Power system operation considering detailed modelling of energy storage systems

The power system operation considering energy storage systems (ESS) and renewable power represents a challenge. In a 24-hour economic dispatch, the generation resources are dispatched to meet demand requirements considering network restrictions. The uncertainty and unpredictability associated with renewable resources and storage systems represents challenges for power system operation due to operational and economical restrictions. This paper developed a detailed formulation to model energy storage systems (ESS) and renewable sources for power system operation in a DCOPF approach considering a 24-hour period. The model is formulated and evaluated with two different power systems (i.e. 5-bus and IEEE modified 24-bus systems). Wind availability patterns and scenarios are used to assess the ESS performance under different operational circumstances. With regard to the systems proposed, there are scenarios in order to evaluate ESS performance. In one of them, the increase in capacity did not represent significant savings or performance for the system, while in the other it was quite the opposite especially during peak load periods.

INTRODUCTION Nowadays, the generation portfolio of electricity in power systems is more diversified than some years ago by the integration of renewable resources [1]. Environmental concerns are pushing the integration of technologies to produce electricity with renewable resources [2]. As a result, there is an increasing to spur investments in order to diminish the conventional fossil fuel-based power generation [3][4][5]. Consequently, the international energy agency (IEA) reports that renewable energy sources have increased at an average annual rate of 2.0 % from 1990 [6]. Growth is largely due to solar PV (37.4 %) and wind power (23.4 %) [6].
The inherent features of this type of resources as uncertainty and variability impact power system operation [7][8][9][10]. In this context, power systems require strategies to integrate such intermittent resources with flexibility to meet the demand requirements [11]. The energy storage systems (ESS) represent a technology to store renewable energy according to their availability during the day (i.e., there are high quantities of electricity from PV systems at noon). The ESS can absorb energy when generation exceeds the load especially when this surplus come from renewable sources and supply this energy to the grid during load peak hours [12,13]. Thus, the ESS provides flexibility under the integration of renewable resources given that the power dispatch can be settled to a desirable supply profile [14,15]. The integration of energy storage systems (ESS) represent a challenge for the operation of power systems from different perspectives. The quality and reliability can be compromised due to misuse, misplacing or bad sizing of ESS [16]. Nonetheless, other challenges for power system operation are recognized, such as performance and safety (viewed from its constituent materials, interconnections [17,18], and service life), the distributed generation impacts in the power system coherency [19], the regulatory environment, the investment costs, and the industry acceptance [20]. These issues can occur because system operation involves decisions in different time frames (since minutes to days) including weather-dependent renewable units scheduling and their reserves [21] (e.g. wind [22]) as well as considering other related variables. However, the ESS mathematical modeling and its integration to power systems is a challenge with great impact and importance.
The optimal power flow (OPF) is used widely by power systems operators to dispatch economically the generation resources according to operational and economical restrictions [23]. From this perspective, the power system operation requires a detailed modeling of storage systems in order to be included in the OPF mathematical formulation. There are several reasons for including these energy storage models in the economic dispatch. One of them is the more efficient integration of renewable energy sources, since these devices contribute to diminish the effects of the stochastic nature of these sources [24]. Also, the ESS contribute to maintain the stability in the power system operation, due to they restrict the fluctuation of instantaneous power coming mostly from renewable sources [25,26]. Likewise, they allow a more efficient economic dispatch since these devices provide flexibility that reduces the amount of power coming from more expensive sources (i.e., they deliver when there is a lack of energy, and store when there is a surplus), being cheaper and with less waste [27].
However, the integration of ESS's into an OPF model introduces inter alia, time interdependence. That is to say the ESS can charge in periods of high wind or low demand (i.e. is absorbing power from the grid), and discharge in periods of low wind availability or load peak (i.e is injecting power to the grid). This choice depends on the charge status (i.e. SoC) at the previous time interval and their respective efficiency. Also, technical and economical conditions are required to avoid unexpected situations as charging and discharging simultaneously. In other words, this situation implies that ESS would be paid for charging and discharging at once [11]. Among others, the dual feature of absorbing and generating power requires a precise modelling for power system operation.
This paper proposes a detailed formulation to include ESS in the optimal power flow with multiple generation sources to provide a 24-hour dispatching to meet demand requirements. Since energy storage systems could be defined as a generator and load due to the dual feature and also are time-correlated as mentioned above. The proposed formulation determines the optimal outputs for all generation portfolio as well as ESS charging/discharging schedules seen through its SoC, all of them under different operation conditions and scenarios.
The paper is organized as follows. The problem description and formulation are presented in Section 2. In Section 3, the 5-bus and IEEE 24-bus modified systems and their parameters are described. Then, the proposed procedure is tested using the systems described above. At the end of this section, the results are analyzed and discussed. Section 4 provides some concluding remarks about this topic.
-Literature review The optimal power flow for dispatching generation resources including renewable sources has been widely discussed. The DC multi-period optimal power flow (DCOPF) formulation have been extended to include the variable nature of renewable power generation, elements such as uncertainty in electricity demand and wind availability [28][29][30][31]. Also, in some works other features such as branches and generation constraints are explicitly included in the formulation such as presented in [32][33][34]. Other authors have made comparisons and analysis between this approach and conventional methods without these variables [35]. On the other hand, some works employs heuristic approaches including deterministic and stochastic methods (e.g Montecarlo simulation) to solve the optimal dispatching [36][37][38][39][40][41].
Several studies [42][43][44][45] have researched the integration of intermittent wind power using a probabilistic approach. In order to provide better tools for the construction of generation scenarios and stochastic dispatch models [46][47][48]. Consequently, optimal power flow has also been used with ESS in order to assess the power system operation flexibility [49], due to these units can absorb energy in case of excessive generation or low electricity prices, mitigating the uncertainty in the renewable sources. Also in this research topic, studies such [50,51] have found other issues such as inclusion of ESS in distributed generation (DG) and RES with their respective modelling and sizing.

