Keywords

1 Introduction

Fossil fuels are the main source of power generation throughout the world. However, they are the major reason for emission of greenhouse gases, causing global warming and associated natural calamities. Various technical, environmental, and economical effects of fossil fuels lead to the advancement in renewable energy (RE), which are clean, environmental friendly, and sustainable in nature. Since RE sources such as solar and wind are intermittent in nature, storage system along with power electronic converter becomes necessary to connect RE sources to power grid. Management of both loads and generating systems is considered to be a strategic approach for optimal operation of the grid [3]. Proper scheduling of grid connected PV system with BES can operate the grid optimally. The BES can act as both generator (in discharging mode) and load (in charging mode) [2].

In power system, load demand will not be constant all the time. Fluctuating loads lead to deviations in frequency. Energy storage system helps in maintaining the frequency. Unscheduled generation and withdrawal of electricity put the whole grid and many other electrical equipment to danger by creating large fluctuation in frequency. Unscheduled interchange (UI) is the mechanism developed to improve grid efficiency, grid discipline, accountability, and responsibility by imposing charges on those who defer from their scheduled generation or withdrawal. Unscheduled interchange cost (UI cost) is a frequency-dependent cost of electrical energy. With increase in frequency, UI cost reduces and vice versa [6].

In [10], optimal operating strategy is discussed for cost and emission minimization with generation and storage system. Two simple and straightforward methods to handle multiobjective optimization problems are the weighted sum and the \(\mu \)-constrained method, both applied in this paper. The weighted sum method provides sufficient conditions for Pareto optimally, but it is not always possible to compute the optimal solution (i.e., non-convex Pareto optimal set) [8]. Sousa et al. proposed a simulated annealing (SA) approach to address energy resources scheduling from the point of view of a virtual power player (VPP) operating in a smart grid [11].

A scheduling algorithm is proposed in [12] for minimizing the expected electric energy cost according to the price variation and the charging demand. It determines the amount of energy to purchase in each time slot, according to the price and the PEV charging demands. The dispatch algorithm determines the time slots where each PEV will be charged. Microgrid intelligent online energy management under cost and emission minimization has been investigated by Chaouachi et al. in [4].

A trading mechanism was introduced in which smart retail consumers submit short-term demand response offers to a retailer. This demand response helps to increase or decrease retailer’s energy consumption, through load management with self-production of renewable energy, for every time period, at favorable prices [5]. Demand-side management assistance can enhance microgrid planning and operation. Residential microgrid load management is one way to optimally operate microgrid. Bhamidi and Sivasubramani investigated the impact of demand-side management on distribution system [1].

The problem formulation includes optimal battery scheduling, taking into account the uncertainty of the microgrid exogenous variables and forecasted entities. An artificial neural network ensemble is developed to predict 24 h ahead photovoltaic generation and 1 h ahead wind power generation and load demand.

This paper deals with the optimal scheduling of grid connected PV system with BES, to reduce the cost of total power generation and amount of power imported from upstream grid. Here, a modified algorithm for scheduling of grid connected PV system with BES is developed. MATLAB simulation tool MATPOWER is used for optimal power flow (OPF) calculation.

Rest of the paper is organized as follows. Section 2 discusses the modified algorithm developed for scheduling of grid connected PV system with BES. Section 3 gives a brief description of the system used to test the proposed algorithm. Section 4 deals with results of scheduling of grid connected PV system with BES. Section 5 concludes the paper.

2 Methodology

A modified algorithm is formulated for optimal scheduling of grid connected PV system with BES. The algorithm is tested by generating various scenarios, viz. (i) case 1: grid without PV system and BES, (ii) case 2: grid with BES, and (iii) case 3: grid with PV system and BES. To solve the minimization problem subject to the desired constraints, MATPOWER, a MATLAB simulation tool is used.

2.1 Modified Algorithm for Optimal Scheduling of Grid Connected PV System with BES

A detailed algorithm for scheduling of grid connected PV system with BES is developed (Figs. 1 and 2). Main aim of this algorithm is scheduling of grid connected PV system with BES to minimize the cost of total power generation and amount of power imported from upstream grid. In the algorithm, UI cost is also considered.

