Active distribution network planning considering shared demand management

Abstract

Due to the necessity of using distributed generation and storage devices in the operation of power systems and with the advancement of technology and industry in the distribution networks, network operators are trying to transform these systems from passive distribution networks to active ones. To this aim, the present study introduces a novel model to exploit an active distribution network from the cost, operation conditions, and reliability points of view. A shared demand management procedure in the presence of storage devices and price-responsive loads is used to improve operational efficiency, and it is presented using a sensitivity matrix. Probability density functions (PDFs) are used to model uncertainty in power generated by wind systems and PVs, and the fuzzy membership function is used to improve the voltage profile of the network. To optimize the objective function, given that the problem goals are not of the same kind, the multi-objective genetic algorithm, based on the non-dominated concept, is implemented. Proposed optimal planning and exploiting of the active distribution network based on the shared demand management procedure, not only maximize profit, because of peak shaving, upgrade deferral, power exchange, and loss reduction but also, technical indexes and reliability improvement are obtained due to energy storage systems (ESS) and price-responsive loads simultaneous management. The rationality and effectiveness of the proposed method are verified by the simulation results of a 33-bus active distribution network.

Keywords

Active distribution network energy storage non-dominated sorting shared demand management

1 Introduction

During recent years, the distribution network’s service providers have been switching from passive distribution networks to the active ones, which can economically and efficiently contribute to the high levels of the distributed energy resources (DER), as well as providing opportunities for more network management and avoiding or deferring network upgrades. Also, the load growth in advanced societies along with the technical and economic concerns drives the distribution systems towards smarter networks and the implementation of new power delivery systems. In some cases, attempts to re-engineer the planning process, along with the addition of necessary methods and tools for supporting the advancement and growth of the active distribution networks seems necessary [1]. Nowadays, the energy storage systems (ESS) as one of the essential requirements for the implementation and improvement of the smart network, have had rapid development in terms of both technical maturity and economic justification [2]. The various applications of ESS have been discussed in many references some of which are load leveling [3, 4], renewable resources integration, load curve flattening, time shift and peak load shaving curves [5 –8], network upgrade deferral [9 –15], steady-state and transient voltage control [16, 17] and loss reduction [18 –20]. Due to the high investment cost of ESSs, simultaneous use of the ESS benefits is essential in planning the scheme for increasing its profits. Two hourly scheduling models for the centralized and distributed energy storages have been introduced in the daily electricity market in [21] without the participation of the distributed generation sources. The CONVEX model for the development planning of the active distribution network has been studied in [22] by considering four active management schemes including distributed generation resources, demand-side management, under load tap changer and reactive power compensation along with the optimization of distributed generation resources for peak load shaving and also operating costs reduction. under load tap changer and reactive power compensation along with the optimization of distributed generation resources for peak load shaving and also operating costs reduction. The combination of RES’s participation with energy storage systems has been investigated in [23] together with the distribution network reconfiguration. The concurrent planning of ESS and DG has been presented considering the ability to distribute their reactive power for maximizing the profit of the distribution network operator (DISCO) [24]. The multi-stage planning model of the active distribution network with the participation of energy storage resources has been proposed in [25], which suggests that ESS be installed on all the network buses and in the suggested model, the long-term planning decisions including the replacing and constructing feeders and installing the energy storage resources have been optimized together with the short-term operation strategies including charging and discharging the energy storage resources. The work [8] has evaluated the contribution parameters of the energy storage resources to the distribution network planning including the location, capacity and operation indicators, such as flattening the daily load demand and improving the voltage profile along with the penetration of the PV distributed generation resources. Authors in [10] try to perform the distribution network planning, taking into account all the benefits of installing and optimal allocation of ESS units alongside the PV distributed generation sources with the consideration of the seasonal loads. Nonetheless, the co-ownership between non-network solutions and demand-side management (DSM) in the two recent references could improve the planning process from both the economic and technical aspects. The traditional network charging methods will not be price-responsive in smart networks with active subscribers. In this regard, the European distribution system operator (EDSO) has recommended the necessity of the transparent motivation creation for convincing the subscribers to change the consumption pattern for the smart grids. Also, it has shown that the network tariffs must be designed to ensure fair participation (with distribution network prices) of the subscribers who generate their electricity [26]. A method has been presented to ensure network cost compensation while improving the network’s utilization and investment [27]. The design of the network charging method consists of the two components of the peak coincidence network charge (PCNC) and fixed charging. Minimizing the total cost in any charging design method has been performed by taking into account the possibility of purchasing electricity from the network and investing in local generations or load limiting with the use of linear programming. A method for optimal planning and operation of the energy storage system is introduced in [28] that strategy of the energy storage charging and discharging is determined based on RES output. The intelligent optimization method, based on harmony search, was proposed in [29] to solve the energy operation management in the renewable micro-grids with different types of sources including photovoltaic, fuel-cell, micro-turbine, wind turbine, and the energy storage system. The modification technique consists of three sub-modification methods were defined in a recent paper that each of them improves the system condition from a specific point of view. Also, it can be deduced that adequate work has been conducted concerning allocating and scheduling ESS operation for developing large penetration levels of RESs [8]. On the other hand, few works have investigated diverse profits due to ESS implementation in active distribution networks, such as peak load shaving, upgrade deferral, energy arbitrage, and loss reduction at the same time [10]. Furthermore, limited works have been conducted for appraising the reliability of ESSs in distribution systems [30]. However, the literature reveals that the problem of improving system reliability by determining the most cost-effective along with technical characters’ enhancement and shared-demand management in active distribution networks, has not yet been addressed considering both the long-term planning and the short-term operation conditions. Therefore, the need for participation and coordination of the different resources, and demand management in order to deal with uncertainties necessitates simultaneous multi-objective planning and utilization of the active distribution network. Accordingly, a novel multi-objective active distribution network planning method is proposed in this paper to optimally maximize economic benefit, improve technical indices and network reliability by incorporating shared demand management. To effectively model storage resources and price-responsive loads, hourly operational issues are considered in the distribution network planning problem, and a sensitivity analysis matrix is introduced to determine the priority of energy storages and price-responsive loads in dealing with uncertainties. Besides, fuzzy technical membership is used to improve the network voltage profile. The multi-objective optimization problem is solved by an algorithm based on the non-dominated method which successfully obtains the optimalsolution.