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ISSN: 2088-8708 Other studies [11,[52][53][54] propose approaches in the economic dispatch using multi-period OPF due to specific challenges to the traditional OPF such as the modeling of charge/discharge of ESS, or a specific ESS technology featuring [55]. Other studies have included more variables in order to bring the problem closer to a more precise context such as [56,57] using power losses constraints on the transmission branches to evaluate different generation scenarios. On the other hand, in [58] adds an environmental approach, modeling the social cost using variables such as emission generation in order to optimize the total production costs, using as little as possible the thermal generation, without neglecting the reliability in the system, all of this cases working under a DC approach.

2.
DC-BASED OPTIMAL POWER FLOW WITH ESS This section includes the notation and the mathematical formulation for the multiperiod DCOPF dispatching model including the ESS modeling. This model also includes thermal and wind power generation.
Voltage angle of the i-bus at time t (rad).
Energy stored in the i-bus at time t (MWh).
Power Charged/discharged to/from ESS connected to the i-bus at time t (MW).

Formulation
The formulation is expressed as optimization problem to address a minimum total operating cost associated with producing electricity to meet the demand for a 24-hour period described by (1). In (2) indicates the total cost of energy production with g thermal units during an interval of time T . In (3) refers to the production costs associated with not taking full advantage of the source of wind generation available during this same interval of time. In (4) represents a condition that requires that the ESS are not charged and discharged simultaneously, this prevents the payment of an ESS for charging and discharging simultaneously [11,29,59], situation that cannot occur.

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ISSN: 2088-8708 Ì 185 The restrictions for the dispatching model are given by the power flow equations. This paper uses the DC approach to include power flow calculations. The power flow balance is given by (5). The power flowing on each line is given by (6). The power flow restrictions are given by the boundaries in the (7).
The dual variable associated to (5) correspond to the locational marginal price (LMP) of each bus hourly. On the other hand, the restrictions for thermal generation units are defined in (8), (9), and (10), where (8) corresponds to the operational range of thermal generators. On the other hand, (9) and (10) indicates the maximum up and down ramps limits that each of the thermal generators can perform from one hour to the next.
P Gen The energy level (i.e. State of charge) of ESS were defined per unit in the i-bus at time interval t, depends on the difference between the ESS charged and discharged power with their respective operating efficiencies, as defined in (11). The maximum and minimum limits of ESS charge/discharge, and ESS Capacity were defined in (12), (13) and (14) respectively.
The restrictions for wind generation (i.e. wind power loss) are defined in (15). The expression corresponds to the reduction of use of potentially available wind energy. In (16) describes the minimum and maximum power range that a wind generator can produce, considering placing and wind availability.

