THE METHOD FOR DETERMINING THE EFFECTIVE TOTAL LOAD SHEDDING FOR UNDER-FREQUENCY LOAD SHEDDING OF THE POWER SYSTEM
This paper suggests a method for determining the effective total amount of load disconnection in case of major frequency drop and under-frequency load shedding (UFLS) activation.  A mathematical model of power balance in emergency areas has been developed, which uses the structure of th...
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| Дата: | 2025 |
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| Формат: | Стаття |
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Institute of Renewable Energy National Academy of Sciences of Ukraine
2025
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Репозитарії
Vidnovluvana energetika| _version_ | 1871103865654345728 |
|---|---|
| author | Lytvynchuk, V. Kaplin , M. Karmazin , O. |
| author_facet | Lytvynchuk, V. Kaplin , M. Karmazin , O. |
| author_institution_txt_mv | [
{
"author": " V. Lytvynchuk",
"institution": "Institute of Renewable Energy of the National Academy of Sciences of Ukraine, Kyiv, Ukraine"
},
{
"author": "M. Kaplin ",
"institution": "Institute of General Energy of the National Academy of Sciences of Ukraine, Kyiv, Ukraine"
},
{
"author": "O. Karmazin ",
"institution": "Institute of Renewable Energy of the National Academy of Sciences of Ukraine, Kyiv, Ukraine"
}
] |
| author_sort | Lytvynchuk, V. |
| baseUrl_str | https://ve.org.ua/index.php/journal/oai |
| collection | OJS |
| datestamp_date | 2026-07-18T06:32:21Z |
| description | This paper suggests a method for determining the effective total amount of load disconnection in case of major frequency drop and under-frequency load shedding (UFLS) activation. 
A mathematical model of power balance in emergency areas has been developed, which uses the structure of the electric network scheme. 
The UFLS is presented in the model by a set of frequency relays with fixed consumer loads behind feeders along the year and binary variables triggering their operation. 
The solution of the integer linear programming problem provides the optimal set of the relays needed to balance all emergency areas given the minimum total load shedding (TLS). 
This determines both the TLS and the placement of individual relays in the electrical network. 
The method involves pre-measurement of the consumer loads behind feeders, as well as power flows in the network for its characteristic modes. 
For this purpose, standard specialized software is used to calculate stationary modes and contingency analysis. 
The input data for the simulation is also a set of electrically unconnected emergency areas. 
This information should be provided by the user of the proposed method by indicating the overhead line cross-sections in electric network. 
The developed method allows to determine the TLS of UFLS and the most efficient set of frequency relays for any power system in order to align these indicators with the requirements of the National Electricity Transmission System Operator. 
  |
| doi_str_mv | 10.36296/1819-8058.2025.1(80).13-21 |
| first_indexed | 2025-07-17T11:39:48Z |
| format | Article |
| fulltext |
13
Відновлювана енергетика. №1/2025 | Комплексні проблеми енергетичних систем на основі НВДЕ
UDC 621.316.786 https://doi.org/10.36296/1819-8058.2025.1(79)13-21
THE METHOD FOR DETERMINING THE EFFECTIVE TOTAL LOAD SHEDDING FOR UNDER-FREQUENCY
LOAD SHEDDING OF THE POWER SYSTEM
Received Oct. 09, 2024; accepted Mar. 14, 2025
Available online Apr. 01, 2025
Lytvynchuk V.1, Kaplin M.2, Karmazin O.3
Author for correspondence: Lytvynchuk Volodymyr,
e-mail: volyt@ukr.net
Abstract. This paper suggests a method for determining the effec-
tive total amount of load disconnection in case of major frequency
drop and under-frequency load shedding (UFLS) activation.
A mathematical model of power balance in emergency areas has
been developed, which uses the structure of the electric network
scheme.
The UFLS is presented in the model by a set of frequency relays
with fixed consumer loads behind feeders along the year and binary variables triggering their operation.
The solution of the integer linear programming problem provides the optimal set of the relays needed to balance
all emergency areas given the minimum total load shedding (TLS).
This determines both the TLS and the placement of individual relays in the electrical network.
The method involves pre-measurement of the consumer loads behind feeders, as well as power flows in the
network for its characteristic modes.
For this purpose, standard specialized software is used to calculate stationary modes and contingency analysis.
The input data for the simulation is also a set of electrically unconnected emergency areas.
This information should be provided by the user of the proposed method by indicating the overhead line cross-
sections in electric network.
The developed method allows to determine the TLS of UFLS and the most efficient set of frequency relays for
any power system in order to align these indicators with the requirements of the National Electricity Transmis-
sion System Operator.
Keywords: Under Frequency Load Shedding (UFLS), Low Frequency Demand Disconnection (LFDD), Total Load
Shed, Total Percentage Demand LFDD.
МЕТОД ВИЗНАЧЕННЯ ЕФЕКТИВНОГО ОБСЯГУ АВТОМАТИЧНОГО ЧАСТОТНОГО
РОЗВАНТАЖЕННЯ ЕНЕРГОСИСТЕМИ
Отримано 09 жов. 2024 р.; рекомендовано до публікації 14 бер. 2025 р.