The remainder of this paper is organized as follows: Section 2 provides modeling and mathematical formulation for the planning method. In Section 3, the proposed method of shared demand management, as well as operation procedure, are further developed for the planning strategy. Solution method and computational results are discussed in section 4. Eventually, Section 5 concludes the paper by highlighting the major conclusions and results of the work.

2 Modeling and formulation

This paper aims to optimal planning and exploiting of active distribution network simultaneously considering three main objectives, including maximizing economic profit, technical indices, and reliability improvement. As these three points of view are the main concerns of active distribution network planning, all of them are considered as a multi-objective function to supply the growing demand and provide an overview of the planning arrangement to the planners to evaluate planning and operation condition in three divers objectives. In the planning process, renewable and energy storage sources are optimally allocated. Simultaneously, according to resources size and place along with system status, a new method has been proposed in the operation process to deal with uncertainties and the time-variable characteristic of load and REGs. Shared demand management regarding energy storages and price-responsive loads is also performed for peak shaving. To improve the voltage profile of the network, fuzzy technical membership function is used and sensitivity matrix analyze is carried out to determine the priority of energy storage and price-responsive loads as well as their participation amount in every specific critical hour of the planninghorizon.

In the following subsections, we first introduce the probabilistic models of wind and solar generation unit. To address the existent uncertainties in the system loads the probability density function (PDF) method is used. To improve PDF for the related period of one year, 12 days are selected as representatives of each month of that year. Each selective day, which is the representative of a month, is divided into 24-hour sections, each of which has a PDF for the corresponding load at that hour [20]. Moreover, the electrical pricing is based on the Queensland, Australia electric price in 2015 [10]. The average electrical prices for a day from every month are calculated in a way that every 24-hour price represents a corresponding month (12*24). Then, the detail formulation of the multi-objective problem as well as its associated constraints are described. Shared demand management regarding energy storages and price-responsive loads is presented in Section 3.

2.1 A probabilistic model of the wind turbine

The wind speed is continuously changing. The average amount specified for a region cannot solely determine the generation amount of the wind turbine installed in that area. In this case, one can use the probabilistic distribution functions in order to determine the frequency of wind speed in an area. The Weibull probability density function is the one that is widely used in wind speed modeling. In many conducted studies, this function has been suggested to be used as the probability distribution function of the wind speed [11]. The general relation for a Weibull distribution with variable X, scale parameter λ and shape parameter k, can be definedas (1). $weibull (λ K) = λ {KX}^{(K - 1)} \exp [- λ X^{K}]$ (1)

For the wind speed, the probabilistic distribution is used according to (2). $f (v) = \frac{h}{c} {(\frac{v}{c})}^{h - 1} exp [{- (\frac{v}{c})}^{h}]$ (2)

Where, c and h represent the shape and scale parameters for the wind velocity (v), respectively. Here, the values of h and c are considered to be 2 and 9, respectively. In a wind turbine, the output power is affected by wind speed, and there is a nonlinear relationship between these two parameters. The power-speed characteristic curve of the wind turbines indicates the generated active power for various wind velocities and can be defined as (3). $P_{W_{T}} (V) = {\begin{matrix} 0 & 0 \leq V \leq V_{ci} or V_{co} \leq V \\ P_{WTr} \times \frac{V^{2} - V_{ci}^{2}}{V_{r}^{2} - V_{ci}^{2}} & V_{ci} \leq V \leq V_{r} \\ P_{WTr} & V_{r} \leq V \leq V_{co} \end{matrix}$ (3)

Here, V_ci, V_r, and V_co, denote the cut in, rated and cut out speeds, respectively. Also, P_WTr stands for the rated speed of the wind turbine. Figure 1 describes the PDF of the wind turbine’s generation power.

