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Management of charging cycles for grid-connected energy storage batteries
Journal of Energy Storage 18 (2018) 380–388
Contents lists available at ScienceDirect
Journal of Energy Storage journal homepage: www.elsevier.com/locate/est
Management of charging cycles for grid-connected energy storage batteries
T
Mohammed Jasim M. Al Essa Faculty of Engineering, University of Kufa, P.O. Box (21), Najaf Governorate, Iraq
A R T I C LE I N FO
A B S T R A C T
Keywords: Battery energy storage systems Distribution grids Energy management Load flow Optimization Voltage control
The use of renewable energy requires a certain level of energy management in electricity distribution grids. Gridconnected energy storage batteries (ESBs) can be utilized to keep this level of management by charging and discharging them accordingly. Grid-connected ESB users schedule their usage based on time-of-use tariffs to follow economic charging cycles. However, charging several grid-connected ESBs during off-peak tariff interval may cause a decline of grid voltage below its limit. Therefore, this paper suggests a management scheme to maintain voltage-sag magnitude within its threshold, while minimizing the aggregated cost of charging the gridconnected ESBs. A sequential quadratic programming technique is employed to solve the objective function, considering an IEEE test system of 37 node. According to optimization results, the management scheme reduces the operational cost of different ESB penetration in the test system, taking into consideration ESB state of charge and grid voltage.
1. Introduction Grid-connected energy storage systems were reported in the literature [1] as emerging technologies that have an impact on revenues considering their ability of increasing demand side flexibility, while implementing scheduling algorithms in electricity grids [2]. A sustainable low-carbon electric pattern can be achieved in power grids using backup energy systems to contain intermittent renewable energy efficiently. Energy storage systems (ESSs) are able to enhance the management of power grids in order to improve efficiency and reduce cost. The de-carbonization of energy sector needs an adequate electricity market of renewables to maintain acceptable variations of voltage and frequency [3]. Fig. 1 shows different combinations of electrochemical energy storage batteries (ESBs), which were used to provide grid support in transmission and distribution power systems based on their capacity and discharging timescale [4]. Grid-integrated ESSs were presented in [5] considering their applications and services for connecting variable energy resources to distribution grids. ESSs were surveyed in [6] as a promising entity to increase the flexibility of energy sector with high penetration of renewable resources. For example, ESSs were investigated in [7] to increase the deployment of solar panels in low-voltage distribution grids using their ability of load clipping, peak shaving and energy shifting. Stationary batteries of ESSs were assessed in [8] to decrease peak demand in low voltage grids. It was concluded that the grid-integrated ESSs have the capability of providing quick and economic reserves, as compared to traditional load shifting ones [9]. A simplified algorithm
E-mail address: [email protected]. https://doi.org/10.1016/j.est.2018.05.019 Received 23 January 2018; Received in revised form 12 May 2018; Accepted 28 May 2018 2352-152X/ © 2018 Elsevier Ltd. All rights reserved.
was proposed in [10] to increase the revenue of grid-scale ESSs while participating in a particular reserve market. Grid-level ESBs were discussed in [11] to investigate their impact on power management and voltage control based on field-trial results across different distribution grids. High numbers of grid-integrated renewable sources (e.g. residential solar panels) can cause voltage fluctuations. Grid-integrated ESBs were used in [12] to maintain grid voltage within its boundaries using quadratic programming of scheduling their charging cycles. Distributed control strategies were proposed in [13] to mitigate the impact of solar panels on grid voltages, considering energy storage. ESSs were presented in [14] to facilitate demand response of residential users based on electricity prices, while connecting solar panels and plug-in hybrid electric vehicles to distribution grids. It was conclude in [14] that a utility corporation has a good control on peak load with a compromised level of consumer comfort considering time-of-use tariff and real time price. An energy management scheme of charging batteries was implemented in [15] based on genetic algorithm to reduce energy costs, accommodating solar panels and plug-in electric vehicles in distribution grids. Re-chargeable batteries were studied in [16] to evaluate their impact on a distribution feeder. A quadratic convex optimization of optimal energy storage scheduling was addressed in [16] to accomplish an efficient use of solar panels and batteries, considering transformer losses and voltage variations. Energy management algorithms of valley-filling and peak-shaving methods were developed in [17] to achieve an intelligent scheduling framework of three-phase ESSs in a low-voltage distribution grid, embedding a dayahead forecasting model.
Journal of Energy Storage 18 (2018) 380–388
M.J.M. Al Essa
(n − 1) by the following formula: v (n − 1) (t ) = vn (t ) + z (n − 1) n ×
Pn (t ) vn (t )
(2)
where v (n − 1) (t ) is the voltage at the node (n − 1) at the time step t. vn (t ) is the voltage at the node n at the time step t. z (n − 1) n is the impedance of the line segment between the node (n − 1) and the node n. Pn (t ) is the power drawn by aggregated loads at the node n at the time step t [18]. Eq. (3) determines loading power of the distribution transformer at each time step t. NF
PL (t ) =
k=1
in (t ) = In this study, the impact of re-charging ESBs on voltage sag in electricity grids is highlighted. The business as usual scenario of the residential stationary ESBs is to charge them during low-price interval of electricity. The energy stored in the ESBs is later discharged over high-price term of electricity to gain revenue. However, this scenario leads to increase demand while delivering low-priced electricity because end-user customers tend to charge their ESBs utilizing low costs. To overcome such problem, this paper proposes a management scheme of charging ESB in residential grids using first principles and optimization techniques. Distribution grids were generally classified into interconnected and radial ones, focusing on the radial systems. A linear mathematical model of load flow calculations is developed considering radial feeders, while embedding synthesized ESB loads over a day. The problem is formulated using an objective function of cost reduction, which is thereafter solved with sequential quadratic programming. This paper is structured as follows. Load flow calculations of electricity feeders are firstly developed considering an IEEE test system of 37 node. The raw data used in studying residential load profiles are then described. The algorithmic steps of generating ESB loads are afterwards demonstrated. Problem formulation was thereafter presented while explaining the installation of the proposed management scheme in electricity grids. Simulation results, conclusion and future work are later discussed.