Доступно онлайн 01 квіт. 2025 р.
Литвинчук В. А.1, Каплін М. І.2, Кармазін О. О.3
Автор для кореспонденції: Литвинчук Володимир,
e-mail: volyt@ukr.net
Анотація. Система автоматичного частотного розван-
таження (АЧР) є єдиним засобом, який широко застосову-
ється в енергосистемах для стримування швидкого па-
діння частоти. Система АЧР здатна майже раптово
відключити частину споживачів та зупинити падіння час-
тоти в районах енергосистеми, які утворилися в резуль-
таті каскадного відключення ліній і генераторів. Для підтримки тимчасового балансу активної по-
тужності в аварійних ситуаціях в енергосистемі повинна бути передбачена кількість навантаження
на відключення.
1 Scientific researcher
https://orcid.org/0000-0003-4727-7800
2 Cand. of Tech. Science
https://orcid.org/0000-0001-9328-4257
3 Cand. of Tech. Science
https://orcid.org/0000-0002-7628-6880
1, 3 Institute of Renewable Energy of the
National Academy of Sciences of Ukraine,
Kyiv, Ukraine
2 Institute of General Energy of the National
Academy of Sciences of Ukraine, Kyiv, Ukraine
1 наук співр.
https://orcid.org/0000-0003-4727-7800
2 канд. техн. наук
https://orcid.org/0000-0001-9328-4257
3 канд. техн. наук
https://orcid.org/0000-0002-7628-6880
1, 3 Інститут відновлюваної енергетики НАН
України, м. Київ, Україна
2 Інститут загальної енергетики НАН України,
м. Київ, Україна
14
Відновлювана енергетика. №1/2025 | Комплексні проблеми енергетичних систем на основі НВДЕ
Тому оператори систем передачі або мережа операторів систем передачі електроенергії встанов-
люють так званий загальний обсяг розвантаження (ЗОР). Найчастіше в стандартах та норматив-
них документах енергосистем цей показник розраховується в умовах загального пікового попиту. Во-
дночас ЗОР рекомендують розмістити в енергосистемі рівномірно, з урахуванням географії мережі.
Такий спосіб розміщення загального обсягу розвантаження не враховує електричної структури елек-
тромережі, добової та сезонної зміни генерувальних потужностей і споживання, не зважаючи на те,
що стандарти та нормативні документи вимагають це враховувати.
В роботі запропоновано математичну модель і спосіб визначення ЗОР системи АЧР та його розмі-
щення в мережі енергосистеми з урахуванням розподіленої генерації, ймовірних варіантів аварійного
поділу енергосистеми, контрольованих перетинів вимог міжнародних стандартів та нормативних
документів, що регулюють функціонування систем протиаварійного захисту в галузі електроенер-
гетики. Модель являє собою задачу цілочисельного (бінарного) лінійного програмування, що здійснює
вибір оптимального набору пристроїв АЧР, які розміщені у наперед заданих вузлах енергосистеми й
спрацювання яких забезпечує баланс потужності в аварійних районах її поділу. Електричні параметри
усталених режимів, а також ефективність оптимального обсягу та розподілу розвантаження в ме-
режі визначаються й перевіряються (верифікуються) у серії апріорних та апостеріорних розрахунків
на точних математичних моделях, визнаних у світовій практиці програмних продуктів електроене-
ргетики.
Отриманий таким чином розподіл обсягів розвантаження підвищує ймовірність балансування якнай-
більшої кількості аварійних районів енергосистеми за умови задоволення вимог щодо частотно-часо-
вої зони відповідних перехідних процесів.
Ключові слова: енергосистема, автоматичне частотне розвантаження, знеструмлення, блекаут.
I. Introduction
Over the last decades, all large-scale accidents in national
TSOs with a large frequency drop, were cascading failures
[1-3].
The emergency was initiated by cascading lines tripping. As
a result, the system split into electrically unconnected areas
not balanced by the emergency automation system. And
for that reason, the operation of part of the TSOs ceased.
[3, 4].
At the same time, there has been no frequency collapse in
the entire power system (without cascade shutdown in the
power system) in recent decades.
This can be explained by the fact that modern power sys-
tems have such a large total capacity of generating units
that the failure of a single one or even an aggregation can
reduce the frequency but will not cause a fast frequency
drop.
For example, let us consider the 2019 emergency in the UK
[10] or the 2021 emergency in the European Network of
Transmission System Operators (ENTSO-E) [11].
In the first case, the UK power system was not divided into
parts. None of the transmission lines were overloaded.
The rate of frequency reduction was slow, but at the time
of the accident there was not enough backup generation to
balance the power system [15].
Therefore, the frequency reduction was suspended by the
first stage Low Frequency Demand Disconnection (LFDD)
with 48.8Hz relay settings (in the report “LFDD” [10] corre-
sponds to “UFLS” [5, 6, 11], and “stage” 10] to “step” [5, 6,
11]).
The first stage of UFLS had 5% of total demand in England
& Wales.
The other emergency divided the power system into two
parts.
After the separation of North-West and South-East electric
power flows by ENTSO-E, the frequency in the North-West
area fell to merely 49.74 Hz.
