VOLTAGE CONTROL IN DISTRIBUTION SYSTEM WITH DISTRIBUTED GENERATION

Abstract

Voltage regulation in distribution system is a control effort for keeping the magnitude of all voltages in the distribution system within prescribed limits. Voltage regulation aims at avoiding two types of violations: overvoltages and undervoltages. An undervoltage (overvoltage) violation happens if magnitude of the voltage is between 80% and 90% (110% and 120%) of the nominal value for longer than one minute. Voltage regulation is usually the responsibility of the network operator. It is important since all devices are optimized to operate in rated voltages and voltage violations may reduce the performance and lifetime of those devices. The main cause of voltage variations is the behaviour of electricity customers and distributed generations. Since the distribution system loads vary over time, the voltage drops on distribution lines also vary. Sometimes, this variation may lead to an undervoltage or an overvoltage situation. In addition, the connection of distributed generation (DG) resources in a distribution network introduces another source of fluctuations in power flow in the network. This also may introduce voltage violations. In the future, due to the environmental and economic considerations, the penetration of DG resources in the distribution system will increase. In addition, electricity consumption will also grow steadily. Consequently, the risk of violations in voltages will be higher in the future. This further emphasizes the importance of voltage regulation in distribution network. The voltage regulation is carried out by different types of controllers such as On-load tap changer (OLTC), shunt capacitor (SC) and static var compensator (SVC). An OLTC is an autotransformer that has multiple taps and, hence, can change its voltage ratio while serving the loads. Shunt capacitors are connected to the network in shunt through appropriate switching mechanism and by varying the number of shunt capacitors the reactive power injected to the system is varied thereby varying the system voltage. At any bus, either a single capacitor or a bank of capacitors may be connected. An SVC is a combination of shunt capacitor, shunt reactor and power electronic devices, which can smoothly change its effective reactance according to the network operating condition and its control strategy. The settings of OLTC (tap setting) and SC (number of SC) are discrete in nature. On the other hand, the setting of an SVC can be discrete (slope) or continuous (reference voltage). Nevertheless, due to power electronic devices, its effective reactance can take continuous values. i For effective voltage regulation, the settings of all the above voltage regulation devices need to be determined in a coordinated manner. These settings are usually determined such that the network is operated optimally in some sense. Depending upon the preference of the network operator, different objectives (such as loss minimization, improvement of system voltage profile etc.) are adopted for optimal operation of the network. Therefore, the voltage regulation problem can be posed as an optimization problem. The solution of the optimization problem gives the optimal and coordinated settings of the controllers. In most of the previous works on voltage regulation in distribution system, SVC has not been considered as most of the distribution networks do not have any SVC installed. Only few works have considered SVC in voltage regulation problem in distribution system. However, these works have considered only balanced network. On the other hand, distribution systems are generally unbalanced networks. Moreover, in the future, the presence of SVC in the distribution system is expected to increase because of its fast response and reduction in price. Consequently, there is a need for a model for SVC that can be used in voltage regulation problem of an unbalanced distribution system. Furthermore, the available works in voltage regulation problem use constant reactive power injection model of SVC. However, another popular operating mode of an SVC is voltage control mode. Hence, a model for SVC operating in voltage control mode for voltage regulation problem in unbalanced distribution system is also required. To address the above issue, a constrained (involving both equality and inequality constraints), multi-objective optimisation problem has been formulated in Chapter 2 for voltage regulation in an unbalanced distribution system. The formulated problem considers single-phase and multiphase OLTC, SC and SVC as voltage control devices. Further, the SVC is assumed to operate in voltage control mode using droop control. In this mode, the slope setting and reference voltage of the SVC need to be determined. It is to be noted that the slope setting is treated as discrete variable while the reference voltage is treated as continuous variable. The objective functions include minimization of power loss in the system and the number of switching of OLTC, SC and SVC. The equality constraints involve the nodal current balance equations and the relations between current and voltages of all elements in the network. The inequality constraints represent the regulatory and physical limits of the network and its elements. The regulatory limits include the limits on voltage magnitudes and amount of unbalance in the system. The physical limits ii involve the operational limits of OLTC, SC and SVC. As the formulated optimisation problem involves both discrete (tap positions of OLTCs, number of SCs, and slope settings of SVC) and continuous (reference voltage of SVC) variables, the formulated optimization problem is a mixed integer non-linear programming (MINLP) problem. To solve the above MINLP problem, a two-stage solution methodology has been developed. In the first stage, the original MINLP is relaxed into a non-linear programming (NLP) problem by considering all the discrete variables as continuous variables and subsequently, the relaxed NLP problem is solved by using