⎞
⎝ j=1
⎠k
⎛⎜ {j = 1, 2, 3, ….,N } ⎟⎞ ⎝ {k = 1, 2, 3, ….,NF } ⎠
(3)
vn (t ) Zn (t )
(4)
where in (t ) is the current drawn by the connected load at the node n in Ampere at time step t. The branch current between the two nodes (n − 1) and n is calculated using Kirchhoff’s current law as follows.
i (n − 1) n (t ) = i (n − 2)(n − 1) (t ) − i (n − 1) (t )
(5)
Meanwhile, the voltage is calculated by the following formula [18]:
v (n − 1) (t ) = vn (t ) + z (n − 1) n × i (n − 1) n (t )
(6)
To start load flow calculations, the voltage at the node n is assumed to be equal to the nominal voltage. Then, the voltage at the source node (v0 ) is calculated by initializing the calculations using the nominal value of voltage. Afterwards, correction factor (CF) is determined using Eq. (7) [18].
CF =
V0 v0
(7)
where V0 is the actual value of the voltage at the source node. The results of final voltages and final currents are determined along the feeder as follows [18].
Vx (t ) = CF × vx (t ) {x = 1, 2, 3, ….,n}
(8)
Ix (t ) = CF × i x (t ) {x = 1, 2, 3, ….,n}
(9)
where Vx (t ) and Ix (t ) are the voltage and current evaluated in load flow calculations using Eq. (1)–(9) at each node along the radial feeder for each time step t.
2. Modelling of electricity feeders, residential appliances and batteries Equations of load flow were presented in this section to accommodate diurnal load profiles of residential appliances and grid-scale batteries into a modified IEEE test system.
2.2. The grid under study A modified IEEE test system of 37 node was used in this paper to study the impact of charging residential ESBs. The grid was adapted from [19] considering different feeders as shown in Fig. 3. A number of distribution transformers were indicated in Fig. 3, serving a finite number of residential customers.
2.1. Electricity feeders Fig. 2 shows the representation of an individual feeder in radial systems, considering the impedance of loads as indicated in Eq. (1) [18].
vn2 (t ) Sn (t )
N
where PL (t ) is the aggregated power of customers at the distribution transformer in kW at time step t. NF is the number of radial feeders. N is the number of residential customers per feeder. pj (t ) is the power consumed by each customers in kW for a unity power factor at time step t.
Fig. 1. Electro-chemical batteries for grid-support applications in transmission and distribution power systems based on their capacity and discharging timescale (adapted from [4]).
Zn (t ) =
⎛
∑ ⎜∑ pj (t ) ⎟
2.3. Residential appliances (1)
Residential loads are modelled considering diurnal load profiles of consumer electronics, cooking appliances, lighting components, space/ water heating systems, wet appliances, and other miscellaneous. Smartplug and circuit-monitoring instrument recorded these data over 10min time steps [20]. Fig. 4 presents these diurnal profiles on a daily basis of 10-min time steps as reported by the source of data [20].
where Zn (t ) is the load impedance at the node n in ohm at time step t. vn (t ) is the voltage at the node n in Volt at time step t. Sn (t ) is the apparent power drawn by aggregated loads at the node n in kVA. Kirchhoff’s laws of voltage and current were used to evaluate load flows of the grid under study. The voltage is calculated at the node 381
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Fig. 2. Representation of an individual feeder in radial grids.
profiles (i.e. L) over a day by synthesizing L rows and 144 columns of “0” and “1” values using uniform probability distribution. The generated matrix of L × 144 elements is subjected to a number of mathematical operations as follows. Summation calculates the aggregated diurnal profile of all ESB charging cycles. The maximum value (i.e. Vm), the root-mean-square value (i.e. RV) and the average value (i.e. AV) are evaluated for the aggregated diurnal profile to verify the logical diversity of the synthesized ESB charging profiles considering sinusoidal characteristics. The state of charge (SOC) level for each ESB unit is calculated as follows.
2.4. Energy storage batteries ESB power profiles were generated to model their consumption for each time step. Loads can be modelled in distribution power systems as follows: constant power, constant current, constant impedance or combination of them [18]. The diurnal charging profiles of residential ESB loads are probabilistically generated as follows. The requested charging cycles of ESBs are generated using uniform probability distribution. The diurnal load profile for each individual ESB unit is synthesized by considering “0” for idle charging cycles, “1” for charging cycles, and “-1” for discharging cycles. A charger of 3 kW is used to re-charge 10 kWh capacity of stationary batteries over a minimum timescale of 10-min (i.e. the successive time slots of generated charging cycles). A number of residential ESB charging profiles were generated over a day. The generated profiles of these ESBs were shifted backward and forward to acquire a logical diversity across the generated individual profiles. It is assumed that the aggregated profiles of ESB charging and discharging cycles form a sinusoidal curve over a day considering off-peak and on-peak electricity price. Accordingly, the peak value of charging ESBs occurs during offpeak tariff term, whereas ESB users prefer discharging their ESBs during on-peak tariff interval to gain revenue. Fig. 5 demonstrates the algorithmic steps that were used to generate charging cycles individually. The algorithm starts with adjusting the number of ESB charging
Μ ⎛SOC + η × ∑i =1 Poi⎞⎟ 0 ⎠ × 100% SOC % = ⎝ SOCR ⎜
(10)
where SOC is the state of charge level of an ESB unit in percentage. SOC0 is the initial state of charge level of the ESB unit in kWh. SOCR is the rated state of charge level of the ESB unit in kWh. Μ is the number of ESB charging time intervals in hours. η is the efficiency of ESB charger. Po is the rated power of the ESB charger in kW. The depth of discharge (DOD) is calculated using the following equation.