RESULT AND DISCUSSION
In order to test this approach to study a wide range of applications, initially, a small case and then a modified IEEE standard case are used to illustrate the ESS modelling in a multi-period dispatching and show their performance according to different operational situations. This section provides a comprehensive explanation of each case and the corresponding analysis to observe ESS performance during a 24-hour period.
All simulations were completed by a computer (PC) running Windows R with an Intel R Core I5+ 8300H processor @2.3 GHz with 12.00 GB RAM, using Gurobi R Solver (8.1.1) [60] under the JuMP 0.20.1 Julia platform [61].

Load curve description
The daily load curves used for the 5-bus (orange) and 24-bus (blue) power systems are plotted in Figure 1. The load curves present four (4) decreasing trend bands with its lowest point at hour 4 (i.e. 787.1 MW and 1950.6 MW respectively), and three (3) increasing trend bands with a load peak at hour 20 (i.e. 1150 MW and 2850 MW respectively).

Wind availability profiles
Three (3) wind profiles are constructed to evaluate the ESS performance during the operation of both power systems considering wind power availability (i.e. low, moderate, and high) as shown in Figure 2. The simulation results of both power systems, such as the the thermal generators scheduling and the ESS performance as well as their respective analysis can be found in the following subsections.

. Case description
The one-line diagram for a 5-Bus system is shown in Figure 3. This system includes thermal generation, wind generation and storage. The thermal unit parameters are listed in Table 1, modifying the information from [49]. The load is distributed in 4 buses.  0  140  17  20  20  2  1  0  170  18  25  25  3  3  0  360  20  30  30  4  5  0  490  21  35  35   Table 2 lists the network grid information such as reactance and rating in MVA (i.e power line constraints), all of them modified from [49]. The 5-bus test system includes a wind power plant connected to the bus 4. The wind power generation site and capacity is listed in Table 3. Also, this system includes an ESS connected in the bus 2. In other words, the ESS is not on the same bus as the wind power plant. The ESS parameters considered are ESS capacity, charging and discharging efficiency, and operating values. Such features are listed in Table 4.

Results
The simulations use the 5-bus power system with the parameters given before (i.e. load curve and wind profiles) to explore and evaluate different operational situations. Initially, the performance of the power system was evaluated according to gradual increases of the ESS capacity, starting from its base capacity (i.e. 25 MW steps, starting at 50 MW up to 200 MW). The analysis highlights changes in the thermal generation scheduling and ESS performance during the 24-hour period.
The ESS performance (i.e State of Charge (SoC)) during a 24-hour period is shown in Figure 4. Likewise, the ESS charging intervals occurs at hours 3 to 7, 16 to 18, and 23 to 24. A one ESS discharging interval occurs in the load peak value (hours 19 to 21). The ESS is charged in valley hours (low demand) and discharged at load peak hours (i.e. time shifting effect and transmission curtailment reduction) as expected. On the other hand, the ESS performance shows a gap when its capacity reaches 150 MWh and the wind availability improves (i.e. moderate and high availability). This finding is presented in hours where there is no charging or discharging behavior (i.e. hours 5 to 16). The description of the ESS performance leads to the analysis that the of ESS installed capacity could be oversized due to wind availability. This could happen in low-wind availability due to wind turbines and On the other hand, the different thermal generation schedules according to the ESS capacity increases during a 24-hour period are shown in Figure 5. Similar performances to the proposed demand curve are presented especially in the low-availability wind pattern. Nonetheless, such performances moved away as wind availability increases (i.e. moderate and high availability patterns) as in the case of ESS performance. Furthermore, it can be appreciated differences in thermal scheduling between ESS capacities on valley hours (i.e hours 2 to 6, and hours 17 and 18) of the load curve for all wind patterns. Also, another difference between scheduling is presented at the peak of the load curve (i.e hours 20 and 21). with a strong dependence on thermal units and low wind power participation. this factor explains the closeness between thermal scheduling and the load curve specially under low wind availability patterns and how similar behaviour is maintained regardless of wind availability. In the same way, the thermal unit scheduling between the highest proposed ESS capacities (e.g. 175 and 200 MW) are similar. This finding proved the misuse of ESS from a certain capacity and wind availability as mentioned above. Likewise, this issue represents a non-improvement of the power system performance as well as a negligible reduction of thermal generation compared with increases in the ESS capacity. Moreover, The ESS performance seen from its SoC during a 24-hour period is shown in Figure 6. Unlike the previous scenario, It shows no differences for some of the proposed availability patterns. Since in low availability pattern, the ESS presents the same behavior regardless of the increase in marginal cost (i.e from 1.0 to 2.0 times). In all cases, charging and discharging patterns are presented depending on the respective wind pattern behavior. However, there is a consistent unloading pattern during peak hours (i.e. from hours 19 to 21). This represents the correct ESS modeling and operation since it delivered power during the load peak as expected. Also, the ESS performance shows a direct influence by wind availability due to the fact that the ESS In other matters, the thermal units dispatch according to wind availability and compared to the load curve is shown in Figure 7. It shows similar behaviors between the thermal scheduling and the load curve for all wind availability profiles, in some cases (i.e. hours 1 to 7 in low-wind availability) the load curve and the thermal units dispatch have matched. Thus, the thermal unit dispatch also shows few changes by increasing the marginal cost to the proposed value. These changes were presented when load falls (i.e. hours 3 to 7 and hours 19 to 24) and exist high wind availability, as shown in c). For all other wind availability patterns, the same thermal units power dispatch was presented. Furthermore, the the wind availability effect on the power system is evident since the difference between load and thermal units power is greater (i.e. differences between low, moderate and high wind availability Ì ISSN: 2088-8708 for all marginal cost increases). In other words, since the generation portfolio of this power system is mostly thermal the dispatched amounts were similar due to the non-existence of meaningful alternative resources to meet demand. Nevertheless, the wind power and ESS would represent a feasible option for mitigating the increased costs of producing with thermal units as proposed.