At the same time, the frequency in the South-East area ini-
tially increased up to 50.6 Hz [11].
It can be argued that frequency drop to the set point of
UFLS is unlikely, if the power system is not divided by the
emergency. A modern power system remains stable until
its cascading division begins.
On the contrary, isolated areas of cascade shutdowns, elec-
trically separated from the main body of the power system,
may experience quite large imbalances of active power.
A large imbalance may cause a blackout if the emergency
automation is not able to balance the mode in some iso-
lated part of the power system and thus complicates the
process of power system restoration.
To reduce the time to restore the power system after a dis-
turbance with large-scale consequences, it is necessary to
balance the separated areas.
Analysis of large-scale emergencies observed during black-
outs worldwide [1] allows us to see the following character-
istic sequence of changes in the power system when the
frequency plummets or soars:
1. Emergency shutdown of a power plant or power plant
unit or power line;
15
Відновлювана енергетика. №1/2025 | Комплексні проблеми енергетичних систем на основі НВДЕ
2. Redistribution of active power deficit between the re-
maining generators;
3. Change of power flow distribution in power lines;
4. Disconnection of the power line due to overload or in-
stability;
5. Sequential cascading disconnection of power lines;
6. Division of the power system into unbalanced areas:
some with excess generation capacity and some with
power deficit.
For their part, emergencies in already island areas have
their own special features depending on their excess or def-
icit of capacity.
I. Development of an emergency in an area with excess
generating capacity:
Scenario 1
1. The frequency has increased by no more than 1.0 Hz;
2. The node voltages are within acceptable values;
3. The automation efficiently regulates frequency and
voltage, the area is well-balanced;
Scenario 2
1. The frequency or the voltage increased up to the level
of automatic tripping of generating units;
2. Automatic tripping of generating units;
3. An area with an excess of generating capacity becomes
an area with a deficit of generating capacity;
4. The emergency develops as in an area with a deficit of
generating capacity.
II. Development of an emergency in an area with a deficit
of generating capacity:
Scenario 1
1. The frequency plummets;
2. The effective operation of UFLS restores power balance.
Scenario 2
1. The frequency plummets;
2. The UFLS disconnects much more power than necessary
for balancing the scheme;
3. An area with a deficit of generating capacity becomes
an area with an excess;
4. The emergency develops as in an area with an excess of
generating capacity.
Scenario 3
1. The frequency plummets;
2. The UFLS cannot stop the frequency drop;
3. A blackout occurs.
It can be seen from the outage scenarios for the course of
accidents, there is a probability that redundant areas at the
beginning of the emergency transition process may be-
come deficient during its further development, and con-
versely, previously deficient areas may become redundant.
Besides that, the system may have successive processes of
subsequent division of selected areas into smaller parts.
Thus, to provide for balancing as many as possible areas
within a system undergoing failure with fluctuating fre-
quency it is necessary to consider the whole volume of the
operating reserves in every isolated area regardless of the
deficit or excess of capacity at the beginning of the transi-
tory period.
An operating reserve of a power system has a fairly wide
time range. However, within the task of distributing the re-
served volume of the automatic frequency demand one can
easily regard only the capacity of the segment operating
jointly with the UFLS system. Thus, Table 1 presents only
the operating reserve of the power system which can be
engaged within the acceptable emergency frequency-time
range, from 0 to 60-100 s.
In order to investigate any accident with frequency fluctu-
ations, the transitory process is divided into two time inter-
vals. In the first one (zero to roughly 5-10 s), the possibility
to contain the frequency decrease is studied, while in the
second one (10 to 60/100 s) the possibility of stabilizing it
at a level close to the nominal value is researched.
The first factor slowing down the rate of frequency de-
crease is the consumers who provide the regulatory effect
of demand (Table 1). The effect depends on the proportion
of engines in the load and the types of mechanisms being
so operated. A 1% decrease in frequency is known to de-
crease the load by 1 to 3%. Thus, when frequency reaches
the UFLS relay without time delay, the power of the load
can drop by 2-6%. The extent of this reserve can not be
foreseen yet it has a perceptible effect if the relative deficit
of active power is not large. It upholds the frequency at a
level above the high UFLS relay without time delay, block-
ing the consumers from being disconnected until the gen-
eration reserve capacity is put into operation (Table 1).
Table 1. The operational reserve of power system
Number and name of frequency reserve
Time required to start of
operation
1. The potential of electrochemical batteries for bulk energy storage in under 1 second
2. Spinning reserve in the form of rotating machines (part-loaded, synchronised plant) 5 – 15 seconds
3. Shunting power 20 – 30 seconds
4. Load reduction due to under Voltage & Frequency (influence on dynamic properties
of the load)
immediate reserve
5. Rate of Change of Frequency (RoCoF) in under 1 second
6. The consumers connected to the UFLS without time delay in under 1 second
7. The consumers connected to the UFLS with time delay more than 5 seconds
16
Відновлювана енергетика. №1/2025 | Комплексні проблеми енергетичних систем на основі НВДЕ
The next reserve to be activated is the additional df/dt
function in UFLS relays [5]. As a rule, this reserve (additional
df/dt function in UFLS relays) is combined with part of the
reserve of the UFLS relay without time delay. As an excep-
tion, this automation can also have its own individual re-
serve. When these two reserves are triggered and depend-
ing on the exact settings of relays in the area, the transient
process follows one of two scenarios. In one case, the local
reserve will slow down the frequency drop in the area, after
that it recovers to its nominal value. In the other case, the
frequency drop is slowed down but its recovery is either
distributed over the reserve generating capacity and the
UFLS relays with disconnection delay or, alternatively, pro-
vided by only one of these reserves alone.
