Online Optimal Power Control of an Offshore OilPlatform Power System
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Abstract
Offshore oilplatform power systems are important infrastructure for the exploitation of maritime oil and gas. However, its current energy management system, with relatively simple control scheme and lowlevel automation, can hardly operate the system in a secure and economic manner to match the rapid progress of offshore oil and gas exploitation. To address this issue, an online multiobjective optimal power control strategy is proposed and implemented based on the existing SCADA system. By incorporating network loss, gas consumption and voltage deviation into a synthesized objective function and taking the various operational constraints into account, the powercontrol task is formulated into a mixedinteger nonlinear optimized problem. And then an efficient procedure that combines the interior point method and the fast branch and bound method is developed to solve the problem. Consequently the optimal control strategy can be obtained online and either system security or operational efficiency is achieved. The developed control system has been put into practical use in the Weixinan offshore oilplatform power system (China’s first of its kind). Field test results show that it can coordinate active and reactive power for online optimal control as per the changes of operating conditions. The improved safety, efficiency and power quality of the power system will definitely promote exploitation of offshore oil and gas in the respect of both security and efficiency.
Keywords
Offshore oilplatform power system Optimal power control Mixedinteger nonlinear problem Interior point method Fast branch and bound methodIntroduction
Offshore oil resource is playing an increasing role in satisfying our fossil fuel needs. It accounts for over one third of the world’s total oil production. For China in 2013, 19% of crude oil is from shallow offshore reserves [1] and the proportion continues to rise at very high speed [2]. In the offshore oil industry, the power supply system is one of the most important infrastructures to ensure safe and efficient production. How to reliably power offshore oil platforms is becoming a critical issue. However, previously and currently, most oil platforms far from the land are powered by standalone power stations built on them. This power supply mode, though simple, is criticized for high investment and low reliability. Moreover, there is a great risk of blackout at the platform once the power station thereon shuts down. Therefore, to improve the reliability of power supply, it becomes a trend to develop offshore oilplatform power system that electrically connect multiple platforms to supply power in a manner of network [3]. In 2010, the first interconnected offshore power system, called the Weixinan offshore oilfiled power system (WOOPS), was established on the South China Sea (SCS) around the Weizhou Island. Since then, more and more offshore platforms have been connected electrically along the coast of China and many regional interconnected offshore power systems have been developed or under construction. Therefore, how to efficiently operate and control those offshore power systems for reliable power supply is critical for the effective and safe operation of offshore oil platforms.
 1)
The control infrastructure is relatively weak. Most of the systems only have the basic function of supervisory control and data acquisition (SCADA) and are short of model support and advanced control functions. It is urgent to improve automation and intelligence of the control system.
 2)
The primary power sources are gas turbine generators and the system is characterized by small inertia, high response speed and closely coupling of active and reactive power. Coordinated control of both active and reactive power is required to reconcile power balance, voltage quality and economic operation within a short period (e.g. 0.5 s) so as to achieve online quasirealtime decisionmaking. This is quite different from the inland power system, in which the online control of AGC and AVC is difficult to coordinate and the time of decisionmaking is relatively long (say minutelevel) due to the huge scale and numerous variables of the power system [6, 7].
 3)
Gas turbine generators have very rapid response, but it is prone to be tripped in case of slight overload due to its limited overloading capability. As for the submarine cables, the charging power is very high and the overloading capacity is limited by the thermal stability. The investment of gas turbines and submarine cables is extremely high. So it is required that the power system operate within the tolerance to guarantee equipment safety and service life.
 4)
The oilfield associated gas, which is used as the fuel of power generation, has very high economic value. In addition, to comply with the strict claim of emission reduction and environment protection on the sea, the power generation cost and energy losses should be minimized.
 5)
Decision variables of power control include continuous variable (such as unit / STATCOM output) and discrete variable (such as on/off status of shunt reactors and transformer tap position). So the optimization problem is generally a mixedinteger nonlinear one. It is a big challenge to find the solution efficiently on line to achieve quasirealtime control. But this difficulty is usually avoided for the inland power system through multistep separate decision.
