## Stochastic Modeling and Analysis of Power System with Renewable Generation

Research output: Research › Ph.D. thesis

### Abstract

Unlike traditional fossil-fuel based power generation, renewable generation such as wind power relies on uncontrollable prime sources such as wind speed. Wind speed varies stochastically, which to a large extent determines the stochastic behavior of power generation from wind farms. With the increasing number of wind turbines (WTs) connected to distribution systems, network operators are concerned about how such a stochastic generation affects power losses of the network. Furthermore, the operators need to estimate how much and when the stochastic generation can reduce the loading of substation transformers and distribution feeders. Moreover, the network operators are interested in evaluating the maximum penetration level of wind power in their network before any technical requirements are violated.

The traditional approach to these studies is based on a deterministic analysis. For instance, the size of a substation transformer is determined by the sum of the maximum loading at individual radial feeders while assuming no generation output from local generators. However, such a deterministic analysis does not provide a realistic evaluation of system steady-state performance. A more realistic evaluation can be achieved through a probabilistic analysis that takes into account the stochastic behavior of wind power generation (WPG) and load demand. Such a probabilistic analysis may help network operators to cut down the cost associated with system planning. Thus, the objective of this thesis is to develop stochastic models of renewable generation and load demand for the optimal operation and planning of modern distribution systems through a probabilistic approach.

On the basis of statistical data, stochastic models of WPG, load and combined heat and power (CHP) generation are developed. The stochastic wind power model is constructed on the basis of an autoregressive integrated moving average (ARIMA) process. The model characterizes WPG by mean level, temporal correlation and driving noise. Such a model is valuable for researchers who do not have access to wind power measurements. The model can be used to evaluate year-to-year variation of wind power generation through a sensitivity analysis and to forecast very short-term wind power through a model-based prediction method. The stochastic load model is established on the basis of a seasonal autoregressive moving average (ARMA) process. It is demonstrated that such a stochastic model can be used to simulate the effect of load management on the load duration curve. As CHP units are turned on and off by regulating power, CHP generation has discrete output and thus can be modeled by a transition matrix based discrete Markov chain. As the CHP generation has a strong diurnal variation, reflecting the heat load and electricity price, it is proposed to use different transition matrices for different periods of a day. These three stochastic models are the main theoretical contributions of this thesis.

With these stochastic models, a realistic evaluation of the system steady-state performance can be carried out through a probabilistic load flow (PLF) analysis. Based on the PLF analysis, several studies are conducted and strategies are proposed to operate and plan a modern distribution system in an optimal way. In the first case study, a stochastic optimization algorithm is proposed that minimizes the expectation of power losses of a 69-bus distribution system by controlling the power factor of WTs. The optimization is subjected to the probabilistic constraints of bus voltage and line current. The algorithm combines a constrained nonlinear optimization algorithm and a Monte Carlo based PLF calculation. In the second case, it is demonstrated through a Danish distribution system (Støvring system) that the probability of transformer overloading and the time of the overloading can be identified through a probabilistic analysis. Based on the analysis, use of a gas turbine is determined as a cheaper solution than transformer expansion in order to solve the overloading problem. In the last case, an optimal constrained load flow algorithm is proposed to determine the maximum WT capacity in the modified Støvring system when allowing reactive power control and energy curtailment of WTs, subject to voltage and current constraints. These developed models and proposed algorithms serve as effective tools to assist network operators in decision-making during the operation and planning of power systems.

The traditional approach to these studies is based on a deterministic analysis. For instance, the size of a substation transformer is determined by the sum of the maximum loading at individual radial feeders while assuming no generation output from local generators. However, such a deterministic analysis does not provide a realistic evaluation of system steady-state performance. A more realistic evaluation can be achieved through a probabilistic analysis that takes into account the stochastic behavior of wind power generation (WPG) and load demand. Such a probabilistic analysis may help network operators to cut down the cost associated with system planning. Thus, the objective of this thesis is to develop stochastic models of renewable generation and load demand for the optimal operation and planning of modern distribution systems through a probabilistic approach.

