Introduction

In hydropower operations, every real-time decision, especially how and when we dispatch power, directly impacts turbine efficiency, generator loading, reservoir usage, and national grid stability. One of the most reliable tools for optimizing these decisions is the turbine hill chart. Far from being a theoretical engineering concept, the hill chart is a practical, day-to-day operational tool that provides a visual map of how different combinations of gate opening (stroke) and net Head influence turbine efficiency.

At Bui Generating Station, our hill chart is specifically designed to reflect our turbine geometry, Head range (up to 84 m), and expected flow profiles under varying operating conditions. It presents a performance contour that helps operators identify the Best Efficiency Zones (BEZ), where water is converted into mechanical energy most effectively, and ensure that this mechanical power aligns safely with the generator’s electrical capacity as defined by the generator's capability curve.

Operators are often required to strike a balance between maximizing output and safeguarding equipment. That means staying efficient without overloading the generator, maintaining system stability without excessive water draw, and adapting to real-time grid voltage and frequency variations. The hill chart, when used side by side with the generator capability curve, becomes a practical roadmap for optimizing output, protecting equipment, and supporting grid conditions intelligently.

This article unpacks how to apply the hill chart in practice, using real-world examples, detailed calculations, and technical insights derived from operations at Bui. Whether you’re an operator setting MW targets or an engineer supporting dispatch decisions, the goal is simple: maximize performance while preserving the long-term integrity of the hydro-mechanical system.

 What is a Hill Chart?

A hill chart is a two-dimensional graphical representation of the turbine’s hydraulic efficiency under varying operational conditions. The chart maps out how turbine efficiency changes with two key parameters:

• Wicket Gate Opening (Stroke or Gate Position): This is plotted on the vertical axis and reflects how wide the turbine wicket gates are opened, controlling the volume of water entering the turbine.

• Net Head: This is plotted on the horizontal axis and represents the available hydraulic Head or pressure differential driving the water through the turbine.
  
  

Efficiency values are displayed as curved contour lines, similar to elevation lines on a topographic map. Each contour represents a zone of constant turbine efficiency, allowing operators to visualize how different combinations of gate stroke and Head affect performance.

The shape of the chart is determined by turbine geometry, guide vane characteristics, and hydraulic design. At Bui, the hill chart is calibrated specifically for our Francis turbines, incorporating data from factory model testing and site commissioning.

The chart helps identify the Best Efficiency Zone (BEZ), the region where the turbine operates at its maximum efficiency. Operating within this zone minimizes water usage per megawatt generated and reduces mechanical stress. When combined with generator capability considerations (e.g., MVA and PF limits), the hill chart becomes a critical tool for real-time performance optimization 

Why Hill Charts Matter in Real-Time Operation

Hill charts matter in real-time hydroelectric operations because they convert abstract design parameters into a tangible, operational framework. At their core, they help answer a daily operational question: given the available Head and a targeted power output, what gate position will yield the most efficient energy conversion?

Turbines respond non-linearly to changes in stroke and Head. For instance, opening the wicket gates wider doesn't always increase efficiency, particularly if the net Head is insufficient or if the operating point moves into regions of low hydraulic performance. The hill chart accounts for this complex interaction, highlighting zones where the turbine operates stably and efficiently, and where it risks cavitation, flow separation, or inefficiency.

In real-time operation, this is invaluable. Grid conditions are not static — voltage, frequency, and system demand fluctuate throughout the day. The operator must be able to adjust power output dynamically while respecting turbine limits and generator capability. Hill charts enable this by guiding operators toward the Best Efficiency Zone (BEZ), which shifts subtly depending on water levels, reservoir inflows, and grid instructions.

At Bui, where turbine efficiency impacts both generation economics and water resource management, hill charts serve as a technical dashboard for dispatch accuracy. They inform load scheduling, especially under peaking plant regimes, and help prevent overloading the generator by correlating turbine output with safe excitation and MVA boundaries. Ultimately, hill charts bridge the gap between theoretical design and on-the-ground performance, enabling smart, situational decision-making that preserves equipment life and improves dispatch outcomes.

Identifying the Best Efficiency Zone (BEZ)

Based on the manufacturer’s Hill chart and live operating experience at Bui, the turbine’s Best Efficiency Zone (BEZ) is centered within:

• 70% – 80% gate stroke, equivalent to approximately 236–270 mm stroke

• 70 – 84 m net Head range

Operating beyond 80% stroke, particularly at higher Heads, risks surpassing generator capacity (148.15 MVA at 0.9 PF), even though turbine efficiency remains high.

Staying within this zone ensures:

• High turbine efficiency (96.5% – 98.2%)

• Safe MW output (Approx. 90 –134 MW)

• Generator and excitation safety

• Optimized water-to-power conversion

Operator Advisory:
Based on practical performance data, turbine efficiency characteristics, and generator capacity limitations, operators are advised to ensure that wicket gate opening does not exceed 75% under normal conditions. This stroke level ensures:

• Operation within the Best Efficiency Zone (BEZ)

• Mechanical power output safely within the generator’s MVA rating

• Sufficient margin for reactive power support

• Protection against thermal overload, excessive excitation, and potential protection trips

• Simplification of operator decision-making and maintaining consistent unit performance

Exceeding 80% gate opening, particularly under high head conditions, significantly increases the risk of surpassing the generator’s 148.15 MVA limit and violating the capability curve boundary. Therefore, the 75% limit is upheld as both a safety safeguard and an efficiency target. It is prudent to maintain at least 3 – 5% MVA headroom to support grid reactive power (VAR) needs and ensure fault ride-through capability.