Fig. 3. A modified IEEE test system of 37 node (adapted from [19]). 382
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M.J.M. Al Essa
Fig. 4. Diurnal load profiles of whole house considering individual appliances [20].
DOD % =
SOCR − SOCt × 100% SOCR
on ESB penetration in the electricity grid. The ESB units were evenly connected to the distribution transformers of the grid under study (see Fig. 3). The peak demand of charging ESB units occurs during the off-peak electricity interval (i.e. the time between 00:00 and 12:00 as shown in Fig. 6) to decrease the operational cost of charging power. However, the absolute peak value of discharging ESB takes place during the on-peak electricity term (i.e. the time between 12:00 and 00:00) to increase
(11)
where DOD is the depth of discharge level of the ESB unit in percentage. SOCt is the state of charge level of the ESB unit in kWh at time step t. Fig. 6 shows the aggregated power of charging residential ESB units based on the algorithmic steps proposed in this paper as shown in Fig. 5. Samples of 750 residential ESB charging profiles were generated over a day. The number of these samples was calibrated up/down based
Fig. 5. The algorithmic steps of generating ESB charging cycles individually. 383
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Fig. 6. Diurnal power of charging and discharging batteries based on the proposed algorithmic steps. Table 1 Key elements and variables of managing charging cycles of energy storage batteries (ESBs), as proposed in this paper. Location
Formulation
Schematic Figure
Description
System Coordinator Level
Constraints
Grid voltage and batteries’ state of charge (SOC) are the constraints of optimization
System Coordinator Level
Constants
Appliances’ power and electricity price are the constants of optimization
System Coordinator Level
Objective
Minimizing the operational cost of charging ESBs is the objective function of optimization
System Coordinator Level
Decision Variables
ESB charging cycles (i.e. “On” and “Off” operation of ESB) are the decision variables of optimization
The ESBs are prioritized in a descending pattern based on their SOC to switch “Off” high SOC batteries when the voltage exceeds its limit
Distributed Level of Managing ESB Charging Cycles
[21], were utilized in this paper. The pricing tariff consists of two level of electricity prices, which are off-peak and on-peak levels in $/kWh [21]. SOCf is the final SOC of aggregated ESB units over a day in kWh. In the meantime, inequality constraints are represented using Eq. (13) considering the operational voltage of residential grids.
revenue. Electricity tariff consists of two levels, which are off-peak and on-peak prices in $/kWh [21]. 3. Problem formulation The objective of this study is to reduce the operational cost of charging the grid-connected ESBs while maintaining grid voltage within its boundaries. This statement is formulated based on optimization methods using first principles as follows.
SOCmin ≤ SOCf ≤ SOCmax Vmin ≤ Vx ≤ Vmax
where SOCmin and SOCmax are the minimum and maximum limits of battery state of charge. The minimum limit was considered 26% of full SOC battery, whereas the maximum limit was adjusted to 86% of full SOC battery as the complete charge/discharge (i.e. full cycle equivalent) has an impact on the aging of battery cells [22]. Vmin and Vmax are the lower/upper limits of voltage magnitudes. According to IEEE standards [23], this voltage tolerance is between ± 5%. Table 1 shows constraints, decision variables and other aspects that
24
⎤ ⎡ Minimize OF = ⎢∑ PSIG × SOCf ⎥ t = 0 ⎦ ⎣
(13)
(12)
where OF is the objective function (i.e. minimizing the operational cost of charging ESBs over a day in $). PSIG is the price signal in $/kWh. The residential time-of-use tariffs, which were presented in the literature 384
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Fig. 7. A theoretical installation of the proposed management strategy in electricity grids.