Fig.1

PDF of the wind turbine’s generated powers.

2.2 The probabilistic model of the solar system

The amount of solar radiation and ambient temperature are the two essential factors which make possible changes and actions in the power generation of the solar cells. Several distribution functions can be used to generate the probability distribution function of these parameters. In this paper, the normal distribution function is used for modeling the corresponding radiation parameter (G_ING) [31] as below. $h (x) = \frac{1}{σ \sqrt{2 π}} e^{\frac{(x - ρ)^{2}}{2 σ^{2}}}$ (4)

In this interpretation, the parameter ρ depicts the mean or the expectation of the distribution, and the parameter σ is the standard deviation. The variable x is solar irradiance. Based on the collected historical data, the mean and standard deviation for hourly solar irradiance are demonstrated in [10]. Eventually, based on Equation (5) photovoltaic produced power is calculated. $P_{pv} = P_{STG} \times \frac{G_{ING}}{G_{STC}} \times (1 + K_{a} (T_{C} - T_{r}))$ (5)

The sun radiation amount and ambient temperature in the standard conditions are considered as $G_{STC} = 1000 \frac{W}{m^{2}}$ and T_r = 25°C, respectively. Also, G_ING, T_c, and k_α, denote the sun radiation rays amount, temperature around the cell and temperature coefficient for the maximum power, respectively. Figure 2 describes the PDF of photovoltaic generation power.

Fig.2

PDF of the solar system’s generated powers.

Finally, according to the mean value method, photovoltaic output, wind power, and load amount for every related hour are computed.

2.3 Problem formulation associated with the proposed active distribution network

The multi-objective function comprises three significant functions including economic objective, technical membership, and reliability index as Equation (6).

$F_{total} = MAX {Fit, Technical membership, \frac{1}{F_{R}}}$ (6)

The first part (Fit) is economic profit due to the suggested planning and operation method, that is including peak shaving, upgrade deferral, energy arbitrage, and loss reduction profits, and investment, maintenance and demand management costs, that are explained more in detail in the following paragraphs. The second part (technical membership) is the technical indices, that is including voltage profile and feeder current that is elaborated more in detail in section 2.3.5. Besides, F_R is the reliability index for a power outage that must be minimized and is expanded in section 2.3.6. Economic profit and technical membership amount are supposed to be maximized, and F_R should be minimized. Accordingly, in the third part, 1/F_R is used to maximize the whole multi-objective function.

2.3.1 Economic objective function

The economic objective function is formulated as Equation (7).

$\begin{matrix} Fit = \sum_{t} ({PPG}_{t} + {PEA}_{t} + {PLOSSR}_{t} + {PTDB}_{t} \\ - {CINV}_{t} - {CM}_{t} - {CCL}_{t}) \end{matrix}$ (7)

2.3.1.1.

Power generation profit Considering the importance of the consumption reduction at peak time, one of the main priorities is the use of energy storage sources and demand management at the peak. Aforementioned reduces the utilization cost of the fuel consumption of thermal power plants. This cost reduction can be converted into an economic benefit due to the installation of energy storage sources and demand management as Equation (8). Since this cost is calculated in the form of the current cost, the coefficient is implemented to estimate the equivalent present value of that.

$\begin{matrix} {PPG}_{t} = \sum_{n = 1}^{N_{yr}} (fpw)^{n} \times \\ (\sum_{i = 1}^{n_{ESS}} {PG}_{ESS, i} + \sum_{n = 1}^{n_{DM}} {PG}_{DM, i}) \times LCT \end{matrix}$ (8)

$fpw = \frac{1 + inf r}{1 + int r}$ (9)

Here, N_yr is the planning horizon, P_{GESS, i}, average annual generated peak power by ESS, n_ESS, the number of energy storage sources, P_{GDM, i}, the average annual reduced power at peak load by system’s price-responsive loads, n_DM, the number of price-responsive loads and LCT stands for the annual cost of the gas consumption. Also, the values of infr and intr in the fpw coefficient, describe the inflation and interest rates of the understudy system.

