Probabilistic Reliability Enhancement Strategies of Hydro Dominant Power Systems Under Energy Uncertainty

sustainability

Article Probabilistic Reliability Enhancement Strategies of Hydro Dominant Power Systems under Energy Uncertainty

Fang Fang, Rajesh Karki * and Prasanna Piya

Power System Research Group, University of Saskatchewan, Saskatoon, SK S7N5A9, Canada; [email protected] (F.F.); [email protected] (P.P.) * Correspondence: [email protected]

Received: 3 April 2020; Accepted: 27 April 2020; Published: 1 May 2020

Abstract: Climatic hydrological changes cause considerable seasonal and yearly energy variation in hydro dominant electric power systems. Extreme weather events are becoming more frequent in recent years causing dramatic impacts on energy availability in such systems. A significant amount of energy is often wasted due to reservoir overflow during wet seasons. By contrast, the scarcity of water in dry seasons results in inadequate power generation to meet the system demand, and therefore degrades overall system reliability. The high risks associated with an extreme dry hydrological condition should not be ignored in long term system adequacy planning of hydro dominant utilities. This paper presents a probabilistic method to incorporate diurnal, seasonal and yearly energy management strategies in run-of-river and storage type hydropower plant planning and operation in order to minimize the adverse impact of energy uncertainty and maintain long-term system adequacy. The impacts of reservoir capacity and demand side management on water utilization and system reliability are investigated with case studies illustrated using the IEEE Reliability Test System modified to create a hydro dominant system. The achieved benefits of reliability enhancement strategies are analyzed and compared in this paper.

Keywords: power system reliability; generation planning; hydropower; energy uncertainty; demand-side management

1. Introduction Hydropower is one of the most efficient, cost-effective, and clean source of electricity generation. The worldwide installed capacity of hydropower rose to 1292 GW in 2018 [1]. China, United States, Brazil and Canada are the countries with the highest hydropower installed capacity. Hydropower generation is growing rapidly in East Asia, followed by South America, South, and Central Asia, Europe, Africa, and North and Central America. Canada had 81 GW of installed hydropower capacity in 2018. Approximately 63% of Canada’s total electricity demand and most of Canada’s electricity exports come from hydropower [2]. Canada has the potential of another 160 GW of hydro capacity. In addition to clean and low-cost energy production, hydropower has a high ramp rate and a quick start capability which support the integration of highly intermittent renewable energy resources such as wind and solar into the conventional grid [3]. A hydro unit can be unavailable or only partially available due to river inflow restrictions. In a hydro dominant power system, the scarcity of water in the dry season can cause inadequate generation to meet the load demand. This issue is even more severe in a dry year. Furthermore, there has been an increase in the occurrence of extreme adverse weather in recent years. The energy uncertainty will have an adverse impact on system reliability [4]. Therefore, the high risks associated with the extreme

Sustainability 2020, 12, 3663; doi:10.3390/su12093663 www.mdpi.com/journal/sustainability Sustainability 2020, 12, 3663 2 of 18 dry hydrological condition should not be ignored in long term system adequacy planning of hydro dominant utilities. Many approaches have been explored and developed to properly model energy uncertainty as a constraint in hydro units in their reliability models. In [5,6], the models are developed to represent an energy source with limited energy input for generation reliability evaluation. The energy management of hydro units due to energy uncertainty is studied and applied mainly into two areas. The first area of study is to develop the operating policy based on energy uncertainty of hydro plants to optimize the operating cost of the system. In reference [7,8], with limited energy, the usage of a hydro unit as a base unit and/or peak shaving unit are compared based on reliability and production cost factors. In reference [9], the optimal allocation of stored energy resulting from random river inflows to the different sub-periods of a year to sell in the energy market as well as to cover any unplanned outages of thermal units is presented. The main objective of this work is to manage the energy generation from the hydro units and to assess the impact of the market rules on the reliability of the system. However, these researches did not consider the coordination of energy management among different hydro units in a hydro dominant system when facing energy uncertainty. The main focus of these works was on optimizing the operating cost. The second area of study is to coordinate the periodic energy uncertainty of hydro units with other types of generation in a mixed generation system. An integrated model for long term operation planning and reliability evaluation of hydrothermal systems is presented in [10]. An optimal amount of discharge of hydro units and energy output of thermal units is developed in that work with the objective of minimizing the total cost of the energy. A simple multivariable weather model is developed in [11] to include rainfall for hydro units. The hydropower plant is used as energy storage to study wind and solar penetration into the system from a reliability point of view. Three types of weather conditions, wet, dry and normal, were modeled in [12] with equal probability of occurrence and randomly chosen during the simulation. The operation incorporated the coordination with thermal and wind power systems to show the system adequacy depending on the capacity and number of hydro units assigned to operate in coordination with wind power. The focus of the existing literature is either on the energy management of hydropower for optimizing the operation cost or on the coordination of hydropower with other types of generation to manage the energy uncertainty due to hydrological conditions. However, the impact of energy uncertainty caused by hydrological variability from year to year on system reliability in the hydro dominant system has not been studied. Moreover, there is a need for research in the field of reliability enhancement strategies under energy limitation for hydro plants without getting assistance from other types of energy sources. This paper develops a new probabilistic method to incorporate diurnal, seasonal and yearly management strategies of run-of-river and storage hydro units in a hydro dominant system. The impacts of reservoir size and demand side management on water utilization and system reliability are investigated. The proposed strategies consider energy uncertainty and strategically manage energy utilization, based on water availability patterns to minimize reliability issues in energy deficient seasons [13]. Two analytical methods are developed and integrated for reliability evaluation of hydro dominant systems. A diurnal energy management method [14] is applied to the run of river hydro units to manage energy to follow the daily load variation. A seasonal energy management method [15] is applied to large storage hydro units to transfer energy so that it follows seasonal load variation. These two methods are integrated and used simultaneously to maximize the utilization of limited energy and minimize the reliability impact of energy uncertainty in order to enhance long-term system adequacy. The contribution of this paper is to provide an appropriate adequacy evaluation methodology for long term resource planning of hydro dominant systems. The short-term operational aspects of market forces and cost optimization are out of scope of this paper. The proposed strategies are applied to the modified IEEE Reliability Test System (RTS) [16] which incorporates the hydrological data of wet year, normal year, dry year and extreme dry year. The proposed methodology Sustainability 2020, 12, 3663 3 of 18 and illustrative results will be useful in planning and policy decisions in long-term investment and utilization of hydro resources for the sustainable growth of reliable hydro dominant systems.

2. Reliability Evaluation of Hydro Dominant Power System This generation system reliability can be deﬁned as the ability of total installed power generation to meet the total system load considering generating unit failures and load variations. The energy availability is also considered for energy-based generations, such as hydro units. The generation model is developed by combining hydro units and other conventional units in the system to create a probability distribution of generation capacity states, commonly known as the capacity outage probability table (COPT) [17]. The loss of load expectation (LOLE) and loss of energy expectation (LOEE) are the most widely used reliability indices, which are calculated by convolving the COPT with the load model of the system. The LOLE is the expected time that the system load exceeds the available generating capacity, and LOEE is the expected amount of energy that is not supplied when needed due to power interruptions [17]. The LOLE and LOEE can be calculated using Equations (1) and (2), respectively. Xn LOLE = p t (1) k × k k=1 Xn LOEE = p E (2) k × k k=1 th where n is the number of capacity outage states, pk is the probability of the k outage state, Ek is the energy not supplied in the outage state, and tk is the time of load loss due to the outage. The monthly energy availability of a hydropower plant varies due to river inﬂow variations from one month to another in the wet, normal, dry and extreme dry years. Therefore, the reliability indices are evaluated in monthly intervals in this paper. The annual LOLE and LOEE are then determined by summing the monthly LOLEs and LOEEs in the study year.

2.1. Modeling of a Hydro Unit The water level in the reservoir of a hydropower plant depends on the discharge rate of the hydro unit and the river inﬂow rate into the reservoir. The output ability of the hydro unit depends on the availability of the unit and the water operating policy based on available energy and water usage regulations at the instant. The turbine discharge rate Q (i) in the ith hour can be adjusted to generate a steady output power P as shown in (3).

P = g α H(i) Q(i) s (3) ∗ ∗ ∗ ∗ where g is the gravitational constant, α is the overall efficiency of the turbine generator, and s is the specific weight of water. The net head H (i) in the ith hour can be obtained by dividing the reservoir volume V (i) by its area A as shown in (4). The reservoir volume changes continuously depending on the river inflow and outflow and is obtained from (5).