Fig. 1
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Algorithm for scheduling of grid connected PV system with BES

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Fig. 2
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Algorithm for scheduling of grid connected PV system with BES (continuation of Fig. 1)

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In this algorithm, the following assumptions are considered. (i) Energy storage systems such as battery are charged from PV panel during the daytime, (ii) only stored energy in the energy storage system is discharged during peak hours, (iii) RE cost is constant, and (iv) power from solar energy is constant for an hour. 24 h scheduling period is divided into 24 time slots of one hour each. Power from PV panel at time t (\(P_{(\text {pv},t)}\)), power generated from main grid (\(P_{(\text {grid},t)}\)), and grid load (\(L_{(\text {grid},t)})\) are obtained from day ahead scheduling. (\(\text {soc}_{t}\)) is SOC level of battery at instant t. Cost of energy from PV system (\( C_{(\text {pv})}\)), cost of energy from battery storage system (\(C_{(\text {batt},t)}\)), and threshold UI cost \((\text {UI}_{\text {Th}})\) are considered constant and are given in $/MWh. Threshold UI cost \((\text {UI}_{\text {Th}})\) is the UI cost at nominal frequency.

According to the availability of PV power, time slots are categorized into two (i) time slot 1 (1–9 and 18–24 h) and (ii) time slot 2 (10–17 h). For the time slot 1, if UI cost \(C_{\text {UI}} < \text {UI}_{\text {Th}}\), battery will be charged from the grid (Fig. 2). If UI cost \(C_{\text {UI}} > \text {UI}_{\text {Th}}\), the battery will be discharged. In daytime (10–17 h), energy storage systems are charged from the PV panel, 20% of load is injected into grid by PV panel, and remaining power is used to charge the battery.

2.2 Determination of UI Cost

The perfect balance of scheduled generation and scheduled load results in nominal frequency. Any deviations from schedule will result in deviation from nominal frequency. Unscheduled interchange cost (UI cost) is a frequency-dependent cost. Let \(f_{\text {nom}}\) be the nominal frequency, f be the current frequency, and \(f_{\text {max}}\) be the maximum frequency, where \(\text {UI}_{\text {Th}}\) cost of electricity at nominal frequency.

$$\begin{aligned} \text {UI cost} = \text {UI}_{\text {Th}}\times \frac{f_{\text {max}}-f}{f_{\text {max}}-f_{ {\text {nom}}}} \end{aligned}$$
(1)

Equation 1 shows that UI cost is higher for frequencies below nominal value (i.e., when load is greater than generation) and lower for frequencies above nominal value (i.e., when generation is greater than load).

2.3 Optimal Power Flow Using MATPOWER

MATPOWER is a package of MATLAB M files for solving power flow and optimal power flow problems [13]. The standard version of each takes the following form:

$$\begin{aligned} \min _{x} z(x) \end{aligned}$$
(2)

subjected to

$$\begin{aligned} g(x)=0 \quad \quad \quad \quad h(x) \le 0 \quad \quad \quad \quad x_{\min } \le x \le x_{\max } \end{aligned}$$
(3)

The objective function z(x) consists of the polynomial cost of generator injections, the equality constraints g(x) are the power balance equations, the inequality constraints h(x) are the branch flow limits, and the \(x_{\min }\) and \(x_{\max }\) bounds include reference bus angles, voltage magnitudes (for AC), and generator real and reactive power injections.