2.3.1.2 Profit of energy exchange.

$\begin{matrix} PEA = \sum_{n = 1}^{Nyr} (fpw)^{n} \times \\ (\sum_{i = 1}^{n_{ESS}} \sum_{m = 1}^{12} \sum_{t = 1}^{24} (P_{ESi, m, t}) . {TD}_{m} . E_{Pr ice, t} \\ + \sum_{i = 1}^{n_{DM}} \sum_{m = 1}^{12} \sum_{t = 1}^{24} (P_{DMi, m, t}) . {TD}_{m} . E_{Pr ice, t}) \end{matrix}$ (10)

Knowing that in the using the energy storage resources, energy is stored at times with the lowest electricity prices and discharged at peak times or high price periods, the profit due to the difference in the electricity’s sales price by the saving energy will be paid to the electricity company. This part of the cost function is within the form of the present cost, therefore, we estimate the equivalent present value of this cost using the fpw coefficient. This profit is calculated based on the daily loading forecast scenarios and it is changed by ESSs timing and price-responsive loads management based on Equation (10). The power generated by the energy storage resources and the demand management, which result in load consumption time-shifting and reduction of the purchased-power from the electricity market, are also included in the cost function. P_ESi,m,t is the power that is charged and discharged by the ith energy storage system, P_DMi,m,t is reduced power by the ith price-responsive load in the nth year, mth month and time t. E_price,t describes the energy price at time t and TD_m stands for the number of days associated with the mth month.

2.3.1.3.

The loss reduction profit Peak load shaving and load consumption reduction in this planning period will reduce the network losses in the peak load. The loss reduction will bring benefits to the system. This benefit is based upon the difference in the cost of the network losses in the initial state before adding the equipment to the system and after using ESS and demand management that is formulated as Equation (11). $\begin{matrix} {PLOSS}_{R} = \sum_{n = 1}^{Nyr} (fpw)^{n} \\ \times [\sum_{m = 1}^{12} \sum_{t = 1}^{24} (P_{LOSS 0, t} - P_{LOSS, t}) . {TD}_{m} . E_{Price, t}] \end{matrix}$ (11)

P_LOSS 0,t is the initial power losses before, and P_LOSS,t is the power losses after the installing of the energy storage sources and employing demand management at time t.

2.3.1.4.

Profit of network upgrade deferral The profit obtained from the network upgrade deferral is due to the scheduling the energy storage sources and price-responsive loads, and discharging the energy storage at peak time postpones the upgrade of the network. The profit that is acquired from network upgrade deferral is the annual cost required for the network upgrade, which can be calculated with the net present value, depending on the deferred years based on Equation (12). $PTDB = \sum_{n = 1}^{Nyr} {fpw}^{n} . C_{T & D} . UP$ (12)

C_T&D, is the average investment cost for each additional MW of the distribution network, and UP is the system’s upgrade capacity.

2.3.1.5.

Annual investment and maintenance cost This cost contains the installation costs of the energy storage sources (ESSs) to the load buses, costs of installing the distributed generations and maintaining them which are formulated in Equation (13). $\begin{matrix} CINV = \sum_{i = 1}^{n_{ESS}} (C_{invESS} + \sum_{n = 1}^{N_{yr}} (fpw)^{n} . C_{MESS}) \\ + \sum_{i = 1}^{n_{DG}} (C_{invDG} + \sum_{n = 1}^{N_{yr}} (fpw)^{n} . C_{MDG}) \end{matrix}$ (13)

C_invESS and C_invDG are Energy storage system and DG investment costs. Also, CM_DG and CM_ESS are maintenance cost of distributed generation and energy storage system, respectively.

2.3.1.6.

The demand management cost It includes the costs related to the loads involved in the load responding. ${CCL}_{t} = \sum_{i = 1}^{n_{DM}} \sum_{n = 1}^{N_{yr}} \sum_{m = 1}^{12} \sum_{t = 1}^{24} P_{DMi n, m, t} . {PC}_{DM}$ (14)

PC_DM is the cost which must be paid to the subscriber for the load responding operations, which is 130% of the corresponding hourly price.

2.3.2 Technical fuzzy membership function

The main goal of this membership function is to minimize the deviation value of the bus voltage as Equation (15) indicates. $Y_{i} = max | V_{s} - V_{i, j} | for i = 2, 3, \dots, NB$ (15)

Where, V_i,j is the voltage domain of the ith node at jth load level, V_s stands for each bus voltage domain in the unit and NB is the number of system buses. If the maximum value of the voltage deviation of the nodes is low, the higher membership amount is determined and vice versa.

In this paper, the values of Y_max and Y_min have been considered as 0.1 and 0.05, respectively. This means that if the secondary bus voltage is 1 p.u, the minimum system voltage will be 0.95 p.u, and according to Fig. 3, if the minimum voltage is equal or more than 0.95 p.u, the membership value is determined as 1. In a similar manner, if Y_max = 1, the minimum system voltage will be 0.9 p.u, and if the minimum voltage is equal or less than 0.9 p.u, the membership value is assumed to be 0. Also, the corresponding fuzzy membership function for the lines loading is calculated according to Equation (16).