Table 2 A comparative table of this study considering other studies in terms of objectives, constraints and algorithms of grid-integrated energy storage management. Studies
Objectives
Constraints
Algorithms
This study
Minimizing the operational cost of charging ESBs Maximizing economic revenue Minimizing CO2 emissions Minimizing peak demand Maximizing operational savings Minimizing transformer loading Minimizing power cost Minimizing battery life cycle cost Minimizing peak demand Minimizing energy consumption
Grid voltage and battery state of charge
Sequential quadratic programming
Energy storage capabilities
Linear programming
Power balance of batteries and grids
Quadratic programming
Power balance, battery state of charge, and battery life-cycle cost
Quadratic programming
Battery state of charge and battery depth of discharge Battery state of charge and grid power capacity
Heuristic forecasting-based programming Hyper-heuristic and evolutionary programming Fuzzy and particle swarm optimization (PSO)
[1] [12] [16]
[17] [26] [27]
Minimizing active power losses Mitigating voltage fluctuations
Battery state of charge, battery depth of discharge, and grid power flow limit
4. Installation of proposed management scheme
Table 3 The case studies of ESB penetration levels at the grid under study. Case studies
Maximum values of ESB loads (kW)
Maximum value of residential loads (kW)
Penetration (%)
Case1 Case2 Case3
750.00 1500.00 2250.00
3485.00 3485.00 3485.00
21.52 43.04 64.56
Fig. 7 explains a theoretical installation of the actual management strategy proposed in this paper, considering a radial feeder in electricity grids. The centralized coordinator requires communications between its location and ESBs to accomplish the task of managing their charging cycles. Meanwhile, the distributed operators need sensors to detect the SOC levels of ESBs. Smart meters provide a potential solution for these requirements, while implementing the proposed management scheme in electricity grids. The management strategy proposed in this paper improves a straightforward technique of ESB load shedding, as it detects which battery can be switched-off without affecting the use of batteries. In other words, the simple management method can lead to unsystematic ESB load shedding when grid voltage starts to drop below 95%, whereas the proposed algorithm detects relatively high SOC batteries to be switched-off. Moreover, the basic management scheme of ESB charging cycles increases the number of full cycle equivalents, shortening the lifetime of batteries. Simplified management techniques often interrupt ESB charging cycles when batteries reach 100% SOC, whilst the proposed strategy schedules ESB charging cycles considering the maximum SOC of 86% as shown in Eq. (13). Table 2 shows different studies as compared to this study in terms of objectives, constraints and algorithms that were used to manage the charging cycles of grid-connected ESBs.
were considered to solve the problem of managing ESB charging cycles in coordination and distribution levels. The proposed objective function can be solved using probabilistic method (e.g. genetic algorithm) or deterministic technique (e.g. sequential quadratic regulator) [24]. In this study, the deterministic programing method (i.e. sequential quadratic programming) was used to solve the problem with visual basic application, because unreliable results were observed while solving the problem using the probabilistic method. The optimal value of aggregated charging demand was used to shift individual ESB loads considering the state of charge. A sequential elimination detector prioritizes all ESBs based on their state of charge in a descending pattern. This detector compares the aggregated demand of ESBs with and without optimization. If the optimized demand is less than or equal the requested demand, all ESBs will be normally charged without interruption. Otherwise, charging cycles of high SOC batteries will be shifted to the next time slot (i.e. whenever the grid voltage exceeded its limit). Voltage correlation method can be used to detect the value of SOC for ESBs as illustrated in [25]. 385
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Fig. 8. Diurnal voltage profiles at the node 37 of the grid under study for basic case (i.e. residential load only) and the three case studies of ESB penetration levels.
Fig. 9. Diurnal voltage profiles at the node 37 of the test system using the management scheme proposed in this paper.
5. Simulation results
this paper. The upper curve of Fig. 8 shows the diurnal voltage profile at the node 37 of the grid under study (see Fig. 3), considering energy consumption by residential appliances only without the ESB demand. In addition, the diurnal voltage profiles of Case 1, 2 and 3 are demonstrated in Fig. 8. It can be noticed that, the operational voltages vary within the range of ± 5% tolerance of voltage for basic case (i.e. without ESB loads) and Case1. However, the voltage exceeds the lower limit (i.e. 95%) when additional ESBs are re-charged, as shown for Case2 and 3, because the users tend to re-charge their batteries during low-tariff interval of electricity, as shown in Fig. 8. To maintain the voltage profile within its limits considering different penetration levels of ESBs, the proposed management scheme is used to re-schedule their charging cycles sequentially. Fig. 9 illustrates
Three case studies were considered to determine the performance of the proposed management scheme. The case studies were evaluated using different penetration levels of ESBs at the grid under study. ESB penetration was defined based on the maximum value of the aggregated ESB loads and the maximum value of residential demand, as follows.
P% =
max × 100% Dmax
(14)
where P % is the penetration level of ESBs at the grid under study in percentage. max is the maximum value of the aggregated ESB loads in kW. Dmax is the maximum value of the aggregated residential demand. Table 3 shows the case studies and the penetration levels considered in 386
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Fig. 10. The aggregated values of ESB state of charge with and without the proposed optimization.
Fig. 11. Comparative cost reductions of charging ESBs with and withoout the proposed method.
of ESB penetration (see Table 3). Although the ESBs were re-charged during off-peak tariff interval, the proposed management scheme kept the voltage above 95% of its nominal value. Sequential quadratic programming was used to minimize the ESB operational cost (see Fig. 11) without exceeding voltage limit as shown in Fig. 9. The ESBs were prioritized based on their state of charge to schedule the charging cycles sequentially, as demonstrated in Table 1. The future work will aim to maximize the revenue of discharging ESBs while keeping the grid voltage below 105% of the nominal voltage, considering feed-in tariffs and batteries’ depth of discharge. Prosumers, who are able to produce and consume electricity, can use the proposed technique to accomplish a profitable energy management, taking into consideration voltage boundaries.