On the basis of statistical data, stochastic models of WPG, load and combined heat and power (CHP) generation are developed. The stochastic wind power model is constructed on the basis of an autoregressive integrated moving average (ARIMA) process. The model characterizes WPG by mean level, temporal correlation and driving noise. Such a model is valuable for researchers who do not have access to wind power measurements. The model can be used to evaluate year-to-year variation of wind power generation through a sensitivity analysis and to forecast very short-term wind power through a model-based prediction method. The stochastic load model is established on the basis of a seasonal autoregressive moving average (ARMA) process. It is demonstrated that such a stochastic model can be used to simulate the effect of load management on the load duration curve. As CHP units are turned on and off by regulating power, CHP generation has discrete output and thus can be modeled by a transition matrix based discrete Markov chain. As the CHP generation has a strong diurnal variation, reflecting the heat load and electricity price, it is proposed to use different transition matrices for different periods of a day. These three stochastic models are the main theoretical contributions of this thesis.

With these stochastic models, a realistic evaluation of the system steady-state performance can be carried out through a probabilistic load flow (PLF) analysis. Based on the PLF analysis, several studies are conducted and strategies are proposed to operate and plan a modern distribution system in an optimal way. In the first case study, a stochastic optimization algorithm is proposed that minimizes the expectation of power losses of a 69-bus distribution system by controlling the power factor of WTs. The optimization is subjected to the probabilistic constraints of bus voltage and line current. The algorithm combines a constrained nonlinear optimization algorithm and a Monte Carlo based PLF calculation. In the second case, it is demonstrated through a Danish distribution system (Støvring system) that the probability of transformer overloading and the time of the overloading can be identified through a probabilistic analysis. Based on the analysis, use of a gas turbine is determined as a cheaper solution than transformer expansion in order to solve the overloading problem. In the last case, an optimal constrained load flow algorithm is proposed to determine the maximum WT capacity in the modified Støvring system when allowing reactive power control and energy curtailment of WTs, subject to voltage and current constraints. These developed models and proposed algorithms serve as effective tools to assist network operators in decision-making during the operation and planning of power systems.

### Details

Unlike traditional fossil-fuel based power generation, renewable generation such as wind power relies on uncontrollable prime sources such as wind speed. Wind speed varies stochastically, which to a large extent determines the stochastic behavior of power generation from wind farms. With the increasing number of wind turbines (WTs) connected to distribution systems, network operators are concerned about how such a stochastic generation affects power losses of the network. Furthermore, the operators need to estimate how much and when the stochastic generation can reduce the loading of substation transformers and distribution feeders. Moreover, the network operators are interested in evaluating the maximum penetration level of wind power in their network before any technical requirements are violated.

The traditional approach to these studies is based on a deterministic analysis. For instance, the size of a substation transformer is determined by the sum of the maximum loading at individual radial feeders while assuming no generation output from local generators. However, such a deterministic analysis does not provide a realistic evaluation of system steady-state performance. A more realistic evaluation can be achieved through a probabilistic analysis that takes into account the stochastic behavior of wind power generation (WPG) and load demand. Such a probabilistic analysis may help network operators to cut down the cost associated with system planning. Thus, the objective of this thesis is to develop stochastic models of renewable generation and load demand for the optimal operation and planning of modern distribution systems through a probabilistic approach.

On the basis of statistical data, stochastic models of WPG, load and combined heat and power (CHP) generation are developed. The stochastic wind power model is constructed on the basis of an autoregressive integrated moving average (ARIMA) process. The model characterizes WPG by mean level, temporal correlation and driving noise. Such a model is valuable for researchers who do not have access to wind power measurements. The model can be used to evaluate year-to-year variation of wind power generation through a sensitivity analysis and to forecast very short-term wind power through a model-based prediction method. The stochastic load model is established on the basis of a seasonal autoregressive moving average (ARMA) process. It is demonstrated that such a stochastic model can be used to simulate the effect of load management on the load duration curve. As CHP units are turned on and off by regulating power, CHP generation has discrete output and thus can be modeled by a transition matrix based discrete Markov chain. As the CHP generation has a strong diurnal variation, reflecting the heat load and electricity price, it is proposed to use different transition matrices for different periods of a day. These three stochastic models are the main theoretical contributions of this thesis.