$$\begin{aligned} z\left( P_{\text {g}}, Q_{\text {g}}\right) =\sum _{i=1}^{n_{\text {q}}} z_{\text {P}}^{i}\left( p_{\text {g}}^{i}\right) +z_{\text {Q}}^{i}\left( q_{\text {g}}^{i}\right) \end{aligned}$$
(4)
$$\begin{aligned} g_{\text {P}}\left( \theta , V_{\text {m}}, P_{\text {g}}\right) =P_{\text {ba}}\left( \theta , V_{\text {m}}\right) +P_{\text {d}}-C_{\text {g}} P_{\text {g}}=0 \end{aligned}$$
(5)
$$\begin{aligned} g_{\text {Q}}\left( \theta , V_{\text {m}}, Q_{\text {g}}\right) =Q_{\text {ba}}\left( \theta , V_{\text {m}}\right) +Q_{\text {d}}-C_{\text {g}} Q_{\text {g}}=0 \end{aligned}$$
(6)
$$\begin{aligned} \theta _{i}^{\text{ ret }} \le \theta _{i} \le \theta _{i}^{\text{ ret }}, \quad t \in \mathcal {I}_{\text{ ref }} \end{aligned}$$
(7)
$$\begin{aligned} V_{\text {m}}^{{i,\max }} \le V_{\text {m}} \le V_{\text {m}}^{{i,\max }}, \quad i=1 \ldots n_{\text {b}} \end{aligned}$$
(8)
$$\begin{aligned} P_{\text {g}}^{{i,\max }} \le P_{\text {g}} \le P_{\text {g}}^{{i,\max }}, \quad i=1 \ldots n_{\text {g}} \end{aligned}$$
(9)
$$\begin{aligned} Q_{\text {g}}^{{i,\max }} \le Q_{\text {g}} \le Q_{\text {g}}^{{i,\max }}, \quad i=1 \ldots n_{\text {g}} \end{aligned}$$
(10)

3 System Description

Test system consists of IEEE 14 bus system as upstream grid. Seventh bus is considered as a distribution substation where PV system with BES is connected. PV system with BES can act as generator (in discharging mode) and load (in charging mode).

IEEE 14 bus system comprised of five generators of total capacity 490 MW, total scheduled generation 266 MW, and total scheduled load of 259 MW. Table 1 shows the generator data and load data of test system. For generating the scheduled power of 266 MW, generators at buses 1, 2, and 3 are made ON, and the other two generators are made OFF.

Table 1 Generator and load data of IEEE 14 bus system
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3.1 PV System with Battery Energy Storage

PV system with BES comprised of PV panel of 98 MW (20% of total generation capacity of upstream grid) capacity and BES system of 300 MWh capacity. Battery size is selected such that it can fulfill the excess load demand during evening hours. PV panel capacity is selected such that it can meet 20% of load demand during daytime along with battery charging. A 35 MVA inverter is used to convert PV panel DC power to AC, and it is also used for reactive power support. Equation 11 shows the maximum energy capacity of BES (\(E_{\text {B}}\)) to fulfill the excess load demand at night peak hours (6–11 p.m.). Equation 12 shows the maximum PV panel capacity (\(P_{\text {PV}}\)) to meet the 20% load demand during daytime along with battery charging, where DoD is the depth of discharge and \(\eta _{\text {ch}}\) and \(\eta _{\text {disch}}\) are battery efficiency during charging and discharging mode, respectively.

$$\begin{aligned} E_{\text {B}}=\frac{\text {Extra energy consumption at night peak hours}}{\text {DoD} \times \eta _{\text {ch}} \times \eta _{\text {disch }}} \times 1.2 \end{aligned}$$
(11)
$$\begin{aligned} P_{\text {PV}}=20\% \ (\text {Total generation capacity of upstream grid}) \end{aligned}$$
(12)

Solar Irradiance The hourly solar irradiance in kWh/\(\text {m}^{2}\)/day for the PV system is obtained from [9]. The highest average solar irradiance of 6.04 kWh/\(\text {m}^{2}\)/day is in the month of February, whereas the lowest average solar irradiance of 3.44 kWh/\(\text {m}^{2}\)/day is in the month of July.

BES System and Inverter PV system with BES consists of 30 MW/300 MWh battery with 98 MW PV plant. It is a 10 h battery storage system which delivers maximum 30 MW at an instant. 35 MVA inverter is used to convert DC power to AC power. Here battery cost is considered as 60 $/MWh. Table 2 shows the specification of battery and inverter.