H(i) = V(i)/A (4)

V(i) = V(i 1) + InV(i) OutV(i 1) (5) − − − where, V (i 1) is the reservoir volume in the previous hour, InV(i) is the inﬂow water volume − into the reservoir at ith hour, and OutV(i 1) is the outﬂow water volume from the reservoir in the − previous hour. It is assumed that the reservoir is a cuboidal shape to illustrate the method developed in this work. Sustainability 2020, 12, 3663 4 of 18

The total period of study is divided into sub-periods with similar hydrological conditions. The generation output varies in the diﬀerent sub-periods based on hydrological condition and water operating policy. The total energy output E of the study period can be found by summing up the Sustainability 2020, 12, x FOR PEER REVIEW 4 of 18 energy outputs in the sub-periods as given in (6)

푖 Xi E퐸== ∑P푃i 푖 ((6)6) 1 1 푡ℎ where 푃푖 is the output power and 푡푖 is the duration of theth 푖 sub-period. where Pi is the output power and ti is the duration of the i sub-period.

2.2.2.2. DiurnalDiurnal and and Seasonal Seasonal Energy Energy Management Management Modeling Modeling AA run-of-river run-of-river hydro hydro plant plant has has a a small small head head pond pond with with limited limited storage storage capacity. capacity. The The underlying underlying conceptsconcepts used used in in evaluating evaluating thethe powerpower outputoutput fromfrom aa run-of-riverrun-of-river hydrohydro plantplant areare describeddescribed inin [[1144].]. ItIt usually usually has has limited limited ability ability to to manage manage water water resource resource to to follow follow the the load load variation variation within within aa day day to to enhanceenhance system system reliability reliability [ 18[18].]. The The generating generating capacity capacity in in each each hour hour of of the the day day can can be be calculated calculated by by (3),(3), and and the the total total available available energy energy of of the the day day can can be be calculated calculated by by (6). (6). The The hydro hydro unit unit is is operated operated at at rated capacity C for ℎ푝푒푎푘 hours during peak hours of the day, and the remaining energy in the rated capacity C for hpeak hours during peak hours of the day, and the remaining energy in the reservoir isreservoir utilized tois utilized supply loadto supply at a constant load at reduceda constant generation reduced capacitygeneration D thatcapaci is calculatedty D that is in calculated (7). in (7). E C hpeak 퐸−− 퐶∗∗ ℎ푝푒푎푘 D퐷== (7) 24 hpeak (7) 24−− ℎ푝푒푎푘 AnAn example example of of diurnal diurnal energy energy management management of a of run-of-river a run-of-river plant plant is shown is shown in Figure in 1Figure. The hydro 1. The unithydro operates unit operates at rated at capacity rated capacity during peak during load peak hours load from hours Hour from 17 toHour Hour 17 20 to andHour at 20 40% and of at its 40% rated of capacityits rated during capacity the during oﬀ-peak the load off-peak hours. load hours.

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 Load p.u.

Gneration/Load (p.u.) Gneration/Load 0.2 Gen Cap Before Diurnal Energy Management 0.1 Gen Cap After Diurnal Energy Management 0

Hours

Figure 1. Diurnal energy management modeling. Figure 1. Diurnal energy management modeling. A large storage type hydro unit has the ability to carry water from one season to another. It can, A large storage type hydro unit has the ability to carry water from one season to another. It can, therefore, be operated to save water by reducing generation output during high inflow and low load therefore, be operated to save water by reducing generation output during high inflow and low load periods. The accumulated water can be carried to next year and utilized to increase the generation periods. The accumulated water can be carried to next year and utilized to increase the generation capacity output during peak load periods in the dry months. Figure2 depicts the monthly water inflow capacity output during peak load periods in the dry months. Figure 2 depicts the monthly water of a large storage type hydro plant and the total system load variation over a year. The figure shows inflow of a large storage type hydro plant and the total system load variation over a year. The figure that there is plenty of water from April to August that can be saved and used in the months of scarce shows that there is plenty of water from April to August that can be saved and used in the months of water with peak loads from October to March. scarce water with peak loads from October to March. Sustainability 2020, 12, 3663 5 of 18 Sustainability 2020, 12, x FOR PEER REVIEW 5 of 18

1.2

0.8

0.6 System Load 0.4 Reservoir Inflow Rate

Inflow Rate/Load (p.u.) Rate/Load Inflow 0.2

0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Months FigureFigure 2. 2.Monthly Monthly reservoir reservoir inﬂow inflow rate rate and and system system load. load.

The method described in [19] is used to integrate the diurnal and seasonal energy management The method described in [19] is used to integrate the diurnal and seasonal energy management strategies of hydro dominant systems. The study year is divided into p periods consisting of a number strategies of hydro dominant systems. The study year is divided into p periods consisting of a number of days with similar load and river inflow. The p period is divided into the q sub-periods as energy of days with similar load and river inflow. The p period is divided into the q sub-periods as energy limitation days and energy adequate days. The energy limitation days represent days when the limitation days and energy adequate days. The energy limitation days represent days when the generation capacity output is not adequate to satisfy the load demand resulting in a high number in generation capacity output is not adequate to satisfy the load demand resulting in a high number in loss of load. The q sub-periods are further divided into two diurnal sub-periods of peak and off-peak loss of load. The q sub-periods are further divided into two diurnal sub-periods of peak and off-peak periods in hours. The generation models of run-of-river are created for two diurnal sub-periods in the periods in hours. The generation models of run-of-river are created for two diurnal sub-periods in energy-limited months, so it can increase capacity in peak load hours of the day. The generation models the energy-limited months, so it can increase capacity in peak load hours of the day. The generation of storage type hydro are created for each sub-period to manage the energy in the energy-limited period. models of storage type hydro are created for each sub-period to manage the energy in the energy- During the q sub-periods, the run-of-river hydro generation model in peak load period is combined limited period. During the q sub-periods, the run-of-river hydro generation model in peak load with the storage type hydro generation model in the same month to get the overall generation model period is combined with the storage type hydro generation model in the same month to get the overall in peak period. The system load models are created as load duration curves for each diurnal peak generation model in peak period. The system load models are created as load duration curves for and off-peak period in each sub-period. The system generation models are convolved with each each diurnal peak and off-peak period in each sub-period. The system generation models are corresponding load model in the sub-period to obtain the risk index Rij, with i period and j sub-period, convolved with each corresponding load model in the sub-period to obtain the risk index 푅푖푗, with i where j q and ni is the number of the days in period qi. The annual reliability index of combined period ∈and j sub-period, where 푗 ∈ 푞 and 푛푖 is the number of the days in period 푞푖. The annual run-of-river and storage hydro units can be obtained by using (8). reliability index of combined run-of-river and storage hydro units can be obtained by using (8). p q q 푞 2 X− X X R = R + n R 2 (8) 푝−푞 j i × ij 푅 = ∑j=1 푅푗 + i∑=1 푛j=1푖 × ∑ 푅푖푗 (8) 푗=1 푗=1 th th where, ni is the number of days in the i sub-period,푖=1 and Rij is the risk index calculated for the j period of the ith sub-period of the year. 푡ℎ where, 푛푖 is the number of days in the 푖 sub-period, and 푅푖푗 is the risk index calculated for the 푗푡ℎ period of the 푖푡ℎ sub-period of the year. 3. Proposed Method 3. ProposedThis section Method presents a probabilistic method to incorporate diurnal, seasonal and yearly energy management strategies to operate the run-of-river and storage type hydro units to minimize the This section presents a probabilistic method to incorporate diurnal, seasonal and yearly energy impact of energy uncertainty and maintain long-term system adequacy. The impacts of reservoir size management strategies to operate the run-of-river and storage type hydro units to minimize the and demand side management on water utilization and system reliability are also investigated in impact of energy uncertainty and maintain long-term system adequacy. The impacts of reservoir size this section. and demand side management on water utilization and system reliability are also investigated in this 3.1.section. Year to Year Energy Management

