Optimal operation of microgrid using hybrid differential evolution and harmony search algorithm

Abstract

This paper proposes the generation scheduling approach for a microgrid comprised of conventional generators, wind energy generators, solar photovoltaic (PV) systems, battery storage, and electric vehicles. The electrical vehicles (EVs) play two different roles: as load demands during charging, and as storage units to supply energy to remaining load demands in the MG when they are plugged into the microgrid (MG). Wind and solar PV powers are intermittent in nature; hence by including the battery storage and EVs, the MG becomes more stable. Here, the total cost objective is minimized considering the cost of conventional generators, wind generators, solar PV systems and EVs. The proposed optimal scheduling problem is solved using the hybrid differential evolution and harmony search (hybrid DE-HS) algorithm including the wind energy generators and solar PV system along with the battery storage and EVs. Moreover, it requires the least investment.

Keywords

battery storage / electric vehicles (EVs) / microgrid (MG) / optimal scheduling / solar photovoltaic (PV) system / wind energy conversion system

Introduction

Microgrid (MG) is a local power grid formed either in the medium or low voltage distribution system. By abstracting the MG as an intelligent agent network, each component (generators, loads, and storage entities) is abstracted as an agent, and the objective is to develop a fully distributed solution to the MG coordination problem [ 1]. The objective is to develop collaborative distributed optimization techniques for efficient resource management in microgrids. Recently, because of the increase in load, and the increased interest in clean and green energy, the need for MG is increasing day by day. The optimal management and operation of MG involves optimum sizing and scheduling of distributed generators (DGs) as per the demand pattern, import and export regulations followed by the local power utility. Optimal decision need to be taken for better utilization of renewable energy resources (RERs) such as wind and solar energy. The objectives of optimal management of MG are to minimize economic factor, to minimize environmental impact, optimal dispatch of schedulable loads, and to maximize delivery to utilizing grid (including ancillary services, reserve margin, etc.) [ 2, 3].

The MG considered in this paper includes conventional generators, wind energy generators, solar photovoltaic (PV) systems, battery storages, and electric vehicles (EVs). The EVs may play dual roles (i.e., bidirectional energy flow) when they are plugged into the MG. These EVs will appear as load demands in the charging period, and as the storage units to supply energy to the remaining load demands in the MG, if the batteries have enough spare energy [ 4]. Because of the intermittent nature of wind and solar PV energy, fixed capacity of storage batteries in a MG may not make the load and generation balance in the real time. However, the oversize of storage devices may smooth the fluctuation of output power resulted from the uncertainty of RERs, which will increase the investment cost of the system [ 5]. An overview of solving an economic dispatch (ED) problem in the MG consisting of renewable energy is presented in Ref. [ 6] presents. A stochastic optimal energy and spinning reserve scheduling approach for the MG considering different types of demand-side reserve offers is proposed in Ref. [ 7]. A joint power and heat MG system including the wind generators, PV arrays, micro-turbine, diesel engines, fuel cell and battery is established in Ref. [ 8]. Optimal scheduling of an isolated system by a virtual power producer (VPP) with the objective of deciding the best VPP management strategy to optimize storage charging and discharging time and to minimize the generation costs is proposed in Ref. [ 9]. A stochastic problem is proposed to optimize the total cost of MG, which includes the conventional generation cost and the expected transaction cost due to the uncertainty in the wind power in Ref. [ 10].

An optimal scheduling strategy is proposed which uses all the storage facilities to perform demand response in order to minimize the daily energy costs sustained by the entire MG in Ref. [ 11]. A dynamic ED approach for the MGs considering the MG as a discrete time system is presented in Ref. [ 12]. A multi-objective ED model considering generation, reliability and environmental impact is proposed in Ref. [ 13]. The logical and functional modeling of various strategies and components of MGs is proposed; hence an objective function is developed to obtain an optimum scheduling and sizing of distributed energy resources (DERs) in the MG [ 14]. A probabilistic approach for estimating the reserve requirement in the MGs is presented in Ref. [ 15]. The amount of spinning reserve required is determined by a trade-off between the economics and the reliability. The mathematical model of MG economic scheduling is presented considering the integration of plug-in hybrid electric vehicles (PHEVs) and the influence of different charging, while discharging modes on MG economic operation is analyzed in Ref. [ 16]. The problem of economic operation of co-generation system including wind energy, solar PV, heat recovery boiler and battery is dealt with in Ref. [ 17]. The state-of-the-art stochastic modeling and optimization tools for MG planning, operation and control are presented in Ref. [ 18]. The tools can be used to address the randomness in renewable power generation, the buffering effect of energy storage devices and the mobility of plug-in EVs in vehicle-to-grid systems.