The efficiency of use of these reserves determines whether
the frequency can be maintained within the acceptable
time-frequency area until the reserve generating capacity
and UFLS relays with disconnection delay are engaged.
The generation capacity reserves and UFLS relays with dis-
connection delay should ensure that the frequency is in-
creased without breaking the limits of the time-frequency
area. To this end, it is necessary to have such reserve ca-
pacity in every given area. The lack of exactly this kind of
reserve capacity can lead to secondary frequency drop and
subsequent blackout.
Most power systems in the world do not employ UFLS re-
lays with disconnection delay, including the systems of EN-
TSO-E member countries [5, 6]. In these power systems, the
preference is given to consumers, that is, the number of
disconnections is minimized through installation of suffi-
cient reserve of generating capacity. According to the au-
thors, this reduces the power system's reliability as the ad-
equacy of generating capacity reserve for the power system
as a whole does not always guarantee its adequacy in every
single area and for any single power supply mode.
Currently, UFLS relays with disconnection delay are used
only where resource constrains do not allow for some op-
erational reserve of generating capacity to balance the
power system.
With this in mind, we conclude that among all kinds of ca-
pacity reserves presented in Table 1, only the operational
reserve of consumers connected to the UFLS relay without
time delay can halt a rapid frequency drop given substantial
deficit of active power.
Therefore, the UFLS relay without time delay is the only
anti-emergency automation tool in the power system capa-
ble of containing the frequency plummeting. Within a few
seconds, UFLS relay without time delay can disconnect a
sufficient portion of consumers and balance the deficient
areas of the power system formed as a result of a cascading
failure involving the disconnection of lines and generators.
II. Problem statement
The UFLS disconnects groups of consumers sequentially
and according to the assigned categorical value. To success-
fully prevent a deep frequency drop, the system should be
outfitted with the required amount of load-shedding capac-
ity to guarantee a temporary active power balance in every
isolated area of the power system.
With this aim in view, the national transmission system op-
erators (TSOs) or the network of transmission system oper-
ators (NTSO) set the value known as the total load shed
(TLS) [7] or total load quantity (TLQ) [6]. In various power
systems worldwide, between 30% and 60% of the total con-
sumer capacity is connected to the UFLS system [5, 7, 10,
12]. This value is entered into the power system’s standards
in a general and prescriptive manner through policy regula-
tions. As a result, it is not always clear from which consumer
capacity the specified percentage is calculated. Most often,
TLS is calculated as a percentage of the maximum system
load. This approach, for instance, is used in the power sys-
tems of the Great Britain and Ukraine [10, 14].
TLS thus defined is commonly advised to be distributed over
the system uniformly and according to the so-called “geo-
graphic principle” [5,6,10]. However, despite the possibility
to “geographically distribute” frequency relays over a coun-
try’s territory or a power system, it is in any case essential to
integrate the UFLS-connected consumers’ capacities based
on their weights in some basic electricity transmission modes
with appropriate justification for selecting the same modes
specifically for evaluating the load shed limits.
It is clear that the above-mentioned ways to determine TLS
and its distribution in the power system do not take in con-
sideration the specific features of the structure of its elec-
trical connection scheme or daily and seasonal variations in
generating and consuming capacities despite the fact that
power system standards require these factors to be ad-
dressed [5, 6, 8]. Another overlooked parameter is the
probability of the design fracturing into unbalanced emer-
gency areas.
Thus, when constructing the UFLS system, the load shed is
shared over as many consumers as possible. Clearly, the ca-
pacity connected to every single relay varies throughout
the year. Therefore, while the total load shed depends on
the current power system operating mode, at any given
moment its value in relative units cannot be lesser than the
value stated in the requirements of the system operator or
the joint power system [5, 8]. Hence, the above-mentioned
TLS value in % can be regarded only as a generalized poten-
tially attainable limit for the UFLS system of the entire
power system. The value does not provide informative in-
sight into the efficiency of the involved consumer load ca-
pacity. Using TLS as an indicator of the sufficiency of load
shedding in the general case does not guarantee prevent-
ing a failure since in the event of the power system scheme
split and the activation of frequency load shedding in the
emergency mode, some areas may turn out to be insuffi-
ciently outfitted with the required amount of load shed due
to the specifics of the power system scheme and the
boundaries of electrically isolated emergency areas.
To provide a sufficient load shedding in every emergency
area at any TLS activation time, it is needed to determine
its value taking into account the structure and amounts of
generating and consuming capacities, schemes of the elec-
trical connections, variable capacity of consumers con-
nected to frequency relays, basic modes’ parameters (in-
cluding those occurring at the maximum and minimum
power system load).
