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1 INTRODUCTION

There is currently a growing trend towards the

introduction of photovoltaic and wind power plants

in Electric Power Systems (EPS). This responds to the

need to replace conventional units that use fossil fuels,

as a measure to reduce the growing environmental

pollution and its depletion. However, solar generation

has an inherently intermittent character, due to solar

irradiation behavior incident on the panels [1-4].

Two causes can be distinguished in solar daily

irradiation pattern. The first one corresponds to the

diurnal variation cycle and the second one is related

to local effects caused by rapid low clouds movement

over the panels [2-5]. Large variations in solar

irradiance due to the first cause are easily predictable

and relatively slow, typically less than 1%/min, while

those due to the second cause can reach values greater

than 10%/min and are difficult to forecast [1]. The

beginning and end of shadows, due to these clouds,

cause large variations in solar irradiation incident on

the photovoltaic panels. This can be detrimental to

their operation, not allowing them to follow the

maximum power point programmed in their work

algorithm (MPPT), as well as causing rapid active

power imbalances in the system to which they are

connected, with frequency deviations from their

nominal values, negatively affecting the quality of the

energy delivered to the system, as well as their safe

operation.

The increasing penetration of generation from

renewable energy sources, especially solar,

significantly amplifies the problems mentioned above

and is therefore a reason for research aimed at

Solar Generation Estimation in Electric Power Systems

for Prospective Frequency Control Studies

A.A. Martínez

-García

, O.E. Torres-Breffe

, M. Vilaragut-Llanes

, O. Delgado-Fernandez

Szpytko

& Y. Salgado-Duarte

Technological University of Havana "José Antonio Echeverría", Havana, Cuba

AGH University of Science and Technology, Kraków, Poland

ABSTRACT: Increasing the presence of non-conventional clean energy sources in Electrical Power Systems

(EPS) is a global strategic goal. Particularly, photovoltaic systems are attractive due to their versatility, low

maintenance cost, easy installation, noiselessness, etc. However, the integration of photovoltaic systems into

EPS increases the necessary regulation actions performed by system generators due to stochastic fluctuations of

solar radiation, especially on cloudy days. Even using complex models that consider many variables, solar

irradiation and its corresponding photovoltaic power generation are difficult variables to forecast with accuracy

in cloudy day scenarios. To address this problem, Energy Storage Systems (BESS) have been proposed as a

solution to mitigate the variability of photovoltaic generation, which reduce the need to use traditional spinning

reserves and provide auxiliary grid services. The BESS selection required to mitigate photovoltaic generation is

directly related to the worst-case daily variability of photovoltaic generation in the short term. This paper

proposes a practical estimation of daily perspective photo voltage solar generation curve in Electrical Power

Systems.

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promoting quality regimes and safe system operation

[5]. In many countries, restrictions have been

established to control power fluctuations of grid-

connected photovoltaic power plants to ensure the

reliability and quality of the generated active power.

An example of the above statement is the case of

Puerto Rico, where a maximum limit of photovoltaic

power generated variation has been established in

10% of their nominal capacity per minute [6].

Similarly, in Germany, transmission grid operators

have imposed a ramp variation limit of 10% per

minute like the case of Puerto Rico [6].

Multiple studies have measured, by means of

irradiation sensors, the variability of irradiation in

photovoltaic power plants, proving that it can vary

more than 50% of its nominal values in 1 second

intervals [7-8]. This makes the use of BESS energy

storage sources necessary to satisfy the constraints of

ramp variations of generated power in different

countries, since conventional units are not capable of

varying their generation in such small-time intervals

with the necessary speed. Furthermore, BESS function

is to reduce the ramp variations in either direction of

photovoltaic power generation plants to the stipulated

values [9].

The effect of solar radiation variability on

photovoltaic power plants is different when analyzing

a single plant or a set of plants distributed in a certain

region. Previous studies have been reported in

different scenarios that when a set of plants is

considered, there is a strong effect of generated power

variability reduction, which is called "smoothing

effect" [7-10]. This effect derives from the typical

cloud dimensions (1-10 Km) and its velocity.