the diurnal voltage at the node 37 of the grid under study while charging the ESB using the proposed management scheme. It can be seen that the voltage drops below 95% for Case2 and for Case3 without using the optimization, as shown in Fig. 8. With the optimization, the diurnal voltage is kept within its limit (i.e. above 95%) for all case studies (see Fig. 9). Fig. 10 depicts the aggregated values of ESB state of charge over a day of 10-min resolution for all case studies with and without the proposed management scheme. In the meantime, the aggregated costs of charging ESBs were decreased as indicated in Fig. 11 (i.e. based on the tariff used), maintaining the grid voltage above the limit of 95%. 6. Conclusion and future work
Acknowledgement
A management scheme of charging cycles for grid-connected energy storage batteries (ESBs) was proposed to maintain voltage magnitude within its limit in radial systems. The problem of voltage sag was mitigated using the proposed method, while considering three case studies
The generous comments of the anonymous reviewers are greatly appreciated. 387
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Appendix A. Supplementary data
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Journal of Energy Storage journal homepage: www.elsevier.com/locate/est
Management of charging cycles for grid-connected energy storage batteries
T
Mohammed Jasim M. Al Essa Faculty of Engineering, University of Kufa, P.O. Box (21), Najaf Governorate, Iraq
A R T I C LE I N FO
A B S T R A C T
Keywords: Battery energy storage systems Distribution grids Energy management Load flow Optimization Voltage control
The use of renewable energy requires a certain level of energy management in electricity distribution grids. Gridconnected energy storage batteries (ESBs) can be utilized to keep this level of management by charging and discharging them accordingly. Grid-connected ESB users schedule their usage based on time-of-use tariffs to follow economic charging cycles. However, charging several grid-connected ESBs during off-peak tariff interval may cause a decline of grid voltage below its limit. Therefore, this paper suggests a management scheme to maintain voltage-sag magnitude within its threshold, while minimizing the aggregated cost of charging the gridconnected ESBs. A sequential quadratic programming technique is employed to solve the objective function, considering an IEEE test system of 37 node. According to optimization results, the management scheme reduces the operational cost of different ESB penetration in the test system, taking into consideration ESB state of charge and grid voltage.
1. Introduction Grid-connected energy storage systems were reported in the literature [1] as emerging technologies that have an impact on revenues considering their ability of increasing demand side flexibility, while implementing scheduling algorithms in electricity grids [2]. A sustainable low-carbon electric pattern can be achieved in power grids using backup energy systems to contain intermittent renewable energy efficiently. Energy storage systems (ESSs) are able to enhance the management of power grids in order to improve efficiency and reduce cost. The de-carbonization of energy sector needs an adequate electricity market of renewables to maintain acceptable variations of voltage and frequency [3]. Fig. 1 shows different combinations of electrochemical energy storage batteries (ESBs), which were used to provide grid support in transmission and distribution power systems based on their capacity and discharging timescale [4]. Grid-integrated ESSs were presented in [5] considering their applications and services for connecting variable energy resources to distribution grids. ESSs were surveyed in [6] as a promising entity to increase the flexibility of energy sector with high penetration of renewable resources. For example, ESSs were investigated in [7] to increase the deployment of solar panels in low-voltage distribution grids using their ability of load clipping, peak shaving and energy shifting. Stationary batteries of ESSs were assessed in [8] to decrease peak demand in low voltage grids. It was concluded that the grid-integrated ESSs have the capability of providing quick and economic reserves, as compared to traditional load shifting ones [9]. A simplified algorithm
E-mail address: [email protected]. https://doi.org/10.1016/j.est.2018.05.019 Received 23 January 2018; Received in revised form 12 May 2018; Accepted 28 May 2018 2352-152X/ © 2018 Elsevier Ltd. All rights reserved.
was proposed in [10] to increase the revenue of grid-scale ESSs while participating in a particular reserve market. Grid-level ESBs were discussed in [11] to investigate their impact on power management and voltage control based on field-trial results across different distribution grids. High numbers of grid-integrated renewable sources (e.g. residential solar panels) can cause voltage fluctuations. Grid-integrated ESBs were used in [12] to maintain grid voltage within its boundaries using quadratic programming of scheduling their charging cycles. Distributed control strategies were proposed in [13] to mitigate the impact of solar panels on grid voltages, considering energy storage. ESSs were presented in [14] to facilitate demand response of residential users based on electricity prices, while connecting solar panels and plug-in hybrid electric vehicles to distribution grids. It was conclude in [14] that a utility corporation has a good control on peak load with a compromised level of consumer comfort considering time-of-use tariff and real time price. An energy management scheme of charging batteries was implemented in [15] based on genetic algorithm to reduce energy costs, accommodating solar panels and plug-in electric vehicles in distribution grids. Re-chargeable batteries were studied in [16] to evaluate their impact on a distribution feeder. A quadratic convex optimization of optimal energy storage scheduling was addressed in [16] to accomplish an efficient use of solar panels and batteries, considering transformer losses and voltage variations. Energy management algorithms of valley-filling and peak-shaving methods were developed in [17] to achieve an intelligent scheduling framework of three-phase ESSs in a low-voltage distribution grid, embedding a dayahead forecasting model.
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(n − 1) by the following formula: v (n − 1) (t ) = vn (t ) + z (n − 1) n ×
Pn (t ) vn (t )
(2)
where v (n − 1) (t ) is the voltage at the node (n − 1) at the time step t. vn (t ) is the voltage at the node n at the time step t. z (n − 1) n is the impedance of the line segment between the node (n − 1) and the node n. Pn (t ) is the power drawn by aggregated loads at the node n at the time step t [18]. Eq. (3) determines loading power of the distribution transformer at each time step t. NF
PL (t ) =
k=1
in (t ) = In this study, the impact of re-charging ESBs on voltage sag in electricity grids is highlighted. The business as usual scenario of the residential stationary ESBs is to charge them during low-price interval of electricity. The energy stored in the ESBs is later discharged over high-price term of electricity to gain revenue. However, this scenario leads to increase demand while delivering low-priced electricity because end-user customers tend to charge their ESBs utilizing low costs. To overcome such problem, this paper proposes a management scheme of charging ESB in residential grids using first principles and optimization techniques. Distribution grids were generally classified into interconnected and radial ones, focusing on the radial systems. A linear mathematical model of load flow calculations is developed considering radial feeders, while embedding synthesized ESB loads over a day. The problem is formulated using an objective function of cost reduction, which is thereafter solved with sequential quadratic programming. This paper is structured as follows. Load flow calculations of electricity feeders are firstly developed considering an IEEE test system of 37 node. The raw data used in studying residential load profiles are then described. The algorithmic steps of generating ESB loads are afterwards demonstrated. Problem formulation was thereafter presented while explaining the installation of the proposed management scheme in electricity grids. Simulation results, conclusion and future work are later discussed.