From the above literature review, it can be observed that there is a need for the optimum scheduling of MG. In this paper, the MG with conventional generators, wind energy generators, solar PV system, battery storages and EVs have been considered. This problem is solved using the hybrid differential evolution and harmony search (hybrid DE-HS) algorithm. In this hybrid algorithm, the DE based update policy of existing chromosomes and the HS based generation strategy of new chromosomes are merged together. Besides, to accelerate the convergence of the regular DE, a hybrid DE-HS algorithm is proposed.

Proposed optimal scheduling approach

The problem formulation for the proposed optimal scheduling of MG is presented.

Minimize, total cost, i.e.,

(1) {\displaystyle \sum _{t=\mathrm{1}}^T[{\displaystyle \sum _{i=\mathrm{1}}^{N_G}{C}_{Gi}(P_{Gi}^t}})+{\displaystyle \sum _{i=\mathrm{1}}^{N_W}{C}_{Wi}(P_{Wi}^t)+{\displaystyle \sum _{j=\mathrm{1}}^{N_S}{C}_{Sj}(P_{\mathrm{Sj}}^t)]+{\displaystyle \sum _{t=\mathrm{1}}^T[{\displaystyle \sum _{k=\mathrm{1}}^{N_{\mathrm{EV}}}[C_{\mathrm{EV},k}^{\mathrm{Ch}}(P_{\mathrm{Ch},\mathrm{EV}}^{k,t})+C_{\mathrm{EV},k}^{\mathrm{Dch}}(P_{\mathrm{Dch,EV}}^{k,t})}}}}.

The first term in Eq. (1) is the fuel cost function of conventional generators, which is assumed as a second order polynomial function,

(2) C_i(P_{Gi}^t)=a_i+b_i{P}_{Gi}^t+c_i{(P_{Gi}^t)}^{\mathrm{2}}.

The second term in Eq. (1) is the cost associated with scheduled wind power [ 19], which is expressed as

(3) C_{Wi}(P_{Wi}^t)= d_i{P}_{Wi}^t.

The third term in Eq. (1) is the cost associated with scheduled solar PV power, which is given by

(4) C_{Sj}(P_{Sj}^t)=t_j{P}_{Sj.}^t

.

The fourth term in Eq. (1) is the cost associated with the charge power of EV [ 20], which is given by

(5) C_{\mathrm{EV},k}^{\mathrm{Ch}}(P_{\mathrm{Ch},\mathrm{EV}}^{k,t})={\pi }_{\mathrm{ch}}^t\times P_{\mathrm{Ch},\mathrm{EV}}^{k,t}.

The last term in Eq. (1) is the cost associated with the discharge power of EV [ 20], which is given by

(6) C_{\mathrm{EV},k}^{\mathrm{Dch}}(P_{\mathrm{Dch},\mathrm{EV}}^{k,t})=({\pi }_{\mathrm{OM}}^t-{\pi }_{\mathrm{Dch}}^t)\times P_{\mathrm{Dch,EV}}^{k,t}.

The above optimization problem is solved subjected to the equality and inequality constraints discussed in Section 2.1.

Equality or nodal power balance constraints

These constraints include both active and reactive power balance equations.

(7) P_i=V_i\underset{j-1}{\overset{n}{\mathrm{\Sigma }}}\left[V_j[G_{ij}\sin ({\delta }_i-{\delta }_j)+B_{ij}\cos ({\delta }_i-{\delta }_j)]\right]-P_{Gi}-P_{Di}\text{},

(8) Q_i=V_i{\displaystyle \sum _{j=\mathrm{1}}^n[V_j[G_{ij}\sin ({\delta }_i-}{\delta }_j)-B_{ij}\cos ({\delta }_i-{\delta }_j)]]-Q_{Gi}-Q_{Di},

where i = 1, 2, ..., n. P_Di and Q_Di are the active and reactive power demands of ith load.

Inequality constraints

The inequality constraints present the system operating limits. The solar power output can be controlled by using power tracking control or storage batteries. Hence, the maximum penetration of solar PV power to the system is expressed by

(9) P_S\le P_S^{\max },

where P_S is the solar PV power generation and P_S^{\max } is the available maximum power generation subject to the solar irradiation and temperature. The power generation of wind energy generator is limited by

(10) \mathrm{0}\le P_{Wj}\le P_{rj}\hspace{1em}\hspace{1em}j=\mathrm{1},\mathrm{2},\mathrm{...},{{\displaystyle N}}_W.

The state of charge (SOC) limits of battery [ 21] is given by

(11)

Modeling of wind and solar energy systems

In the proposed optimal scheduling of MG problem, some characterization of uncertain nature of solar irradiation and wind speed are required. The variability of solar PV and wind power is the main barrier to the integration into the electrical grid. The proper forecasting of solar and wind power plays a major role in the integration of solar PV and wind power.