The variability reduction (VR) is defined in [10] as

the ratio between the variances calculated at a present

time interval according to the expression:

∆

(1)

where σ

Δt is the generated power variance in a

photovoltaic power plant in the time interval Δt; σ

Δt

is the total generated power variance in the set of

photovoltaic power plants in the time interval Δt.

Studies reported in [10] for time intervals of 10

minutes show that variability reduction ranges from

1.7 to 3.3 times. The study period was 1 year. In

similar studies [1], performing calculations in 5-

minute intervals, in one year period, report values

between 2.4 and 4.1. This shows that the variability

depends on considered time interval. The longer the

time interval, the smaller the reduction of variability,

i.e., the smaller the flattening effect of the generated

power. In [12-13] it is shown that, with no correlation

between generated photovoltaic plants powers,

variability of a set N of farms can be calculated as:

∆

(2)

The correlation between the powers generated by

the set of farms will depend on the geographical

separation between their locations. In [14] it is shown

that the correlation coefficient between photovoltaic

farms decreases as the distance between their

locations increases. In [15] it is established that in

order to perform perspective calculations it is of

utmost importance to estimate the maximum variation

of the generated power of the future set of farms,

considering their locations and the corresponding

flattening effect of the summary generation, to avoid

oversizing BESS capacities of necessary units for an

effective frequency control under these conditions,

with the corresponding economic effects. In [16] it is

verified that high values of irradiance variation,

measured by sensors in photovoltaic generation plants

in small time intervals, are not reflected in similar

values of power variations in the complete plant or to

sets of plants, which could be impacting in system

behavior.

What would be then the time intervals that should

be considered, to estimate power variation in

photovoltaic power plants, to determine their

interaction with the system to which they are

connected and therefore their influence on frequency

control?

In [16] it is stated that time intervals depend on the

type of study to be executed, for the case of frequency

regulation studies the intervals would be in the order

of seconds to minutes. In the case of load covering

studies, the intervals to be analyzed correspond to

tens of minutes and in the case of economic dispatch

and planning of electric power systems, the variability

associated with the diurnal cycle is the necessary to be

considered.

To estimate BESS nominal values, (Power and

Energy), necessary to perform primary and secondary

control of frequency, with important increases of

photovoltaic penetration, it is necessary to start from

perspective estimates of photovoltaic power

generated in the days of greater variations, where

intervals of several seconds to minutes are considered.

This implies starting from current simultaneous

measurements of power in existing installations that

have a sampling time of at least one second. From

these measurements it is possible to estimate the

future behavior when solar photovoltaic penetration

in the system increases. The estimation must consider

the flattening effect of the photovoltaic generation, the

existence or not of correlation between different

plants generated power, as well as different climatic

seasons during the year and the possible variations

from one year to another. Similar calculations must be

made for wind power plants if the total installed

power does not allow to disregard the variations

caused by the randomness of the wind in perspective

calculations.

From these calculations and using concentrated

models of the considered power system [17-18], it is

possible to estimate BESS nominal values that ensures

an adequate frequency performance. In these models,

photovoltaic and wind generated powers should be

included, by means of "lookup" tables during the days

of greater variability in intervals of the order of one

second. In analyzed works, studies are reported to

select BESS nominal values that globally compensate

active power variations resulting from an important

penetration of photovoltaic power plants. The

213

selection criterion, under these conditions, is the

system frequency behavior.

In the present work, daily average solar power

generation curve is estimated in per unit (p.u.) with

respect to installed capacity under 2030 system

conditions. For this purpose, it is necessary to assume

that it´s shape is like that of the current average curve

of maximum daily variations obtained from database

processing of years 2019 and 2020. In subsequent

works, estimates of Cuban System frequency behavior

for different nominal values of BESS will be

presented.