⎞
⎝ j=1
⎠k
⎛⎜ {j = 1, 2, 3, ….,N } ⎟⎞ ⎝ {k = 1, 2, 3, ….,NF } ⎠
(3)
vn (t ) Zn (t )
(4)
where in (t ) is the current drawn by the connected load at the node n in Ampere at time step t. The branch current between the two nodes (n − 1) and n is calculated using Kirchhoff’s current law as follows.
i (n − 1) n (t ) = i (n − 2)(n − 1) (t ) − i (n − 1) (t )
(5)
Meanwhile, the voltage is calculated by the following formula [18]:
v (n − 1) (t ) = vn (t ) + z (n − 1) n × i (n − 1) n (t )
(6)
To start load flow calculations, the voltage at the node n is assumed to be equal to the nominal voltage. Then, the voltage at the source node (v0 ) is calculated by initializing the calculations using the nominal value of voltage. Afterwards, correction factor (CF) is determined using Eq. (7) [18].
CF =
V0 v0
(7)
where V0 is the actual value of the voltage at the source node. The results of final voltages and final currents are determined along the feeder as follows [18].
Vx (t ) = CF × vx (t ) {x = 1, 2, 3, ….,n}
(8)
Ix (t ) = CF × i x (t ) {x = 1, 2, 3, ….,n}
(9)
where Vx (t ) and Ix (t ) are the voltage and current evaluated in load flow calculations using Eq. (1)–(9) at each node along the radial feeder for each time step t.
2. Modelling of electricity feeders, residential appliances and batteries Equations of load flow were presented in this section to accommodate diurnal load profiles of residential appliances and grid-scale batteries into a modified IEEE test system.
2.2. The grid under study A modified IEEE test system of 37 node was used in this paper to study the impact of charging residential ESBs. The grid was adapted from [19] considering different feeders as shown in Fig. 3. A number of distribution transformers were indicated in Fig. 3, serving a finite number of residential customers.
2.1. Electricity feeders Fig. 2 shows the representation of an individual feeder in radial systems, considering the impedance of loads as indicated in Eq. (1) [18].
vn2 (t ) Sn (t )
N
where PL (t ) is the aggregated power of customers at the distribution transformer in kW at time step t. NF is the number of radial feeders. N is the number of residential customers per feeder. pj (t ) is the power consumed by each customers in kW for a unity power factor at time step t.
Fig. 1. Electro-chemical batteries for grid-support applications in transmission and distribution power systems based on their capacity and discharging timescale (adapted from [4]).
Zn (t ) =
⎛
∑ ⎜∑ pj (t ) ⎟
2.3. Residential appliances (1)
Residential loads are modelled considering diurnal load profiles of consumer electronics, cooking appliances, lighting components, space/ water heating systems, wet appliances, and other miscellaneous. Smartplug and circuit-monitoring instrument recorded these data over 10min time steps [20]. Fig. 4 presents these diurnal profiles on a daily basis of 10-min time steps as reported by the source of data [20].
where Zn (t ) is the load impedance at the node n in ohm at time step t. vn (t ) is the voltage at the node n in Volt at time step t. Sn (t ) is the apparent power drawn by aggregated loads at the node n in kVA. Kirchhoff’s laws of voltage and current were used to evaluate load flows of the grid under study. The voltage is calculated at the node 381
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Fig. 2. Representation of an individual feeder in radial grids.
profiles (i.e. L) over a day by synthesizing L rows and 144 columns of “0” and “1” values using uniform probability distribution. The generated matrix of L × 144 elements is subjected to a number of mathematical operations as follows. Summation calculates the aggregated diurnal profile of all ESB charging cycles. The maximum value (i.e. Vm), the root-mean-square value (i.e. RV) and the average value (i.e. AV) are evaluated for the aggregated diurnal profile to verify the logical diversity of the synthesized ESB charging profiles considering sinusoidal characteristics. The state of charge (SOC) level for each ESB unit is calculated as follows.
2.4. Energy storage batteries ESB power profiles were generated to model their consumption for each time step. Loads can be modelled in distribution power systems as follows: constant power, constant current, constant impedance or combination of them [18]. The diurnal charging profiles of residential ESB loads are probabilistically generated as follows. The requested charging cycles of ESBs are generated using uniform probability distribution. The diurnal load profile for each individual ESB unit is synthesized by considering “0” for idle charging cycles, “1” for charging cycles, and “-1” for discharging cycles. A charger of 3 kW is used to re-charge 10 kWh capacity of stationary batteries over a minimum timescale of 10-min (i.e. the successive time slots of generated charging cycles). A number of residential ESB charging profiles were generated over a day. The generated profiles of these ESBs were shifted backward and forward to acquire a logical diversity across the generated individual profiles. It is assumed that the aggregated profiles of ESB charging and discharging cycles form a sinusoidal curve over a day considering off-peak and on-peak electricity price. Accordingly, the peak value of charging ESBs occurs during offpeak tariff term, whereas ESB users prefer discharging their ESBs during on-peak tariff interval to gain revenue. Fig. 5 demonstrates the algorithmic steps that were used to generate charging cycles individually. The algorithm starts with adjusting the number of ESB charging
Μ ⎛SOC + η × ∑i =1 Poi⎞⎟ 0 ⎠ × 100% SOC % = ⎝ SOCR ⎜
(10)
where SOC is the state of charge level of an ESB unit in percentage. SOC0 is the initial state of charge level of the ESB unit in kWh. SOCR is the rated state of charge level of the ESB unit in kWh. Μ is the number of ESB charging time intervals in hours. η is the efficiency of ESB charger. Po is the rated power of the ESB charger in kW. The depth of discharge (DOD) is calculated using the following equation.
