Improved methods of power systems availability indices determination
M. Stojkov Ph.D.
HEP group, Distribution, Area Slavonski Brod, Croatia
S. Nikolovski Ph.D.
Faculty of Electrical Engineering
University of Osijek, Croatia
I. Mravak M.Sc.Eng.
HEP group, Distribution, Zagreb, Croatia
ABSTRACT: This paper presents a role of reliability aspect in the power system supply quality. Increasing importance of availability indices in quality improvement evaluation in power delivering and some cost savings at the same time is given here. The evaluation method has been developed to solve a real technical and management problem – define optimal power system switching state. The evaluation method is based on Markov state space model of power lines as system components, enumerating all possible power system states and composed of an independent power system components failures time-series data, their coincidence of the first, second and the third order for the branches (lines and transformers), storing in a relational system database. Some input variables and detailed reliability results calculated for all buses in the distribution power system of area Slavonski Brod are a part of this paper too.
1 INTRODUCTION
1.1 Power quality
Anyone with a technical background can define power delivering as a dynamic process depending on customer demands during any time period. So, power quality consists of the several main variables describing some kind of a dynamic process according to EN 50160. One of these variables describing power system reliability is maximum allowed failures number per year and the second one is maximum allowed duration of voltage interruption per year for each end-user. To determine the above mentioned systems parameters, the power system (nodes and branches) has to be permanently monitored day by day during the whole year. The object of this approach are only components failures, which cause the power interruption to the end-users.
According to the EN 50160 voltage drop period starts when voltage drops down to a level less then 1% of the nominal voltage level. There are two possible voltage absence periods: planned maintenance (consumers are informed a days in advance) and accident failures. The last one can be divided further in long term (permanent failure) and short voltage interruptions (transient failure, duration is less then 3 minutes). The latter failures are expected to last about several hundreds, but duration of 70% of them should be less then 1 s. Long term non voltage periods should not be more then 10-50 per year.
The power system is given with its branches (power lines and transformers) and buses (nodes) describing actual topology order. The nodes are the points with load feed (generators and load input from a higher voltage network), load output points from the distribution network to the customer, branching points or points of the power line type changeability (like overhead line – buried line, isolation technology type, radius and conductor material).
1.2 Reliability aspect
The power system is composed of a great number of mechanical and electrical components, which can be removed when a failure occurs or even in a maintenance process (periodic maintenance or when any component parameter deviate outside of the regulated range). There are also some organizations imperfections and human faults as possible failure causes.
The power system is an open dynamic technical system with a number of strong connections with its environment. The environment is structured in two parts: technical with material parameters and physics essentials in one side and probability variables (demands, weather conditions) at the other side. However, at any time, the system is in one and only one possible state that is completely described by a set of variables.
The power delivering is object process we monitored within the system and its states. If the next system state can be predicted for sure on the base of physical process low, it is deterministic system. If we only know probability distribution of a next system state, it is stochastic system. The power system is exactly a stochastic technical system. Some uncertainties in the power demand, external temperature, other weather conditions, pollution and other factors become into consideration here.
2 relational power system data base
2.1 Introduction
All time-series events about systems and components states and their changes have been continually recorded in the power system management documents obligated by the law. It was very hard and slow to retrieve data from these documents based on only one component state in a particular moment in the past. All recorded data were extremely unconnected, hard readable and unsorted. So, the relational power system database is designed to solve above mentioned problems and to provide greater accuracy Figure 1. Relationships scheme in the database kikaE2.mdb
in the power system availability. Now, all the information about power system and its components faults are recorded in the place where it could be simultaneously available to several users. The other advantage is in a recording immediately after faults occur, which give us fresh and accurate data. The traditional approach on a faults registration till now was to collect and store these data after some time, some of the important facts used to be neglected, based on a subjective men opinion or memory.
2.2 Main parts
The relational database KikaE2.mdb (Microsoft Access) with its main parts – tables and relationships is illustrated in figure 1. The most of the data in database is structured, interconnected, fast accessed, non redundant and sorted, describing events (faults, maintenance), system states (switching states, failure type, failure cause) and objects (components, power lines and transformer substations).
The relation between two tables depends on the connection key determination, with its connection properties and rules. By means of data base queries, it is very easy to filter out desired information. For example, it is easy to filter only one power line faults a user wants from all power system lines faults, and to take into account only faults in desirable time period between two dates by users choice. It is possible to do further filtration by selecting only faults with the same cause, faults of the same components, faults with duration more then 5 or 20 minutes and so on.
