Fuzzy Total Power Quality Index for Electric Networks

1

Fuzzy Total Power Quality Index for Electric Networks P.A. Langouranis, S.D. Kaminaris, G.A. Vokas, T.E. Raptis, G.Ch. Ioannidis

Abstract

- Electric network Power Quality (PQ), which is

a current interest to several power utilities all over the world, is severely affected by many disturbances caused in an electric network like harmonics, over and under-voltages, frequency fluctuations, etc. Many voltage, current and frequency characteristics must follow pre-specified limits (according to the disturbance), for an acceptable power quality. However, the energy sector development (increased use of power electronics and non-linear loads, increased integration of Renewable Energy Sources - RES) and the weak electric networks (as the majority of the Greek islands have) indicate the need to face power quality issues with a broadened perspective. This paper proposes a novel Fuzzy Total Power Quality Index (FTPQI) for representing the level of electric network PQ status. Existing traditional power quality indices for assessing the status of the PQ need improvement in terms of their versatility, reliability, and accuracy. Fuzzy representations can be successful for PQ studies, giving a reliable and scientific way to check the total PQ of electric networks in general and at specified points, as well as, providing the possibility of ad-hoc network improvement remedies. Index Terms: Electric Networks, Expert System, Fuzzy Logic, Multicriteria Decision Making, Power Quality.

I. INTRODUCTION

E

lectrical Power is considered –among others- as an indicator of the stage of development of a country. The conventional design of power systems based on centralized production is replaced by the increasing integration of distributed generation. But the dependence of power system on distributed energy sources, including renewable and non-conventional, has made the control of the system sufficiently intricate. With the use of modern power electronic devices the complexities in system control are made more efficient, user-friendly and reliable also. But the usage of these devices has pushed a power system in serious quality problem. Since the use of sophisticated electronic gadgets has increased in every sphere of life, for their good longevity, requirement of quality power has become a predominant criterion to the

consumers in the present deregulated competitive power market. Therefore, electric PQ has become a main concern of utilities, end users as well as manufacturers [1]. Many definitions for PQ are found in the literature [2-4]. In general, PQ can be considered as the combination of Voltage and Current quality; i.e. the non-deviation from the ideal sinusoidal waveform [3]. The main disturbances that influence the network’s PQ are [2]: short and long interruptions, frequency variation, voltage magnitude variations, rapid voltage changes, supply voltage dips, voltage swells, voltage imbalance, transient overvoltage, harmonics, interharmonics, notching and noise. The deviations of PQ parameters from the accepted values may lead to losses because of decreasing of planned production, decreasing of the lifetime of consumer's machineries and equipment, decreasing of transmission and distribution network availability, etc [5]-[8]. Research since now, is focused on analyzing the impact of each disturbance separately. A combined evaluation has never been applied till now. But the question of an acceptable PQ and the level of acceptance according to various disturbances remains. The aim of this paper is to propose a novel FTPQI for representing the level of electric network PQ status. It could be used to evaluate the most important PQ disturbances that occur in a network, so that to estimate the proposed FTPQI of an examined site. This approach proposes a combined evaluation of PQ using a Fuzzy Expert System (FES) Model (FESM) that is based mainly on: a) Literature survey and analysis and b) Collection and analysis of the Experience of significant users (large consumers, producers, system administrator). It will be calibrated with on-site measurements and statistical recordings. Final methodology will be a useful evaluation tool for the users and the administrators of electric networks that does not currently exist. II. PROPOSED METHODOLOGY A. General

This research has been co-financed by the European Union (European Social Fund - ESF) and Greek national funds through the Operational Program "Education and Lifelong Learning" of the National Strategic Reference Framework (NSRF) – Research Funding Program: ARCHIMEDES III. Investing in knowledge society through the European Social Fund. G.A. Vokas, S.D. Kaminaris, G.Ch. Ioannidis, are with the Departments of Electronics & Electrical Engineering, Technological Educational Institute (TEI) of Piraeus, P.Ralli & Thivon 250, 122 44 Egaleo, Greece (e-mail: [email protected] ). P.A. Langouranis is a MSc Electrical Engineer and T.E. Raptis is a Physist, Researcher in Demokritos Research Institute, Greece.

PQ is an issue that is becoming increasingly important to electricity consumers at all levels of usage. Poor PQ causes inefficiency and reduces productivity in business and industry. High PQ helps insure reliable operation of electronic and computer-controlled equipment. High PQ is essential for business and industries to be competitive in local and world markets. One of the most important indices for industries is the Gross Domestic Product (GDP) per hour worked that is directly connected with the PQ level.