3.1.The Year energy to Year management Energy Management of hydro units depends on the reservoir size, load variation proﬁles and hydrological conditions in the study year. The objective of this method is to save water in a The energy management of hydro units depends on the reservoir size, load variation profiles normal or wet year with minimal adverse impact on the system reliability by incorporating diurnal, and hydrological conditions in the study year. The objective of this method is to save water in a seasonal and yearly energy management, such that a maximum amount of water will be available for normal or wet year with minimal adverse impact on the system reliability by incorporating diurnal, the upcoming energy uncertainty year. The uncertainty in the hydrological condition in an upcoming seasonal and yearly energy management, such that a maximum amount of water will be available for the upcoming energy uncertainty year. The uncertainty in the hydrological condition in an upcoming SustainabilitySustainability 20202020,, 1122,, x 3663 FOR PEER REVIEW 66 of of 18 18 Sustainability 2020, 12, x FOR PEER REVIEW 6 of 18 year is represented by an expected monthly or seasonal variation in hydrological data in this work, yearwhichyear is is isrepresented represented obtained using by by an an Equation e expectedxpected (9). monthly monthly or or seasonal seasonal variation variation in in hydrological hydrological data data in in this this work, work, whichwhich is is obtained obtained using using Equation Equation (9). (9). 푊 = ∑ 푃(푋) × 푊푋 ∀ 푋 ∈ {wet year, normal year, dry year, extreme dry year} (9) X W푊== ∑푋P(푃X(푋) ) ×W푊X ∀X 푋 ∈ wet{wet year, year, normal year year,, dry dry year year,, extreme extreme dry dry year year} (9) × 푋 ∀ ∈ (9) where X representsX 푋 the hydrological condition of the year, W_X is the average monthly or seasonal whydrologicalwherehere XX representsrepresents data for the the the hydrological hydrological year with hydrological condition condition of of conditionthe the year, year, W_XW_XX as isshownis the the average average in Figure monthly monthly 3, and or orP( seasonalX seasonal) is the hydrologicalprobabilityhydrological that data data a foryear for the thewill year year have with with hydrological hydrological hydrological condition condition condition X whichXX asas shown shown is shown in in Figure Figurein Figure 3, and 4 for PP(( XXthe)) is isfour the the probabilitydifferentprobability hydrological that that a a year year conditions: will will have have hydrological hydrologicalwet year, normal condition condition year, dryXX whichwhich year andis is shown shown extreme in in Figuredry Figure year. 4 for the four differentdiﬀerent hydrological hydrological conditions: conditions: wet wet year, year, normal year, dry year and extreme dry year. wet year 1 wetnormal year year 1 normaldry year year 0.8 dryextreme year dry year 0.8 extremeexpected dry hydrological year data 0.6 expected hydrological data 0.6 0.4 0.4

Hydrological Data (pu) Data Hydrological 0.2

Hydrological Data (pu) Data Hydrological 0.2 0 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Months Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Months Figure 3. Monthly variation in hydrological data. FigureFigure 3. 3. MonthlyMonthly variation variation in in hydrological hydrological data data.. 1 0.784 0.81 0.784 0.80.6

0.60.4 Probability 0.40.2 0.108

Probability 0.054 0.054 0.108 0.20 0.054 0.054 0 wet year normal year dry year extreme wet year normal year dry year extremeyear

Figure 4. The occurrence probability of diﬀerent hydrologicalyear condition. Figure 4. The occurrence probability of different hydrological condition . The algorithmFigure involved 4. The in occurrence implementing probability the methodology of different hydrological is shown incondition Figure5. and described in the followingThe algorithm steps: involved in implementing the methodology is shown in Figure 5 and described in theThe following algorithm steps: involved in implementing the methodology is shown in Figure 5 and described 1. The hydrological condition of the current year is known. Determine the expected hydrological in the following steps: 1. Thedata hydrological of the upcoming condition year using of the the current probabilistic year is hydrologicalknown. Determine model obtainedthe expected from hydrological Equation (9). 1.2. ThedataIntegrate hydrological of the the upcoming diurnal condition andyear seasonal usingof the thecurrent energy probabilistic managementyear is known. hydrological strategy Determine ofmodel the the hydro obtained expected dominant from hydrological Equation system as data(9).described of the inupcoming Section2 intoyear the using hydro the operating probabilistic simulation. hydrological Evaluate model the systemobtained reliability from Equation indices,

2. (9).Integratesuch as the the LOLE, diurnal for and each seasonal sub-period energy of themanagement current year strategy and following of the hydro year usingdominant Equation system (8) 2. Integrateasto described understand the diurnalin theSection characteristics and 2 seasonalinto the of energyhydro the system. operatingmanagement simulation. strategy Evaluateof the hydro the dominantsystem reliability system indices, such as the LOLE, for each sub-period of the current year and following year using 3. asIf described the reservoir in Section is full at 2 theinto end the of hydro the current operating year, simulation. further energy Evaluate management the system is not reliability needed. Equation (8) to understand the characteristics of the system. indices,Otherwise, such sortas the the LOLE, LOLE for values each ofsub the-period sub-period of the incurrent the current year and year following in ascending year using order. 3. If the reservoir is full at the end of the current year, further energy management is not needed. EquationCheck the (8) reservoir to understand capacity the of characteristics the sub-period of with the thesystem. lowest LOLE. If it is not full, decrease the Otherwise, sort the LOLE values of the sub-period in the current year in ascending order. Check 3. Ifhydropower the reservoir output is full inat the sub-periodend of the current to save year, more further water inenergy the reservoir. management Then is run not the needed. whole the reservoir capacity of the sub-period with the lowest LOLE. If it is not full, decrease the Otherwise,year simulation sort the again LOLE to evaluatevalues of the the LOLE sub-period values in and the reservoircurrent year levels in ascending for each sub-period. order. Check the reservoir capacity of the sub-period with the lowest LOLE. If it is not full, decrease the Sustainability 2020, 12, 3663 7 of 18

4. If the hydro operating simulation results in reservoir full in the lowest LOLE sub-period, then follow the ascending order and ﬁnd the next lowest LOLE sub-period with water storage capability in a reservoir in the current year, and modify year to year energy management strategy to reduce the amount of generation in the sub-period. In the following year, the generation output capability of the hydro unit is increased in the sub-periods with the highest LOLE values by utilizing saved water from the year to year energy management in the previous year. Then run the two-year simulation again to update the LOLE values for each sub-period and the water level in reservoirs. 5. If the total two-year LOLE value after applying the most recent year to year energy management is lower than the previous LOLE value, then repeat step 3. 6. If the total two-year LOLE value after applying the most recent year to year energy management is higher than the previous LOLE value, then slightly increase the hydropower output in the sub-period in the descending order of the LOLE values of the current year. If the small amount of increase of hydropower output will result in a huge amount of LOLE increase, then move to the next highest LOLE value sub-period. Again, run the two-year simulation to identify the total LOLE values. 7. Repeat step 5 and 6 to keep adjusting the year to year energy management until the maximum storage of water is reached with the lowest two-year total LOLE values.

The year to year energy management is applied to the modified IEEE RTS system consisting of six hydro plants (with three run-of-river and three storage hydro plants) and two thermal plants. The historical river flow pattern of BC province in Canada [20] was used in the study. The data includes the inflow rate at monthly intervals for the different rivers in different hydrological years as shown in Figure3. The generation output capability can be calculated using Equation (3) based on the inflow pattern for each month in Figure3 and the reservoir condition of every hour can be updated using Equations (4) and (5). A study was done assuming the current as a normal hydrological year which has a wet season from May to October, and a dry season from November to April. The following year was assumed as a dry year in the study with reduced water in the wet season and inadequate water in the dry season as shown in Figure3. Without the year to year energy management, November and December in the current year were simulated at its rated generation capacity to meet peak load demand as shown in Figure6. As a result, the reservoir was full until October and the stored water in the reservoir began to rapidly decrease from the November of the current year due to low river inflow in the dry season. The generation capacity output dropped each month from the current year to the next year in the dry season. With the implementation of the year to year energy management, the amount of water that can be carried from one year to another is very restricted due to the reservoir capacity as shown in Figure7. However, the amount of water can be distributed at critical times between January to March to mitigate the scarcity of energy during the dry months of the following dry year. The contribution of the saved water can be seen in Figure6. The water saved by reducing generation in the current year is used to increase the generation capacity output from January to March in the following year to meet the load demand.

3.2. Increase of Reservoir Size The size or capacity of the reservoir is one of the main limitations in energy management, as discussed in Section 3.1. With current reservoir size restraints, a large amount of water in the wet season is wasted as spillage. The reliability can be enhanced by increasing the reservoir size to avoid water spillage. It can store and manage additional energy from year to year as needed. SustainabilitySustainability2020 2020, ,12 12,, 3663 x FOR PEER REVIEW 88 of of 18 18

Hydrological condition of the current year known. Determine the expected hydrological condition for the upcoming year using Equation (9).