Fig. 3. A modified IEEE test system of 37 node (adapted from [19]). 382
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Fig. 4. Diurnal load profiles of whole house considering individual appliances [20].
DOD % =
SOCR − SOCt × 100% SOCR
on ESB penetration in the electricity grid. The ESB units were evenly connected to the distribution transformers of the grid under study (see Fig. 3). The peak demand of charging ESB units occurs during the off-peak electricity interval (i.e. the time between 00:00 and 12:00 as shown in Fig. 6) to decrease the operational cost of charging power. However, the absolute peak value of discharging ESB takes place during the on-peak electricity term (i.e. the time between 12:00 and 00:00) to increase
(11)
where DOD is the depth of discharge level of the ESB unit in percentage. SOCt is the state of charge level of the ESB unit in kWh at time step t. Fig. 6 shows the aggregated power of charging residential ESB units based on the algorithmic steps proposed in this paper as shown in Fig. 5. Samples of 750 residential ESB charging profiles were generated over a day. The number of these samples was calibrated up/down based
Fig. 5. The algorithmic steps of generating ESB charging cycles individually. 383
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Fig. 6. Diurnal power of charging and discharging batteries based on the proposed algorithmic steps. Table 1 Key elements and variables of managing charging cycles of energy storage batteries (ESBs), as proposed in this paper. Location
Formulation
Schematic Figure
Description
System Coordinator Level
Constraints
Grid voltage and batteries’ state of charge (SOC) are the constraints of optimization
System Coordinator Level
Constants
Appliances’ power and electricity price are the constants of optimization
System Coordinator Level
Objective
Minimizing the operational cost of charging ESBs is the objective function of optimization
System Coordinator Level
Decision Variables
ESB charging cycles (i.e. “On” and “Off” operation of ESB) are the decision variables of optimization
The ESBs are prioritized in a descending pattern based on their SOC to switch “Off” high SOC batteries when the voltage exceeds its limit
Distributed Level of Managing ESB Charging Cycles
[21], were utilized in this paper. The pricing tariff consists of two level of electricity prices, which are off-peak and on-peak levels in $/kWh [21]. SOCf is the final SOC of aggregated ESB units over a day in kWh. In the meantime, inequality constraints are represented using Eq. (13) considering the operational voltage of residential grids.
revenue. Electricity tariff consists of two levels, which are off-peak and on-peak prices in $/kWh [21]. 3. Problem formulation The objective of this study is to reduce the operational cost of charging the grid-connected ESBs while maintaining grid voltage within its boundaries. This statement is formulated based on optimization methods using first principles as follows.
SOCmin ≤ SOCf ≤ SOCmax Vmin ≤ Vx ≤ Vmax
where SOCmin and SOCmax are the minimum and maximum limits of battery state of charge. The minimum limit was considered 26% of full SOC battery, whereas the maximum limit was adjusted to 86% of full SOC battery as the complete charge/discharge (i.e. full cycle equivalent) has an impact on the aging of battery cells [22]. Vmin and Vmax are the lower/upper limits of voltage magnitudes. According to IEEE standards [23], this voltage tolerance is between ± 5%. Table 1 shows constraints, decision variables and other aspects that
24
⎤ ⎡ Minimize OF = ⎢∑ PSIG × SOCf ⎥ t = 0 ⎦ ⎣
(13)
(12)
where OF is the objective function (i.e. minimizing the operational cost of charging ESBs over a day in $). PSIG is the price signal in $/kWh. The residential time-of-use tariffs, which were presented in the literature 384
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Fig. 7. A theoretical installation of the proposed management strategy in electricity grids.
Table 2 A comparative table of this study considering other studies in terms of objectives, constraints and algorithms of grid-integrated energy storage management. Studies
Objectives
Constraints
Algorithms
This study
Minimizing the operational cost of charging ESBs Maximizing economic revenue Minimizing CO2 emissions Minimizing peak demand Maximizing operational savings Minimizing transformer loading Minimizing power cost Minimizing battery life cycle cost Minimizing peak demand Minimizing energy consumption
Grid voltage and battery state of charge
Sequential quadratic programming
Energy storage capabilities
Linear programming
Power balance of batteries and grids
Quadratic programming
Power balance, battery state of charge, and battery life-cycle cost
Quadratic programming
Battery state of charge and battery depth of discharge Battery state of charge and grid power capacity
Heuristic forecasting-based programming Hyper-heuristic and evolutionary programming Fuzzy and particle swarm optimization (PSO)
[1] [12] [16]
[17] [26] [27]
Minimizing active power losses Mitigating voltage fluctuations
Battery state of charge, battery depth of discharge, and grid power flow limit
4. Installation of proposed management scheme
Table 3 The case studies of ESB penetration levels at the grid under study. Case studies
Maximum values of ESB loads (kW)
Maximum value of residential loads (kW)
Penetration (%)
Case1 Case2 Case3
750.00 1500.00 2250.00
3485.00 3485.00 3485.00
21.52 43.04 64.56
Fig. 7 explains a theoretical installation of the actual management strategy proposed in this paper, considering a radial feeder in electricity grids. The centralized coordinator requires communications between its location and ESBs to accomplish the task of managing their charging cycles. Meanwhile, the distributed operators need sensors to detect the SOC levels of ESBs. Smart meters provide a potential solution for these requirements, while implementing the proposed management scheme in electricity grids. The management strategy proposed in this paper improves a straightforward technique of ESB load shedding, as it detects which battery can be switched-off without affecting the use of batteries. In other words, the simple management method can lead to unsystematic ESB load shedding when grid voltage starts to drop below 95%, whereas the proposed algorithm detects relatively high SOC batteries to be switched-off. Moreover, the basic management scheme of ESB charging cycles increases the number of full cycle equivalents, shortening the lifetime of batteries. Simplified management techniques often interrupt ESB charging cycles when batteries reach 100% SOC, whilst the proposed strategy schedules ESB charging cycles considering the maximum SOC of 86% as shown in Eq. (13). Table 2 shows different studies as compared to this study in terms of objectives, constraints and algorithms that were used to manage the charging cycles of grid-connected ESBs.