The present work is structured as follows. Section

II presents information of processing tool required to

estimate photovoltaic generation in 2030. Section III

presents the necessary requirements for BESS nominal

values estimation. Section IV presents the estimated

maximum daily solar generation curve and Section V

presents conclusions.

2 PROCESSING TOOL DEVELOPMENT

In the Republic of Cuba, a significant penetration is

planned for the coming years, bringing the generation

by non-conventional plants to around 25% of the total

generated power in 2030. To estimate the future

behavior of the photovoltaic power generated in a

daily cycle, considering its variation in intervals of

several seconds to minutes, it is necessary to start

from the information of the current generation

performance in the system in different actual existing

installations, which requires the processing of

extensive databases. This is practically impossible if

there are no computer programs developed for this

purpose.

In Cuban Electrical System, power of most of the

installed photovoltaic generation plants ranges

between 4 and 6 MW and they are planned to be

separated from each other by no less than 8 km to

make the correlation between the generated powers

negligible [19].

FREDAT V1.0 tool developed by the authors for

this purpose is presented. This tool, based on

simultaneous measurements of active power

generated every second in different solar generation

plants in the form of Excel tables, performs the

following actions:

− Filters the database, eliminating erroneous values

and making interpolations between values when

losses of measurements are detected in the

database.

− Determines the curves corresponding to the

highest power variation observed on the day of the

solar farm under study, on the days with the

highest incidence of clouds, previously selected

using adjustable length windows.

− From the set of solar farms under study in a day,

the combination of solar farms with the highest

and lowest generation variation corresponding to

different combinations of a selected number of

solar farms, as well as the summary power curve

in one-second intervals. From these curves, an

average variation power curve is obtained for the

analyzed day from the combinations with the

highest and lowest variation.

− For adjustable time windows, curves of average

power values are calculated, and from them the

sum of power values above and below these

average values, calculated as:

(

)

PP t−∆

(3)

where P

i is the instantaneous power and Pm is the

mean value calculated using the adjustable

window and Δt is the time interval between

measurements. In this way it is possible to estimate

the energy value during the day, necessary to

cover the variability of the generated power with

respect to the average values previously calculated.

− Maximum and minimum values of energy during

the day are calculated for isolated farms or

combinations of N farms previously selected in the

main screen.

To better understand the performance of the

developed tool, Figure 1 shows it main screen. The

database must be stored in a folder with known

address in Excel format. To start the work, the

location of this folder must be placed in the upper left

part of the screen.

Figure 1. Main tool screen of FREDAT V1.0.

214

Next, all the files in the database are displayed,

which are selected by clicking on the arrow and the

files corresponding to generated powers during

different days in the different PV plants of the system

are loaded, which are listed in the third column by

their names when analyzed day is selected.

The buttons in the fourth column allow selected

plants deletion. The second button eliminates any

errors that may exist in the database and fills in the

missing measurement information by linear

interpolation. The last button saves the database ready

to start calculations.

Before starting it is necessary to set the common

power base, because the farms have different powers,

and it is necessary to take a common base. This is

done in the space under the “Potencia Base” (Power

Base) sign. Under the option "Ventana de variabilidad

(min)" (Variability window (min)) the size of the

window for the calculations is selected. If a farm is

selected and the variability key is pressed, the result

shown in Figure 2 appears for the selected farm, in

this case 11, which corresponds to Santa Teresa Farm.

Figure 2. Power generated from Santa Teresa Farm.

Figure 3 shows how the program calculates the

maximum variation, which in this case is by moving a

5-minute window over the database and calculating

the maximum power variation in that window and

updating it as the window moves through all the data

so that at the end the highest generated power in the

window for the selected generating plant on the day is

selected.

Figure 3. Calculation of the largest power variation by

moving a 5-minute window over the data base.

To calculate the variation of several plants of the

total number of plants loaded, click on the “Múltiple

Variabilidad” (Multiple Variability) key and mark the

number of plants to calculate this variation as shown

in Figure 4.

Figure 4. Maximum variation for combinations of four

farms by 5-minute window movement over the database.