Integrate diurnal and seasonal energy management into hydro operating simulation for 2 years.

Calculate LOLE for each sub-period of current and upcoming year and 2-year total LOLE (퐿푂퐿퐸2푌(1)).

YES Is reservoir full at the end of the current year?

Sort LOLE of each sub-period for the current year in ascending order and select sub-period with lowest LOLE.

Is reservoir full at YES Select next sub-period from the the sub- period? sorted list after current sub-period. NO Decrease hydro output in this sub-period of current year. Increase hydro output in sub-period with highest LOLE 퐿푂퐿퐸2푌(1) = 퐿푂퐿퐸2푌(2 ) in the upcoming year.

Integrate diurnal and seasonal energy management into hydro operating simulation for 2 years.

Calculate LOLE for each sub-period Increase the hydro output in of current and upcoming year and 2- sub-period in descending order year total LOLE (퐿푂퐿퐸2푌(2)). of LOLE in the current year.

YES NO NO |퐿푂퐿퐸 − 퐿푂퐿퐸 | 2푌(2) 2푌(1) 퐿푂퐿퐸2푌(2) > 퐿푂퐿퐸2푌(1) <=Tolerance?

YES

STOP

Figure 5. Flow chart for year to year energy management methodology. LOLE: Loss of load expectation.

The year to year energy management is applied to the modified IEEE RTS system consisting of six hydro plants (with three run-of-river and three storage hydro plants) and two thermal plants. The historical river flow pattern of BC province in Canada [20] was used in the study. The data includes the inflow rate at monthly intervals for the different rivers in different hydrological years as shown in Figure 3. The generation output capability can be calculated using Equation (3) based on the inflow pattern for each month in Figure 3 and the reservoir condition of every hour can be updated using Equations (4) and (5). A study was done assuming the current as a normal hydrological year which has a wet season from May to October, and a dry season from November to April. The following year Sustainability 2020, 12, x FOR PEER REVIEW 9 of 18

was assumed as a dry year in the study with reduced water in the wet season and inadequate water in the dry season as shown in Figure 3. Without the year to year energy management, November and December in the current year were simulated at its rated generation capacity to meet peak load demand as shown in Figure 6. As a result, the reservoir was full until October and the stored water in the reservoir began to rapidly decrease from the November of the current year due to low river inflow in the dry season. The generation capacity output dropped each month from the current year to the next year in the dry season. Sustainability 2020, 12, x FOR PEER REVIEW 9 of 18 350 Before EM After EM was assumed as a 300dry year in the study with reduced water in the wet season and inadequate water in the dry season as250 shown in Figure 3. Without the year to year energy management, November and December in the current year were 200 simulated at its rated generation capacity to meet peak load demand as shown in Figure 6. As a result, 150 the reservoir was(MW) full until October and the stored water in the reservoir began to rapidly decrease from the November100 of the current year due to low river inflow in the dry season. The generation Sustainability 2020, 12, 3663 9 of 18 capacity output dropped50 each month from the current year to the next year in the dry season.

Generation Capacity Output Capacity Generation 0 350 Before EM After EM 300 Normal Year to Dry Year 250 Figure200 6. Simulated generation capacity output variation from one year to another. 150 With the implementation(MW) of the year to year energy management, the amount of water that can be carried from one100 year to another is very restricted due to the reservoir capacity as shown in Figure 7. However, the amount50 of water can be distributed at critical times between January to March to mitigate the scarcity of energy during the dry months of the following dry year. The contribution of Generation Capacity Output Capacity Generation 0 the saved water can be seen in Figure 6. The water saved by reducing generation in the current year is used to increase the generation capacity output from January to March in the following year to meet the load demand. Normal Year to Dry Year FigureFigure 6.6. SimulatedSimulated generationgeneration capacitycapacity outputoutput variationvariation fromfrom oneoneyear yearto toanother. another. Reservior water with No Year-Year EM With the implementation of the year to year energy management, the amount of water that can 6E+09 Reservior water with Year-Year EM be carried from one year to another is very restricted due to the reservoir capacity as shown in Figure

7. However, the5E+09 amount of water can be distributed at critical times between January to March to m3) m3) mitigate the scarcity4E+09 of energy during the dry months of the following dry year. The contribution of the saved water can be seen in Figure 6. The water saved by reducing generation in the current year is used to increase3E+09 the generation capacity output from January to March in the following year to meet the load 2E+09demand.

1E+09 Reservior Water ( Water Reservior Reservior water with No Year-Year EM 0 6E+09 Reservior water with Year-Year EM 5E+09 m3) m3) Normal Year to dry Year Months 4E+09 Figure 7. Reservoir water variation by applying energy management. 3E+09Figure 7. Reservoir water variation by applying energy management. Figure8 shows a reservoir head and water spillage for 300 MW storage type hydro plant. A study 3.2. Increase of2E+09 Reservoir Size was carried out by increasing the reservoir size by 30%. With the increased size, it takes a longer time 1E+09 to fill theThe reservoir size( Water Reservior or capacity to its maximum of the reservoir head in Julyis one as shownof the main in Figure limitations8. More waterin energy is saved management, during the as wetdiscussed season duein Section to reduced0 3.1. With spillage current in July, reservoir and the size stored restraints, water is a carried large amount over from of thewater current in the year wet toseason the upcoming is wasted year. as spillage. The saved The reliability water is distributed can be enh inanced the dryby increasing months from the reservoir January tosize March to avoid of thewater following spillage. dry It yearcan store where and there manage is a severe additional shortage energ ofy water. from Atyear the to end year of as April, needed. the saved water is all used up and the head value reachesNormal its lowest Year to limit. dry Year The Months corresponding MW capacity output of the 300 MW hydro unit after the increase in reservoir size is shown in Figure9. Starting with the same head, the reservoirFigure with 7. Reservoir 30% increased water variation size stores by applying more water energy in management the reservoir. and yields more capacity output in the energy-limited months than the original size reservoir from January to April in 3.2. Increase of Reservoir Size the current year. With the increased reservoir size, the capacity output in the dry months from January to AprilThe of size the or following capacity dry of yearthe reservoir will increase is one significantly of the main due limitations to additional in energy water management, stored from the as currentdiscussed year in to Section use in the3.1. upcomingWith current year. reservoir size restraints, a large amount of water in the wet season is wasted as spillage. The reliability can be enhanced by increasing the reservoir size to avoid 3.3.water Demand spillage. Side It Management can store and manage additional energy from year to year as needed. A winter peaking load and a summer peaking load represent two distinctly different load patterns. They are studied in this paper to investigate the impact of correlation between load pattern and generation capacity output on the system reliability. Figure 10 shows the winter peaking load and summer peaking load patterns, and the generation output capability of the hydro dominant system with the dry year hydrological pattern. The hydro units can generate rated output during the wet Sustainability 2020, 12, x FOR PEER REVIEW 10 of 18

Figure 8 shows a reservoir head and water spillage for 300 MW storage type hydro plant. A Sustainability 2020, 12, x FOR PEER REVIEW 10 of 18 study was carried out by increasing the reservoir size by 30%. With the increased size, it takes a longer time to fillFigure the reservoir 8 shows to aits reservoir maximum head head and in Julywater as shownspillage in for Figure 300 MW8. More storage water type is saved hydro during plant. A the wetstudy season was carrieddue to reducedout by increa spillagesing in the July, reservoir and the size stored by 30%. water With is thecarri increaseded over from size, theit takes current a longer year timeto the to upcoming fill the reservoir year. The to its saved maximum water head is distributed in July as inshown the dry in Figure months 8. fromMore January water is tosaved March during of thethe following wet season dry due year to wherereduced there spillage is a severe in July, shortage and the ofstored water. water At theis carri ended of over April, from the thesaved current wateryear is allto theused upcoming up and the year. head The value saved reaches water is its distributed lowest limit. in the The dry corresponding months from MWJanuary capacity to March outputof theof the following 300 MW dry hydro year unitwhere after there the isincrease a severe in shortage reservoir of size water. is shown At the in end Figure of April, 9. Starting the saved withwater the same is all head, used theup reservoirand the head with value30% increasedreaches its size lowest stores limit. more The water corresponding in the reservoir MW capacityand yieldsoutput more of capacity the 300 outputMW hydro in the unit energy after -thelimited increase months in reservoir than the size original is shown size in reservoir Figure 9. from Starting Januarywith to the April same in thehead, current the reservoir year. With with the 30% increased increased reservoir size storessize, the more capacity water output in the inreservoir the dry and Sustainability 2020, 12, 3663 10 of 18 monthsyields from more January capacity to April output of the in following the energy dry-limited year will months increase than significantly the original due size to reservoiradditional from waterJanuary stored tofrom April the in current the current year toyear. use With in the the upcoming increased year. reservoir size, the capacity output in the dry seasonmonths from from May January to September to April of but the generate following reduced dry yea outputr will increase during thesignificantly dry season due from to Decemberadditional Reservior head with original reservoir size towater April. stored from the currentReservior year to head use inwith the increased upcoming size year. of reservoir Water spillage with original reservoir size WaterReservior Spillage headwith increasedwith original size reservoir of reservoir size 60 Reservior head with increased size of reservoir Water spillage with original reservoir size 12 Water Spillage with increased size of reservoir 40 60 8 12

20 40

4 8 Reservoir Head (m) (m) Head Reservoir 20

0 0 4 m3) million (x Spillage Water Reservoir Head (m) (m) Head Reservoir

0 0 m3) million (x Spillage Water Figure 8. Net head and water spillage of the reservoir before and after increase size of the reservoir.