were considered to solve the problem of managing ESB charging cycles in coordination and distribution levels. The proposed objective function can be solved using probabilistic method (e.g. genetic algorithm) or deterministic technique (e.g. sequential quadratic regulator) [24]. In this study, the deterministic programing method (i.e. sequential quadratic programming) was used to solve the problem with visual basic application, because unreliable results were observed while solving the problem using the probabilistic method. The optimal value of aggregated charging demand was used to shift individual ESB loads considering the state of charge. A sequential elimination detector prioritizes all ESBs based on their state of charge in a descending pattern. This detector compares the aggregated demand of ESBs with and without optimization. If the optimized demand is less than or equal the requested demand, all ESBs will be normally charged without interruption. Otherwise, charging cycles of high SOC batteries will be shifted to the next time slot (i.e. whenever the grid voltage exceeded its limit). Voltage correlation method can be used to detect the value of SOC for ESBs as illustrated in [25]. 385
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Fig. 8. Diurnal voltage profiles at the node 37 of the grid under study for basic case (i.e. residential load only) and the three case studies of ESB penetration levels.
Fig. 9. Diurnal voltage profiles at the node 37 of the test system using the management scheme proposed in this paper.
5. Simulation results
this paper. The upper curve of Fig. 8 shows the diurnal voltage profile at the node 37 of the grid under study (see Fig. 3), considering energy consumption by residential appliances only without the ESB demand. In addition, the diurnal voltage profiles of Case 1, 2 and 3 are demonstrated in Fig. 8. It can be noticed that, the operational voltages vary within the range of ± 5% tolerance of voltage for basic case (i.e. without ESB loads) and Case1. However, the voltage exceeds the lower limit (i.e. 95%) when additional ESBs are re-charged, as shown for Case2 and 3, because the users tend to re-charge their batteries during low-tariff interval of electricity, as shown in Fig. 8. To maintain the voltage profile within its limits considering different penetration levels of ESBs, the proposed management scheme is used to re-schedule their charging cycles sequentially. Fig. 9 illustrates
Three case studies were considered to determine the performance of the proposed management scheme. The case studies were evaluated using different penetration levels of ESBs at the grid under study. ESB penetration was defined based on the maximum value of the aggregated ESB loads and the maximum value of residential demand, as follows.
P% =
max × 100% Dmax
(14)
where P % is the penetration level of ESBs at the grid under study in percentage. max is the maximum value of the aggregated ESB loads in kW. Dmax is the maximum value of the aggregated residential demand. Table 3 shows the case studies and the penetration levels considered in 386
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Fig. 10. The aggregated values of ESB state of charge with and without the proposed optimization.
Fig. 11. Comparative cost reductions of charging ESBs with and withoout the proposed method.
of ESB penetration (see Table 3). Although the ESBs were re-charged during off-peak tariff interval, the proposed management scheme kept the voltage above 95% of its nominal value. Sequential quadratic programming was used to minimize the ESB operational cost (see Fig. 11) without exceeding voltage limit as shown in Fig. 9. The ESBs were prioritized based on their state of charge to schedule the charging cycles sequentially, as demonstrated in Table 1. The future work will aim to maximize the revenue of discharging ESBs while keeping the grid voltage below 105% of the nominal voltage, considering feed-in tariffs and batteries’ depth of discharge. Prosumers, who are able to produce and consume electricity, can use the proposed technique to accomplish a profitable energy management, taking into consideration voltage boundaries.
the diurnal voltage at the node 37 of the grid under study while charging the ESB using the proposed management scheme. It can be seen that the voltage drops below 95% for Case2 and for Case3 without using the optimization, as shown in Fig. 8. With the optimization, the diurnal voltage is kept within its limit (i.e. above 95%) for all case studies (see Fig. 9). Fig. 10 depicts the aggregated values of ESB state of charge over a day of 10-min resolution for all case studies with and without the proposed management scheme. In the meantime, the aggregated costs of charging ESBs were decreased as indicated in Fig. 11 (i.e. based on the tariff used), maintaining the grid voltage above the limit of 95%. 6. Conclusion and future work
Acknowledgement
A management scheme of charging cycles for grid-connected energy storage batteries (ESBs) was proposed to maintain voltage magnitude within its limit in radial systems. The problem of voltage sag was mitigated using the proposed method, while considering three case studies
The generous comments of the anonymous reviewers are greatly appreciated. 387
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Appendix A. Supplementary data
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