IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 19, NO. 3, JULY2004 1393 Decision Theory Process for Making a Mitigation Decision on Harmonic Resonance G. Atkinson-Hope and K. A. Folly Abstract—A three-stage process for making a harmonic reso- nance mitigation decision in an end-user power plant is developed. Two new indices are developed to assist in making the decision. The first index assesses the severity of resonance and the second is used to make a mitigation decision. In Stage 1, a quantitative model is developed to structure and represent the decision problem with the harmonic resonance severity index as the objective func- tion. In Stage 2, “Utility Theory” is used as the decision criterion to select the most desirable capacitor size. In Stage 3, the mitiga- tion index is applied to assess whether mitigation is needed or not for the chosen capacitor. A case study, based on a model made up of three end-users is conducted to demonstrate the effectiveness of this new process. Index Terms—Decision table, decision theory process, mitigation decision, severity of harmonic resonance, utility theory. I. INTRODUCTION S HUNT capacitor banks for power factor correction are ap- plied to end-users for the efficient operation of power plants [1]. Capacitor-network resonance at harmonic frequencies can cause magnification of harmonic levels to well above accepted limits. System designers are interested to know if the proposed capacitor installation would cause resonance and what is the ex- tent of the problem. The method commonly used to find the res- onant frequency is to determine the ratio of the system fault level to the capacitor size [1]–[3]. This approach has the following shortcomings. a) The method does not reveal the extent of the problem (severity of resonance). Even though a harmonic reso- nance exists, this does not imply that damage to the ca- pacitor will incur. The results can be misleading. It is not always necessary to mitigate harmonic resonance even if the capacitor resonates with system fault level. Also, the method will not give the correct resonant harmonic fre- quency for systems containing upstream capacitances and inductances [2], [4]. b) How to make a decision on the size of capacitor in terms of severity of resonance is not disclosed. A measurement procedure is proposed in [2] to improve on the fault level/capacitor size method. It emphasizes that it is impor- tant to assess the severity of harmonic resonance in addition to determining the resonant frequency. The severity of resonance Manuscript received March 7, 2003. G. Atkinson-Hope is with Cape Technikon, Cape Town, Cape Province 8000, South Africa (e-mail: Garyah@ctech.ac.za). K. A. Folly is with the University of Cape Town, Cape Town, Cape Province 7701, South Africa (e-mail: Kfolly@ebe.uct.ac.za). Digital Object Identifier 10.1109/TPWRD.2004.829142 is not quantified and the procedure is limited to a real system in which a capacitor exists. In this paper, a systematic way is proposed to deal with the shortcomings: a) a new index to quantify the level of severity of resonance at key harmonic frequencies is introduced; b) a new structured decision making process based on a sci- entific method is introduced to help make a decision on the severity of resonance and to decide between different sizes of capacitors as to which size is the most desirable; c) a new index to quantify the level at which mitigation is needed is introduced; d) the new process is applied to decide if mitigation is needed or not. II. DECISION ANALYSIS Decision analysis or the decision theory process is a rational methodology for conceptualizing, analyzing, and solving deci- sion problems [5]. There are three zones for making decisions uncertainty, risk, and certainty, respectively. When probabilities are assigned to each state of nature the decision moves from uncertainty to the risk zone and the model is called a “determin- istic model.” If the outcome measure is a nonmonetary value, the “Utility Theory”(UT) decision criterion is used. “UT” in- corporates preferences toward risk, so that the most desirable decision alternative is identified [6]. III. DECISION THEORY PROCESS The main stages and components of the “decision theory process” are shown in Fig. 1 and are [7]: a) quantitative model building stage which relates control- lable (decision alternatives) and uncontrollable (states of nature) inputs to the outcome (result variable/objective); b) decision table stage; c) decision making stage. A. Define the Problem and Objectives (Block A in Fig. 1) Problem: Will the resonance be severe enough to result in damage to the pf correction capacitors? Objectives: Determine the severity of resonance caused by the installation of pf correction capacitors at key harmonic fre- quencies for a given range of power demand (steady-state) oper- ating conditions. Make a decision between different sizes of ca- pacitors as to which is the most desirable and should be chosen. Furthermore, if high levels of severity of resonance are found, make a decision on mitigation. 0885-8977/04$20.00 © 2004 IEEE