An optimization approach to determining the power of active filters

. The coal grading plants in Vietnam extensively apply asynchronous motors with frequency control. They consume reactive power and non-sinusoidal current from the supply network. The non-sinusoidal currents and voltages lead to additional energy losses in electrical equipments, reduce their service life and cause an economic damage. Because of the low load power factor the companies with such plants pay penalties to power supply utilities. These problems can be solved by the active filters. The paper suggests an optimization algorithm to calculate the power of the active filter, which provides a load power factor corresponding to the normative documents and power quality indices corresponding to the standard requirements. The algorithm is used to calculate the power of the active filter for the coal grading plant owned by the company "Kua Ong-Vinakomin".


Introduction
Coal mining is one of the most important economic industries of Vietnam. Mines and quarries have coal grading plants. The manufacturing equipment of the plants is driven by asynchronous motors, primarily with frequency control. They are nonlinear loads for power supply systems and distort power quality. The harmonic factors of voltage exceed the established standards [1]. Voltages and currents contain both harmonics and interharmonics. The load power factors are lower than the value agreed by the normative documents [2].
The paper presents an analysis of the power supply system of the coal grading plant, results of the tests of electric power, formulates an optimization problem and describes an algorithm to determine the power of the active filter, presents results of calculation of the power of active filter for the coal grading plant of the company "Kua Ong-Vinakomin".

Characteristic of the power supply system and loads of the coal grading plant
Coal is mined in the quarry and transported to the warehouse of the coal grading plant. Fig.1 presents a scheme of the power supply of the plant. Electric power from the 22 kV substation buses of the power supply utility (node 6643) is supplied to the 0.4 kV network of the power supply system of the plant (node 4143) by the 1000 kVA step-down transformer that belongs to the coal grading plant. The distance between nodes 4143 and 45038 is 60 meters. The total length of the 0.4 kV electric network exceeds 12 km. The plant has two coal grading shops (shop No.1, shop No. 2), a shop of power and water supply, a coal warehouse. In the warehouse the excavator loads coal on the conveyer, which delivers coal to the shops for grading coal pieces by size. The manufacturing equipment of the shops is put into operation by 58 asynchronous motors with a capacity from 4 to 185 kW primarily with frequency control.  To assess the quality of voltage and current in the 0.4 kV network, the following indices and norms for their values were established in [1]:  deviation of the voltage value -δU ≤ ±5.0%;  the total harmonic distortion -KU ≤ 6.5%;  the n-th harmonic factor of voltage -KU(n) ≤ 3%;  the n-th harmonic factor of current KI(n) ≤12%. In [2] the load power factor (cosφ) at the connection node of the plant to the supply network should comply with the condition: cosφ ≥0.85. If this condition is not fulfilled, the company with the plant pays penalties to the power supply utility. The value of cosφ can be low because of large reactive power consumption by the electric motors of the plant, active power losses when transmitted over the electric network and losses caused by harmonics and interharmonics. The power quality and the value of cosφ at node 4143 were tested.

Results of the electrical energy tests
The tests included measurements of the indices of voltage and current quality and cosφ by the device PQ-Box150 [8] for 24 hours with a time interval of measurements equal to 1 second. Table 1 presents the measured values of δU, which correspond to the requirements [1]. The Table also shows the measured values of KU and their normative values from [1].The measured values of KU exceed the norm more than twice. They are shown in bold type.  Table 2 presents the measured and normative values of KU(n) and KI(n) for the harmonics with the most frequent excess of the norms [1]. The measured values of KI(n) are not higher than the normative value. The measured values of KU(m) for interharmonics and the values of currents I(m)max of interharmonics (m -the number of the interharmonic) are given in Table 3. The normative values for them are not determined. The measured values of cosφ and its normative value determined in [2] are shown in Table 4. At phase В the value of cosφ is lower than the norm. The problems caused by harmonics, interharmonics and cosφ can be resolved using the active filter that is connected to the network in parallel to the nonlinear load.

Optimization problem to determine the power of the active filter
The power of the active filter is determined by the reactive power that it must generate to compensate for the reactive power of the load and the apparent power required to get rid of harmonics and interharmonics of the current at the point of its connection to the network. This can be achieved by solving an optimization problem with the objective function assumed to be the minimum active power losses in the power system network after installation of the active filter, i.e.
where N -the highest number of harmonic, M -the highest number of interharmonic. In this case the following constraints are to be met: where i -the network node number; The optimization problem consists of three subproblems: 1) calculation of the apparent power of the active filter to provide the normative cosφ; 2) calculation of the apparent power of the active filter to eliminate current harmonics; 3) calculation of the apparent power of the active filter to eliminate current interharmonics.
The first subproblem is formulated in such a way: the total active power losses in the network of the fundamental frequency ( Constraints (2) and (3) in this case should be fulfilled. If the node for active filter installation is not assigned, all nodes of the network must be considered as candidates for the active filter installation. The algorithm must consider transformer capabilities of voltage control on the lower side with the connected load. The suggested algorithm was developed based on the software "SDO" to calculate electric network modes of the fundamental frequency [9,10]. The block-diagram of the algorithm is presented in Fig. 2 where "d" abbreviated from "desired". The value of c φ tg is determined based on cosφc. The value of d φ tg is calculated using constraint (2). As far as the admissible value of cosφ is within the interval cosφmin ≤ cosφ ≤ cosφmax. The value of the reactive power of the active filter is also within the interval The required phase angle φd should be calculated using cosφmin and cosφmax. The highest and lowest values of Block 9. Calculation of the total active power losses in the network on the basis of results obtained by the software "SDO".
Block 10. Comparison of the active power losses of the preceding calculation step with the losses of the current step to determine minimum losses, namely, if  The management company of the coal grading plant has chosen node 45038 for installation of an active filter in power supply system (Fig. 1). The transformer supplying electric energy to the  Table 7. The active filter to eliminate harmonics of current must be no less than 17 kVA in each phase.  Table 8 presents the values of phase powers of interharmonics and the total powers of three phases that were calculated by the measured parameters. The apparent power of interharmonics at three phases accounts for 313.7 VA.

Conclusions
The measurements have shown that the load current contains harmonics and interharmonics, the indices KU(n) and KU exceed the normative values, and cosφ is lower than the norm.
The total harmonic distortion reduction and the load power factor increase can be achieved by installation of the active filter. The power of the active filter was determined by the developed optimization algorithm and using the results of measurements of mode parameters of network.
The power of the active filter was determined for the coal grading plant of the company "Kua Ong-Vinakomin".