Fig.3

Technical membership value.

$\begin{matrix} μ V_{j} = \frac{(y_{max} - y_{j})}{(y_{max} - y_{min})} for y_{min} \leq y_{j} \leq y_{max} \\ μ V_{j} = 1 for y_{i} \leq y_{min} \\ μ V_{j} = 0 for y_{j} \geq y_{max} \end{matrix}$ (16) $Technical membership = μ I_{j} + μ V_{j}$ (17)

The reason for using this function is to achieve the best possible solution with the least deviation from the network limitations. In this case, a system is presented in which the best response with the lowest possible risk and the highest amount of fuzzy membership is achieved. Finally, the value of the technical membership function is obtained from the sum of these two parameters, according to Equation (17). In this case, this function enables us to provide a response to be operated with the lowest possible risk and maximum network’s profit.

2.3.3 Reliability function (F_R)

A reliable electric power system means a system is having enough electrical power to supply the load demand over a specific period, taking into account the technical constraints, or, in other words, a system with the low loss of power supply probability (LPSP). In this study, the LPSP function is considered as the main index of the reliability objective function, F_R. LPSP is a probability when the insufficient power supply occurs, and the system cannot provide the demand (P_load), taking into account the technical constraints. The LPSP value from zero to time T is estimated from Equation (18). $\begin{matrix} F_{R} = \sum_{t = 0}^{8760} \frac{Power . failure . time}{8760} \\ = \frac{\sum_{t = 0}^{8760} time (P_{available} (t) < P_{load} (t))}{8760} \end{matrix}$ (18)

Power failure time is the number of hours in a year which demand load cannot be supplied. The system cannot be operated in the case of the excessive voltage drop; Therefore, the reliability index is investigated here based on the outages due to the voltage drop.

2.4 Constraints

In addition to the parameters of the cost function, we should consider a series of limitations in operating the distribution network. The general form of the constraints is as follows.

2.4.1 Restrictions on renewable generation sources

It includes the maximum and minimum generated power of each wind energy and photovoltaic unit concerning the radiation and wind limitations. $P_{{DG}_{i}} \leq P_{{DG}_{t}}^{max}$ (19)

$P_{{DG}_{t}}^{max}$ describes the maximum output power of distributed generation.

2.4.2 Functional constraints of the ESS

These constraints include the balance of the power and batteries energy, stored power limitations, and the charging and discharging limits of the battery as given in Equations (20 and 21). $P_{{Ess}_{i}} \leq P_{{Ess}_{i}}^{max}$ (20) $E_{{Ess}_{i}} \leq E_{{Ess}_{i}}^{max}$ (21)

$P_{{Ess}_{i}}^{max}$ and $E_{{Ess}_{i}}^{max}$ are the maximum discharged power and energy at every time, respectively.

2.4.3 Demand management limitation

It includes the maximum amount of the participant power in the demand management as well as the maximum time of the consumption shifting for the peak load shaving. $P_{DMi} \leq {XP}_{n}$ (22)

X is a percentage of the nth bus’s peak load (P_n).

3 Shared demand management

In order to provide the network loads at the peak time when all of the system’s bus voltages are within the allowed range, ESSs will act in a price-based manner and be discharged. In the case where there are busses in the system whose voltages are not within the allowed range (less than 0.95 p.u), the storage devices will enter based on the sensitivity analysis matrix.

3.1 Sensitivity analysis matrix

In this situation, depending on the bus in which the storage system is located, as well as the amount of the current charge and the maximum capacity to be discharged at that time by the storage, its impact on the network is determined through calculating the difference between the maximum and minimum network voltages after the inclusion of this storage according to Equation (23). ${SR}_{i} = {SR}_{i}^{\max} - {SR}_{i}^{\min}$ (23)

SR_i is the voltage after entering the ith ESS. Therefore, in order to regulate the voltage, the difference between the maximum and minimum voltages depends on the loads involved in the demand management program. Now, the sensitivity analysis vector is defined as Equation (24). $\begin{matrix} Sensitivity Matrix \\ = [{SR}_{1}, {SR}_{2}, {SR}_{3}, \dots, {SR}_{n_{ESS}}] \end{matrix}$ (24)

n_ESS describes the number of ESSs available in the network.

3.2 Threshold and price-responsive load

In the present research, the threshold value method is implemented for importing the load responsibility into the planning and system operation. The threshold value can be determined based on various factors, including the decision for the network reservation capacity, which is a security margin to avoid the outage. It can also be the equivalent of the capacity required for the network boosting. Using the shared load management by energy storage sources, demand-side management and determining the optimal threshold value, it is aimed to manage the additional load by an optimal entry of the price-responsive loads when the load exceeds the threshold value. The optimal threshold value will be determined with the goal of maximizing the profit, technical membership function, and reliability improvement. ESSs will operate in both of the normal (with the aim of peak shaving) and critical modes (simultaneously with the price-responsive loads) of the distribution network.