Figure 8. Net head and water spillage of the reservoir before and after increase size of the reservoir. Figure 8. Net head and water spillage of the reservoir before and after increase size of the reservoir. Original Size 30% Enlargement 350 300 Original Size 30% Enlargement 250 350 200 300 150 250 100 200 50 150 100 Gneration Capcity Output (MW) Output Capcity Gneration 0 50

Gneration Capcity Output (MW) Output Capcity Gneration 0 Months FigureFigure 9. Corresponding 9. Corresponding 300 MW 300 capac MW capacityity output output of reservoir of reservoir enlargement enlargement.. Months 3.3. DemandA winterSide Management peaking load pattern shows a negative correlation with the generation capability of the hydro generationFigure output9. Corresponding as depicted 300 inMW Figure capac 10ity. output The system of reservoir peak enlargement load occurs. during the dry monthsA winter (Dec–Jan) peaking when load the and generating a summer units peaking have load derated represent outputs, two which distinctly increases different the loss load of load patterns.probability.3.3. Demand They are OnSide studied the Management other in hand,this paper the system to investigate oﬀ-peak the load impact occurs of during correlation the wet between months load (May–Jul) pattern when and thegeneration generationA winter capacity units peaking haveoutput load rated on and capacitythe asystem summer output reliability. peaking which Figure is load not necessary represent10 shows to twothe meet winter distinctly the lightpeaking different load load demand. load and patterns. summerFor aThey peaking system are load withstudied patterns, the in summer this andpaper peaking the to generationinvestigate load pattern, outputthe impact the capability system of correlation peak of the load hydrobetween occurs dominant load in thepattern wet seasonand generation where the capacity hydro units output can on generate the system the rated reliability. capacity Figure output 10 to shows meet thethe highwinter load peaking demand. load In theand dry summer season, peaking the generation load patterns, output capability and the generation is derated, butoutput the load capability is also of at the minimum hydro dominant during the period, so the loss of load mainly depends on random failures of the generating units during this period. It is desired that the load variation pattern and the generation output capability have a positive correlation so that the hydro units have adequate energy in time sequence to satisfy the system peak load. Applying demand side management is one of the eﬀective ways to slow the increase in electricity demand and transform the system load pattern toward to the desired trend, in this case, following positive correlation with the hydropower output capability. Sustainability 2020, 12, x FOR PEER REVIEW 11 of 18 system with the dry year hydrological pattern. The hydro units can generate rated output during the wet season from May to September but generate reduced output during the dry season from Sustainability 2020, 12, 3663 11 of 18 December to April.

Generation Output Capability in Dry Year Winter Peaking Load 3500 Summer Peaking Load

3000

2500

2000 Generation/Load (MW) Generation/Load

1500 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Generation Output Capability in Dry Year Winter Peaking Load 3500 Summer Peaking Load

3000

2500

2000 Generation/Load (MW) Generation/Load

1500 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Figure 10. Load and generation correlation. Figure 10. Load and generation correlation. Therefore, a strong positive correlation between the generation output capability and the load A winter peaking load pattern shows a negative correlation with the generation capability of the pattern has a great positive impact on system reliability. Application of the demand side management hydro generation output as depicted in Figure 10. The system peak load occurs during the dry to change the system’s load pattern to obtain the desired correlation with the hydrological condition months (Dec–Jan) when the generating units have derated outputs, which increases the loss of load can signiﬁcantly improve the reliability of the hydro dominant system. probability. On the other hand, the system off-peak load occurs during the wet months (May–Jul) 4.when Simulation the generation Results units of Applying have rated the capacity Developed output Models which to is the not Test necessary System to meet the light load demand. Long term reliability analysis of a power system is normally carried out every year for a planning For a system with the summer peaking load pattern, the system peak load occurs in the wet horizon of several years using annual indices. Such analysis can also be conducted for a season, a year season where the hydro units can generate the rated capacity output to meet the high load demand. or a longer period of time. This paper considers long term energy uncertainty of hydro dominant power In the dry season, the generation output capability is derated, but the load is also at the minimum system due to hydrological uncertainty. Since proper management of reservoir water usage requires during the period, so the loss of load mainly depends on random failures of the generating units the knowledge of energy availability and demand scenarios in the immediate future years, a two-year during this period. study period was chosen to incorporate the current year and future year’s hydrological conditions. It is desired that the load variation pattern and the generation output capability have a positive A modiﬁed IEEE RTS system as described in Section3 is used for reliability studies. A calendar correlation so that the hydro units have adequate energy in time sequence to satisfy the system peak year is assumed to have one of the four hydrological conditions, namely wet, normal, dry and extreme load. Applying demand side management is one of the effective ways to slow the increase in dry year as shown in Figure3, with the probabilities shown in Figure4. This data was obtained electricity demand and transform the system load pattern toward to the desired trend, in this case, from hydrological information obtained for the Canadian province of British Columbia. The normal following positive correlation with the hydropower output capability. hydrological year has the highest occurrence probability of 0.78. Therefore, the study is assumed to start with a normal hydrological year, but in fact, the hydrological condition of the current year is Sustainability 2020, 12, x FOR PEER REVIEW 12 of 18

Therefore, a strong positive correlation between the generation output capability and the load pattern has a great positive impact on system reliability. Application of the demand side management to change the system’s load pattern to obtain the desired correlation with the hydrological condition can significantly improve the reliability of the hydro dominant system.

4. Simulation Results of Applying the Developed Models to the Test System Long term reliability analysis of a power system is normally carried out every year for a planning horizon of several years using annual indices. Such analysis can also be conducted for a season, a year or a longer period of time. This paper considers long term energy uncertainty of hydro dominant power system due to hydrological uncertainty. Since proper management of reservoir water usage requires the knowledge of energy availability and demand scenarios in the immediate future years, a two-year study period was chosen to incorporate the current year and future year’s hydrological conditions. A modified IEEE RTS system as described in Section 3 is used for reliability studies. A calendar year is assumed to have one of the four hydrological conditions, namely wet, normal, dry and extreme dry year as shown in Figure 3, with the probabilities shown in Figure 4. This data was obtained from hydrological information obtained for the Canadian province of British Columbia. The Sustainability 2020, 12, 3663 12 of 18 normal hydrological year has the highest occurrence probability of 0.78. Therefore, the study is assumed to start with a normal hydrological year, but in fact, the hydrological condition of the current yearknown is known with relativelywith relatively low uncertainty. low uncertainty. A winter A winter peaking peaking load pattern load pattern as shown as shown in Figure in Figure10[ 21] 10 was [21used] was considering used considering a peak loada peak of load 2380 of MW 2380 in MW the following in the following studies. studies. TheThe proposed proposed methodology methodology of ofwater water management management for for reliability reliability enhancement enhancement was was applied applied to to thethe modified modiﬁed RTS RTS system system to investigate to investigate the thereliability reliability impacts. impacts. Figure Figure 11 shows 11 shows the LOLE the LOLEfor the for four the hydrologicalfour hydrological condition condition years years with with and withand withoutout implementing implementing the the energy energy management management strategy. strategy. FigureFigure 11 11 also also shows shows the the expected expected LOLE LOLE for for the upcoming yearyear obtainedobtained byby multiplying multiplying the the LOLE LOLE for foreach each of of the the four four hydrological hydrological conditions conditions by by the the probability probability of of its its occurrence. occurrence. TheThe expectedexpected LOLELOLE is is 0.48 0.48 h h/year./year. This This is equivalentis equivalent to LOLE to LOLE of 0.1 of days 0.1 / days/year,year, which which is the widelyis the widely used reliability used reliability planning planningcriterion criterion [22] in major [22] in power major utilities. power utilities.