2 The impact of the PQ problems on system operation and customer satisfaction have been recognized by the utilities, which have adopted several strategies to deal with the causes and consequences of deficient PQ [9]. PQ problems have many characteristics that can exploit the advantages of a FES methodology. By its very nature, an estimation for PQ at a site of a distribution system is a problem that needs an expert’s look at various facets, and a FES approach for this can serve as a surrogate expert in helping not only the utility engineer. The all estimation process is a complex, time-consuming task which requires skilled and experienced engineers. This approach lead to high cost practices. In such a way, an intelligent system containing as much knowledge as possible concerning the above-mentioned task, with efficient and quick reasoning would be very useful and helpful to utility engineers [9]. Intelligent Techniques (ITs) are algorithms and methods that are to some extent autonomous and mimic the behaviors of human experts. Among the most successful ITs are those based on Expert Systems and Fuzzy Logic, which are able to mimic the informal reasoning processes of human experts in a way that makes it relatively straight – forward to incorporate direct human experience. The application of ITs to power systems can tackle problems, previously considered as human tasks. Several such systems are developed so far [11]-[12]. Fuzzy logic is often used for reasoning in knowledgebased systems, such as FESs. The knowledge is typically represented in terms of IF-THEN rules. An example is: IF A and B THEN C. The if-part of the rule is called the “premise” and the then-part the “consequent”. The truth value of the rule’s premise describes to what degree the rule applies in a given situation. The so-called fuzzy inference mechanism is used to determine the consequent fuzzy set based on the truth value of the premise (this is often called the degree of fulfillment). Consequent fuzzy sets of individual rules are then combined (aggregated) into a single fuzzy set. In most practical applications, the resulting fuzzy set is converted (defuzzified) in to a real (crisp) value. Fuzzy logic implements experience and preferences through membership functions. The membership functions have different shapes depending on the designer's preference and experience. Fuzzy rules may be formed that describe relationships linguistically as antecedentconsequent pairs of IF-THEN statements. Basically, there are four approaches to the derivation of fuzzy rules: (1) from expert experience and knowledge, (2) from the behavior of human operators, (3) from the fuzzy model of a process, and (4) from learning. Linguistic variables allow a system to be more understandable to a non-expert operator. In this way, fuzzy logic can be used as a general methodology to incorporate knowledge, heuristics or theory into controllers and decision-making.

B. Fuzzy Variables Determination The main purpose of this phase is to determine the fuzzy variables for PQ level assessment. Taking into consideration the international standards [18]-[24] and experts’ opinion [24]-[26], [12]-[13] the following variables have been selected: i. Long Interruptions (li) ii. Short Interruptions (si) iii. Frequency Variations (f) iv. Harmonics (H) v. Supply Voltage Unbalance (un) vi. Voltage dips and swells (d) vii. Supply Voltage Variations (v) viii. Flicker severity (fl) For the above selected fuzzy variables the following questions have to be clarified: • Which are the acceptable limits for each one? • What are the consequences for the users? • Is there any connection among the variables? • Which of them is the most important for the PQ level at a site and which is the less? There is not a crisp answer to these questions. To bypass this hurdle a FES is required. Backbone of this Expert System is the experience obtained by: - Literature - International standards for each disturbance - Experience of significant users of the system For the above selected fuzzy variables the following five categories as far as fuzziness is proposed: VR (Very Common), C (Common) M (medium), U (Uncommon) and VU (Very Uncommon). A correlation between these five linguistic values and fuzzy variables is analyzed in each membership function definition. C. Fuzzy Expert System Presentation The proposed FESM involves the following major steps: - Definition of membership functions for every fuzzy variable - Definition and evaluation of the importance of each fuzzy variable - FTPQI Computation In this context, the FESM requires three parameters: - Specification of the limits for each disturbance - Definition of the correlation between frequency of appearances and effects for each disturbance - Definition of the significance of each disturbance for the Total PQ The first two parameters contribute to the design and specification of the membership functions. The last one is essential in order to define a Multi-Criteria Decision Making Model. The specification of the limits could be obtained mainly from the standards, but it could be confirmed through experience gathered by key personnel (experts) of power systems. This experience is essential in order to correlate