Table 2 Specification of battery and inverter
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3.2 Power Generated by PV Panel

Power generated by PV panel (\(P_{\text {PV}}(t)\)) is calculated by Eq. 13 [7].

$$\begin{aligned} P_{\text {PV}}(t) = N_{\text {PV}} * V_{\text {oc}}(t) * I_{\text {SC}}(t) * {\text {FF}} \end{aligned}$$
(13)

where \(N_{\text {PV}}\) represents number of PV panel, \(V_{\text {oc}}(t)\) is the open circuit voltage of PV panel, and \(I_{\text {sc}}(t)\) is the short circuit current of PV panel.

$$\begin{aligned} V_{\text {oc}}(t)=V_{\text {OCS}}-\tau \left( T_{\text {PV}}(t)-25^{\circ }\right) \end{aligned}$$
(14)
$$\begin{aligned} I_{\text {sc}}(t)=\left[ I_{\text {SCS}}+\varepsilon \left( T_{\text {PV}}(t)-25^{\circ }\right) \right] * \frac{Q_{\text {PV}}(t)}{1000} \end{aligned}$$
(15)
$$\begin{aligned} T_{\text {PV}}(t)=T_{\text {amp}}(t)+\frac{T_{\text {PVmn}}(t)-20}{800} * Q_{\text {PV}}(t) \end{aligned}$$
(16)

where \(V_{\text {OCS}}\) and \(I_{\text {SCS}}\) stand for open circuit voltage and short circuit current under standard test condition, respectively, \(\tau \) is the open circuit voltage temperature coefficient, \(\varepsilon \) is the short circuit current temperature coefficient, \({Q_{\text {PV}}(t)}\) represents solar irradiance \((\text {W}/\text {m}^{2})\) incident on PV panels, \(T_{\text {PV}}(t)\) is solar cell operational temperature, and \(T_{\text {PVnm}}(t)\) is the nominal temperature of solar cell in \(^\circ {\text {C}}\), respectively, and \(T_{\text {amb}}(t)\) is an ambient temperature (\(^\circ {\text {C}}\)). Fill factor (FF) of PV panel is computed using Eq. 17. Specification of PV panel is provided in Table 3

$$\begin{aligned} \text {FF} = \frac{V_{\text {MPP}} * I_{\text {MPP}}}{V_{\text {OC}} * I_{\text {SC}}} \end{aligned}$$
(17)
Table 3 Specifications of PV panel
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3.3 Frequency Calculation

Load variation in a power system leads to frequency variation. Frequency of IEEE 14 bus system is calculated using the following equations.

$$\begin{aligned} {\Delta } {f}=\frac{-{\Delta } P}{D1+D2+D3+1/ R_{1}+1/ R_{2}+1/ R_{3}} \end{aligned}$$
(18)
$$\begin{aligned} f_{\text {new}}=f+{\Delta } {f} \end{aligned}$$
(19)

where \({\Delta } P\) change in load in p.u., \({\Delta } {f}\) is the change in frequency due to load change, R is the droop, and D represents the frequency dependency of load. For case 1 (grid without PV system and BES)

$$\begin{aligned} {\Delta } {P}=(L_{\text {gridnew}} +\text {loss}_{\text {new}})-L_{\text {sche}}+\text {Loss}_{\text {sche}} \end{aligned}$$
(20)

where \(L_{\text {gridnew}}\) represents grid load demand at the instant of frequency change and \(L_{\text {sche}}\) is the scheduled load demand. Losses are also varying with variation of load. \(\text {Loss}_{\text {sche}}\) and \(\text {Loss}_{\text {new}}\) are loss for load \(L_{\text {sche}}\) and \(L_{\text {gridnew}}\), respectively.

$$\begin{aligned} L_{\text {gridnew}}=L_{\text {grid}} \pm P_{\text {BES}} \end{aligned}$$
(21)
$$\begin{aligned} L_{\text {gridnew}} =L_{\text {grid}}\pm P_{\text {BES}}-P_{\text {PV}} \end{aligned}$$
(22)

For case 2 (grid with BES), \(L_{\text {gridnew}}\) is the sum of grid load demand (\(L_{\text {grid}}\)) and charging (+) or discharging (−) power of energy storage system (\(P_{\text {BES}}\)) as shown in Eq. 21. For case 3 (grid with PV system and BES), \(L_{\text {gridnew}}\) is the grid load demand (\(L_{\text {grid}}\)), charging (\(+\)) or discharging (−) power of energy storage system (\(P_{\text {BES}}\)), and power from PV panel (\(P_{\text {PV}}\)) as shown in Eq. 22.