ESS performance in the IEEE 24-Bus System 3.4.1. Case description
The one-line diagram for a modified IEEE 24-bus power system is shown in Figure 8. As above, this system includes thermal generation, wind generation and storage. The thermal unit features are listed in Table 5, modifying the information from [49]. The load is distributed in 16 buses.   Table 6 lists the network grid information such as reactance, power line constraints and interconnections, all of them directly from [49].

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ISSN: 2088-8708 Ì 193  Table 7. Likewise, the system includes two ESS connected to buses 19 and 21 respectively (i.e. the ESS are in buses where wind power plants are located, unlike the case above), where their features (i.e. charging/discharging efficiency, capacity, among others) are listed in Table 8.

Results
The simulations use the 24-bus power system with the parameters (load curve and wind profiles) given above. The analysis highlights changes in thermal units scheduling and ESS performance during the 24-hour period as above.
The ESS performance during a 24-hour period is shown in Figure 9. It shows different performances for all wind patterns tested. In other words, the initial charging behavior for each wind availability pattern occur at different times (i.e. hours 4 to 7 in low availability, hours 1 to 8 in moderate availability, and hours 6 to 8 in high availability). However, the discharging behavior that occurs at the peak area of the purposed load curve (hours 18 to 21) remains the same. Likewise, the increase in the capacity of the ESS has no effect on the general ESS performance. Moreover, the proper performance of the mathematical modeling of the ESS also was verified.
Likewise, the ESS capacity installed in this power system presents an adequate capacity unlike the 5-bus case. This is due to the fact that regardless of the purposed wind availability profile, the ESS provides energy at the time when the load peak occurs (i.e. an average of 150 MW of the 2850 MW of load). Another fact to support that statement is the ESS capacity presented in each increment and wind availability pattern is totally used (minimum and maximum allowed ESS capacities) avoiding misusing. In fact, this result motivates to increase the ESS base capacity to achieve lower total operating costs. On the other hand, the different thermal generation units schedules according to ESS capacity increases during the 24-hour period for this system are shown in the Figure 10. Similar performances to the proposed load curve are presented especially in the low-availability wind pattern (except for hours 5 to 7, due to excess electrical energy of this technology subsequently stored in the ESS). Also it can be appreciated differences in thermal scheduling between ESS capacities on valley hours (i.e hours 2 to 6, and hours 17 and 18) of the load curve for all wind patterns. Likewise, another difference between scheduling is presented at the peak of the load curve (i.e hours 20 and 21).
Additionally, the thermal units dispatching under different wind availability patterns shows that wind availability strongly determines the thermal units dispatch. As well as the 5-bus system, this system presents a portfolio with a predominance of electricity produced by thermal units and lower wind power participation. This situation is highlighted in the system especially in the low wind availability, because the thermal units must produce above the load to satisfy the programming of the whole 24-hour period (i.e. hours 5 to 7). Fortunately, since the power system has ESS with adequate capacity, it can store this amount of excess energy to deliver when required. Like the previous case, the power system performance also was evaluated under the effect of gradually increasing the marginal cost per MW of thermal units until doubling its value (i.e. 0.2 times steps, from 1.0 to 2.0 times). This analysis explores this operational situation with more expensive thermal generation due to increment in the cost of fuel such as coal or gas, and how this affects the dispatching performance. This analysis highlights changes in the 24-bus system thermal generation scheduling and ESS performance during the 24-hour period.
The ESS performance seen from its SoC during a 24-hour period is shown in Figure 11. It shows no differences for the proposed wind availability profiles. Due to the ESS presents the same behavior regardless of the increase in marginal cost (i.e from 1.0 to 2.0 times). In all cases, charging patterns appear depending on the respective wind pattern behavior. However, again there is a consistent discharging pattern during peak hours (i.e. hours 19 to 21) and different charging patterns at the beginning of the analysis period (i.e. hours 5 to 7 in low availability, 2 to 5 in moderate availability, and 6 to 7 in high availability).