Wind energy system modeling

In this paper, it is considered that wind speed follows the Weibull probability density function (PDF) and then it is converted to the wind power distribution for use in the proposed generation scheduling problem. The derived wind power will then follow the stochastic/intermittent nature. For every wind energy generator, the power output for a specific input, i.e., wind speed (v) is expressed as [ 22, 23]

(12)

In the present paper, Weibull PDF is used to model the wind power conversion system, and the probabilistic modeling of wind energy generator is presented in Ref. [ 24].

Solar energy system modeling

The power output of solar PV module depends on hourly solar irradiation. The hourly data are required to model the solar energy system. Figure 1 depicts the solar PV energy system with battery storage considered in this paper [ 19].

The total power output of solar PV energy system is expressed as

(13) P_S=P_{\mathrm{PV}}(G)+P_b-P_u,

where P_PV(G) is the power output from the solar PV cell, which is expressed as [ 19, 25]

(14)

where the spillage power of solar PV generator (P_u(MW)) and the aggregated battery are ignored. P_S is either positive or negative. The positive value of P_S denotes the power flow from the solar PV module to the utility/grid. The maximum discharge and charge powers of aggregated battery are given by

(15) \underline{P_b}\le P_b\le \overline{P_b},

where \overline{P_b} is the discharging power limit (MW), \underset{\_}{P_b} is the charging power limit (MW), and P_b is the power charge/discharge to/from battery (MW), which is positive during the discharging period and negative during the charging period.

If C_init and C are the SOC of all the batteries (kAh) at starting and ending of scheduling period, the power output from the solar PV module to the utility/grid in the interval Δt (i.e., 1 h) is expressed as [ 21]

(16) P_S=P_{\mathrm{PV}}(G)+{\displaystyle \frac{(C_{\mathrm{init}}-C)V_b}{{\eta }_b\Delta t}}-P_u.

The aggregated battery is connected to the solar PV system using a DC/DC chopper, and to the grid using a DC/AC inverter and a transformer. The discharge/charge equation for aggregated battery is given by [ 19, 21]

(17) C=C_{\mathrm{init}}+[{\displaystyle \frac{\Delta t\times {\eta }_b}{V_b}}(P_{\mathrm{PV}}(G)-P_S-P_u)],

(18) C=C_{\mathrm{init}}+\left[{\displaystyle \frac{\Delta t \times {\eta }_b}{V_b}}(P_b)\right].

The optimal generation scheduling problem involves determining the minimum/optimum cost trajectory (i.e., SOC of the battery at every time interval).

The charge and discharge of a battery is fixed by its starting and final SOC, which are expressed as

(19) {{\displaystyle C}}_{t|t=\mathrm{0}}={{\displaystyle C}}_S\hspace{1em}initialSOC,

(20) {{\displaystyle C}}_{t|t={{\displaystyle N}}_t}={{\displaystyle C}}_f\hspace{1em}finalSOC\mathrm{.}

The hourly solar irradiation distribution follows a bi-modal distribution which can be obtained by using two uni-modal distributions that can be modeled using Weibull, Log-normal and Beta probability density functions. In this paper, Weibull PDF is used, and the discussion on probabilistic solar PV modeling is mentioned in Refs. [ 15, 19].

Modeling of electric vehicle (EV)

The MG considered in the present paper includes conventional generators, wind farms, solar PV plants, battery storages and EVs. The wind turbines and solar PV modules, which are intermittent, convert the wind and solar energy to the electrical power and, whereas storage batteries and EVs guarantee the reliable operation of MG. Compared to the stationary storage devices (fixed batteries), the EVs have many advantages [ 4]. EVs have four SOCs. {\mathrm{SOC}}_{\min }^{\mathrm{EV}} and {\mathrm{SOC}}_{\max }^{\mathrm{EV}} are the charge and discharge limits of EVs. The EVs should satisfy {\mathrm{SOC}}_{\min }^{\mathrm{EV}}\le {\mathrm{SOC}}^{\mathrm{EV}}\le {\mathrm{SOC}}_{\max }^{\mathrm{EV}} at any time to ensure the sustainable capacity usage. However, when the EVs are connected to the MG, the SOC of the EVs should be detected at every constant interval to meet {\mathrm{SOC}}_{\mathrm{low}}^{\mathrm{EV}}\le {\mathrm{SOC}}^{\mathrm{EV}}\le {\mathrm{SOC}}_{\mathrm{high}}^{\mathrm{EV}} .