17
Відновлювана енергетика. №1/2025 | Комплексні проблеми енергетичних систем на основі НВДЕ
In this study, the criterion of TLS distribution efficiency is
the minimum load shed required in the power system, con-
sidering the probability of its split into, generally speaking,
arbitrary isolated emergency areas.
To solve the problem of TLS minimization, it is necessary to use
a model of the power system to calculate its common regimes.
A mathematical model allows to compute the net power flow
through power lines at the split points of the emergency areas
and the deficit of active power in them. To incorporate load
shed changes created by TLS it is proposed to analyze three
basic power system modes: the maximum and minimum loads
and also the mode in which the share of distributed generating
capacity from renewable energy sources is maximized in the
structure of the total generating capacity.
Using the scheme of power system’s connections, the
boundaries of the affected areas are shown, and, using the
informational model of the UFLS system, the sets of load
shedding devices are determined together with the respec-
tive amount of capacity of connected consumers in these
areas. The UFLS dataset is shown in Table 2 based on meas-
urements taken in the distribution network for the three
basic modes chosen.
Table 2. Fragment of the list UFLS relays with settings and amount of load shedding in three basic modes
Nodes of network
The frequency and time of
the relay setpoints
Mode of Power System
Substation Feeders Hz S 1* 2** 3***
MW
DTS 110/35 -1 169 49,0 0,15 2,4 2,5 3,2
169-01 49,0 0,15 0,1 0,3 0,1
169-05 49,0 0,15 0,3 0,5 0,6
169-14 49,0 0,15 0,1 0,2 0,2
169-10 49,0 0,15 0,3 0,3 0,5
169-11 49,0 0,15 0,3 0,5 0,8
169-17 49,0 0,15 0,2 0,6 0,7
169-19 49,0 0,15 0,1 0,1 0,3
DTS 330/35- 5 166 48,2 0,15 0,3 0,7 0,9
166-06 48,2 0,15 0,2 0,6 0,8
166-08 48,2 0,15 0,1 0,1 0,1
DTS 330/35-2 165 48,7 0,15 1,1 0,7 2,5
165-05 48,7 0,15 0,3 0,4 0,7
165-06 48,7 0,15 0,5 0 0,8
165-07 48,7 0,15 0,3 0,3 0,6
_________________________________________________________________________________________________
*1 – the mode of the total peak demand of the power system;
**2 – the mode of the total low demand of the power system;
***3 – the mode with the total peak capacity of distributed generation.
Thus, the task of determining TLS and its placement in the
distribution power system has its own specifics for every
power system under study. To find an efficient solution, a
certain sequence of steps must be followed including calcu-
lation, preparation and organization of the data support,
modeling the capacity balance in the power system divided
into arbitrary emergency sections, and a final computa-
tional verification of the efficiency of load shedding given
the capacities determined earlier during the balancing of
capacities and UFLS devices’ arrangement phase.
For ease of use, the sequence is presented as a coherent
algorithm of TLS determination shown as a flowchart in
Fig. 1.
Block 1 describes the operation of measuring consumer ca-
pacities for the three basic power system modes - the max-
imum and minimum load and the mode with the maximum
share of distributed generation. The measurement results
obtained in the distribution network at this stage are
recorded in Table 2 which has the following structure. The
Mode column includes:
1. capacity of the substations and connections when the
power system operates in the minimum load mode:
2. capacity of the substations and connections when the
portion of distributed generation of renewable energy
sources is maximum in the generating structure;
3. capacity of the substations and connections when the
power system operates in the maximum load mode.
The Relay column contains the de facto frequencies and
times of engagement of the acting settings of the UFLS.
Block 2 shows the preparatory stage of the set of possible
scenarios for dividing the power system into emergency ar-
eas, which are subject to analysis to define and adjust the
TLS distribution. To this list, we add the scenarios of power
system division, each presented as a list (set) of lines of the
protection scheme that could sequentially disconnect in
18
Відновлювана енергетика. №1/2025 | Комплексні проблеми енергетичних систем на основі НВДЕ
the event of a cascading failure. Primarily, such lines could
include the controlled crossings (see Fig. 2, secants IV-IV
and V-V). Besides that, considering the fact that it is practi-
cally impossible to predict exactly which lines and in what
sequence are going to be disconnected as the failure devel-
ops [9], it is advisable to consider scenarios involving some-
what arbitrary divisions shown in Fig. 2 by secants 1-1, 2-2,
3-3 and 4-4.
Fig. 1. Simplified block diagram of an integral algorithm
The third stage is shown as Block 3. It is a scheme of algo-
rithm to determine (obtain) the output data for an optimiz-
ing mathematical model of capacity balances in emergency
areas when the UFLS settings are engaged. There, calcula-
tions for the three basic modes are performed with the help
of standard software. In particular, these calculations use a
common mathematical model of the balance of active and
reactive power system capacities to obtain the relevant
power flows in the protection scheme for the maximum
and minimum daily load modes and the mode of the maxi-
mum share of distributed generation.