Furthermore, It also shows an influence by wind availability due to the ESS finds some operation flexibility by increasing wind availability, delivering the stored energy when it is really needed (i.e. load peak Ì ISSN: 2088-8708 hours). This fact is evidenced by the decrease in the amount of charging and discharging interactions when the highest wind availability occurs. However, the marginal cost increase has no impact on the performance of the ESS and does not prevent the use of all the capacity that this device allows. Figure 11. (a) Comparison of ESS performance with regard to the marginal cost increasing for a 24-bus system, between the low-wind availability, (b), the moderate wind availability, (c) and high-wind availability The thermal units dispatch according to wind availability for the 24-bus system and compared to the load curve is shown in Figure 12. It shows similar performances between the thermal scheduling and the proposed load curve for all wind pattern. Again the thermal units dispatch exceeds the load to complete the 24-hour scheduling period (i.e. hours 6 to 7 in low-wind availability graph). Also, the thermal units dispatch is unchanged when increasing the marginal cost to the proposed value for all wind availability patterns. The difference between the load curve and thermal unit scheduling for all cases and wind patterns corresponds to the variable wind power participation and the charging/discharging interactions carried out by the ESS included in the system.
Likewise, the impact of wind availability in this power system is evident since the difference between load and thermal units power is greater. The generation portfolio of this power system is mostly thermal where the dispatched amounts were similar due to the non-existence of meaningful amount of alternative resources power to meet demand. This fact suggests a possible expansion of the total ESS capacity in this system, either by increasing the existing ones or by placing new ones in other buses, due to the reduction of operational costs and thermal unit dependence that these devices represent as shown in the previous scenario. However, the location and capacity of these systems must be optimal to achieve this goal. This consideration involves solving a new optimization problem with that approach. Figure 12. (a) Comparison of thermal scheduling with regard to the marginal cost increasing for a 24-bus system, between the low-wind availability, (b) the moderate wind availability, (c) and high-wind availability

CONCLUSION
In this article, a detailed multi-period DCOPF model for a 5-bus and a 24-bus power system was presented that includes renewable power (i.e wind power) and energy storage systems (ESS) under different operational scenarios for a 24-hour period. It has been shown that the mathematical modeling presented for the ESS charging and discharging behavior, corresponds to a valid approach of these elements for a planning process since it satisfies the dual features of this type of devices.
It was observed the great incidence of the wind availability for the proposed power system since it affects the ESS participation in load meeting, and thermal units dispatch even if the marginal cost is increased. It is due to the limited generation portfolio that is mostly thermal, being more susceptible to these changes. However, this feature causes the same thermal power to be dispatched even through marginal costs increase for Ì ISSN: 2088-8708 both systems, since both systems does not have meaningful alternative resources. Moreover, when increasing the capacity of the ESS, different situations arose for the systems used. In the 5-bus system, above a certain ESS capacity, the system did not improve its performance or significantly reduce its operating cost. Consequently, an investment in ESS with such capacities would not be fully exploited, which could represent economic losses and higher cost for users. On the other hand, for the 24-bus system all the proposed increases in ESS capacity represented significant savings and improved system performance. Thus, the existence of an efficient use of the ESS was verified from all wind availability patterns and capacities tested. This is because all proposed ESS capacities are fully used. Thus, an investment in increasing ESS capacity from base capacity to target value (from 300 MW to 450 MW) represents meaningful operational cost savings as well as lower costs for users.