Before Energy Management LOLE(hrs/year)

2 After Energy Management (hrs/year) criteria 1.5

1 LOLE (hrs/year)LOLE 0.5

0 wet normal dry extreme dry Expected LOLE

Figure 11. System LOLE with and without year to year energy management. Figure 11. System LOLE with and without year to year energy management. Figure 11 shows that the LOLE is the lowest in the wet year. The LOLE in the normal year almost reachesFigure the 11 criterion shows that value the even LOLE before is the applying lowest in the the energy wet year. management The LOLE strategy.in the normal After year applying almost the reachesyear to the year criterion energy value management even before strategy, applying LOLE the decreases energy management to 0.35 h/year. strategy. The LOLE After values applying in dry the and yearextreme to year dry energy years aremanagement very high. strategy, Although LOLE the year decreases to year to energy 0.35 h management/year. The LOLE in these values conditions in dry andcan extreme significantly dry years improve are the very system high. reliability, Although it the is not year able to to year transfer energy enough management energy to in meet these the conditionsreliability can criterion. significantly It should, improve however, the system be noted reliability, that the expected it is not able LOLE to meetstransfer the enough reliability energy criterion to meetafter the the reliabilityyear to year criterion. energy management. It should, however, The widely be acceptednoted that LOLE the criterion expected may LOLE be suitable meets the for a reliabilityparticular criterion year, but after its compliancethe year to wouldyear energy require management. significant capital The widely investment accepted in dry LOLE and criterion extremely maydry be years. suitable An for appropriate a particular value year, of but expected its compliance LOLE considering would require the di significantfferent hydrological capital investment years can be used as a planning criterion for hydro dominant systems. Figure 11, however, shows that the equivalent of 0.1 days/year may not be an acceptable value since the LOLE in the dry and extreme dry year cases are very high. A reliability cost worth analysis in the dry and extreme dry scenarios is needed to determine the suitable criterion values. The peak load carrying capacity (PLCC) [17] of a system is the peak load that the system can carry without violating its reliability planning criterion. The PLCCs of the system are shown in Figure 12 for the four hydrological conditions assuming a planning criterion of LOLE = 0.48 h/year. The system can carry a higher peak load after applying the year to year energy management in all hydrological conditions. Another study was carried out to investigate the impact of reservoir capacity on the system reliability in the different hydrological years with year to year energy management. Three different reservoir sizes were considered: (1) the original size, (2) a 30% increase in reservoir volume, and (3) a reservoir with infinite volume. The results are shown in Figure 13. Sustainability 2020, 12, x FOR PEER REVIEW 13 of 18

in dry and extremely dry years. An appropriate value of expected LOLE considering the different hydrological years can be used as a planning criterion for hydro dominant systems. Figure 11, however, shows that the equivalent of 0.1 days/year may not be an acceptable value since the LOLE in the dry and extreme dry year cases are very high. A reliability cost worth analysis in the dry and Sustainabilityextreme 20 20dry, 1 2scenarios, x FOR PEER is REVIEWneeded to determine the suitable criterion values. 13 of 18 The peak load carrying capacity (PLCC) [17] of a system is the peak load that the system can in dry and extremely dry years. An appropriate value of expected LOLE considering the different carry without violating its reliability planning criterion. The PLCCs of the system are shown in Figure hydrological years can be used as a planning criterion for hydro dominant systems. Figure 11, 12 for the four hydrological conditions assuming a planning criterion of LOLE = 0.48 h/year. The however, shows that the equivalent of 0.1 days/year may not be an acceptable value since the LOLE system can carry a higher peak load after applying the year to year energy management in all in the dry and extreme dry year cases are very high. A reliability cost worth analysis in the dry and hydrological conditions. extreme dry scenarios is needed to determine the suitable criterion values. The peak load carrying2600 capacity (PLCC) [17] of a system is Beforethe peak Energy load Management that the system can carry without violating its reliability planning criterion. The PLCCs of the system are shown in Figure 12 for the four hydrological conditions assuming a planning criterion of LOLE = 0.48 h/year. The After Year to Year Energy system can carry a higher peak load after applying the year to year energy management in all Sustainability 2020, 12, 36632400 Management 13 of 18 hydrological conditions.

26002200 Before Energy Management PLCC(MW)

After Year to Year Energy 24002000 Management Wet Year Normal Dry Year Extreme Expected Year Dry Year PLCC

2200 PLCC(MW) Figure 12. Increase in peak load carrying capacity (PLCC) after year to year energy management.

Another study2000 was carried out to investigate the impact of reservoir capacity on the system reliability in the differentWet hydrological Year Normal years withDry year Year to year energyExtreme management.Expected Three different reservoir sizes were considered: (1) the Yearoriginal size, (2) a 30% Dryincrease Year in reservoirPLCC volume, and (3)

a reservoirFigure with 12. Increaseinfinite involume. peak load The carrying results capacity are shown (PLCC) in Figure after year 13. to year energy management. Figure 12. Increase in peak load carrying capacity (PLCC) after year to year energy management. Original Reservoir Size Another study was carriedIncrease out to investigate30% of Reservoir the impact Size of reservoir capacity on the system Infinite Reservoir Size reliability in the different1 hydrological years with year to year energy management. Three different reservoir sizes were considered: criteria(1) the original size, (2) a 30% increase in reservoir volume, and (3) a reservoir with infinite volume. The results are shown in Figure 13.

Original Reservoir Size 0.1 Increase 30% of Reservoir Size Infinite Reservoir Size

LOLE (hrs/year)LOLE 1 criteria

0.01 Wet Year Normal Dry Year Extrme Expected 0.1 Year Dry Year LOLE

LOLE (hrs/year)LOLE Figure 13. Improvement of system reliability by the increase of reservoir size. Figure 13. Improvement of system reliability by the increase of reservoir size. The LOLE in the normal hydrological year is 0.46 h/year which scarcely meets the reliability The LOLE0.01 in the normal hydrological year is 0.46 h/year which scarcely meets the reliability criterion of 0.48 h/year without any changes in the reservoir size. When the reservoir size is increased criterion of 0.48 h/year withoutWet Year any changesNormal in Drythe reservoirYear Extrme size. WhenExpected the reservoir size is increased by 30%, there is an additional 30% of stored water volume in the current year. The additional 30% by 30%, there is an additional 30% of Yearstored water volumeDry inYear the currentLOLE year. The additional 30% increase in reservoir size improved the system reliability by lowering the LOLE to 0.08 h/ year. Similar increase in reservoir size improved the system reliability by lowering the LOLE to 0.08 h/year. Similar reliability improvements are observed for the dry and extreme dry years as shown in Figure 13. An reliability improvementsFigure 13. Improvement are observed of system for thereliability dry and by theextreme increase dry of yearsreservoir as shownsize. in Figure 13. An infinite reservoir has sufficient size to prevent the spillage of water that makes the hydro system as infinite reservoir has sufficient size to prevent the spillage of water that makes the hydro system as a aThe non-energy LOLE in limited the normal system hydrological with energy year management. is 0.46 h/year In thiswhich case, scarcely the LOLE meets is mainlythe reliability caused by criterionthe forced of 0.48 outages h/year without of the generating any changes units. in th Thee reservoir infinite size. reservoir When has the lower reservoir expected size is LOLE increased than an by 30%,increase there 30% is an of reservoiradditional size 30% as of shown stored in water Figure volume 13. in the current year. The additional 30% increase Figurein reservoir 14 shows size improved the PLCC the of thesystem system reliability considering by lowering the impact the LOLE of the to three 0.08 reservoirh/year. Similar sizes and reliabilitythe four improvements hydrological are condition observed years. for Thethe dry PLCC and increased extreme fordry all years hydrological as shown conditionin Figure years13. An with infinite30% reservoir increase has of reservoir sufficient size size and to prevent infinite the reservoir spillage size. of water The PLCC that makes increased the hydro significantly system inas aa dry year from 2240 MW to 2520 MW for 30% increase of reservoir, and in an extreme dry year from 2150 MW to 2420 MW. With infinite reservoir size, the PLCC increased to 2630 MW in a dry year and 2540 MW in extreme dry year. Sustainability 2020, 12, x FOR PEER REVIEW 14 of 18 Sustainability 2020, 12, x FOR PEER REVIEW 14 of 18 non-energy limited system with energy management. In this case, the LOLE is mainly caused by the forcednon-energy outages limited of the system generating with energy units. management. The infinite reservoirIn this case, has the lower LOLE expected is mainly LOLE caused than by thean increaseforced outages 30% of reservoir of the generating size as shown units. in TheFigure infinite 13. reservoir has lower expected LOLE than an increaseFigure 30% 14 of shows reservoir the PLCC size as of shown the system in Figure considering 13. the impact of the three reservoir sizes and the fourFigure hydrological 14 shows conditionthe PLCC years.of the Thesystem PLCC considering increased the for impact all hydrological of the three condition reservoir years sizes with and 30%the fourincrease hydrological of reservoir condition size and years. infinite The reservoirPLCC increased size. The for PLCC all hydrological increased significantly condition years in a withdry year30% fromincrease 2240 of MW reservoir to 2520 size MW and for infinite 30% increase reservoir of reservoir,size. The andPLCC in increasedan extreme significantly dry year from in a2150 dry MWyear tofrom 2420 2240 MW. MW With to infinite2520 MW reservoir for 30% size, increase the PLCC of reservoir, increased and to in 2630 an extremeMW in a dry dry year year from and 25402150 MW to 2420 MW. With infinite reservoir size, the PLCC increased to 2630 MW in a dry year and 2540 MWSustainability in extreme2020, 12dry, 3663 year. 14 of 18 MW in extreme dry year. Original Reservoir Size IncreaseOriginal Reservoir30% of Reservoir Size Size 2700 InfiniteIncrease Reservoir 30% of Reservoir size Size 2700 2600 Infinite Reservoir size 2600 2500 2500 2400 2400 2300