In this case, the maximum and minimum variation

of four farms combinations are calculated from the set

of 11 farms loaded in the program. The values of

maximum variation in p.u. with respect to the

capacity of the farms in the case of one farm is 0.847pu

for the Santa Teresa Farm and in the case of four farms

it is lower.

The above is the result of the flattening effect

resulting in 0.51pu, corresponding to the farms Pinar

2, Caguagua, Guasimal and Santa Teresa, in the case

of the four farms shown in Figure 4.

The program also calculates farms combination

considered to cause the lowest power variation during

the day as shown in Figure 5, for three farms

combinations. From the curves of maximum and

minimum variation calculates curve of average values

of power variation.

In the case of three farms combinations, from the

total of 11 farms in the database, 165 combinations are

required to determine the group with maximum

variation. In the case of five farms combinations, the

number of required combinations for comparison

reaches 462.

Figure 5. Minimum, mean and maximum variation for

combinations of three generating plants from a database of

11 units.

The objective of processing the databases of the

generating plants is to estimate the values of the

highest power variation of a set of N plants that

would work connected to the grid at a future date to

estimate the nominal values of the BESS that could

compensate these variations.

In multiple works [10-13] it is found that the

maximum power variation of a set of plants decreases

as the number of plants increases. In [20] it is

established that an acceptable estimate of this

variation can be estimated from successive operations

for all combinations of plants in the data. Thus, it is

possible to determine with sufficient accuracy the

trend of the maximum power variations. Carried out

calculations show that from a given number of farms

in the data the results tend to practically the same

values.

215

The developed tool provides this possibility by

adjusting the trend of the maximum variation curve of

the generated power as a function of the number of

grouped farms, just by pressing the "Variability

Curve" key. Figure 6 shows the results for groupings

from 1 to 11 farms on a selected day. In this case, the

values of the different groupings for the maximum

power variation on the selected day is estimated as

follows:

( )

0.36386

0.66956 0.22119

−

= +

(4)

where N is the corresponding number of grouped

plats.

If the number of plants is large then it can be

considered that the value of maximum variation of the

generated power would correspond to the

independent term of the equation 0.2212 p.u., which

corresponds to 22.12% of N plants power connected to

the system. The above can be seen in Figure 6 where

the curves for minimum and average power variation

for different groupings are also shown.

Figure 6. Results of the perspective calculation of the

variation of the generated power for the case of 10 plants

connected to the system for the selected day.

Days with the highest variability in the year(s), are

selected as the initial database, see Table I in

Appendix. Maximum power variation will be an

upper limit to be considered for necessary BESS

nominal values to compensate these power variations.

For the above-mentioned reasons, it is possible to

know the average values so that the specialist can

decide the values to be considered in BESS selection.

In the case of the energy necessary values to

compensate the power variations around the average

are calculated with 15-minute windows, the program

looks for the sum of the instantaneous powers that

exceed or not this average value to then calculate the

energies delivered or consumed with respect to this

average value and the sum of these accumulated

energies, each one with its sign allow us to estimate

the maximum energy that a BESS would produce to

compensate for the power variations of the

photovoltaic plants.

Figure 7 shows this procedure graphically, where

the red curve represents the average values and below

the red areas correspond to the energy consumed by

the BESS and in blue the energy that should be

delivered. The values of interest would be the

maximum accumulated values during the day,

consumed or delivered.

Figure 7. Maximum energy calculation process to cover

variations in power generated by photovoltaic plants.

Similar procedures can be performed for different

combinations of farms working with the total

generated power and proceed in a similar way as in

the case of calculating the maximum variation of the

power when N plants are tended. Figure 8 shows the

results.

Figure 8. Energy trend as a function of number of plants.

3 REQUIREMENTS FOR BESS NOMINAL VALUES

SELECTION

The BESS used in frequency control must not only

compensate the variability of the power generated by

the photovoltaic plants but also be able to, in cases of

important active power deficits in the system,

maintain the frequency at acceptable values until

measures can be taken to restore the normal working

regime of the system, and this condition is usually the

one that determines the energy values of the BESS

required to be implemented in the system [20].