Therefore, the power control method widely used in inland power systems is almost inappropriate for the offshore system. A special power control strategy and system is in urgent need. However, very few research was done in this aspect. References [8, 9] investigated the impact of wind power on the operation of offshore oilplatform power systems, however, without optimal control of the overall system. In [10], security and stability control system for offshore power grids was analyzed, however, not touching the topic of operating the power system optimally.
 1)
The developed power control system is of a serviceoriented architecture (SOA) [11] and based on common information model (CIM). So all its basic functions such as topology analysis, state estimation and advanced control applications such as online power optimization are plugandplay.
 2)
The optimal power control task is formulated into a constrained, mixedinteger nonlinear programming problem. The goal is to synthetically minimize power generation cost, network loss rate and bus voltage deviation. Moreover, the gas consumption of generators can be updated online based on operation data.
 3)
An efficient algorithm combining the interior point method (IPM) and the fast branchandbound method (BBM) is designed to solve the optimization problem and thus rapid decisionmaking and online power control is achieved.
 4)
The online optimal power control system is put into operation in China’s first offshore oilplatform power system, i.e., WOOPS. Field test results verify its practicability and effectiveness.
The rest of the paper is organized as follows: In “The Offshore OilPlatform Power System and its Improved Power Control System” section, an improved configuration of the power control system is proposed based on the analyses of the status quo of WOOPS and its existing control strategy. “Formulation of the Optimal Power Control Problem” section details the formulation of the power control problem. In “Solution to the Optimization Problem” section, IPM and fast BBM are combined to solve the optimization problem efficiently. In “Implementation of OPC and its Application Results” section, the developed control system is applied to the target system to investigate its actual performance. Finally, brief conclusions are drawn in the sixth section.
The Offshore OilPlatform Power System and its Improved Power Control System
Description of the Target Offshore OilPlatform Power System
Active/reactive power ranges of generators and STATCOM
Generator/STATCOM  Active power(MW)  Reactive power(Mvar) 

G1~G7  0~3.5  1~2.5 
G8~G9  0~2.5  −0.5~1.8 
G10~G11  0~4.5  0~3.5 
STATCOM  0  −3.0~3.0 
The Originally SCADA System and Power Control Strategy
In order to monitor and control the power system, a simple energy management system (EMS) is originally deployed. It only has basic SCADA functions and power control strategy. The SCADA collects operation data of the power system by the way of polling. The data includes switching status, RMS voltage and current, active and reactive power, etc. They are acquired from the measuring points of system at fixed intervals. Then the data and status are directly displayed on the singleline diagram for the users to monitor the current conditions of the system.
The reactive power of each generator is regulated with either of the three methods: i) Maintaining the terminal voltage, which is achieved by the automatic voltage regulation (AVR) of the excitation system by tracking a predefined voltage reference. ii) Dispatching the reactive power, which is fulfilled by EMS through sending reactive power order for each generator. 3) Keeping the power factor constant. For a generator, its reactive power control mode can be switched among these 3 ones as required by the operator at different operating conditions or time period.
 1)
SCADA just displays the acquired data to the users. The acquisition and transmission of data is asynchronously conducted and inevitably introduces errors. Lack of basic functions such as topology analysis and state estimation tend to make inconsistent and inaccurate presentation of the system. As a result, accurate system state information is not available and the resultant operation may be deviated or even incorrect, which definitely endangers the safety and stability of the whole power system.
 2)
The power control strategy is derived from the original singleplatform power supply system, without considering the various constraints in a power grid, for instance, stability of the whole system, the capacity limit of cables and transformers. So under unfavorable conditions, such a simple control strategy would cause overload of equipment or even weaken system stability.
 3)
Economy and efficiency of system operation are not fully considered. With the existing control strategy, the active power of each generator only depends on the total load and its capacity. No consideration is given to the difference in generation cost and network loss caused by the transmission of power. When the distribution of loads is not matched with the capacity of deployed generator(s) on each platform or the operation cost of generator varies greatly, the existing control strategy would cause high fuel cost, increased network loss, and thereby degraded operation efficiency.