In this condition, depending on the bus in which the price-responsive load is selected, its impact on the network is determined through calculating the difference between the maximum and minimum network voltages after the inclusion of this price-responsive load according to Equations (25 and 26). ${SDR}_{i} = {SDR}_{i}^{\max} - {SDR}_{i}^{\min}$ (25) $\begin{matrix} Sensitivity Matrix = [{SR}_{1}, {SR}_{2}, {SR}_{3}, \dots, \\ {SR}_{nb}, \dots {SDR}_{1}, {SDR}_{2}, \dots, {SDR}_{n_{DM}}] \end{matrix}$ (26)

SDR_i is the voltage after entering the ith price-responsive load. The influence of all the storage systems and price-responsive loads are stored in a comprehensive vector as in the following based on a sensitivity matrix. Finally, the vector is sorted according to the effectiveness of the parameters as in the previous section and analyzed in operation stage to determine the priority of price-responsive loads.

To analyze this problem, it is assumed that when the load decreases, only the active power of the load demand is reduced, and the reactive one remains unchanged. Generally, the distribution network planners design the electrical networks in such a way that they can meet the predefined limits and constraints under normal conditions. However, in the case of an emergency such as the protective system disconnection or overloads, these constraints may not be met with the storage systems discharging. Following this, some of the buses may exceed the allowable range, and in this case, the use of load reduction option can be a feasible approach. If the customers associated with the load reduction program can change their load consumption as needed, DSO can return the voltage of the critical nodes to the permitted range. More details on implementing the load reduction program in the distribution system’s function, as well as the timing of the energy and auxiliary services, are discussed in [32].

4 Solution method and numerical studies

Here, one of these algorithms, which is the second version of the multi-objective genetic algorithm with the non-dominated sorting (NSGA II), is used for solving the planning problem of the active distribution network. The suggestive method will be applied to the standard test systems such as IEEE 33-bus standard one.

4.1 Problem optimization based on NSGA II

Since the genetic algorithm search for the response space via several points in a parallel manner, it can be desirably used for finding a subset of the efficient responses. NSGA II is an edition of the genetic algorithm designed for solving multi-criteria optimization problems. In NSGA II, the population members are ranked based on the non-dominated concept. Non-dominant members in the existing population, form the first level (R = 1). Then, these members are temporarily removed from the population and the new non-dominant ones forming the second level (R = 2), are identified out of the remaining population. This process continues until all levels are identified and each member of the population is assigned to one of these levels. Figure 4 displays a graphical representation of the ranking and non-dominant levels in a minimization problem with two objective functions.

Fig.4

Graphical representation of the ranking and non-dominant levels.

4.2 Numerical studies

The proposed method was tested on the IEEE 33-bus radial distribution test system. The investigated radial network contains one feeder with 33 buses [33]. The candidate locations of wind, photovoltaic resources, and energy storages with their related allowed capacity and economic parameters in the studied distribution system are demonstrated in Tables 1 and 2.

Table 1
DGs and ESS information

Items Allowable installation capacity (KW) Installation location Maintenance cost ($/KW)

PV 40,80,140,200 13,22,33 0.20820

WT 150,240,300,400 8,17,30 0.52500

ESS 100,200,300 5,12,19,26,32 0.08618

DM – 11,15,18,28,31

Items	Allowable installation capacity (KW)	Installation location	Maintenance cost ($/KW)
PV	40,80,140,200	13,22,33	0.20820
WT	150,240,300,400	8,17,30	0.52500
ESS	100,200,300	5,12,19,26,32	0.08618
DM	–	11,15,18,28,31

Table 2

Economical parameters

Parameter (Unit)	Value	Parameter (Unit)	Value
C_invEss ($/KVA)	813	LCT ($/KW)	162
C_invEss ($/KWh)	543	UP (KW)	2000
C_invPV ($/KW)	1000	N _yr	10
C_invW ($/KW)	1650	$C_{T & D} (Mil $ / MW)$	2
inf r (%)	0.13	intr (%)	1
Annual demand growth(%)	5

General steps of NSGA II for solving the optimization problems in the distribution network are based on the flowchart in Fig. 5.

Fig.5

NSGA II algorithm flowchart.

Daily calculated price of electricity for depicted 12 months of the year is shown in Fig. 6. At first, place and size for ESSs and DGs along with threshold value are determined by every population. Then, for the existing system, the method of operation is performed for the related population, and the objective functions are calculated. Ultimately, based on NSGA II, optimal solutions are extracted.