Block 4 is dedicated to determining TLS: here, the calcula-
tions yield the set of UFLS devices (frequency relays) and the
relevant amount of load capacity connected to them neces-
sary for the most complete balancing of all affected areas of
the power system’s division for all versions of division con-
sidered at the second stage of the algorithm (Block 2). In or-
der to do this, a mathematical model of balancing the capac-
ities in the emergency-divided power system is used, which
contribution is considered below in greater detail. Using the
model allows for analyzing and increasing the efficiency of
distribution and determination of the minimum total
amount of balancing capacity of frequency load shed for all
possible divisions of the power system. In fact, this process
identifies a set of relays with non-zero (binary) integer use
intensities that are most essential for load shedding. Concur-
rently, activation of other relays which do not coincide with
19
Відновлювана енергетика. №1/2025 | Комплексні проблеми енергетичних систем на основі НВДЕ
the chosen ones in the optimal solution of the linear pro-
gramming problem for this model is fairly improbable in any
emergency situation. From the experience of using the algo-
rithm in practice, this probability depends on the
comprehensiveness of the power system division scenarios
set developed at Stage 2 (Block 2). The obtained frequency
appropriate for load shedding of a set of relays are then used
to draw a table of analyzing modes and areas (Table 3).
─ the transmission line cross-sections in the electric network;
─ transmission lines which got into the cross-section.
Fig. 2. Variants for arbitrary separation of the power system
At the fifth stage (Block 5), analysis of calculations is per-
formed according to Table 3, in particular, the lack or excess
of load shedding is determined for every distribution net-
work, every operator of the distribution network (ODN).
Table 3. The fragment of the table the evaluation of TLS placement in the power system
ІІІ. Mathematical model of capacity balance in an emer-
gency-divided power system
According to the described algorithm to solve the prob-
lem, the minimum required capacity is calculated by the
formula
,
1
=
=
UN
LS opt
min i i
i
P P x , (1)
where , 1, ,opt
i Ux i N= – is the set of optimal
values of binary variables of device i usage or not usage
to remedy the consequences of an arbitrary emergency
which has led to frequency drop in a power system with
a pre-determined set of power modes with measured
capacities of load-shedding devices that determines the
network distribution of used load-shedding capacity and
is found as the solution of the problem of integer opti-
mization that is to minimize the value of the function
( )
1
1
UN
i i
i
k x min
=
− →
(2)
Number
of basic
mode
Section of
emergency
Number of
region
Reserve of load
shedding
Total amount of load
shedding in area
Amount of load shedding
that was calculated
MW MW MW
1 2 1 922 1764 1662
1 3 2 -146 1080 1080
2 20 1 761 2203 2101
1 17 1 637 1895 1793
1 9 1 395 1995 1995
3 14 2 -19 438 438
2 8 1 201 2071 2071
20
Відновлювана енергетика. №1/2025 | Комплексні проблеми енергетичних систем на основі НВДЕ
if ( )
1 1,
1,
U
R
T
N
RES
ri i i i r
i r N
N
A P G x D
−
= =
=
−
; (3)
where ( )
1 1,
1,
U
R
T
N
RES cons
ri i i i r
i r N
N
A P G x s P
+
= =
=
− , (4)
𝐴ri is an element of the matrix of the affiliation of load-
shedding devices (frequency relays) to the isolated areas:
𝐴ri = 1, if the device i belongs to the isolated area r and
𝐴ri = 0 if not;
𝑃𝑖𝜏 is the capacity of load connected to device i measured
in regime 𝜏;
RES
iG is the determined active power of renewable en-
ergy sources which provide capacity for points active in the
area covered by device i in mode 𝜏;
rD is the deficit of active capacity of area r in regime 𝜏,
resulting from the division of the power system by an emer-
gency followed with frequency drop;
s is the % of load that is set by the system operator to en-
gage consumers in load shedding;
cons
rP is the total active capacity load of the surplus re-
gion r in mode 𝜏;
𝑘𝑖 is the consumer categorization factor / active setting for
frequency of the consumer connected to device i;
𝑥𝑖 is the sought binary variable of state of the device i: х𝑖 =
1, if device i is involved in unloading the power system;
𝑁𝑈 is the number of unloading devices (relays) in the power
system;
R
N − is the number of isolated areas of the power system
deficit in active power;
R
N + is the number of isolated areas of the power system
with surplus active power;
𝑁𝑇 is the number of measurements on devices during the
calculation period T.
ІV. An example
A scheme of power system is shown on Fig. 3. It has two
controlled crossings IV-IV and V-V which were disconnected
resulting in respective emergency areas (Fig. 3). Besides
that, we considered other, fairly different system divisions
to demonstrate various cases of arbitrary emergency re-
gions formation (1-1, 2-2, 3-3, 4-4). When the problem was
solved according to the proposed algorithm, we obtained a
Table of analysis of areas and modes (see the description of
Stages 4 and 5 of the algorithm of TLS determination), a
fragment of which is shown in Table 3.
If the described power system were required to follow the
ENTSO-E policy requirements [5] for TLS, then no less than
45% load, +/- 7%, would have to be connected to UFLS. The
minimum TLS should thus be 38%, while the maximum
should be 52%.