3 the frequency of appearance and the effects on the users. The importance (weight) of each disturbance is one the results of this activity. MEMBERSHIP FUNCTIONS For each fuzzy variable a membership function should be defined. The Membership function should answer to the following question: What is the level of PQ IF (fuzzy variable) is (VC, C, M, U, or VU)? For PQ level the following five categories as far as fuzziness are proposed: VH (very High), H (High), M (Medium), L(Low) and VL (Very Low). The relationship definition between PQ values and these five linguistic variables is heuristically defined and shown in Table I. TABLE I RELATIONSHIP BETWEEN PQ VALUES & LINGUISTIC VARIABLES Linguistic variable PQ VL (Very Low) [0.0,0.2] L (Low) [0.2,0.4] M (Medium) [0.4,0.6] H (High) [0.6,0.8] VH (Very High) [0.8,1.0]

For each fuzzy variable (FV) their contribution to PQ level is expressed through the following linguistic rules: -

IF (FV) is VU THEN PQ is VH IF (FV) is U THEN PQ is H IF (FV) is M THEN PQ is M IF (FV) is C THEN PQ is L IF (FV) is VC THEN PQ is VL

Each fuzzy variable contributes to the PQ level through its membership function. i.

Long Interruptions (li) An interruption is classified as a network’s isolation from any kind of supply. Long interruption may occur in a network and may last from few (at least three) minutes to few hours. “The less interruptions the better the PQ level is” [14]-[16]. According to international standards and experts’ opinion up to ten long interruptions a year is acceptable. If more than fifty long interruptions occur in a network, the impact will be huge not only for industrial users. Forming these data to mathematical equation:

ii.

0, 1 𝜇1 (𝑙𝑖) = �1 − � � × (𝑙𝑖 − 10), 40 1,

𝑙𝑖 ≥ 50

10 ≤ 𝑙𝑖 ≤ 50 (1) 𝑙𝑖 ≤ 10

Short Interruptions (si) Short interruption may occur in a network and may last from few seconds to few minutes (maximum three). “The less short interruptions the better the PQ level is” [20]. According to international standards and experts’ opinion up to ten short interruptions a year is acceptable. If more than some hundreds short interruptions occur in a network, the proper operation of network-users will be set under consideration. Forming this data to mathematical equation:

iii.

0, ⎧ 0.55 ⎪0.55 − � � × (𝑠𝑖 − 50), 250 𝜇2 (𝑠𝑖) = 0.45 ⎨ 1−� � × (𝑠𝑖 − 10), ⎪ 40 ⎩ 1,

𝑠𝑖 ≥ 300

50 ≤ 𝑠𝑖 ≤ 300 10 ≤ 𝑠𝑖 ≤ 50 𝑠𝑖 ≤ 10

(2)

Frequency Variation (f) Power Frequency Variation happens when the balance between generators and their loads changes. Frequency Variation is rarely met in the Union for the Coordination of the Transmission of Electricity (UCTE). The appearance of such an event may lead to dangerous situation. However the enormous increase of distributed generation and the lack of communication between different Power Producers may lead to such deviations. The linguistic rule for this event is: “The less Frequency Variation the better PQ level is” [24]. The limits for the membership functions are different and depend on the location. In Greece, for a non-interconnected inland grid a deviation of ±1% from nominal frequency is allowed (frequency should be kept between 49.5 Hz and 50.5 Hz). According to international standards [18] at least the 99.5% of 10 minutes mean values measured in a week time have to be inside these boundaries. Taking this into consideration the membership function is: 0, 1 𝜇3.1 (𝑓) = �� � × (𝑓 − 0.95), 0.045 1,

𝑓 ≤ 95%

95% ≤ 𝑓 ≤ 99.5% (3.1)

99.5% ≤ 𝑓 ≤ 100%

Respectively for island grid it is allowed to deviate ±2% from nominal frequency. Frequency should be kept between 49 Hz and 51 Hz. According to international standards [18] at least the 95% of 10 minutes mean values measured in a week time have to be inside these boundaries. Taking this into consideration the membership function is: 0, 1 𝜇3.2 (𝑓) = �� � × (𝑓 − 0.90), 0.085 1,

𝑓 ≤ 90%

90% ≤ 𝑓 ≤ 98.5%

98.5% ≤ 𝑓 ≤ 100%

(3.2)

iv. Harmonics(H) As known, any periodic deviation of a pure sinusoidal voltage waveform can be presented with the sum of sinusoids of the power frequency and its integer multiples. The presence of harmonics is evaluated through the total harmonic distortion (THD) index. The impact of harmonics in network operation is significant. Harmonics lead to energy losses but also they are responsible for protections devices tripping, overheating of neutral line, premature aging of system components and other. There are limits for each single multiple of power frequency that should be kept. In linguistic rules this is described as follows: “The fewer Harmonic, the better PQ level is”. According to international standards [18], [24] at least the 95% of 10 minutes mean values measured in a week time have to be inside these boundaries. Taking this into consideration the membership function is:

4 0, 1 𝜇4 (𝐻) = �� � × (𝐻 − 0.90), 0.085 1,

𝐻 ≤ 90%

90% ≤ 𝐻 ≤ 98.5% (4)

98.5% ≤ 𝐻 ≤ 100%

v. Supply Voltage Unbalance (un) Supply voltage unbalance arises when rms values or phase angles between consecutive phases are not equal. Voltage unbalance affects three phase asynchronous motors causing overheating and tripping of protective devices [6]. Industries that base their production line to such motors may have huge problems because of this event. Supply voltage unbalance should be less that 2%. According to international standards [24] at least the 95% of 10 minutes mean values measured in a week time have to be inside these boundaries. Taking this into consideration the membership function is: 0, 1 𝜇5 (𝑢𝑛) = �� � × (𝑢𝑛 − 0.90), 0.085 1,

𝑢𝑛 ≤ 90%

90% ≤ 𝑢𝑛 ≤ 98.5% (5)

98.5% ≤ 𝑢𝑛 ≤ 100%

vi. Voltage Dips (d) Many Voltage dips and swells represent a temporary change of voltage below or above a threshold. Thousands of Voltage dips may occur in a year time period. In linguistic rules this is described as follows: “The less Voltage dips, the better PQ level is” [20]. The membership function is: 0, 1 𝜇6 (𝑑) = �1 − � � × (𝑑 − 10), 990 1,

𝑑 ≥ 1000

10 ≤ 𝑑 ≤ 1000 (6) 𝑑 ≤ 10

vii. Supply Voltage Variation (v) The magnitude of the supply voltage is represented with a rms value of voltage during an aggregation period (10 minutes). Any variation in the magnitude of the supplied voltage outside the acceptable limits (±10%) can cause premature ageing, preheating or malfunction of connected equipment. According to international standards [24] at least the 95% of 10 minutes mean values measured in a week time have to be inside these boundaries. Taking this into consideration the membership function is:

viii.

0, 1 𝜇7 (𝑣) = �� � × (𝑣 − 0.90), 0.085 1,

𝑣 ≤ 90%

90% ≤ 𝑣 ≤ 98.5%

98.5% ≤ 𝑣 ≤ 100%

(7)

Flicker Severity (fl) Flicker is a visual sensation caused by unsteadiness of a light. The level of the sensation depends on the frequency and magnitude of a light and on the observer. There are indices calculating this event. For long term analysis the Plt index is essential. Plt should be below 1. According to international standards [24] at least the 95% of 10 minutes mean values measured in a week time have to be inside these boundaries. Taking this into consideration the membership function is: 0, 1 𝜇8 (𝑓𝑙) = �� � × (𝑓𝑙 − 0.90), 0.085 1,

𝑓𝑙 ≤ 90%

90% ≤ 𝑓𝑙 ≤ 98.5% (8)

98.5% ≤ 𝑓𝑙 ≤ 100%

MULTI-CRITERIA DECISION MAKING METHODOLOGY The aim of Multi-Criteria Decision Making (MCDM) methodology is to determine the optimal alternative with the highest degree of desirability with respect to all relevant criteria and constraints. Basically MCDM consist of two phases: I. The aggregation of the judgment with respect to all criteria and per decision alternatives. II. The rank ordering of the decision alternatives according to the aggregation judgment. In crisp MCDM models it is usually assumed that the final judgments of the alternatives are expressed as real numbers. In this case the second phase does not pose any particular problems and, therefore, suggested algorithms concentrate on phase I. Studying PQ level we will concentrate on phase I. The aggregation of judgment leads to the TPQI. Phase II is a ranking system of TPQI [10]. Yager–Saaty method is implemented in this study in order to combine different criteria to estimate the PQ level under phase I. It is assumed a finite set of alternative locations 𝑋 = {𝑥𝑖 }, i = 1,2,3, … , n and a finite set of criteria 𝐺 = �𝑔�𝑗 �, j = 1,2,3, … ,8. The 𝐺 = �𝑔�𝑗 �, j = 1,2,3, … ,8, are fuzzy sets the degrees of membership of which represent the normalized degrees of attainment of the jth criteria by alternative xi. The fuzzy set � , is then the intersection of all fuzzy criteria, that decision, 𝐷 is, 𝜇 𝐷� (𝑥𝑖 ) = min �𝜇𝑗 (𝑥𝑖 )� , 𝑖 = 1,2,3, … , 𝑛 (9) 1