Power system simulation

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Power system simulation models are a class of computer simulation programs that focus on the operation of electrical power systems. These computer programs are used in a wide range of planning and operational situations including:

  1. Long-term generation and transmission expansion planning
  2. Short-term operational simulations
  3. Market analysis (e.g. price forecasting)

These programs typically make use of mathematical optimization techniques such linear programming, quadratic programming, and mixed integer programming.

Key elements of power systems that are modeled include:

  1. Load flow (Load Flow Calculation)
  2. Short circuit (Short Circuit Analysis)
  3. Transient stability (Transient Stability Simulation)
  4. Optimal dispatch of generating units (unit commitment).
  5. Transmission optimal power flow.

Layered on top if this physical framework are models of competition such as Cournot, Bertrand competition, and Supply Function Equilibrium.

Contents

[edit] Load Flow Calculation

The load-flow calculation is the most common network analysis tool for examining the undisturbed and disturbed network within the scope of operational and strategical planning. On the basis of the network topology with the impedances of all devices as well as with the infeeds and the consumers, the load-flow calculation can provide voltage profiles for all nodes and loading of network components, such as cables and transformers. With this information, the compliance of the operating conditions relating to permissible voltage ranges and maximum loads, or the violation of these conditions, can be examined. This is, for example, important for determining the transmission capacity of underground cables, where the influence of cable bundling on the load capability of each cable has to be taken also into account. Due of its ability to determine losses and reactive-power allocation, load-flow calculation also supports the planning engineer in the investigation of the most economical operation mode of the network. When changing over from single and/or multi-phase infeed low-voltage meshed networks to isolated networks, load-flow calculation is essential for operational and economical reasons. Load-flow calculation is also the basis of all further network studies, such as motor start-up or investigation of scheduled or unschedulded outages of equipment within the outage simulation. Especially when inevstigating motor start-up, the load-flow calculation results give helpful hints, for example, of whether the motor can be started in spite of the voltage drop caused by the start-up current.

[edit] Short Circuit Analysis

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[edit] Transient Stability Simulation

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[edit] Unit Commitment

The problem of unit commitment involves finding the least-cost dispatch of available generation resources to meet the electrical load.

Generating resources can include a wide range of types:

  1. Nuclear
  2. Thermal (using coal, gas, or other fossil fuels])
  3. Renewables (including hydro, wind, wave-power, and solar)

The key decision variables that are decided by the computer program are:

  1. Generation level (in megawatts)
  2. Number of generating units on

The latter decisions are binary (0,1), which means the mathematical problem is not continuous.

In addition, generating plant are subject to a number of complex technical constraints, including:

  1. Minimum stable operating level
  2. Maximum rate of ramping up or down
  3. Minimum time period the unit is up and/or down

These constraints are amenable to mathematical programming as linear or mixed-integer constraints.

[edit] Optimal Power Flow

Electricity flows through an AC network according to Kirchhoff's Laws. Transmission lines are subject to thermal limits (simple megawatt limits on flow), as well as voltage and electrical stability constraints.

The simulator must calculate the flows in the AC network that result from any given combination of unit commitment and generator megawatt dispatch, and ensure that AC line flows are within both the thermal limits and the voltage and stability constraints. This may include contingencies such as the loss of any one transmission or generation element - a so-called security-constrained optimal power flow (SCOPF), and if the unit commitment is optimized inside this framework we have a security-constrained unit commitment (SCUC).

[edit] Models of Competitive Behavior

The cost of producing a megawatt of electrical energy is a function of:

  1. fuel price
  2. generation efficiency (the rate at which potential energy in the fuel is converted to electrical energy)
  3. operations and maintenance costs

In addition to this, generating plant incur fixed costs including:

  1. plant construction costs, and
  2. fixed operations and maintenance costs

Assuming perfect competition, the market-based price of electricity would be based purely on the cost of producing the next megawatt of power, the so-called short-run marginal cost (SRMC). This price however might not be sufficient to cover the fixed costs of generation, and thus power market prices rarely show purely SRMC pricing. In most established power markets, generators are free to offer their generation capacity at prices of their choosing. Competition and use of financial contracts keeps these prices close to SRMC, but inevitably offers price above SRMC do occur (for example during the California Energy Crisis of 2001).

In the context of power system simulation, a number of techniques have been applied to simulate imperfect competition in electrical power markets:

  1. Cournot competition
  2. Bertrand competition
  3. Supply function equilibrium
  4. Residual Supply Index analysis

Various heuristics have also been applied to this problem. The aim is to provide realistic forecasts of power market prices, given the forecast supply-demand situation.