 4)
Relatively lowlevel automation and intelligence cannot comply with the growing expansion trend of offshore oilplatform power systems. Currently, there are huge number of nonautomatic operations in the existing system, for instance, setting the var. reference of generators/STATCOM, switching transformer tap positions and reactors. The reliance on human experience and manual operations, on the one hand, seriously lowers the automation of the power system, and on the other hand, certainly threaten the security and reliability of the system. This is especially the case when the scale of the offshore oil platforms increases steadily.
Configuration of the Improved Power Control System
Formulation of the Optimal Power Control Problem
 1.
Objective function
 2.
Constraints
 i)
Power flow constraint: For each bus or node, the active/reactive power should be balanced, i.e.,
 ii)
Generator power constraint: The active/reactive power of each generator should be within its allowed range, or:
 iii)
Constraint on the capacity of cables: The power transmitted through a cable is limited by its physical condition:
 iv)
Bus voltage constraint: The magnitude of bus voltage should be within its upper and lower limits, namely
 v)
Constraint on STATCOM var. output: STATCOM’s var. output should be within its capacity range, or
 vi)
Constraint on tap positions of OLTC transformers: There are only a finite number of tap positions, or
 vii)
Reactor state constraint: There are two states for each reactor, namely 0 for off and 1 for on, or
 3.
The integrated mathematical model
Solution to the Optimization Problem
The controldesign problems (15) and (16) are both mixedinteger nonlinear optimization problems. It is hard for conventional methods to find a proper solution directly. Current solutions to such a problem generally include deterministic algorithms [18] and heuristic algorithms [19]. Heuristic algorithms, for instance, the particle swarm optimization method [20, 21] and genetic algorithm [22, 23], can handle discrete variables well. However, due to its relatively lower speed of converging and uncertainty in reaching optimal solution, the heuristic algorithm can hardly meet the need of online optimal power control. So in this paper the deterministic algorithm is adopted to solve the control problem. In previous literature [24], the interior point method (IPM) and the branchandbound method (BBM) were combined to find the solution of similar problems. Its basic procedure is as follows: relax discrete variables first and solve the relaxed problem by IPM; then if any discrete variable in said solution does not meet its discrete constraint, break the original problem into several branch ones by BBM; next, branch problems are solved to update the upper and lower limits of the objective function; by repeating the former steps, the boundary of decisive variables will be narrowed gradually and the feasible optimal solution can be obtained in the end. In theory, this combined method can be used to solve the optimization problem (16). In practice, however, it has an obvious drawback: with the growth of the scale of the problem, the branches will increase dramatically, which in turn leads to very slow computation speed and poor converging performance. As a result, online execution of the optimal power control can hardly be achieved.
 Step 1:
Input parameters necessary for establishing the optimization model, including the parameters of power networks, the upper/lower operational limits of generators, transformers, submarine cables, the online updated parameters of gas consumption curve for each generator, and the weights in the objective function.
 Step 2:Formulate the optimal power control task into the mathematical problem as shown in (15), which is later transformed into the general form of (16).
 Step 3:
Set the initial values for all decision variables. Although the primaldual IPM is insensitive to initial conditions, the results of current state estimation are assigned as the initial values so that the convergence speed can be greatly accelerated.
 Step 4:
Relax the optimization problem. The IPM requires all variables be continuous while the power optimization model (16) has many a discrete variables (for instance, transformer tap positions, reactor on/off states). So the process of relaxing is necessary for the use of IPM.
 Step 5:
Solve the relaxed problem (19) with IPM. We have developed an IPM solver based on the open source package IPOPT (Interior Point Optimizer) [27] of COINOR community to effectively solve the optimization problem. It is fulfilled with the 4 substeps, of which the flow chart is also shown in Fig. 5.
 Substep 51:
Calculate the firstorder derivative of the objective function (▽_{x}f(x)) and the Jacobian matrices of the constraint functions (▽_{x}h(x), ▽_{x}g(x)).
 Substep 52:
Calculate the secondorder derivative of the objective function (▽2 xf(x)) and the Hessian matrices of constraint functions (▽2 xh(x), ▽2 xg(x)) by using the quasiNewton approximation [27].