PLCC (MW) PLCC 2300 2200 PLCC (MW) PLCC 2200 2100 2100 2000 2000 Wet Year Normal Year Dry Year Extreme Dry Expected Wet Year Normal Year Dry Year ExtremeYear Dry ExpectedPLCC Year PLCC Figure 14. Increase in PLCC after increase of reservoir size. Figure 14. Increase in PLCC after increase of reservoir size. Figure 14. Increase in PLCC after increase of reservoir size. TheThe correlation correlation between between the the system system load loadvariation variation pattern pattern and the andhydrological the hydrological pattern determines pattern The correlation between the system load variation pattern and the hydrological pattern determinesthe energy limitation the energy levels limitation in a hydro levels dominant in a hydro system. dominant A study system. was carried A study out was considering carried twoout determines the energy limitation levels in a hydro dominant system. A study was carried out consideringdifferent load two variation different patterns: load variation (1) a winter patterns: peaking (1) load a winter which peaking has a poorload correlation which has with a poor the considering two different load variation patterns: (1) a winter peaking load which has a poor correlationhydrological with pattern, the hydrological and (2) a summer pattern, peaking and (2) loada summer system peaking which hasload a system high correlation which has with a high the correlation with the hydrological pattern, and (2) a summer peaking load system which has a high correlationhydrological with pattern. the hydrological The impact pattern. on system The reliability impact on of system the correlations reliability ofof thethe loadcorrelations and river-flow of the correlation with the hydrological pattern. The impact on system reliability of the correlations of the loadpatterns and river in the-flow years patterns with the in t diheff yearserent with hydrological the different conditions hydrological is reflected conditions in the is LOLE reflected results in the as load and river-flow patterns in the years with the different hydrological conditions is reflected in the LOLEshown results in Figure as shown 15. in Figure 15. LOLE results as shown in Figure 15. Winter Peaking Load 2 PatternWinter Peaking Load 2 SummerPattern Peaking Load 1.5 PatternSummer Peaking Load 1.5 criteriaPattern criteria 1 1 LOLE (hrs/year)LOLE 0.5 LOLE (hrs/year)LOLE 0.5 0 0 Wet Year Normal Dry Year Extrme Expected Wet Year NormalYear Dry Year DryExtrme Year ExpectedLOLE Year Dry Year LOLE FigureFigure 15. 15. LOLELOLE of of different different load load patterns patterns and and hydrological hydrological conditions conditions.. Figure 15. LOLE of different load patterns and hydrological conditions. ForFor the the winter winter peaking peaking load load pattern, pattern, LOLE LOLE in in the the normal normal year year is is 0.46 0.46 h h/yea/year.r. This This value value is is within within thethe rel reliabilityForiability the winter criterion peaking ofof 0.480.48 load hh//year.year. pattern, InIn the the LOLE dry dry year inyear the and and normal extreme extreme year dry dry is year,0.46 year, h the/yea the LOLE r.LOLE This values valuevalues exceed is exceed within the thethereliability reliabilityreliability criterion criterioncriterion of the ofof the system0.48 system h/year. due due toIn the theto energythe dry energy year limitation and limitation extreme of the of dry hydrothe year, hydro system the system LOLE caused causedvalues by the exceedby poor the poorthecorrelation reliability correlation between criterion between the of river-flow the the system river and- flowdue load to and the variation load energy variation patterns.limitation patterns. However,of the hydro However, for system the summer for caused the summer peaking by the peakingpoorload pattern, correlation load pattern, the wetbetween the year, wet t normalhe year, river normal year-flow and andyear even loadand dry even variation year dry have year patterns. high have system high However, system reliability for reliability the with summer LOLE with peakingof 0.04 h /loadyear, pattern, 0.04 h/year the wet and year, 0.06 hnormal/year, respectively.year and even The dry LOLE year ofha theve high extreme system year reliability is 0.21 h /withyear which shows that the capacity reserve is well above that required by the reliability criterion. Figure 16 shows the PLCC at the LOLE criterion of 0.48 h/year. For winter peaking load pattern, the PLCC varies from 2570 MW in the wet year to 2150 MW in the extreme dry year. The difference in capacity reserve requirements in the two extreme hydrological conditions is at least 420 MW, which amounts to huge capacity investments under uncertainty. For the summer peaking load pattern, the PLCC values of the hydro system reduce gradually from 2650 MW in the wet year to 2470 MW in the extreme dry year. It should be noted that the peak load of the test system is 2380 MW, but the system can carry 90 MW additional system load even in an extreme dry year if the load variation is in high correlation with Sustainability 2020, 12, x FOR PEER REVIEW 15 of 18

LOLE of 0.04 h/year, 0.04 h/year and 0.06 h/year, respectively. The LOLE of the extreme year is 0.21 h/year which shows that the capacity reserve is well above that required by the reliability criterion. Figure 16 shows the PLCC at the LOLE criterion of 0.48 h/year. For winter peaking load pattern, the PLCC varies from 2570 MW in the wet year to 2150 MW in the extreme dry year. The difference in capacity reserve requirements in the two extreme hydrological conditions is at least 420 MW, which amounts to huge capacity investments under uncertainty. For the summer peaking load pattern, the PLCC values of the hydro system reduce gradually from 2650 MW in the wet year to 2470 MW in the extreme dry year. It should be noted that the peak load of the test system is 2380 MW, but the system Sustainability 2020, 12, 3663 15 of 18 can carry 90 MW additional system load even in an extreme dry year if the load variation is in high correlation with the river-flow variation. With the summer peaking load, the difference in PLCC in thethe river-flow two extreme variation. hydrological With conditions the summer is peakingonly 180 load,MW, the capacity difference costs inPLCC of which in thecantwo be compared extreme hydrologicalto the costs of conditions 420 MW for is only the winter 180 MW, peaking the capacity load. A costs demand of which side canmanagement be compared policy to the to improve costs of 420the MWcorrelation for the winterof the load peaking with load. the river A demand-flow variation side management is highly desired policy to in improve a hydrothe dominant correlation power of thesystem. load with the river-flow variation is highly desired in a hydro dominant power system.