interior point method (IPM). The major purpose of this stage is reduction in the size of the discrete search space. From the solution of the NLP relaxation, the two closest possible discrete values are selected. In this manner, the discrete search space is reduced significantly. In the second stage, from the selected discrete values, a smaller MINLP is formulated involving only binary discrete values. This smaller MINLP is solved using branch and bound (BB) method. With this two-stage approach, the formulated problem has been solved for one-hour-ahead study. The effectiveness of the developed method has been investigated on a modified IEEE 123 bus unbalanced radial distribution system. This system has one single-phase OLTC, one two-phase OLTC, two three-phase OLTCs, three single-phase SC, one three-phase SC, and one three-phase SVC. In addition, it has many photovoltaic (PV) generations as well. Further, while solving the optimization problem, both uniform and non-uniform operations of the multi-phase control devices have been considered. When a multi-phase device operates uniformly, its settings for all its phases are kept the same. On the other hand, in non-uniform operation, the settings in different phases are allowed to be different. The performance of the developed two-stage algorithm has been investigated on several test cases in this system. It was found that to solve the formulated optimization problem for 24 one-hour periods, the proposed algorithm takes less than 10 minutes. Further, the performance of the developed algorithm has also been tested for the case of fast moving clouds. In this case, one-step-ahead optimization has been used to solve the problem and the optimal solution could be found within 2 minutes. This is a significant improvement considering that the original MINLP problem was unsolved even after 8 hours (using a branch-and-bound solver). As a result, the proposed two-step solution method has the potential for practical application. In Chapter 2, the one-hour-ahead optimization study has been conducted assuming that the iii load and generation patterns remain fixed during the one-hour period of study. However, during this one-hour period, loads and generations can vary significantly. Therefore, upon implementation of the settings of the controllers (obtained assuming fixed load and generation pattern), there may be voltage violations or suboptimal operation of the network. To avoid this possibility, it is important to consider the uncertainties in load and generation in the voltage regulation problem. In Chapter 3, application of robust optimization technique is proposed to consider these uncertainties. To apply the robust optimization (RO) technique, the property of monotonicity of the voltage magnitudes against the variation of load and generation has been used. Following this property, the extreme values of magnitudes of voltages correspond to the situations in which loads and generations are also at their corresponding extreme values. Therefore, in the robust optimization method, different extreme scenarios are considered and if the solution obtained by the RO method ensures the acceptable operation of the network in all these extreme scenarios, then it can be safely concluded that the operation of network would be acceptable under the actual load and generation variation within the limiting values. In Chapter 3, from the extreme values of loads and generations, 32 extreme scenarios have been generated. Furthermore, the optimization problem discussed in Chapter 2 has been extended to consider all of these extreme scenarios at once. This chapter conjectures that the optimal solution of the problem corresponds to the robust settings of the controllers. The settings are robust if the network remains feasible for all possible values of load and generation as long as these values remain within the intervals defined by the extreme scenarios. However, the robust optimization problem cannot be solved using the method described in Chapter 2. Therefore, a new two-stage approach has been proposed based on the absolute values constraint method. The first stage of Chapter 3 is same as that of Chapter 2. However, in the second stage, the binary MINLP are reformulated again. Each binary variable is replaced by a continuous variable that are constrained to have binary values using the absolute value constraints. The new problem is an NLP in which all variables are continuous. Using the new proposed methodology, the RO problem has been solved to compute the controller settings in the modified IEEE 123 bus system. Moreover, Monte Carlo Simulation (MCS) studies have been carried out to verify the above conjecture. The boundaries of magnitudes of voltages calculated using RO method have been compared with those calculated using MCS studies. It was found that the discrepancies iv between the values obtained by the RO method and the MCS method are small for all practical purpose thereby validating the above conjecture. Furthermore, the performance of the proposed method has also been tested for a representative day with fast moving clouds and the performance was found to be quite satisfactory. However, as the price of the robustness, the robust solution is a little bit worse than the non-robust solution in terms of the optimal value of the objective function. Further, the best operating strategy corresponding to robust solution differs from that corresponding to non-robust solution discussed in Chapter 2. In Chapters 2 and 3, the topology of the system has been assumed to be fixed. However, due to various reasons, such as enhancement of network efficiency, restoration of supply after the occurrence of a fault etc., the configuration of the system is altered. Because of this change in topology, the controller settings obtained in one configuration may not be feasible in other configuration(s). Therefore, it is important to ensure that the obtained controller settings remain feasible for all possible, pre-selected configurations of the network. However, in the literature, no