However, Table 3 (lines 1 and 3) shows that after the defi-
cits were covered, the remained 24% (1334 MW) and 33%
(1758 MW) is less than the minimum required reserve of
38%. In the second line, the reserve was 39% (1423 MW),
exceeding the minimum capacity required. Given these re-
serve values, it is possible to calculate the amount of con-
sumer capacity in megawatts which requires load shedding
in every isolated area, and, consequently, the TLS of the
power system as a whole.
V. Conclusions
1. The analysis conducted in this study of large-scale power
failures involving frequency drop and the properties of var-
ious types of operating reserve in power systems allows us
to state that the system of automatic frequency load shed-
ding is currently the only way to balance a power system in
the event of large and sudden imbalances of active power
regardless of their causes. An essential condition for the ef-
fective operation of the automated frequency load-shed-
ding system is the sufficiency of amounts and expediency
of capacity distribution of consumers connected to the sys-
tem. Determination of sufficient load shed should be based
solely on a comprehensive analysis of both the specifics of
the power network structure and the power flow distribu-
tion for a sufficiently diverse set of power modes. This ap-
proach allows to obtain precise values of capacity deficit
and the appropriate sources to address their recovery
within the set of means of the available operating reserve.
2. In this paper, we propose a method and an algorithm to
determine the appropriate capacity of the UFLS operating
reserve, as well as a mathematical model for its optimal bal-
ancing considering the possible division of the power sys-
tem into arbitrary electrically disconnected emergency ar-
eas. The application of these tools for evaluating and
adjusting load shed substantially reduces the likelihood of
21
Відновлювана енергетика. №1/2025 | Комплексні проблеми енергетичних систем на основі НВДЕ
a total blackout in emergency areas due to complex cascad-
ing failures followed by significant frequency drops. The se-
quential algorithm of formal procedures to solve the prob-
lem, alongside the proposed specific data structures and
mathematical model for balancing the emergency areas
equip the maintenance services and control centers of
power systems with a tool to precisely model and construct
a UFLS system.
3. Using a real power system as an example, we proved,
quantitatively, that the value of the total load shed man-
dated by the current standards and regulatory documents
in the applicable energy legislation is an insufficiently trust-
worthy parameter for defining the UFLS systems’ basic
properties. In order to determine the reasonable value of
this parameter and the consequent distribution of load-
shedding capacities in the system, it is necessary to use a
toolkit for accurate calculation of the system’s operational
mode states. One such toolkit and a case of its implemen-
tation is proposed in our research.
Fig. 3. Single Line Diagram of Power System (fragment)
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|
| id | veorgua-article-501 |
| institution | Vidnovluvana energetika |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-07-19T01:14:59Z |
| publishDate | 2025 |
| publisher | Institute of Renewable Energy National Academy of Sciences of Ukraine |
| record_format | ojs |
| resource_txt_mv | veorgua/4d/ec880860d5a0ffc918821e46f774a04d.pdf |
| spelling | veorgua-article-5012026-07-18T06:32:21Z THE METHOD FOR DETERMINING THE EFFECTIVE TOTAL LOAD SHEDDING FOR UNDER-FREQUENCY LOAD SHEDDING OF THE POWER SYSTEM МЕТОД ВИЗНАЧЕННЯ ЕФЕКТИВНОГО ОБСЯГУ АВТОМАТИЧНОГО ЧАСТОТНОГО РОЗВАНТАЖЕННЯ ЕНЕРГОСИСТЕМИ Lytvynchuk, V. Kaplin , M. Karmazin , O. Under Frequency Load Shedding (UFLS), Low Frequency Demand Disconnection (LFDD), Total Load Shed, Total Percentage Demand LFDD. енергосистема, автоматичне частотне розвантаження, знеструмлення, блекаут. This paper suggests a method for determining the effective total amount of load disconnection in case of major frequency drop and under-frequency load shedding (UFLS) activation.  A mathematical model of power balance in emergency areas has been developed, which uses the structure of the electric network scheme.  The UFLS is presented in the model by a set of frequency relays with fixed consumer loads behind feeders along the year and binary variables triggering their operation.  The solution of the integer linear programming problem provides the optimal set of the relays needed to balance all emergency areas given the minimum total load shedding (TLS).  This determines both the TLS and the placement of individual relays in the electrical network.  The method involves pre-measurement of the consumer loads behind feeders, as well as power flows in the network for its characteristic modes.  For this purpose, standard specialized software is used to calculate stationary modes and contingency analysis.  The input data for the simulation is also a set of electrically unconnected emergency areas.  