a Multi-Carrier Energy System

Hierarchical genetic optimization of a fuzzy logic system for energy flows management in microgrids

Appl. Soft Comput.

Distributed power management for dynamic economic dispatch in the multi-micro-grids environment

IEEE Trans. Control Syst. Technol.

Second-order continuous-time algorithms for economic power dispatch in smart grids

IEEE Trans. Syst. Man Cybern. Syst.