 Substep 53:
 Substep 54:
Judge the convergence of IPM: If the criterion, or x^{k + 1}x^{k} ≤ 10^{−8}, is met, the iteration converges and the optimal solution to the relaxed problem (19) is obtained, which are denoted as (x* c,x* d). Otherwise, go back to Substep 5–1 and proceed to next iteration, where the last updated variables will be used as the new initial values.
 Step 6:
Discretize the solution. If any of the discrete variables is not assigned with its allowed value (later called: untreated), the fast BBM will be called to discretize that variable. Unlike the conventional BBM, which, in the worst case, has to traverse each branch, the fast BBM used here only considers the smaller branch of the objective function. Its basic procedure, as illustrated in Fig. 4, is carried out by the following substeps.
 Substep 61:
Sort the untreated discrete variables of the optimal solution obtained in the previous step. Since the tap positions of OLTC transformers have greater impact on system voltage and reactive power flow, they will be discretized first. Moreover, priority should be given to the taps of higher voltage levels. For the transformers at the same voltage level, their tap variables should be treated according to the order from that with the largest distance to its discrete value. Reactors go next. Similarly, they are treated in the descending order of their deviation from the discrete values. Suppose the sorted discrete variables are x_{d,k}, k = 1,…,N_{d}, where N_{d} is the number of discrete variables to be treated; fast BBM will be applied successively to each of them. By setting k = 1, the first untreated discrete variable will be processed in the next substep.
 Substep 62:
Discretize the kth untreated variable x_{d, k}. Suppose its current value as a continuous variable is x* d,k. After fixing the treated discrete variables, two relaxed subproblems are formulated for those untreated discrete variables:
 Substep 63:
Judge if k>N_{d}, or all discrete variables have already treated. If yes, go to Step 7; otherwise, go back to Substep 6–3 and continue to determine untreated discrete variables by the fast BBM.
 Step 7:
Output the final optimal solution to the problem.
Compared with the conventional method, the fast BBM only keeps the minimum branch of the objective function instead of traversing all branches in the worst case. So the calculation burden and the required memory can be considerably reduced and the efficiency greatly improved. Although an optimal solution is not guaranteed in theory, in control practice suboptimal decision is generally acceptable because the practical requirements of power system and the extensive experience of BBM have been taken into full consideration during the designing procedure.
Implementation of OPC and its Application Results
The general structure of the control system and the basic procedure of OPC has been previously described. Here some specific aspects for its implantation will be discussed.
Online Update of the GasConsumption Parameters
In (4), the parameters, namely a_{i}, b_{i} and c_{i}, are the key to the accurate calculation of the fuel cost. In the offshore oilplatform power system, each gas turbine generators has different generation efficiency, which changes (generally declines) with the increase of service time. These parameters are initially set according to the efficiency curve provided by the manufacturer. Then during the longterm operation, the generation output and the gas consumption are measured in the field. These field measurements are next processed with a curvefitting identification procedure to update the parameters on line. Since the online updated curves reflect the change of the actual working condition, the obtained gas consumption is much more precise.
Parameters of gas consumption curves (p.u)
Generators  a  b  c 

G1~G7  0.02  0.85  0.13 
G8~G9  0.05  1.26  0.33 
G10~G11  0.45  0.52  0.26 
Selection of the Weights in the Objective Function

Mode 1: w_{p} = 1, w_{c} = w_{v} = 0, that is, only the network loss is selected as the optimization goal.

Mode 2: w_{v} = 1, w_{p} = w_{c} = 0, that is, only the voltage deviation is selected as the optimization goal.

Mode 3: w_{c} = 1, w_{p} = w_{v} = 0, that is, only the gas consumption is selected as the optimization goal.

Mode 4: w_{c} = w_{p} = 0, w_{v} = 0, that is, the gas consumption and the network loss are equally taken as the optimization goal.

Mode 5: w_{c} = 0.05, w_{p} = 0.8, w_{v} = 0.15, that is, all three subobjectives are taken into account by a composite set of weights, which actually are determined through trial and error.