This information should be provided by the user of the proposed method by indicating the overhead line cross-sections in electric network.  The developed method allows to determine the TLS of UFLS and the most efficient set of frequency relays for any power system in order to align these indicators with the requirements of the National Electricity Transmission System Operator.    Система автоматичного частотного розвантаження (АЧР) є єдиним засобом, який широко застосовується в енергосистемах для стримування швидкого падіння частоти. Система АЧР здатна майже раптово відключити частину споживачів та зупинити падіння частоти в районах енергосистеми, які утворилися в результаті каскадного відключення ліній і генераторів. Для підтримки тимчасового балансу активної потужності в аварійних ситуаціях в енергосистемі повинна бути передбачена кількість навантаження на відключення.  Тому оператори систем передачі або мережа операторів систем передачі електроенергії встановлюють так званий загальний обсяг розвантаження (ЗОР). Найчастіше в стандартах та нормативних документах енергосистем цей показник розраховується в умовах загального пікового попиту. Водночас ЗОР рекомендують розмістити в енергосистемі рівномірно, з урахуванням географії мережі. Такий спосіб розміщення загального обсягу розвантаження не враховує електричної структури електромережі, добової та сезонної зміни генерувальних потужностей і споживання, не зважаючи на те, що стандарти та нормативні документи вимагають це враховувати.   В роботі запропоновано математичну модель і спосіб визначення ЗОР системи АЧР та його розміщення в мережі енергосистеми з урахуванням розподіленої генерації, ймовірних варіантів аварійного поділу енергосистеми, контрольованих перетинів вимог міжнародних стандартів та нормативних документів, що регулюють функціонування систем протиаварійного захисту в галузі електроенергетики. Модель являє собою задачу цілочисельного (бінарного) лінійного програмування, що здійснює вибір оптимального набору пристроїв АЧР, які розміщені у наперед заданих вузлах енергосистеми й спрацювання яких забезпечує баланс потужності в аварійних районах її поділу. Електричні параметри усталених режимів, а також ефективність оптимального обсягу та розподілу розвантаження в мережі визначаються й перевіряються (верифікуються) у серії апріорних та апостеріорних розрахунків на точних математичних моделях, визнаних у світовій практиці програмних продуктів електроенергетики.  Отриманий таким чином розподіл обсягів розвантаження підвищує ймовірність балансування якнайбільшої кількості аварійних районів енергосистеми за умови задоволення вимог щодо частотно-часової зони відповідних перехідних процесів.   Institute of Renewable Energy National Academy of Sciences of Ukraine 2025-03-31 Article Article application/pdf https://ve.org.ua/index.php/journal/article/view/501 10.36296/1819-8058.2025.1(80).13-21 Vidnovluvana energetika ; No. 1(80) (2025): Scientific and applied Journal renewable energy ; 13-21 Возобновляемая энергетика; ##issue.no## 1(80) (2025): Scientific and applied Journal renewable energy ; 13-21 Відновлювана енергетика; № 1(80) (2025): Науково-прикладний журнал Відновлювана енергетика; 13-21 2664-8172 1819-8058 10.36296/1819-8058.2025.1(80) en https://ve.org.ua/index.php/journal/article/view/501/410 Copyright (c) 2025 V. Lytvynchuk, M. Kaplin , O. Karmazin https://creativecommons.org/licenses/by-nc-nd/4.0 |
| spellingShingle | Under Frequency Load Shedding (UFLS) Low Frequency Demand Disconnection (LFDD) Total Load Shed Total Percentage Demand LFDD. Lytvynchuk, V. Kaplin , M. Karmazin , O. THE METHOD FOR DETERMINING THE EFFECTIVE TOTAL LOAD SHEDDING FOR UNDER-FREQUENCY LOAD SHEDDING OF THE POWER SYSTEM |
| title | THE METHOD FOR DETERMINING THE EFFECTIVE TOTAL LOAD SHEDDING FOR UNDER-FREQUENCY LOAD SHEDDING OF THE POWER SYSTEM |
| title_alt | МЕТОД ВИЗНАЧЕННЯ ЕФЕКТИВНОГО ОБСЯГУ АВТОМАТИЧНОГО ЧАСТОТНОГО РОЗВАНТАЖЕННЯ ЕНЕРГОСИСТЕМИ |
| title_full | THE METHOD FOR DETERMINING THE EFFECTIVE TOTAL LOAD SHEDDING FOR UNDER-FREQUENCY LOAD SHEDDING OF THE POWER SYSTEM |
| title_fullStr | THE METHOD FOR DETERMINING THE EFFECTIVE TOTAL LOAD SHEDDING FOR UNDER-FREQUENCY LOAD SHEDDING OF THE POWER SYSTEM |
| title_full_unstemmed | THE METHOD FOR DETERMINING THE EFFECTIVE TOTAL LOAD SHEDDING FOR UNDER-FREQUENCY LOAD SHEDDING OF THE POWER SYSTEM |
| title_short | THE METHOD FOR DETERMINING THE EFFECTIVE TOTAL LOAD SHEDDING FOR UNDER-FREQUENCY LOAD SHEDDING OF THE POWER SYSTEM |
| title_sort | method for determining the effective total load shedding for under-frequency load shedding of the power system |
| topic | Under Frequency Load Shedding (UFLS) Low Frequency Demand Disconnection (LFDD) Total Load Shed Total Percentage Demand LFDD. |
| topic_facet | Under Frequency Load Shedding (UFLS) Low Frequency Demand Disconnection (LFDD) Total Load Shed Total Percentage Demand LFDD. енергосистема автоматичне частотне розвантаження знеструмлення блекаут. |
| url | https://ve.org.ua/index.php/journal/article/view/501 |
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