4 Results and Discussion

IEEE 14 bus system is chosen as main grid with PV system and BES integrated at bus number 7. Parameters of system described are shown in Table 4. Optimal scheduling of grid with PV system and battery energy storage is done using MATPOWER. The following three different cases were considered for testing the proposed algorithm. (i) Case 1: Grid without PV system and BES, (ii) case 2: Grid with BES, and (iii) case 3: Grid with PV system and BES OPF results for scheduled generation and scheduled load are shown in Table 5.

Table 4 System parameter
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Table 5 OPF results for scheduled load and generation
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Table 6 Hourly load demand, power generation, cost of generation, and power loss
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As shown in Table 6, grid load demand varies every hour. During charging, BES also acts as load. During daytime (time slot 2), battery is charged from PV system. In both cases 2 and 3, the battery energy storage is used to regulate the frequency at peak and off-peak hours.

Amount of power taken from upstream grid is reduced when PV panel is connected into the grid. Upstream grid power generation for each time is given in Table 6. PV panel generates power during time slot 2 (Fig. 3a). PV power is used to supply 20% load demand of upstream grid and charge the battery.

Fig. 3
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Power output of PV and energy stored in BES

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Energy level of BES is shown in Fig. 3b. During daytime, battery is charged to its maximum capacity using PV panel power or from grid. For grid with BES, during evening peak hours, generation is limited to scheduled generation, battery is discharged for extra power needed, and thus frequency is regulated. During evening or night off-peak hours, the BES is charged from the grid. This stored energy is discharged during morning peak hours. For the three test cases, cost of power generated is shown in Table 6.

Frequencies of the system for the three cases are shown in Fig. 4a. For case 1, frequency deviation from its nominal value is high. For case 2, frequency <50 Hz during daytime because battery is charging from the grid. During evening peak hours, battery discharges, and during evening off-peak hours, battery charges to maintain the frequency at 50 Hz. For case 3, daytime frequency is greater than 50 Hz because PV is also generating. Frequency deviation (\({\Delta }f\)) for three cases is shown in Fig. 4. Positive value \({\Delta }f\) implies frequency greater than 50 Hz, and negative value \({\Delta }f\) implies frequency less than 50 Hz. In the case of grid with storage system, during some time slots, frequency deviation is negative because actual load is greater than scheduled load, and frequency is less than 50 Hz. In the case of grid with both PV and storage system, frequency deviation is positive because actual load is less than scheduled load and frequency is greater than 50 Hz (Eqs. 18–20).

Figure 5a shows the UI cost for the three test cases. UI cost at 50 Hz (\(\text {UI}_{\text {Th}}\)) is 63.91 \(\$\)/MWh. Battery charges from grid when UI cost \(<\text {UI}_{\text {Th}}\) and discharges when UI cost is high. As shown in Fig. 5a, during time slot 2, \(f>50\) Hz. In this scenario, grid can sell power to other neighboring power systems to balance the system and gain profit.

Table 6 shows the power loss in each hour for the three cases. For case 2, power loss is increased by 5% than case 1 because of battery charging during off-peak hours. For case 3, power loss is reduced by 20.95% than case 1 because (i) 20\(\%\) grid load is supplied by PV panel during daytime and (ii) discharging of BES at bus 7. Both of these reduce the power loss by reducing the distribution loss.

Figure 5b shows the minimum bus voltage of IEEE 14 bus system for three cases. Voltage of the system drops below 1 p.u. when grid load is greater than the scheduled load and rises above 1 p.u. when grid load is less than scheduled load. For case 2, charging and discharging of BES maintain the voltage magnitude. For case 3, increase in voltage is due to the PV source at bus 7.

Fig. 4
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System frequency and frequency deviation

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Fig. 5
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UI cost and minimum voltages of IEEE 14 bus system

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5 Conclusions

In this paper, a modified algorithm is formulated for scheduling of grid connected PV system with BES taking UI cost into consideration. Optimal power flow is performed for upstream grid, grid with BES, and for grid connected PV system with BES for various load and generation patterns. BES system was able to regulate the frequency with proper selection of charging and discharging mode based on UI cost. Using the proposed algorithm, it is proved using IEEE 14 bus system that grid connected PV with BES can optimally operate the grid when compared to grid with BES alone. Frequency regulation, reduction in power loss, and improvement of voltage profile are other benefits to grid by the introducing PV system with BES.