such methodology has been proposed to consider topology variation in voltage control problem. To address the above issue, in Chapter 4, a methodology to find the optimal settings of the controllers in voltage control problem has been proposed considering the variation in topology. The method ensures that for any configuration within a set of pre-selected topologies, all bus voltages across the network remain within their specified limits. This method assumes that network reconfiguration is carried out separately from voltage regulation studies and that topological changes of the network occur within one-day period. The optimal settings obtained by the proposed method can be maintained at the same values even when the network changes its topology within the set of pre-selected configurations. Hence, the solution is robust against uncertainty of topologies. Simulation studies have been carried out on the modified IEEE 123 bus system to verify the efficacy of the proposed method. The results obtained show that when more than two topological changes in a day are expected, the proposed method is better than the conventional voltage regulation method that considers no topological change. In most of the previous works in the literature and in Chapters 2-4 of this thesis, all OLTCs are assumed to operate in time-of-day mode. In this mode, the positions of a tap of an OLTC is optimized beforehand in the off-line mode and communicated to the OLTC. The OLTC will change its v tap position based on the schedule communicated to it by the network operator. However, in this mode of operation, a good forecast of future variation of load and generation is required. If the actual load and generation conditions are different from the forecasted values, the degree of optimality may be reduced. In addition, it requires communication infrastructure for communication between the central control centre and the controllers. On the other hand, an OLTC can also be controlled in line drop compensation (LDC) mode. In this mode, the position of a tap of an OLTC is selected by the local controller based on the setting of the LDC and the measured local current and voltage. Hence, if loading condition changes significantly, the OLTC will sense it and adjust the position of its tap according to its LDC settings. However, the settings of LDC are generally chosen based on heuristics rules. Hence, coordination with other OLTCs and controllers cannot be done optimally. Now, in the literature, no optimization model of OLTC operating in LDC mode for voltage regulation studies could be found. To address this issue, Chapter 5 proposes an optimization model of an OLTC operating in LDC mode. The developed model can be integrated into the optimization problems discussed in the previous chapters. As a result, it is possible to coordinate an OLTC operating in LDC mode with other controllers in the network. In the LDC mode, there are four parameters corresponding to each tap of an OLTC. These are: voltage reference, voltage bandwidth, resistance setting and reactance setting. All of these are discrete quantities. Based on the values of these parameters and the measured local current and voltage, the position of a tap of the OLTC can be decided by the microprocessor of the OLTC. Hence, if an OLTC operates in LDC mode, the position of its taps is no longer a control variable as is the case in previous chapters. With the proposed optimization model, the values of the parameters of LDC of an OLTC are calculated once in every 24-hour. Conventionally, the modification of the settings of LDC is done seasonally or when there is a significant change in the loading condition of the network. Hence, the LDC mode does not need the availability of a communication network. However, the optimization problem that considers LDC operation cannot be solved using the methods described in the previous chapters. Hence, another new two-stage method has been proposed. The first stage of Chapter 5 is same as that of Chapter 2. There are two differences between the second stage of Chapter 5 and that of Chapter 3. Firstly, from the solution of the first stage, vi three closest possible discrete values are considered for voltage reference, voltage bandwidth, resistance setting, reactance setting and taps of OLTCs. However, for shunt capacitor and SVC, only two discrete values are considered. Hence, the new MINLP has ternary, binary and continuous variable. Secondly, the exact penalty function method is used to solve the new MINLP. The relaxation is applied for both equality and inequality constraints Simulation studies have been carried out for a number of possible operating strategies of OLTC, SC, and SVC. The results indicate that the proposed model and method can be used to coordinate an OLTC operating with LDC mode with other controllers. Moreover, the computational times for 24-hour-ahead optimization are shorter than 2 minutes. Hence, the proposed model and method can be quite useful in planning and operation in unbalanced distribution system where OLTCs operate in LDC mode. In all the previous chapters, constant power load has been assumed. However, this model is accurate only for industrial loads. On the other hand, commercial and residential loads are voltage dependent. Therefore, it is important to consider different types of loads in voltage regulation problem. Chapter 6 explores this issue in more detail. In this chapter, a polynomial model of voltage-dependent loads is considered and the obtained results have been compared with the results obtained using constant power loads. Detail comparative studies obtained with constant power loads considering multiple topology and line drop compensation have also been carried out. The optimization problem corresponding to voltage-dependent loads are harder to solve than that corresponding to constant-power loads. This is evident because the methods described in Chapters 2, 3 and 4 cannot solve the optimization problem with voltage-dependent loads. However, the method described in chapter 5 solves the