Here, two expected energy not supplied (EENS) evaluations are calculated, traditional (EENS1) based on transformers installed power and new real (EENS2) based on real measured power of the previous day in the same non voltage period of the fault day.
3 Power SYSTEM TOPOLOGY
3.1 Substations and power lines
The analyzed power systems area Slavonski Brod cover 1983 square kilometers and population of 186,000, about 40,000 consumers and 33.13 MW peak power that is between 1.6% and 2% of Croatian National Electricity Board. The distribution power system is presented in figure 2.
There are following transformer substations in distribution network in observed area (Table 1): Podvinje 110/35 kV (80 MW) – basic systems feed point and Bjelis 110/35/10 kV (40 MW) – secondary systems feed point and eight transformer substations 35/10 kV, 66.7 km overhead power lines 35 kV and 10.6 km buried power lines 35 kV (see Table 1-2, and Figure 2). Here, branches are marked by two incident buses.
1
2
9 13 10
12
11
5
14
8
3
7
4
6
Figure 2. Power system's scheme
Table 1. Distribution network nodes
______
Node/Bus Bus name Transformers
number (location) installed (MVA)
______
1 Podvinje110 80.00
2 Podvinje35 80.00
3 Bjelis35 40.00
4 Slavonski Brod1 32.00
5 Slavonski Brod2 16.00
6 Slavonski Brod3 16.00
7 Brodsko Brdo 8.00
8 Oriovac 6.50
9 Brodski Stupnik 0.00
10 Donji Andrijevci 12.00
11 Bebrina 6.50
12 INA-gas 0.00
13 Topolje 0.00
14 Zrinski Frankopan 0.00
______
Table 2. Distribution network branches.
______
Branch Start End Power line/
number node node transformer type
______
1 1 2 Transformer 110/35 kV 40 MVA
2 1 2 Transformer 110/35 kV 40 MVA
3 2 4 NA2XS (F) 2Y 3 x (1x 240) mm2
4 2 12 Overhead line Copper 3 x 70 mm2
5 2 5 Overhead line Al-steel 3 x 150 mm2
6 2 5 Overhead line Al-steel 3 x 120 mm2
7 5 6 NKBA - 3 x 150 m m2
8 4 6 NKBA - 3 x 150 m m2
9 3 5 Overhead line Al-steel 3 x 120 mm2
10 13 10 Overhead line Al-steel 3 x 120 mm2
11 2 9 Overhead line Al-steel 3 x 120 mm2
12 9 11 Overhead line Al-steel 3 x 120 mm2
13 2 7 Overhead line Al-steel 3 x 120 mm2
14 12 14 NA2XS(F)2Y 3 x (1x 240) mm2
15 14 4 NKBA -3 x 240 m m2
16 2 13 Overhead line Al-steel 3 x 95 mm2
17 9 8 Overhead line Al-steel 3 x 120 mm2
______
3.2 The power load flow model
The real yearly load diagram (electric power against days during the year, see oscillating line, figure 3.) for the power system is approximated by the stepwise linear lines presenting load duration (figure 4.). The decreasing line (figure 3.) presents the electric power for all days (D) during the year but sorted by their values from the largest to the lowest value.
Each level is marked by the system peak load level (absolute and relative to peak load of the first level) and its occurrence probability (Table 3). The power systems load duration diagram is specified by 5 levels, where the first level is 100% (33.13 MW). It means, for example that 0.55% of the time (48.18 hours /year) load is PM (33.13 MW).
Figure 3. Electric power load diagram during the year (oscill-
ating) and same decreasing characteristic in Area Slavonski Brod, 1999.
Table 3. Stepwise linear lines load duration, Area Slavonski
Brod, 1999.
Level / P (MW) / Days per year (D) / P/Ppeak / T (%)1 / 33.13 / 2 / 1.00 / 0.55
2 / 28.26 / 45 / 0.85 / 12.33
3 / 24.39 / 155 / 0.74 / 42.46
4 / 20.32 / 154 / 0.61 / 42.19
5 / 16.89 / 9 / 0.51 / 2.47
Figure 4. The stepwise linear lines load characteristic in Area
Slavonski Brod, 1999.