By comparing the control effects of the five control modes, it is obvious that if a single objective is taken as optimization goal, like Mode 1, 2 and 3, the optimized system will has the best performance in the selected aspect. For instance, Mode 1, 2 and 3 exhibit the best result in minimizing the network loss rate, the voltage deviation and the gas consumption, respectively. But they generally perform poorly in other aspects. Mode 4 incorporates both economic indicators (i.e., network loss and gas consumption), however, without the consideration of the voltage quality. As a result, both network loss and gas consumption are reduced after optimization. But the voltage deviation becomes worse to some extent. Mode 5 accommodate all the three goals. In other words, both economic and security criteria are taken into account. So the three objectives are balanced. Compared to the original state of the system, the network loss rate, the gas consumption and the voltage deviation are all reduced in a coordinated way. Actually, such a compromising control mode is exactly what the system operators expect. So the weights defined by Mode 5 are adopted in practice.
 1)
For smaller system, since the voltage fluctuation is relatively larger and the power loss of the networks is not so significant, the weight for voltage should be increased while the weight for the loss should be lowered.
 2)
The fuel cost is quite different from one system to another, depending on the fuel value, transportation cost of the accompany gas. A higher cost of fuel requires a larger value of w_{c}.
 3)
In practice, the three weights are initially determined by trial and error. Firstly, w_{v} is selected to keep the fluctuation of voltage within a limit, for instance ±5% under typical operating conditions. Then, the ratio of w_{c} and w_{p} is set to make the economic value of electricity and fuel comparable. Finally, with some trial and error under different scenarios, the weights are determined. However, they can be adjusted afterward by system operators when more experiences are accumulated in practice.
Typical Field Test Results
System performance before and after OPC
Power Loss Rate (%)  Voltage Deviation (%)  Gas Consumption (p.u.)  

Before OPC  0.34%  0.39%  2.845 
After OPC  0.15%  0.12%  2.371 
It can be found that the power output of each generator has been adjusted after the optimal power control with the recommended weights. In particular, the power of G10 on WZIT platform is reduced to 0 from 3.19 MW before optimization, that is, the generator is shut down after the OPC. The power system has its network loss rate lowered from 0.34% to 0.12%, voltage deviation from 0.39% to 0.12% and the total gas consumption from 2.845 p.u. to 2.371 p.u., which fully demonstrates that the OPC has considerably improved the operation performance of the target system.
For this practical case, if the conventional BBM is used, under the worst circumstance there are 23,328 (2^{5} × 9^{3}) branches to be traversed. It is a huge work. But the fast BBM only need to solve 8 branch problems at most, each for a discrete variables. Consequently the efficiency of the algorithm is enhanced dramatically. In this specific case, the optimization problem is solved with only 23 iterations, which takes the server about 0.08 s. Therefore, the optimal power control can be executed in real time.
Conclusions
Secure and economical operation of the offshore oilplatform power system plays a key role in the efficient exploitation of offshore oil and gas. In this paper, an SOAbased multiobjective optimal power control (OPC) is developed as an advanced control function of the EMS. By incorporating network loss, gas consumption and voltage deviation into a synthesized objective function and taking the various operational constraints into account, the powercontrol task is formulated into a mixedinteger nonlinear optimized problem. To achieve quasirealtime decision making, we have implemented an efficient solution to the problem by combining the interior point method and the fast branch and bound method. Particularly, the parameters of the gas consumption are updated online to reflect the current operating performance of gas turbines. The developed optimal power control system has been put into practical use in the Weixinan offshore oilplatform power system (China’s first of its kind). Field test results show that it can reach an optimized control strategy in less than 0.1 s and thus achieve online optimal control of the system. Compared with system status without the OPC, network loss rate, voltage deviation and gas consumption can be reduced by 55%, 69% and 16%, respectively. This has fully demonstrated the effectiveness of the developed OPC system in enhancing power quality as well as operational efficiency of the offshore oilplatform power system, which in turn will improve the efficiency of offshore oil and gas exploitation.
Notes
Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant No. 51322701) and National High Technology Research and Development Program of China (Grant No. 2012AA050216).
Compliance with Ethical Standards
Conflict of Interest
The authors declare that they have no conflict of interest.
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