With these stochastic models, a realistic evaluation of the system steady-state performance can be carried out through a probabilistic load flow (PLF) analysis. Based on the PLF analysis, several studies are conducted and strategies are proposed to operate and plan a modern distribution system in an optimal way. In the first case study, a stochastic optimization algorithm is proposed that minimizes the expectation of power losses of a 69-bus distribution system by controlling the power factor of WTs. The optimization is subjected to the probabilistic constraints of bus voltage and line current. The algorithm combines a constrained nonlinear optimization algorithm and a Monte Carlo based PLF calculation. In the second case, it is demonstrated through a Danish distribution system (Støvring system) that the probability of transformer overloading and the time of the overloading can be identified through a probabilistic analysis. Based on the analysis, use of a gas turbine is determined as a cheaper solution than transformer expansion in order to solve the overloading problem. In the last case, an optimal constrained load flow algorithm is proposed to determine the maximum WT capacity in the modified Støvring system when allowing reactive power control and energy curtailment of WTs, subject to voltage and current constraints. These developed models and proposed algorithms serve as effective tools to assist network operators in decision-making during the operation and planning of power systems.

The traditional approach to these studies is based on a deterministic analysis. For instance, the size of a substation transformer is determined by the sum of the maximum loading at individual radial feeders while assuming no generation output from local generators. However, such a deterministic analysis does not provide a realistic evaluation of system steady-state performance. A more realistic evaluation can be achieved through a probabilistic analysis that takes into account the stochastic behavior of wind power generation (WPG) and load demand. Such a probabilistic analysis may help network operators to cut down the cost associated with system planning. Thus, the objective of this thesis is to develop stochastic models of renewable generation and load demand for the optimal operation and planning of modern distribution systems through a probabilistic approach.

On the basis of statistical data, stochastic models of WPG, load and combined heat and power (CHP) generation are developed. The stochastic wind power model is constructed on the basis of an autoregressive integrated moving average (ARIMA) process. The model characterizes WPG by mean level, temporal correlation and driving noise. Such a model is valuable for researchers who do not have access to wind power measurements. The model can be used to evaluate year-to-year variation of wind power generation through a sensitivity analysis and to forecast very short-term wind power through a model-based prediction method. The stochastic load model is established on the basis of a seasonal autoregressive moving average (ARMA) process. It is demonstrated that such a stochastic model can be used to simulate the effect of load management on the load duration curve. As CHP units are turned on and off by regulating power, CHP generation has discrete output and thus can be modeled by a transition matrix based discrete Markov chain. As the CHP generation has a strong diurnal variation, reflecting the heat load and electricity price, it is proposed to use different transition matrices for different periods of a day. These three stochastic models are the main theoretical contributions of this thesis.

With these stochastic models, a realistic evaluation of the system steady-state performance can be carried out through a probabilistic load flow (PLF) analysis. Based on the PLF analysis, several studies are conducted and strategies are proposed to operate and plan a modern distribution system in an optimal way. In the first case study, a stochastic optimization algorithm is proposed that minimizes the expectation of power losses of a 69-bus distribution system by controlling the power factor of WTs. The optimization is subjected to the probabilistic constraints of bus voltage and line current. The algorithm combines a constrained nonlinear optimization algorithm and a Monte Carlo based PLF calculation. In the second case, it is demonstrated through a Danish distribution system (Støvring system) that the probability of transformer overloading and the time of the overloading can be identified through a probabilistic analysis. Based on the analysis, use of a gas turbine is determined as a cheaper solution than transformer expansion in order to solve the overloading problem. In the last case, an optimal constrained load flow algorithm is proposed to determine the maximum WT capacity in the modified Støvring system when allowing reactive power control and energy curtailment of WTs, subject to voltage and current constraints. These developed models and proposed algorithms serve as effective tools to assist network operators in decision-making during the operation and planning of power systems.

Original language | English |
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Publisher | Department of Energy Technology, Aalborg University |
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Number of pages | 203 |

ISBN (Print) | 87-89179-89-6 |

State | Published - Feb 2010 |

Publication category | Research |

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