Fig.6

Hourly electricity price of 12 months.

The proposed NSGA II algorithm for minimizing planning and operation cost of the active distribution network is implemented using MATLAB running on a 2.4 GHz Processor with 1 gigabyte of the cache. During the simulation, the parameters in this algorithm are: numbers of search operators and the maximum number of repetitions both equal to 100.

In this paper, three different cases are considered for proving the validity of the proposed model, along with improving considered objectives. These cases are including:

Case I (A): Active distribution network operation without energy storage and price-responsive load.

Case II (B): Active distribution network operation containing energy storage battery without the presence of any price-responsive load.

Case III (C): Active distribution network operation including an energy storage battery and price-responsive load along with attaining optimal threshold.

In the first case, the network is considered with the presence of neither the energy storage nor the price-responsive load which operates in the conventional conditions, and all DGs (RESs or Non-RESs) must meet the anticipated load demand in the evaluated time. Since no energy storage is considered in this case study, to assure constant operation of the system, the output power of DGs and operator must be higher than power demand of the distribution system as an operating reserve. In the second case, energy storages are added to the distribution system operation. The main advantages of energy storage in the active distribution network are maintaining stability, integration of systems, improving power quality, etc. Energy storage starts the time-period without any initial charge so that discharging in every step of the day is restricted to charge rate in previous hours. The minimum charge and discharge rate of the energy storage is considered to be 10% of the total capacity of the related energy storage per hour. In the second case study, to evaluate the effectiveness of selecting one ESS with optimized and appropriate size, the maximum charge rate of the energy storage (C_ESSMAX), and installation locations are considered as a part of control variables which must be optimized in a time-period that is mentioned in Table 1. In other words, the supplied energy in energy storage is in the range of [C_ESSMIN - C_ESSMAX]. As mentioned before, in case C for load controlling in the ADN system, shared demand management, and energy storages are utilized. In this condition, while raising load amount from a specified threshold, for price-responsive loads participation in demand management, the sensitivity matrix is formed according to DGs and ESSs locations. Indeed, the threshold determines the entry range of price-responsive loads participation with energy storages for managing system demand. In this study, the range of threshold change is between 95–99 percent of the peak load. Then, based on every item’s impact on the system (impact rate on the bus with a minimum voltage), energy resources are prioritized in the sensitivity matrix. In this situation, based on the priorities calculated in the matrix, resources are entered, and after entering every resource, the sensitivity matrix is updated in the presence of that item. This process continues until all buses voltages (V_b ≥ 0.95 p.u) and all lines currents (I_L ≤ I_max) are within the range. Because of the costly nature of demand management in operation time of ADN compared to energy storage systems, according to (21) a cost influence is considered in a sensitivity matrix. In Fig. 8, the threshold for case C in the typical daily peak load is illustrated. The optimized threshold is 96% of the peak load in 5th year, which is the load higher than the threshold supplied by sharing the power of price-responsive loads and energy storages. In the case of network inability to sustain buses voltage in the allowed domain, an outage occurs, and reliability function based on outage loads is calculated. Regarding all of these parameters, the optimization problem for the active distribution test system is solved by the NSGA II algorithm. The main objectives of this solution include: optimizing the total profit, technical membership, and reliability objective functions as well as determining the optimal size of ESS and the output power of PV and WT. Figure 7 shows the solution space of objective function in the NSGA II program. Feasible solution space can be opted based on three objective functions and their priorities. A planner can select an appropriate solution based on the foremost objective and planning priorities from feasible solution space. In this paper, the acquired economic objective function values of the active distribution system using the NSGA II algorithm for case C, as mentioned in Table 3, is 6.628380×10⁶ $ for studied time-period. Comparing the calculated results using the NSGA II algorithm for the three cases reveals that installing the initially charged energy storage in case B leads profit of the ADN to 5.897037×10⁶ $.

Fig.7

Feasible response space of objective functions.

Fig.8

Energy supplying by every source for 24 hours of a typical day in case C.

Table 3

Objective function results for three scenarios

No.	Item	Case A	Case B	Case C
1	Produced power by Wind and PV in studied time period (KW)	1.358297×10⁷	1.157797×10⁷	1.04371×10⁷
2	Peak load generation PPG_t	0	4.734608×10⁶	5.131248×10⁶
3	Power exchange profit PEA_t	0	1.364529×10⁵	2.205446×10⁵
4	Loss reduction profit PLOSSR_t	0	1.776085×10⁴	2.139862×10⁴
5	Network upgrade deferral profit PTDB_t	0	3.138352×10⁶	3.138352×10⁶
6	Annual investment and maintain cost CINV_t	1.25764×10⁶	2.129222×10⁶	2.161933×10⁶
7	ADN load management cost CLL_t	0	0	2.115764×10⁴
8	Profit objective function	0	5.897037×10⁶	6.628380×10⁶
9	Technical membership	0.8419512	1.720623	1.794550
10	Optimal Threshold	–	–	0.96
11	LPSP (per year)	0.02	0	0

In addition, in the case C, thanks to the employment of load management in system operation, we have witnessed 731343 $ improvement in the system profit function and 0.0739 in technical membership value compared to the second case. Numerical results of the optimized output power of DGs, energy storages, and their related operation conditions are represented in Fig. 8. In the third case, the threshold value for entering price-responsive load according to what was mentioned in the previous section is 96% of the peak load of 5th year.