problem with voltage-dependent loads successfully. However, it is to be noted that for considering the uncertainties in voltage dependent loads, it is quite difficult to find the intervals of possible values of load power of the voltage dependent loads due to the unknown voltage magnitudes at buses at which those loads are connected. Consequently, uncertainties in voltage dependent loads in voltage regulation problem could not be undertaken in this work. In general, the optimal solution corresponding to constant-power loads differs from those corresponding to voltage-dependent loads. The significance of the difference may depend on the characteristics of each distribution system. However, the simulation studies verify the efficacy and vii the efficiency of the proposed method. Thus, the proposed method has the potential to be used in planning and operation of a distribution system that serves many voltage-dependent loads such as commercial and residential customers. Outline of the thesis Based on the above discussion, the outline of the thesis is as follows: • In Chapter 2, a constrained (involving both equality and inequality constraints), multi-objective optimisation problem has been formulated for voltage regulation in an unbalanced radial distribution system. The formulated problem considers single-phase and multi-phase OLTC, SC and SVC as voltage control devices. The formulated optimisation problem involves both discrete and continuous variables and therefore, it is a mixed integer non-linear programming (MINLP) problem. To solve this MINLP problem efficiently, a two-stage solution method has been developed. A large number of test cases (including a case of fast moving clouds) have been considered on the modified IEEE 123 bus unbalanced radial distribution system to validate the effectiveness of the developed solution procedure. However, the formulated optimization problem in this chapter assumes that both load and generation conditions are accurately known and, also, the topology of the system remains fixed. • In Chapter 3, the uncertainties in both load and generation conditions are considered in the voltage control problem. For considering these uncertainties, the voltage regulation problem is formulated as a robust optimisation problem. As the two-stage solution method developed in Chapter 2 is unable to solve this RO problem satisfactorily, a new two-stage solution procedure has been developed to solve this RO problem. Again, several test cases (including fast moving clouds) have been considered on the modified IEEE 123 bus system to validate the efficacy of the developed solution procedure to solve the robust voltage control problem. However, in this chapter also, it has been assumed that the topology of the system remains fixed. • In Chapter 4, uncertainty in topology has been considered in the voltage regulation problem. However, in this case, no uncertainty in the load and generation conditions has been considered. The solution of the formulated problem ensures that the settings of the controllers can viii be maintained at the same values even when the network changes its topology within the set of pre-defined configurations. Moreover, the controller settings also ensure that the bus voltages in the network remain within the limits for any topology within the set of pre-defined configurations. As in the previous chapters, several studies on the IEEE 123 bus system have been carried out to validate the effectiveness of the proposed method. • In Chapter 5, LDC mode of operation of an OLTC is considered (in Chapters 2-4, time-ofday mode of OLTC has been used). To integrate the LDC mode of OLTC in the voltage regulation problem and find its settings in coordination with the other control devices, a new optimisation model of LDC has been developed. Simulation studies have been carried out on the IEEE 123 bus system to investigate the comparative performances of OLTC operating in time-of-day mode and LDC mode. • In Chapter 6, voltage dependent loads have been considered (in all the previous chapters, constant power loads have been used). To represent the voltage dependent loads, polynomial model of the load has been used. Detailed studies have been carried out on the IEEE 123 bus system to compare the obtained results with those obtained with constant power load corresponding to uncertain topology and LDC mode of operation of OLTC. • In Chapter 7, major conclusions of this work are given and a few suggestions for future work in this field of study are also provided. Contribution of the thesis To summarize, the major contributions of this thesis are as follows: • For including the SVC operating in voltage control mode in voltage regulation in unbalanced radial distribution system, a current-voltage based optimization model using Cartesian coordinate has been developed and a two-stage optimization method has been proposed to solve it. • For considering the uncertainty of load and generation, a robust-optimization-based voltage regulation problem has been formulated and its continuous reformulation that is based on complementarity condition has been proposed. ix • For considering frequent topological changes in distribution system, the exact penalty based relaxation method has been proposed to solve voltage regulation problem considering multiple topologies. • An optimization model of line drop compensation of an OLTC has been developed. The model has been integrated into the model of voltage regulation problem. However, this model introduces an integer-valued state variable corresponding to the position of a tap of an OLTC. A modelling approach to represent the integer state variable using continuous variable has been proposed. • A study on the effect of voltage dependent load on the performance of voltage regulation problem has been carried out to identify the strengths and weaknesses of the popular practice of using constant-power load in voltage regulation problem. The studies corresponding to multiple topology approach and line drop compensation have been carried out.