To reliably select the nominal values of the BESS in

[19] it is established that it is necessary to take into

account: Considerations related to the lifetime of the

battery, such as Depth of Discharge (DoD),

temperature, life cycle as well as other aspects such as

its efficiency and the requirements of its behavior in

the system.

Among these requirements are:

216

− Perform primary and secondary frequency control

by limiting the participation of conventional units

only at times when large power unbalances are

generated. This is possible by adjusting dead bands

in the BESS lower than those of conventional units

and adjusting lower droops in their active power

controls.

− Decrease the primary and secondary regulation

reserves of the conventional units, favoring their

efficient work and increasing the planned

maintenance intervals.

− In case of sudden departures of generating units, it

must be able to maintain acceptable frequency

values for a sufficient period so that measures can

be taken for tertiary frequency control or decision

making by the operators to restore the working

regime to safe conditions.

To verify compliance with all these considerations,

it is necessary to model system behavior under

working conditions that are estimated to occur in the

future, using simplified concentrated models of the

generators, the BESS and its controls, the predicted

daily load curve, the curves of the total power

generated by all the photovoltaic and wind power

plants in one second intervals, which would be

connected to the system at the analyzed time.

4 DAILY PHOTOVOLTAIC GENERATION CURVE

ESTIMATION FOR THE YEAR 2030

In the case of the Cuban System, it is projected that by

the year 2030 the solar installed capacity will be

around 2000MW. To check the behavior of the

frequency using BESS of different nominal values, it is

necessary to study the behavior of its load state

during the day, which avoids the decrease of its

lifetime.

For important capacities of solar generation, curves

of this generation must be obtained by similar

procedures using solar generation databases. The

question to answer then would be:

What would be the maximum power variation in

MW of N farms whose installed power is 2000MW

and from this the summary power curve every

second?

Maximum variation estimated processing

measurements from six photovoltaic farms was

0.3232pu, and its trend for many farms is 0.251pu. If

the base taken to make the current power sums was

20MW, this maximum variation can be estimated as:

max

2000 0.251 20

0.3232 32.48



= ×





(5)

where the factor 20/32.48 reduces the values to p.u.

with respect to the capacity of the six farms and the

factor 0.251/0.3232 considers the flattening of the

maximum variation when the number of farms tends

to a large number.

If we multiply the graph of average generated

power of the six farms in p.u. in the day based on

their sum power by the factor seen above, we will

have the generated power estimation when there is an

installed capacity of 2000MW. The results obtained

from the above estimation in the interval from 7am to

7pm are shown in Figure 9. Maximum power

variation in 5-minute window in the analyzed case is

in the order of 500MW.

Figure 9. Estimated solar generation curve (7am-7pm) with

maximum power variations in the Cuban “Sistema

Electroenergético Nacional” (National Power System) in

2030.

This does not mean that the BESS should have a

capacity of 500MW because it represents a higher

value. To estimate more reliable values it is necessary,

using concentrated models of the system, and the

curves of solar and wind generation in 1 second

intervals, to check the behavior of the frequency for

different nominal values of the BESS, as well as the

time that can maintain the reliable work of the system

before critical conditions of outputs of generating

units, with the objective of allowing the operator to

make decisions for system recovery.

5 CONCLUSIONS

The computational tool developed allows, from a

database of current simultaneous measurements of the

power generated in photovoltaic units, to project into

the future to estimate the maximum variation of this

generation in the day, knowing the total installed

power, as well as the estimation of the curve of

greater variations of power generated in the day.

This curve is necessary for the selection of the

BESS that meets all the requirements for its use in

frequency control in the system. In order to verify the

above, modelling is required to verify the fulfilment

of these requirements, which will be the subject of

future works.

ACKNOWLEDGMENT

The work has been financially supported by the Polish

Ministry of Education and Science.

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