Sample Calculation Using the Hill Chart

Estimating the turbine output using the Bui Unit Rated Data on the Hill chart and applying the basic hydro power formula:
Hydraulic Power (MW) = η × ρ × g × Q × H / 1,000,000
Where:
η = turbine efficiency (rated 0.982)
ρ = water density (1000 kg/m³)
g = acceleration due to gravity (9.81 m/s²)
Q = flow in m³/s ( rated 204.62 m³/s)
H = net Head in meters ( rated 73.7 m)

Power = 0.982 × 1000 × 9.81 × 204.62 × 73.7 / 1,000,000
      ≈ 145.3 MW (Mechanical Power)

Assuming 98% generator efficiency:
Electrical Power = 145.3 × 0.98  = approx.  142.4 MW

This confirms that the generator (rated at 133.34 MW) becomes the limiting factor even at full-rated turbine capacity.

So even if the turbine produces 145.3 MW mechanically, the generator can only safely convert up to 133.34 MW.

 Any excess:

• Must be reduced by reducing stroke or flow (i.e., less mechanical power), or

• Results in generator overloading, risking overheating, protective trips, or reduced equipment life.

Practical Real-Time Application

Let’s say the current Net Head is 81 m. With 75% gate opening and the same flow rate:
Power = 0.982 × 1000 × 9.81 × 0.75 × 204.62 × 81 / 1,000,000
      = Approx.  120 MW (Mechanical Power)

Electrical Power approx.
= 120 × 0.98
= 118 MW
This stays within the generator’s safe limit. However, increasing the stroke to 80% could push output to approximately 136 – 140 MW, risking overload.

Adjusting for System Demand and Grid Conditions

At Bui, operators control the unit output primarily by setting the target MW, not by manually adjusting the wicket gate stroke. Once the MW setpoint is entered, the governor system automatically adjusts the gate stroke to achieve the desired electrical output, based on available water Head and system load demand.

This means the actual stroke percentage is a response, not a manual setting. It reflects how much hydraulic effort the unit needs to meet the MW setpoint under current conditions.

Under normal to high Head conditions (e.g., 75 – 80 m), the unit may operate at or slightly above 75% stroke to meet higher MW demands. However, this must be approached with caution. While the turbine may hydraulically support greater output, the generator is electrically limited to 133.34 MW (148.15 MVA at 0.9 lagging PF). Exceeding these limits, especially during sustained loading, can trigger protective trips, overexcite the field, or degrade insulation over time.

When the Head exceeds 80 m, operators may cautiously increase the MW set-point to take advantage of the increased hydraulic potential. However, this must be done with care. As the governor responds to the higher load demand, the wicket gate opening will increase accordingly. If the resulting stroke approaches the 76 – 77% range, operators must ensure that all generator and excitation parameters remain within safe operating limits.

Specifically, the following must be closely monitored:

• Active power remains below 133.34 MW

• Generator MVA does not exceed 148.15

• Power factor stays within the 0.9 – 0.98 lagging range

• Field current and voltage remain within rated excitation limits

In this mode of operation, MW is the control input, and stroke is the governed output. Monitoring the stroke percentage becomes a practical way to validate that the unit remains within the hydraulic and electrical performance envelope, especially when operating near the top of the Head range.

It’s also critical to recognize that the rated flow of 204.62 m³/s corresponds to 100% wicket gate opening at the rated Head of 73.7 m. However, flow is not solely determined by stroke, it also depends on the available Head. When the Head increases above the rated value, even if the stroke remains constant, the resulting flow may increase slightly, but most of the additional energy is realized as increased pressure, which translates into higher power output, not necessarily large increases in discharge.

In essence, gate stroke controls the flow area, while Head influences the driving force (pressure). Together, they define turbine output. But the relationship between stroke and MW is nonlinear, especially across varying Heads.

Therefore, operators must avoid assuming that increasing stroke always leads to proportionate increases in power or flow. Instead, always base output predictions on live Head measurements and the governor’s dynamic stroke adjustments, validated with the Hill Chart and generator capability limits.

Operational recommendations based on typical Head levels:

• At high Heads (≥80 m): You may approach 75 – 77% stroke, but monitor all generator parameters

• At moderate Heads (73 – 75 m): Aim for 75% stroke to optimize efficiency and generator loading

• At low Heads (68 – 70 m): Maintain 70 – 73% stroke to stay within BEZ and avoid inefficiency

• At very low Heads (<68 m): Watch for reduced efficiency and higher water usage per MW. Don’t go beyond 72% stroke to stay within the BEZ.

 
Summary and Operator Takeaways

Hill charts translate theoretical turbine dynamics into practical, actionable strategies. For operators at Bui, they serve as both a daily planning tool and a real-time adjustment map. By monitoring the current water Head and interpreting the hill chart contours, operators can confidently target the Best Efficiency Zone that balances turbine output, generator loading, and water conservation.

The chart does more than indicate optimal performance, it supports grid stability by enabling accurate dispatch, minimizes unnecessary wear on the turbine, and ensures reactive power reserves are not compromised. When used together with the generator capability curve, the hill chart becomes a precision tool for situational decision-making involving both MW and MVAr management.

Key Operator Takeaways:

• Always confirm the current net Head before adjusting MW targets.

• Operate between 70% and 75% gate stroke (236 – 253 mm) for optimal efficiency.

• Avoid crossing 80% gate stroke at Heads above 75 m to prevent generator overloading.

• Continuously monitor generator MVA, power factor, and field excitation levels.

• Use the hill chart and capability curve side-by-side during peak demand, reservoir transition, or system instability.
  
  

“Operating a generator isn’t just about pushing limits, it’s about staying safe but doing it with intelligence and precision.”
— David Kwaku Boadu