Besides, we have presented how the required distribution network energy is supplied by every energy sources as well as charge and discharge condition of ESSs for three cases. Price-responsive loads bus number priority to participate in peak shaving, based on sensitivity matrix and typical day (January) are 18, 15, 11, 28 and 31, respectively. Optimal energy sources place and size obtained by planning and operation process and also price-responsive loads participation in two hours of January in 10th planning year are indicated in Table 4.

Table 4

Optimal location and size of energy resources

Optimal energy resources place and size	ESS location (bus)	ESS size KW	Wind location (bus)	Wind size KW	PV location (bus)	PV size KW	Price-responsive load (bus)	Price-responsive load reduction in two hours:
								Time 20	Time 21
CASE C	5	300	30	400	13	80	18	51.270	54.30
	12	300			33	200	15	25.620	36.210
	19	300					11	34.170	27.230
	26	300					28	10.230	10.050
	32	–					31	25.560	25.420

Furthermore, for one specific day of the last year (that stands for January), energy supplied by each energy resource is illustrated during 24 hours in Fig. 8 and Table 5. Based on the results, utilizing energy storage has a substantial effect on cost improvement and enhancing obtained profit, that stems from system operation. Predominantly, energy storage systems by entering in peak time, directly cause system profit to increase and power quality to improve. Also, in this condition, demand management shared with energy storage based on sensitivity analyzing matrix are accomplished. In this case, price-responsive loads and energy storages entering are applied simultaneously with their importance of stage degree.

Table 5

System units produced power for case C

Time	PV	WT	BES	CLL	NET
1	0	254707.6	– 125000	0	1411492
2	0	233574.5	– 187500	0	1111725
3	0	228297.8	– 187500	0	1151002
4	0	227482.1	– 375000	0	1386672
5	0	259250.8	– 375000	0	1453816
6	0	268557.2	– 375000	0	2087114
7	0	257020.6	– 125000	0	3257951
8	20696.13	274196.4	– 125000	0	3206250
9	96025.94	284848.3	0	0	3807357
10	175366.3	309851.9	0	0	3716662
11	233981.8	336189.9	0	0	3644693
12	254759.2	344133.7	0	0	3990985
13	271014.6	365920.8	0	0	3982523
14	236958.4	374245.9	0	0	3925848
15	184350	382489.8	0	0	3947615
16	115861.2	380179.1	187500	0	4334882
17	47869.94	383717.9	0	0	3814435
18	1844.903	375869.7	187500	0	3633133
19	0	355132.1	250000	0	3758828
20	0	343441.0	375000	170376	4281155
21	0	317061.7	500000	177659	4392614
22	0	293751.7	375000	0	3762270
23	0	279073.3	0	0	3243498
24	0	273306.8	0	0	2020182

5 Conclusion

In this paper, a new approach is proposed to deal with active distribution network planning and operation based on shared demand management by energy storages and price-responsive loads. To this aim, 12 days were selected as representatives of each month of the year loads, and power prices and every 24-hour represents a corresponding month. For modeling the wind turbine speed, the Weibull distribution function, and for PV output, the normal distribution function was utilized. The objective function contains three major parts including cost, reliability, and technical membership, in which the cost involved planning and operation costs. The results showed that not only 11.033 percent economic profit improvement was achieved compared to the conventional distribution network planning, but also there is a 4.12 percent enhancement in technical membership value without any power outage in planning horizon. These experiments proved that not only the planning and operation cost of ADN has reduced, but also regards to sensitivity analyzing and technical membership function, power quality factors of the network have improved. One of the most significant findings emerged from this study is that the technical risk characters of ADN are minimized. As represented in the results, a shared operation of price-responsive loads and energy storage systems considering the optimal threshold along with sensitivity analyzing matrix have had a superb effect on operation and planning costs, power quality and reliability factors of ADN. Obtained extensive simulations by NSGA II algorithm, which solved this multi-objective problem, confirmed the above claim. Further research could also be conducted to determine the effectiveness of this method. For instance, the effect of participation of electric vehicles (v2g) in ADN planning as an energy source in critical time along with demand response program, could be investigated.

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