Winter Peaking Load Pattern 2700 Summer Peaking Load Pattern 2600 2500 2400 2300

PLCC (MW) PLCC 2200 2100 2000 Wet Year Normal Dry Year Extreme Expected Year Dry Year PLCC

Figure 16. PLCC of the hydro system with winter/summer peaking load patterns. Figure 16. PLCC of the hydro system with winter/summer peaking load patterns. A sensitivity analysis was performed on the modified IEEE RTS to assess the impact of the energyA management sensitivity analysis strategy was on performed the loss of on load the and modified energy IEEE indices RTS by to varying assess the the impact system of peak the demand,energy management reservoir size strategy and system on load the loss variation of load pattern. and energy The expected indices system by varying LOLE the and system LOEE were peak evaluateddemand, withreservoir and withoutsize and implementing system load thevariation year to pattern. year energy The managementexpected system strategy LOLE for and reliability LOEE enhancementwere evaluated on with the base and system.without Theseimplementing indices werethe year also to evaluated year energy considering management 30% increasestrategy for in reservoirreliability volume enhancement and varying on the system base system. peak load These and indices the load were profile also obtained evaluated through considering demand-side 30% managementincrease in reservoir with high volume correlation and varying with the the seasonal system river-flow.peak load and Figures the load 17 and profile 18 respectively obtained through show thedemand expected-side system management LOLE and with LOEE high increasecorrelation with with the increasethe seasonal in the river system-flow. peak Figure load 17 considering and Figure the18 above-mentionedrespectively show factors.the expected As compared system LOLE to the caseand LOEE without increase energy with management, the increase the in year the tosystem year energypeak l managementoad considering results the in above a significant-mentioned reduction factors. in the As system compared LOLE toand the LOEE. case The without figures energy show thatmanagement, there is further the year improvement to year energy in system management reliability results with the in increasea significant in reservoir reduction size in by the 30%, system and theLOLE implantation and LOEE. of The the demandfigures show side management.that there is further It can beimprovement noted that the in applicationsystem reliability of the demandwith the sideincrease management in reservoir provides size by arelatively 30%, and large the implantation improvement of in the the demand reliability side of themanagement. system as shown It can inbe SustainabilityFiguresnoted that 17 20 and the20, 1 18application2, x. FOR PEER of REVIEW the demand side management provides a relatively large improvement16 of 18 in the reliability of the system as shown in Figures 17 and Figure 18. 1.4 Before Energy Management 1.2 Year to Year Energy Management Increase 30% of Reservoir Size 1 Demand Side Management 0.8 0.6

LOLE (hrs/year)LOLE 0.4 0.2 0 2000 2100 2200 2300 2400 2500 System Peak Load (MW)

FigureFigure 17. 17. VariationVariation in in expected expected LOLE LOLE with with the the system system peak peak load load using using different diﬀerent reliability reliability enhancementenhancement strategies. strategies.

140 Before Energy Management 120 Year to Year Energy Management 100 Increase 30% of Reservoir Size Demand Side Management 80 60

40 LOEE (MWhr/year) LOEE 20 0 2000 2100 2200 2300 2400 2500 Syetem Peak Load (MW) Figure 18. Variation in expected loss of energy expectation (LOEE) with the system peak load using different reliability enhancement strategies.

5. Conclusions The reliability of the hydro dominant system is significantly affected by the seasonal and yearly variation of the hydrological conditions. This paper presents a new probabilistic method that accounts for the uncertainties in the hydrological condition in the energy management strategy to improve the reliability of the system. Diurnal, seasonal and yearly energy management strategies are applied in run-of-river and storage type hydropower plant operation to minimize the reliability impact of energy uncertainty and maintain long-term system adequacy. Furthermore, these energy management strategies are incorporated into the year to year energy management strategy to save water in a normal or wet year with minimal impact on the system reliability and to maximize the availability of water in an upcoming energy uncertainty year. Although year to year energy management improves the reliability of the system, the amount of water that can be carried from one year to another is restricted due to the reservoir capacity. Therefore, the result of increasing the reservoir capacity together with the year to year energy management was investigated. Increasing the reservoir capacity results in a larger volume of water that can be carried over from the current year to the upcoming year which further improves the reliability of the system. However, increasing the reservoir capacity is not always a feasible solution. The studies presented in this work show that a strong positive correlation between the river flow pattern and the load has a great positive impact on the system reliability. The application of the demand side management to change the system’s load pattern to follow the hydrological condition can significantly improve the reliability of a hydro Sustainability 2020, 12, x FOR PEER REVIEW 16 of 18

1.4 Before Energy Management 1.2 Year to Year Energy Management Increase 30% of Reservoir Size 1 Demand Side Management 0.8 0.6

LOLE (hrs/year)LOLE 0.4 0.2 0 2000 2100 2200 2300 2400 2500 System Peak Load (MW)

Figure 17. Variation in expected LOLE with the system peak load using different reliability Sustainability 2020, 12, 3663 16 of 18 enhancement strategies.

140 Before Energy Management 120 Year to Year Energy Management 100 Increase 30% of Reservoir Size Demand Side Management 80 60

40 LOEE (MWhr/year) LOEE 20 0 2000 2100 2200 2300 2400 2500 Syetem Peak Load (MW) FigureFigure 18. 18. VariationVariation in in expected expected loss loss of of energy energy expectation expectation ( (LOEE)LOEE) with with the the system system peak peak load load using using differentdifferent reliability reliability enhancement enhancement strategies strategies.. 5. Conclusions 5. Conclusions The reliability of the hydro dominant system is significantly affected by the seasonal and yearly The reliability of the hydro dominant system is significantly affected by the seasonal and yearly variation of the hydrological conditions. This paper presents a new probabilistic method that accounts variation of the hydrological conditions. This paper presents a new probabilistic method that for the uncertainties in the hydrological condition in the energy management strategy to improve accounts for the uncertainties in the hydrological condition in the energy management strategy to the reliability of the system. Diurnal, seasonal and yearly energy management strategies are applied improve the reliability of the system. Diurnal, seasonal and yearly energy management strategies are in run-of-river and storage type hydropower plant operation to minimize the reliability impact of applied in run-of-river and storage type hydropower plant operation to minimize the reliability energy uncertainty and maintain long-term system adequacy. Furthermore, these energy management impact of energy uncertainty and maintain long-term system adequacy. Furthermore, these energy strategies are incorporated into the year to year energy management strategy to save water in a normal management strategies are incorporated into the year to year energy management strategy to save or wet year with minimal impact on the system reliability and to maximize the availability of water water in a normal or wet year with minimal impact on the system reliability and to maximize the in an upcoming energy uncertainty year. Although year to year energy management improves the availability of water in an upcoming energy uncertainty year. Although year to year energy reliability of the system, the amount of water that can be carried from one year to another is restricted management improves the reliability of the system, the amount of water that can be carried from one due to the reservoir capacity. Therefore, the result of increasing the reservoir capacity together with year to another is restricted due to the reservoir capacity. Therefore, the result of increasing the the year to year energy management was investigated. Increasing the reservoir capacity results in a reservoir capacity together with the year to year energy management was investigated. Increasing larger volume of water that can be carried over from the current year to the upcoming year which the reservoir capacity results in a larger volume of water that can be carried over from the current further improves the reliability of the system. However, increasing the reservoir capacity is not always year to the upcoming year which further improves the reliability of the system. However, increasing a feasible solution. The studies presented in this work show that a strong positive correlation between the reservoir capacity is not always a feasible solution. The studies presented in this work show that the river flow pattern and the load has a great positive impact on the system reliability. The application a strong positive correlation between the river flow pattern and the load has a great positive impact of the demand side management to change the system’s load pattern to follow the hydrological on the system reliability. The application of the demand side management to change the system’s condition can significantly improve the reliability of a hydro dominant system. Therefore, all these load pattern to follow the hydrological condition can significantly improve the reliability of a hydro reliability enhancement strategies have significant importance in the operation and planning of the hydro dominant system under hydrological uncertainties. The methodology proposed and the case studies presented in the paper provide a practical approach for a long-term system adequacy planning of the hydro dominant system.

Author Contributions: Conceptualization, F.F. and R.K.; methodology, F.F.; writing-original draft preparation, F.F.; writing-review and editing, R.K. and P.P.; supervision, R.K. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Canada Natural Science and Engineering Research Council (NSERC) grant number RGPIN-2015-06327 And The APC was funded by NSERC grant. Conﬂicts of Interest: The authors declare no conﬂict of interest. Sustainability 2020, 12, 3663 17 of 18

Nomenclature

α turbine efficiency A reservoir area (m2) C rated capacity of hydro unit (W) D reduced generation capacity of hydro unit (W) g gravitational constant m/s2 H net head of hydropower plant (m) InV reservoir inflow water volume (m3) LOLE loss of load expectation (hours/year) LOEE loss of energy expectation (MWhr/year) OutV reservoir outflow water volume (m3) P hydro unit output power (W) PLCC peak load carrying capacity (MW) Q discharge (m3/s) s specific weight of water (kg/m3) V reservoir volume (m3)

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