The most important step in load approximation process is to preserve the area under load curve in load time dependency graph (save equity of distributed electric energy to consumers). Any quantity evaluation for a part of the year (season, month), which is based on load estimation, has to be start from a beginning by raw load data. In that case this approximation is not good enough to cover usual accuracy.
4 reliability evaluation
Although it is not so easy and grateful to make a model of a power system with distributed components in different weather and load conditions, there are several modeling methods used to accomplish that task. Here, reliability evaluation is based on the analytical method of state space enumeration (using Markov’s state space model). This evaluation composes independent failures of the power system components, their coincidence of the first, second and the third order for the branches.
4.1 Reliability output indices
The power system reliability indices we use for quantification adequacy aspect are:
4.1.1 The number and type of supply interruption
Number of contingencies causing split network -Splt
Number of contingencies causing bus isolation - Isol
4.1.2 The load curtailment reliability indices
Probability of load curtailment (Prob x 10-3 )
Frequency of load curtailment (Freq occ./year)
Duration of load curtailment (Dur hours/year)
4.1.3 The Bulk Power Energy Curtailment Index (BPECI, BP MWh/MW,year)
This parameter shows quantity amount of unsupplied energy (MWh) per 1 MW installed load power yearly. It is usually expressed in the system minutes – SM (by multiplying BPECI by 60). It has two interpretations: a) actual system malfunction index SM is presented on an equivalent fault state of power system under the peak load for so many system minutes and b) SM is duration of outage time per each consumer at the system peak load.
4.1.4 The Expected Energy Not Supplied (EENS, ENS)
This parameter is usually shown in MWh/year, but here is in kWh/year. The program does not calculate this parameter directly, and then we calculate it out from BPECI, multiplying with the peak system load (PM = 33.13 MW).
4.2 Output results
Now, we can compare the reliability indices n-1, n-2 and n-3 of the branches failure coincidence level for the observed system. Only the power systems switching states of the same order of the coincidence level during the monitored time period can be compared. It is obvious that reliability evaluation based on the second order for branches (one or two possible failures) include all events of n-1 order of level contingency and all events with two component failures in the power system. Although it is possible to function in closed ring topology (except four transformer substations), the power system can function in the radial topology. Table 4 presents possible radial networks appearance with its marks and branches with open connections between two buses.
Table 4. Distribution network switching states, (radial)
Switching states mark / Openbranch 1 / Open
branch 2 / Open
Branch 3
A / 2-4 / 4-6 / 2-5 II
B / 2-4 / 5-6 / 2-5 II
C / 12-4 / 4-6 / 2-5 II
D / 12-4 / 5-6 / 2-5 II
E / 12-4 / 5-6 / 2-5 I
F / 2-4 / 5-6 / 2-5 I
G / 2-4 / 4-6 / 2-5 I
H / 12-4 / 4-6 / 2-5 I
It is obvious that there are important differences in output reliability indices between different switching states of the distribution network. Reliability indices listed in chapter 4.1 are evaluated and given in tables 5-7 depending on contingency order for different power system switching states mark according to table 4. If the systems switching state C (the best case)
Table 5. Reliability indices of n-1 order, Distribution power
network, area Slavonski Brod (radial topology)
State / A / B / C / D / E / F / G / HSplt / 3 / 5 / 1 / 2 / 2 / 5 / 4 / 3
Isol / 7 / 6 / 8 / 7 / 8 / 6 / 7 / 7
Prob / 4.19 / 7.56 / 4.03 / 4.09 / 7.35 / 7.56 / 7.50 / 7.40
Freq / 24.7 / 50.0 / 23.8 / 24.7 / 48.1 / 50.0 / 49.0 / 49.0
Dur / 36.7 / 66.2 / 35.3 / 35.8 / 64.4 / 66.2 / 65.7 / 64.9
BP / 3.51 / 6.51 / 3.29 / 3.38 / 6.06 / 6.51 / 6.27 / 6.15
ENS / 20.8 / 34.5 / 18.8 / 19.0 / 30.7 / 34.5 / 32.8 / 30.9
is compared with that marked B (the worst switching state by the reliability aspect), it is found out even 53.94% less curtailment load probability, around 45.55% less expected unsupplied electric energy per year, around 52.4% less load curtailment frequency and 46.6% less load curtailment duration for case A. And furthermore, switching states can be sorted by their reliability indices of n-1 order as following: C, D, A, E, H, G, F and B.