The EVs have the bidirectional power flow and mobile storage characteristics (as they can be used as loads and storage devices) under different conditions to smooth the fluctuation of wind and solar PV energy with minimizing the capacity of fixed batteries. The state of EVs at the tth hour depends on the state at the (t–1)th hour and the charge and discharge from the hour (t- 1) to t. During the charging of the EV, the energy of electric vehicle at the tth hour [ 20] is given by

(21) E_{\mathrm{Ch,EV}}^t=E_{\mathrm{EV}}^{t-\mathrm{1}}+[{\displaystyle \frac{t_{\mathrm{char}}}{T}}\times E_{\mathrm{EV}}^{\max }].

During the discharging of the EV, the energy of electric vehicle at the tth hour [ 20] is given by

(22) E_{\mathrm{Dch,EV}}^t=E_{\mathrm{EV}}^{t-\mathrm{1}}+\left[{\displaystyle \frac{t_{\mathrm{dischar}}}{{\eta }_{\mathrm{conv}}}}\times P_{\mathrm{dischar}}\right].

Hybrid differential evolution and harmony search (hybrid DE-HS) algorithm

The differential evolution (DE) algorithm is a robust population-based approach to handle a large variety of optimization problems such as parameter identification, data clustering, power system planning, etc [ 26]. The harmony Search (HS) algorithm is inspired by the underlying principles of musicians’ improvisation of harmony [ 27]. Nowadays, the HS algorithm is used for various applications such as mechanical structure design, function optimization, pipe network optimization, etc. To improve the convergence of the DE algorithm, a hybrid DE and HS algorithm is proposed. In this hybrid DE-HS algorithm, the DE-based update policy of existing chromosomes and the HS-based generation strategy of new individuals/chromosomes are merged together [ 28].

The DE algorithm updates the existing chromosomes based on the differences among the certain randomly selected individuals. This algorithm does not have a mechanism for generating the completely new individuals, whereas, the HS algorithm has a special feature of using the 8 combination of all existing chromosomes to obtain the new chromosomes/ individuals. Hence, the aim is to combine this individual generation method with the original DE algorithm, so that this hybridization can be converged in a faster way. The hybrid HE-HS algorithm is a hybrid approach [ 28] by combining the DE with the HS algorithms, in which the HS memory is a duplication of the DE population, which can effectively provide new individuals for the DE evolution using the HS principles.

The flow chart of the hybrid DE-HS algorithm is presented in Fig. 2. The chromosomes/individuals in the DE population are updated using Eqs. (23) and (24) [ 28].

(23) {S^{\prime }}_i(k)=S_{i\mathrm{1}}(k)+\omega [S_{i\mathrm{2}}(k)-S_{i\mathrm{3}}(k)],

(24) S_i(k+\mathrm{1})={S^{″}}_i(k),

where S_i2(k) and S_i3(k) are the two random chromosomes. These individuals are considered as harmony memory members of the HS algorithm. Besides, the size of the HS memory is the same as that of the DE population. Hence, a new chromosome is generated based on the available HS memory members (i.e., DE population) or in a random manner. This fresh individual is then compared with the worst DE individual for possible replacement. Finally, the entire population is updated, and the DE evolution continues to the next generation [ 28].

Results and discussion

The MG selected in this paper comprises of two conventional generators (synchronous generators), wind farm, solar PV energy system with the battery storage and EVs. The 24 h load demand profile is taken from Ref. [ 6]. The results of the optimal scheduling of the MG with and without battery storage and EVs are obtained for comparison.

Case 1: Optimal scheduling of MG without battery storage and EVs

In Case 1, the objective function consists only the first three terms of Eq. (1), (i.e., costs due to conventional generators, wind farms and solar PV plants). Table 1 presents the optimum objective function values of Case 1. The power outputs of the wind farm and solar PV plant are depicted in Fig. 3. The optimum cost incurred in Case 1 for the 24 h scheduling period is 232410.18 $.

Case 2: Optimal scheduling of MG with battery storage and EVs

In Case 2, the objective function includes all the terms in Eq. (1). Table 1 presents the optimum objective function values of Case 2. The scheduled power outputs of the wind farm and solar PV plant are illustrated in Fig. 3. The optimum cost incurred in Case 2 for the 24 h scheduling period is 214215.73 $, which is 7.83% less than the cost obtained from Case 1.

Conclusions

This paper proposes the optimal generation scheduling of MG considering the conventional generators, wind energy generators, solar PV systems, battery storages and EVs. EVs play two roles when they are plugged into the MG. These EVs appear as load demands during the charging, and are also used as the storage units to supply energy to remaining load demands, if the batteries have sufficient spare energy. The proposed optimization problem is solved using the hybrid differential evolution and harmony search (hybrid DE-HS) algorithm. The MG considered is more stable as it has battery storage and EVs. Besides, the EVs are less expensive because the wind and solar PV energy are included along with the battery storage.

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